id sid tid token lemma pos bracis-28424 1 1 detecting detect VERB bracis-28424 1 2 multiple multiple ADJ bracis-28424 1 3 epidemic epidemic NOUN bracis-28424 1 4 sources source NOUN bracis-28424 1 5 in in ADP bracis-28424 1 6     SPACE bracis-28424 1 7 network network NOUN bracis-28424 1 8 epidemics epidemic NOUN bracis-28424 1 9 using use VERB bracis-28424 1 10 graph graph NOUN bracis-28424 1 11 neural neural ADJ bracis-28424 1 12 networks network NOUN bracis-28424 1 13 | | ADV bracis-28424 1 14 springer springer NOUN bracis-28424 1 15 nature nature PROPN bracis-28424 1 16 link link PROPN bracis-28424 1 17 ( ( PUNCT bracis-28424 1 18 formerly formerly ADV bracis-28424 1 19 springerlink springerlink NOUN bracis-28424 1 20 ) ) PUNCT bracis-28424 1 21 skip skip VERB bracis-28424 1 22 to to ADP bracis-28424 1 23 main main ADJ bracis-28424 1 24 content content NOUN bracis-28424 1 25 advertisement advertisement NOUN bracis-28424 1 26 log log NOUN bracis-28424 1 27 in in ADP bracis-28424 1 28 menu menu NOUN bracis-28424 1 29 find find VERB bracis-28424 1 30 a a DET bracis-28424 1 31 journal journal NOUN bracis-28424 1 32 publish publish VERB bracis-28424 1 33 with with ADP bracis-28424 1 34 us we PRON bracis-28424 1 35 track track VERB bracis-28424 1 36 your your PRON bracis-28424 1 37 research research NOUN bracis-28424 1 38 search search NOUN bracis-28424 1 39 cart cart NOUN bracis-28424 1 40 home home NOUN bracis-28424 1 41 intelligent intelligent ADJ bracis-28424 1 42 systems system NOUN bracis-28424 1 43 conference conference NOUN bracis-28424 1 44 paper paper NOUN bracis-28424 1 45 detecting detect VERB bracis-28424 1 46 multiple multiple ADJ bracis-28424 1 47 epidemic epidemic NOUN bracis-28424 1 48 sources source NOUN bracis-28424 1 49 in in ADP bracis-28424 1 50     SPACE bracis-28424 1 51 network network NOUN bracis-28424 1 52 epidemics epidemic NOUN bracis-28424 1 53 using use VERB bracis-28424 1 54 graph graph NOUN bracis-28424 1 55 neural neural ADJ bracis-28424 1 56 networks network NOUN bracis-28424 1 57 conference conference NOUN bracis-28424 1 58 paper paper NOUN bracis-28424 1 59 first first ADV bracis-28424 1 60 online online ADV bracis-28424 2 1 : : PUNCT bracis-28424 2 2 12 12 NUM bracis-28424 2 3 october october NOUN bracis-28424 2 4 2023 2023 NUM bracis-28424 2 5 pp pp ADP bracis-28424 2 6 331–345 331–345 NUM bracis-28424 2 7 cite cite VERB bracis-28424 2 8 this this DET bracis-28424 2 9 conference conference NOUN bracis-28424 2 10 paper paper NOUN bracis-28424 2 11 access access NOUN bracis-28424 2 12 provided provide VERB bracis-28424 2 13 by by ADP bracis-28424 2 14 university university PROPN bracis-28424 2 15 of of ADP bracis-28424 2 16 notre notre PROPN bracis-28424 2 17 dame dame PROPN bracis-28424 2 18 hesburgh hesburgh PROPN bracis-28424 2 19 library library PROPN bracis-28424 2 20 download download PROPN bracis-28424 2 21 book book NOUN bracis-28424 2 22 pdf pdf PROPN bracis-28424 2 23 download download NOUN bracis-28424 2 24 book book NOUN bracis-28424 2 25 epub epub PROPN bracis-28424 2 26 intelligent intelligent ADJ bracis-28424 2 27 systems system NOUN bracis-28424 2 28 ( ( PUNCT bracis-28424 2 29 bracis bracis NOUN bracis-28424 2 30 2023 2023 NUM bracis-28424 2 31 ) ) PUNCT bracis-28424 2 32 detecting detect VERB bracis-28424 2 33 multiple multiple ADJ bracis-28424 2 34 epidemic epidemic NOUN bracis-28424 2 35 sources source NOUN bracis-28424 2 36 in in ADP bracis-28424 2 37     SPACE bracis-28424 2 38 network network NOUN bracis-28424 2 39 epidemics epidemic NOUN bracis-28424 2 40 using use VERB bracis-28424 2 41 graph graph NOUN bracis-28424 2 42 neural neural ADJ bracis-28424 2 43 networks network NOUN bracis-28424 2 44 download download NOUN bracis-28424 2 45 book book NOUN bracis-28424 2 46 pdf pdf PROPN bracis-28424 2 47 download download NOUN bracis-28424 2 48 book book PROPN bracis-28424 2 49 epub epub PROPN bracis-28424 2 50 rodrigo rodrigo PROPN bracis-28424 2 51 gonçalves gonçalves PROPN bracis-28424 2 52 haddad haddad PROPN bracis-28424 2 53     SPACE bracis-28424 2 54 orcid orcid NOUN bracis-28424 2 55 : : PUNCT bracis-28424 2 56 orcid.org/0009-0006-2171-600x9 orcid.org/0009-0006-2171-600x9 NUM bracis-28424 2 57 & & CCONJ bracis-28424 2 58 daniel daniel PROPN bracis-28424 2 59 ratton ratton PROPN bracis-28424 2 60 figueiredo figueiredo PROPN bracis-28424 2 61     SPACE bracis-28424 2 62 orcid orcid NOUN bracis-28424 2 63 : : PUNCT bracis-28424 2 64 orcid.org/0000-0001-9341-66199 orcid.org/0000-0001-9341-66199 NOUN bracis-28424 2 65     SPACE bracis-28424 2 66 part part NOUN bracis-28424 2 67 of of ADP bracis-28424 2 68 the the DET bracis-28424 2 69 book book NOUN bracis-28424 2 70 series series NOUN bracis-28424 2 71 : : PUNCT bracis-28424 2 72 lecture lecture NOUN bracis-28424 2 73 notes note NOUN bracis-28424 2 74 in in ADP bracis-28424 2 75 computer computer NOUN bracis-28424 2 76 science science NOUN bracis-28424 2 77 ( ( PUNCT bracis-28424 2 78 ( ( PUNCT bracis-28424 2 79 lnai lnai ADJ bracis-28424 2 80 , , PUNCT bracis-28424 2 81 volume volume NOUN bracis-28424 2 82 14197 14197 NUM bracis-28424 2 83 ) ) PUNCT bracis-28424 2 84 ) ) PUNCT bracis-28424 2 85 included include VERB bracis-28424 2 86 in in ADP bracis-28424 2 87 the the DET bracis-28424 2 88 following follow VERB bracis-28424 2 89 conference conference NOUN bracis-28424 2 90 series series NOUN bracis-28424 2 91 : : PUNCT bracis-28424 2 92 brazilian brazilian ADJ bracis-28424 2 93 conference conference NOUN bracis-28424 2 94 on on ADP bracis-28424 2 95 intelligent intelligent ADJ bracis-28424 2 96 systems system NOUN bracis-28424 2 97 530 530 NUM bracis-28424 2 98 accesses access NOUN bracis-28424 2 99 1 1 NUM bracis-28424 2 100 citation citation NOUN bracis-28424 2 101 abstract abstract ADJ bracis-28424 2 102 epidemics epidemic NOUN bracis-28424 2 103 start start VERB bracis-28424 2 104 within within ADP bracis-28424 2 105 a a DET bracis-28424 2 106 network network NOUN bracis-28424 2 107 because because SCONJ bracis-28424 2 108 of of ADP bracis-28424 2 109 the the DET bracis-28424 2 110 existence existence NOUN bracis-28424 2 111 of of ADP bracis-28424 2 112 epidemic epidemic NOUN bracis-28424 2 113 sources source NOUN bracis-28424 2 114 that that PRON bracis-28424 2 115 spread spread VERB bracis-28424 2 116 information information NOUN bracis-28424 2 117 over over ADP bracis-28424 2 118 time time NOUN bracis-28424 2 119 to to ADP bracis-28424 2 120 other other ADJ bracis-28424 2 121 nodes node NOUN bracis-28424 2 122 . . PUNCT bracis-28424 3 1 data datum NOUN bracis-28424 3 2 about about ADP bracis-28424 3 3 the the DET bracis-28424 3 4 exact exact ADJ bracis-28424 3 5 contagion contagion NOUN bracis-28424 3 6 pattern pattern NOUN bracis-28424 3 7 among among ADP bracis-28424 3 8 nodes node NOUN bracis-28424 3 9 is be AUX bracis-28424 3 10 often often ADV bracis-28424 3 11 not not PART bracis-28424 3 12 available available ADJ bracis-28424 3 13 , , PUNCT bracis-28424 3 14 besides besides SCONJ bracis-28424 3 15 a a DET bracis-28424 3 16 simple simple ADJ bracis-28424 3 17 snapshot snapshot NOUN bracis-28424 3 18 characterizing characterizing NOUN bracis-28424 3 19 nodes node NOUN bracis-28424 3 20 as as SCONJ bracis-28424 3 21 infected infect VERB bracis-28424 3 22 , , PUNCT bracis-28424 3 23 or or CCONJ bracis-28424 3 24 not not PART bracis-28424 3 25 . . PUNCT bracis-28424 4 1 thus thus ADV bracis-28424 4 2 , , PUNCT bracis-28424 4 3 a a DET bracis-28424 4 4 fundamental fundamental ADJ bracis-28424 4 5 problem problem NOUN bracis-28424 4 6 in in ADP bracis-28424 4 7 network network NOUN bracis-28424 4 8 epidemic epidemic NOUN bracis-28424 4 9 is be AUX bracis-28424 4 10 identifying identify VERB bracis-28424 4 11 the the DET bracis-28424 4 12 set set NOUN bracis-28424 4 13 of of ADP bracis-28424 4 14 source source NOUN bracis-28424 4 15 nodes node NOUN bracis-28424 4 16 after after SCONJ bracis-28424 4 17 the the DET bracis-28424 4 18 epidemic epidemic NOUN bracis-28424 4 19 has have AUX bracis-28424 4 20 reached reach VERB bracis-28424 4 21 a a DET bracis-28424 4 22 significant significant ADJ bracis-28424 4 23 fraction fraction NOUN bracis-28424 4 24 of of ADP bracis-28424 4 25 the the DET bracis-28424 4 26 network network NOUN bracis-28424 4 27 . . PUNCT bracis-28424 5 1 this this DET bracis-28424 5 2 work work NOUN bracis-28424 5 3 tackles tackle VERB bracis-28424 5 4 the the DET bracis-28424 5 5 multiple multiple ADJ bracis-28424 5 6 source source NOUN bracis-28424 5 7 detection detection NOUN bracis-28424 5 8 problem problem NOUN bracis-28424 5 9 by by ADP bracis-28424 5 10 using use VERB bracis-28424 5 11 graph graph NOUN bracis-28424 5 12 neural neural ADJ bracis-28424 5 13 network network NOUN bracis-28424 5 14 model model NOUN bracis-28424 5 15 to to PART bracis-28424 5 16 classify classify VERB bracis-28424 5 17 nodes node NOUN bracis-28424 5 18 as as ADP bracis-28424 5 19 being be AUX bracis-28424 5 20 the the DET bracis-28424 5 21 source source NOUN bracis-28424 5 22 of of ADP bracis-28424 5 23 the the DET bracis-28424 5 24 epidemic epidemic NOUN bracis-28424 5 25 . . PUNCT bracis-28424 6 1 the the DET bracis-28424 6 2 input input NOUN bracis-28424 6 3 to to ADP bracis-28424 6 4 the the DET bracis-28424 6 5 model model NOUN bracis-28424 6 6 ( ( PUNCT bracis-28424 6 7 node node NOUN bracis-28424 6 8 attributes attribute NOUN bracis-28424 6 9 ) ) PUNCT bracis-28424 6 10 are be AUX bracis-28424 6 11 novel novel ADJ bracis-28424 6 12 epidemic epidemic NOUN bracis-28424 6 13 information information NOUN bracis-28424 6 14 in in ADP bracis-28424 6 15 the the DET bracis-28424 6 16 k k PROPN bracis-28424 6 17 - - PUNCT bracis-28424 6 18 hop hop ADJ bracis-28424 6 19 neighborhoods neighborhood NOUN bracis-28424 6 20 of of ADP bracis-28424 6 21 the the DET bracis-28424 6 22 nodes node NOUN bracis-28424 6 23 . . PUNCT bracis-28424 7 1 the the DET bracis-28424 7 2 proposed propose VERB bracis-28424 7 3 framework framework NOUN bracis-28424 7 4 is be AUX bracis-28424 7 5 trained train VERB bracis-28424 7 6 and and CCONJ bracis-28424 7 7 evaluated evaluate VERB bracis-28424 7 8 under under ADP bracis-28424 7 9 different different ADJ bracis-28424 7 10 network network NOUN bracis-28424 7 11 models model NOUN bracis-28424 7 12 and and CCONJ bracis-28424 7 13 real real ADJ bracis-28424 7 14 networks network NOUN bracis-28424 7 15 and and CCONJ bracis-28424 7 16 different different ADJ bracis-28424 7 17 scenarios scenario NOUN bracis-28424 7 18 , , PUNCT bracis-28424 7 19 and and CCONJ bracis-28424 7 20 results result NOUN bracis-28424 7 21 indicate indicate VERB bracis-28424 7 22 different different ADJ bracis-28424 7 23 trade trade NOUN bracis-28424 7 24 - - PUNCT bracis-28424 7 25 offs off NOUN bracis-28424 7 26 . . PUNCT bracis-28424 8 1 in in ADP bracis-28424 8 2 a a DET bracis-28424 8 3 direct direct ADJ bracis-28424 8 4 comparison comparison NOUN bracis-28424 8 5 with with ADP bracis-28424 8 6 prior prior ADJ bracis-28424 8 7 works work NOUN bracis-28424 8 8 , , PUNCT bracis-28424 8 9 the the DET bracis-28424 8 10 proposed propose VERB bracis-28424 8 11 framework framework NOUN bracis-28424 8 12 outperformed outperform VERB bracis-28424 8 13 them they PRON bracis-28424 8 14 in in ADP bracis-28424 8 15 all all DET bracis-28424 8 16 scenarios scenario NOUN bracis-28424 8 17 available available ADJ bracis-28424 8 18 for for ADP bracis-28424 8 19 comparison comparison NOUN bracis-28424 8 20 . . PUNCT bracis-28424 9 1 this this DET bracis-28424 9 2 work work NOUN bracis-28424 9 3 has have AUX bracis-28424 9 4 received receive VERB bracis-28424 9 5 financial financial ADJ bracis-28424 9 6 support support NOUN bracis-28424 9 7 through through ADP bracis-28424 9 8 research research NOUN bracis-28424 9 9 grants grant NOUN bracis-28424 9 10 from from ADP bracis-28424 9 11 cnpq cnpq NOUN bracis-28424 9 12 and and CCONJ bracis-28424 9 13 faperj faperj PROPN bracis-28424 9 14 ( ( PUNCT bracis-28424 9 15 brazil brazil PROPN bracis-28424 9 16 ) ) PUNCT bracis-28424 9 17 . . PUNCT bracis-28424 10 1 access access NOUN bracis-28424 10 2 provided provide VERB bracis-28424 10 3 by by ADP bracis-28424 10 4 university university PROPN bracis-28424 10 5 of of ADP bracis-28424 10 6 notre notre PROPN bracis-28424 10 7 dame dame PROPN bracis-28424 10 8 hesburgh hesburgh PROPN bracis-28424 10 9 library library PROPN bracis-28424 10 10 . . PUNCT bracis-28424 11 1 download download PROPN bracis-28424 11 2 conference conference NOUN bracis-28424 11 3 paper paper NOUN bracis-28424 11 4 pdf pdf NOUN bracis-28424 11 5 similar similar ADJ bracis-28424 11 6 content content NOUN bracis-28424 11 7 being be AUX bracis-28424 11 8 viewed view VERB bracis-28424 11 9 by by ADP bracis-28424 11 10 others other NOUN bracis-28424 11 11 the the DET bracis-28424 11 12 effect effect NOUN bracis-28424 11 13 of of ADP bracis-28424 11 14 concurrency concurrency NOUN bracis-28424 11 15 on on ADP bracis-28424 11 16 epidemic epidemic NOUN bracis-28424 11 17 threshold threshold NOUN bracis-28424 11 18 in in ADP bracis-28424 11 19 time time NOUN bracis-28424 11 20 - - PUNCT bracis-28424 11 21 varying vary VERB bracis-28424 11 22 networks network NOUN bracis-28424 11 23 chapter chapter NOUN bracis-28424 11 24 © © PROPN bracis-28424 11 25 2019 2019 NUM bracis-28424 11 26 approximate approximate ADJ bracis-28424 11 27 identification identification NOUN bracis-28424 11 28 of of ADP bracis-28424 11 29 the the DET bracis-28424 11 30 optimal optimal ADJ bracis-28424 11 31 epidemic epidemic NOUN bracis-28424 11 32 source source NOUN bracis-28424 11 33 in in ADP bracis-28424 11 34 complex complex ADJ bracis-28424 11 35 networks network NOUN bracis-28424 11 36 chapter chapter NOUN bracis-28424 11 37 © © PROPN bracis-28424 11 38 2020 2020 NUM bracis-28424 11 39 information information NOUN bracis-28424 11 40 source source NOUN bracis-28424 11 41 estimation estimation NOUN bracis-28424 11 42 with with ADP bracis-28424 11 43 multi multi ADJ bracis-28424 11 44 - - ADJ bracis-28424 11 45 channel channel NOUN bracis-28424 11 46 graph graph NOUN bracis-28424 11 47 neural neural ADJ bracis-28424 11 48 network network NOUN bracis-28424 11 49 chapter chapter NOUN bracis-28424 11 50 © © PROPN bracis-28424 11 51 2021 2021 NUM bracis-28424 11 52 explore explore VERB bracis-28424 11 53 related relate VERB bracis-28424 11 54 subjects subject NOUN bracis-28424 11 55 discover discover VERB bracis-28424 11 56 the the DET bracis-28424 11 57 latest late ADJ bracis-28424 11 58 articles article NOUN bracis-28424 11 59 , , PUNCT bracis-28424 11 60 books book NOUN bracis-28424 11 61 and and CCONJ bracis-28424 11 62 news news NOUN bracis-28424 11 63 in in ADP bracis-28424 11 64 related related ADJ bracis-28424 11 65 subjects subject NOUN bracis-28424 11 66 , , PUNCT bracis-28424 11 67 suggested suggest VERB bracis-28424 11 68 using use VERB bracis-28424 11 69 machine machine NOUN bracis-28424 11 70 learning learning NOUN bracis-28424 11 71 . . PUNCT bracis-28424 12 1 complex complex ADJ bracis-28424 12 2 networks network NOUN bracis-28424 12 3 dynamic dynamic ADJ bracis-28424 12 4 networks network NOUN bracis-28424 12 5 graph graph NOUN bracis-28424 12 6 theory theory NOUN bracis-28424 12 7 network network NOUN bracis-28424 12 8 models model NOUN bracis-28424 12 9 network network NOUN bracis-28424 12 10 research research NOUN bracis-28424 12 11 stochastic stochastic NOUN bracis-28424 12 12 networks network NOUN bracis-28424 12 13 1 1 NUM bracis-28424 12 14 introduction introduction NOUN bracis-28424 12 15 epidemics epidemic NOUN bracis-28424 12 16 are be AUX bracis-28424 12 17 among among ADP bracis-28424 12 18 the the DET bracis-28424 12 19 most most ADV bracis-28424 12 20 prominent prominent ADJ bracis-28424 12 21 and and CCONJ bracis-28424 12 22 fundamental fundamental ADJ bracis-28424 12 23 processes process NOUN bracis-28424 12 24 that that PRON bracis-28424 12 25 take take VERB bracis-28424 12 26 place place NOUN bracis-28424 12 27 in in ADP bracis-28424 12 28 networks network NOUN bracis-28424 12 29 since since SCONJ bracis-28424 12 30 they they PRON bracis-28424 12 31 represent represent VERB bracis-28424 12 32 a a DET bracis-28424 12 33 diverse diverse ADJ bracis-28424 12 34 set set NOUN bracis-28424 12 35 of of ADP bracis-28424 12 36 phenomena phenomenon NOUN bracis-28424 12 37 , , PUNCT bracis-28424 12 38 e.g. e.g. ADV bracis-28424 12 39 , , PUNCT bracis-28424 12 40 the the DET bracis-28424 12 41 spread spread NOUN bracis-28424 12 42 of of ADP bracis-28424 12 43 information information NOUN bracis-28424 12 44 in in ADP bracis-28424 12 45 social social ADJ bracis-28424 12 46 media medium NOUN bracis-28424 12 47 or or CCONJ bracis-28424 12 48 biological biological ADJ bracis-28424 12 49 virus virus NOUN bracis-28424 12 50 among among ADP bracis-28424 12 51 the the DET bracis-28424 12 52 global global ADJ bracis-28424 12 53 human human ADJ bracis-28424 12 54 population population NOUN bracis-28424 13 1 [ [ X bracis-28424 13 2 4 4 NUM bracis-28424 13 3 , , PUNCT bracis-28424 13 4 14 14 NUM bracis-28424 13 5 , , PUNCT bracis-28424 13 6 15 15 NUM bracis-28424 13 7 ] ] PUNCT bracis-28424 13 8 . . PUNCT bracis-28424 14 1 in in ADP bracis-28424 14 2 a a DET bracis-28424 14 3 network network NOUN bracis-28424 14 4 epidemic epidemic NOUN bracis-28424 14 5 , , PUNCT bracis-28424 14 6 nodes node NOUN bracis-28424 14 7 have have VERB bracis-28424 14 8 an an DET bracis-28424 14 9 epidemic epidemic NOUN bracis-28424 14 10 state state NOUN bracis-28424 14 11 ( ( PUNCT bracis-28424 14 12 infected infected ADJ bracis-28424 14 13 or or CCONJ bracis-28424 14 14 susceptible susceptible ADJ bracis-28424 14 15 ) ) PUNCT bracis-28424 14 16 that that PRON bracis-28424 14 17 may may AUX bracis-28424 14 18 change change VERB bracis-28424 14 19 over over ADP bracis-28424 14 20 time time NOUN bracis-28424 14 21 while while SCONJ bracis-28424 14 22 contagion contagion NOUN bracis-28424 14 23 occurs occur VERB bracis-28424 14 24 through through ADP bracis-28424 14 25 network network NOUN bracis-28424 14 26 edges edge NOUN bracis-28424 14 27 . . PUNCT bracis-28424 15 1 it it PRON bracis-28424 15 2 is be AUX bracis-28424 15 3 not not PART bracis-28424 15 4 surprising surprising ADJ bracis-28424 15 5 that that SCONJ bracis-28424 15 6 , , PUNCT bracis-28424 15 7 over over ADP bracis-28424 15 8 the the DET bracis-28424 15 9 past past ADJ bracis-28424 15 10 decades decade NOUN bracis-28424 15 11 , , PUNCT bracis-28424 15 12 many many ADJ bracis-28424 15 13 works work NOUN bracis-28424 15 14 have have AUX bracis-28424 15 15 focused focus VERB bracis-28424 15 16 on on ADP bracis-28424 15 17 developing develop VERB bracis-28424 15 18 models model NOUN bracis-28424 15 19 to to PART bracis-28424 15 20 predict predict VERB bracis-28424 15 21 real real ADJ bracis-28424 15 22 network network NOUN bracis-28424 15 23 epidemics epidemic NOUN bracis-28424 15 24 sources source NOUN bracis-28424 15 25 for for ADP bracis-28424 15 26 various various ADJ bracis-28424 15 27 kinds kind NOUN bracis-28424 15 28 of of ADP bracis-28424 15 29 phenomena phenomenon NOUN bracis-28424 15 30 . . PUNCT bracis-28424 16 1 more more ADV bracis-28424 16 2 importantly importantly ADV bracis-28424 16 3 , , PUNCT bracis-28424 16 4 the the DET bracis-28424 16 5 focus focus NOUN bracis-28424 16 6 has have AUX bracis-28424 16 7 also also ADV bracis-28424 16 8 been be AUX bracis-28424 16 9 on on ADP bracis-28424 16 10 understanding understand VERB bracis-28424 16 11 the the DET bracis-28424 16 12 impact impact NOUN bracis-28424 16 13 that that PRON bracis-28424 16 14 different different ADJ bracis-28424 16 15 measures measure NOUN bracis-28424 16 16 have have VERB bracis-28424 16 17 on on ADP bracis-28424 16 18 the the DET bracis-28424 16 19 epidemic epidemic NOUN bracis-28424 16 20 process process NOUN bracis-28424 16 21 , , PUNCT bracis-28424 16 22 such such ADJ bracis-28424 16 23 as as ADP bracis-28424 16 24 quarantine quarantine NOUN bracis-28424 16 25 and and CCONJ bracis-28424 16 26 immunization immunization NOUN bracis-28424 16 27 , , PUNCT bracis-28424 16 28 to to PART bracis-28424 16 29 cite cite VERB bracis-28424 16 30 a a DET bracis-28424 16 31 recent recent ADJ bracis-28424 16 32 example example NOUN bracis-28424 16 33 largely largely ADV bracis-28424 16 34 debated debate VERB bracis-28424 16 35 during during ADP bracis-28424 16 36 the the DET bracis-28424 16 37 coronavirus coronavirus NOUN bracis-28424 16 38 pandemic pandemic ADJ bracis-28424 17 1 [ [ X bracis-28424 17 2 7 7 NUM bracis-28424 17 3 ] ] PUNCT bracis-28424 17 4 . . PUNCT bracis-28424 18 1 an an DET bracis-28424 18 2 epidemic epidemic NOUN bracis-28424 18 3 starts start VERB bracis-28424 18 4 with with ADP bracis-28424 18 5 the the DET bracis-28424 18 6 infection infection NOUN bracis-28424 18 7 of of ADP bracis-28424 18 8 a a DET bracis-28424 18 9 single single ADJ bracis-28424 18 10 node node NOUN bracis-28424 18 11 or or CCONJ bracis-28424 18 12 a a DET bracis-28424 18 13 few few ADJ bracis-28424 18 14 nodes node NOUN bracis-28424 18 15 , , PUNCT bracis-28424 18 16 known know VERB bracis-28424 18 17 as as ADP bracis-28424 18 18 the the DET bracis-28424 18 19 epidemic epidemic NOUN bracis-28424 18 20 sources source NOUN bracis-28424 18 21 . . PUNCT bracis-28424 19 1 from from ADP bracis-28424 19 2 this this DET bracis-28424 19 3 initial initial ADJ bracis-28424 19 4 set set NOUN bracis-28424 19 5 of of ADP bracis-28424 19 6 nodes node NOUN bracis-28424 19 7 , , PUNCT bracis-28424 19 8 the the DET bracis-28424 19 9 epidemic epidemic NOUN bracis-28424 19 10 unfolds unfold VERB bracis-28424 19 11 through through ADP bracis-28424 19 12 the the DET bracis-28424 19 13 edges edge NOUN bracis-28424 19 14 of of ADP bracis-28424 19 15 the the DET bracis-28424 19 16 network network NOUN bracis-28424 19 17 potentially potentially ADV bracis-28424 19 18 reaching reach VERB bracis-28424 19 19 a a DET bracis-28424 19 20 large large ADJ bracis-28424 19 21 fraction fraction NOUN bracis-28424 19 22 of of ADP bracis-28424 19 23 the the DET bracis-28424 19 24 network network NOUN bracis-28424 19 25 nodes nod VERB bracis-28424 19 26 . . PUNCT bracis-28424 20 1 precise precise ADJ bracis-28424 20 2 information information NOUN bracis-28424 20 3 about about ADP bracis-28424 20 4 epidemic epidemic NOUN bracis-28424 20 5 process process NOUN bracis-28424 20 6 is be AUX bracis-28424 20 7 often often ADV bracis-28424 20 8 not not PART bracis-28424 20 9 available available ADJ bracis-28424 20 10 , , PUNCT bracis-28424 20 11 such such ADJ bracis-28424 20 12 as as ADP bracis-28424 20 13 timing timing NOUN bracis-28424 20 14 or or CCONJ bracis-28424 20 15 contagion contagion NOUN bracis-28424 20 16 information information NOUN bracis-28424 20 17 . . PUNCT bracis-28424 21 1 therefore therefore ADV bracis-28424 21 2 , , PUNCT bracis-28424 21 3 a a DET bracis-28424 21 4 fundamental fundamental ADJ bracis-28424 21 5 problem problem NOUN bracis-28424 21 6 in in ADP bracis-28424 21 7 network network NOUN bracis-28424 21 8 epidemic epidemic NOUN bracis-28424 21 9 is be AUX bracis-28424 21 10 identifying identify VERB bracis-28424 21 11 the the DET bracis-28424 21 12 set set NOUN bracis-28424 21 13 of of ADP bracis-28424 21 14 source source NOUN bracis-28424 21 15 nodes node NOUN bracis-28424 21 16 after after SCONJ bracis-28424 21 17 the the DET bracis-28424 21 18 epidemic epidemic NOUN bracis-28424 21 19 has have AUX bracis-28424 21 20 reached reach VERB bracis-28424 21 21 a a DET bracis-28424 21 22 significant significant ADJ bracis-28424 21 23 fraction fraction NOUN bracis-28424 21 24 of of ADP bracis-28424 21 25 the the DET bracis-28424 21 26 network network NOUN bracis-28424 21 27 [ [ X bracis-28424 21 28 11 11 NUM bracis-28424 21 29 , , PUNCT bracis-28424 21 30 20 20 NUM bracis-28424 21 31 ] ] PUNCT bracis-28424 21 32 . . PUNCT bracis-28424 22 1 this this DET bracis-28424 22 2 problem problem NOUN bracis-28424 22 3 is be AUX bracis-28424 22 4 known know VERB bracis-28424 22 5 to to PART bracis-28424 22 6 be be AUX bracis-28424 22 7 hard hard ADJ bracis-28424 22 8 for for ADP bracis-28424 22 9 simple simple ADJ bracis-28424 22 10 epidemics epidemic NOUN bracis-28424 22 11 even even ADV bracis-28424 22 12 when when SCONJ bracis-28424 22 13 it it PRON bracis-28424 22 14 starts start VERB bracis-28424 22 15 on on ADP bracis-28424 22 16 a a DET bracis-28424 22 17 single single ADJ bracis-28424 22 18 node node NOUN bracis-28424 22 19 and and CCONJ bracis-28424 22 20 the the DET bracis-28424 22 21 network network NOUN bracis-28424 22 22 is be AUX bracis-28424 22 23 infinite infinite ADJ bracis-28424 22 24     SPACE bracis-28424 23 1 [ [ X bracis-28424 23 2 18 18 NUM bracis-28424 23 3 , , PUNCT bracis-28424 23 4 19 19 NUM bracis-28424 23 5 ] ] PUNCT bracis-28424 23 6 . . PUNCT bracis-28424 24 1 the the DET bracis-28424 24 2 difficulty difficulty NOUN bracis-28424 24 3 in in ADP bracis-28424 24 4 identifying identify VERB bracis-28424 24 5 the the DET bracis-28424 24 6 source source NOUN bracis-28424 24 7 nodes node NOUN bracis-28424 24 8 strongly strongly ADV bracis-28424 24 9 depend depend VERB bracis-28424 24 10 on on ADP bracis-28424 24 11 the the DET bracis-28424 24 12 observation observation NOUN bracis-28424 24 13 process process NOUN bracis-28424 24 14 , , PUNCT bracis-28424 24 15 i.e. i.e. X bracis-28424 24 16 , , PUNCT bracis-28424 24 17 what what PRON bracis-28424 24 18 is be AUX bracis-28424 24 19 observed observe VERB bracis-28424 24 20 from from ADP bracis-28424 24 21 the the DET bracis-28424 24 22 network network NOUN bracis-28424 24 23 epidemic epidemic NOUN bracis-28424 24 24 . . PUNCT bracis-28424 25 1 a a DET bracis-28424 25 2 common common ADJ bracis-28424 25 3 snapshot snapshot NOUN bracis-28424 25 4 model model NOUN bracis-28424 25 5 consists consist VERB bracis-28424 25 6 of of ADP bracis-28424 25 7 a a DET bracis-28424 25 8 single single ADJ bracis-28424 25 9 and and CCONJ bracis-28424 25 10 instantaneous instantaneous ADJ bracis-28424 25 11 snapshot snapshot NOUN bracis-28424 25 12 that that PRON bracis-28424 25 13 reveals reveal VERB bracis-28424 25 14 the the DET bracis-28424 25 15 epidemic epidemic NOUN bracis-28424 25 16 state state NOUN bracis-28424 25 17 of of ADP bracis-28424 25 18 all all DET bracis-28424 25 19 network network NOUN bracis-28424 25 20 nodes node NOUN bracis-28424 25 21 [ [ X bracis-28424 25 22 11 11 NUM bracis-28424 25 23 , , PUNCT bracis-28424 25 24 20 20 NUM bracis-28424 25 25 ] ] PUNCT bracis-28424 25 26 . . PUNCT bracis-28424 26 1 if if SCONJ bracis-28424 26 2 the the DET bracis-28424 26 3 snapshot snapshot NOUN bracis-28424 26 4 is be AUX bracis-28424 26 5 taken take VERB bracis-28424 26 6 very very ADV bracis-28424 26 7 early early ADV bracis-28424 26 8 in in ADP bracis-28424 26 9 the the DET bracis-28424 26 10 epidemic epidemic NOUN bracis-28424 26 11 process process NOUN bracis-28424 26 12 , , PUNCT bracis-28424 26 13 very very ADV bracis-28424 26 14 few few ADJ bracis-28424 26 15 nodes node NOUN bracis-28424 26 16 will will AUX bracis-28424 26 17 be be AUX bracis-28424 26 18 infected infect VERB bracis-28424 26 19 and and CCONJ bracis-28424 26 20 identifying identify VERB bracis-28424 26 21 the the DET bracis-28424 26 22 source source NOUN bracis-28424 26 23 nodes node NOUN bracis-28424 26 24 is be AUX bracis-28424 26 25 intuitively intuitively ADV bracis-28424 26 26 easier easy ADJ bracis-28424 26 27 . . PUNCT bracis-28424 27 1 on on ADP bracis-28424 27 2 the the DET bracis-28424 27 3 other other ADJ bracis-28424 27 4 hand hand NOUN bracis-28424 27 5 , , PUNCT bracis-28424 27 6 if if SCONJ bracis-28424 27 7 it it PRON bracis-28424 27 8 is be AUX bracis-28424 27 9 taken take VERB bracis-28424 27 10 very very ADV bracis-28424 27 11 late late ADV bracis-28424 27 12 , , PUNCT bracis-28424 27 13 i.e. i.e. X bracis-28424 27 14 , , PUNCT bracis-28424 27 15 once once SCONJ bracis-28424 27 16 all all DET bracis-28424 27 17 nodes node NOUN bracis-28424 27 18 have have AUX bracis-28424 27 19 been be AUX bracis-28424 27 20 infected infect VERB bracis-28424 27 21 , , PUNCT bracis-28424 27 22 there there PRON bracis-28424 27 23 is be VERB bracis-28424 27 24 no no DET bracis-28424 27 25 information information NOUN bracis-28424 27 26 that that PRON bracis-28424 27 27 can can AUX bracis-28424 27 28 be be AUX bracis-28424 27 29 used use VERB bracis-28424 27 30 to to PART bracis-28424 27 31 identify identify VERB bracis-28424 27 32 the the DET bracis-28424 27 33 source source NOUN bracis-28424 27 34 nodes nod VERB bracis-28424 27 35 . . PUNCT bracis-28424 28 1 the the DET bracis-28424 28 2 time time NOUN bracis-28424 28 3 the the DET bracis-28424 28 4 snapshot snapshot NOUN bracis-28424 28 5 is be AUX bracis-28424 28 6 taken take VERB bracis-28424 28 7 can can AUX bracis-28424 28 8 be be AUX bracis-28424 28 9 translated translate VERB bracis-28424 28 10 to to ADP bracis-28424 28 11 the the DET bracis-28424 28 12 moment moment NOUN bracis-28424 28 13 the the DET bracis-28424 28 14 epidemic epidemic NOUN bracis-28424 28 15 reaches reach VERB bracis-28424 28 16 a a DET bracis-28424 28 17 certain certain ADJ bracis-28424 28 18 fraction fraction NOUN bracis-28424 28 19 of of ADP bracis-28424 28 20 nodes node NOUN bracis-28424 28 21 , , PUNCT bracis-28424 28 22 which which PRON bracis-28424 28 23 is be AUX bracis-28424 28 24 the the DET bracis-28424 28 25 model model NOUN bracis-28424 28 26 used use VERB bracis-28424 28 27 in in ADP bracis-28424 28 28 this this DET bracis-28424 28 29 paper paper NOUN bracis-28424 28 30 . . PUNCT bracis-28424 29 1 the the DET bracis-28424 29 2 source source NOUN bracis-28424 29 3 identification identification NOUN bracis-28424 29 4 problem problem NOUN bracis-28424 29 5 can can AUX bracis-28424 29 6 be be AUX bracis-28424 29 7 posed pose VERB bracis-28424 29 8 as as ADP bracis-28424 29 9 a a DET bracis-28424 29 10 classification classification NOUN bracis-28424 29 11 problem problem NOUN bracis-28424 29 12 as as ADP bracis-28424 29 13 , , PUNCT bracis-28424 29 14 given give VERB bracis-28424 29 15 an an DET bracis-28424 29 16 epidemic epidemic NOUN bracis-28424 29 17 snapshot snapshot NOUN bracis-28424 29 18 , , PUNCT bracis-28424 29 19 every every DET bracis-28424 29 20 node node NOUN bracis-28424 29 21 is be AUX bracis-28424 29 22 to to PART bracis-28424 29 23 be be AUX bracis-28424 29 24 classified classify VERB bracis-28424 29 25 as as ADP bracis-28424 29 26 being be AUX bracis-28424 29 27 an an DET bracis-28424 29 28 epidemic epidemic NOUN bracis-28424 29 29 source source NOUN bracis-28424 29 30 , , PUNCT bracis-28424 29 31 or or CCONJ bracis-28424 29 32 not not PART bracis-28424 29 33 [ [ X bracis-28424 29 34 3 3 NUM bracis-28424 29 35 , , PUNCT bracis-28424 29 36 17 17 NUM bracis-28424 29 37 ] ] PUNCT bracis-28424 29 38 . . PUNCT bracis-28424 30 1 besides besides SCONJ bracis-28424 30 2 the the DET bracis-28424 30 3 epidemic epidemic NOUN bracis-28424 30 4 state state NOUN bracis-28424 30 5 of of ADP bracis-28424 30 6 the the DET bracis-28424 30 7 nodes node NOUN bracis-28424 30 8 provided provide VERB bracis-28424 30 9 in in ADP bracis-28424 30 10 the the DET bracis-28424 30 11 snapshot snapshot NOUN bracis-28424 30 12 , , PUNCT bracis-28424 30 13 the the DET bracis-28424 30 14 network network NOUN bracis-28424 30 15 structure structure NOUN bracis-28424 30 16 is be AUX bracis-28424 30 17 also also ADV bracis-28424 30 18 available available ADJ bracis-28424 30 19 to to ADP bracis-28424 30 20 the the DET bracis-28424 30 21 classification classification NOUN bracis-28424 30 22 model model NOUN bracis-28424 30 23 . . PUNCT bracis-28424 31 1 therefore therefore ADV bracis-28424 31 2 , , PUNCT bracis-28424 31 3 a a DET bracis-28424 31 4 natural natural ADJ bracis-28424 31 5 classification classification NOUN bracis-28424 31 6 model model NOUN bracis-28424 31 7 is be AUX bracis-28424 31 8 one one NUM bracis-28424 31 9 that that PRON bracis-28424 31 10 takes take VERB bracis-28424 31 11 advantage advantage NOUN bracis-28424 31 12 of of ADP bracis-28424 31 13 the the DET bracis-28424 31 14 network network NOUN bracis-28424 31 15 over over ADP bracis-28424 31 16 which which PRON bracis-28424 31 17 the the DET bracis-28424 31 18 epidemic epidemic NOUN bracis-28424 31 19 unfolds unfold VERB bracis-28424 31 20 . . PUNCT bracis-28424 32 1 graph graph NOUN bracis-28424 32 2 neural neural ADJ bracis-28424 32 3 networks network NOUN bracis-28424 32 4 ( ( PUNCT bracis-28424 32 5 gnns gnns NOUN bracis-28424 32 6 ) ) PUNCT bracis-28424 32 7 seem seem VERB bracis-28424 32 8 well well ADV bracis-28424 32 9 - - PUNCT bracis-28424 32 10 suited suited ADJ bracis-28424 32 11 for for ADP bracis-28424 32 12 this this DET bracis-28424 32 13 task task NOUN bracis-28424 32 14 since since SCONJ bracis-28424 32 15 this this DET bracis-28424 32 16 model model NOUN bracis-28424 32 17 integrates integrate VERB bracis-28424 32 18 neighboring neighboring NOUN bracis-28424 32 19 information information NOUN bracis-28424 32 20 . . PUNCT bracis-28424 33 1 however however ADV bracis-28424 33 2 , , PUNCT bracis-28424 33 3 two two NUM bracis-28424 33 4 nodes node NOUN bracis-28424 33 5 that that PRON bracis-28424 33 6 have have VERB bracis-28424 33 7 too too ADV bracis-28424 33 8 many many ADJ bracis-28424 33 9 neighbors neighbor NOUN bracis-28424 33 10 in in ADP bracis-28424 33 11 common common ADJ bracis-28424 33 12 are be AUX bracis-28424 33 13 likely likely ADJ bracis-28424 33 14 to to PART bracis-28424 33 15 have have VERB bracis-28424 33 16 similar similar ADJ bracis-28424 33 17 representations representation NOUN bracis-28424 33 18 under under ADP bracis-28424 33 19 classic classic ADJ bracis-28424 33 20 gnn gnn NOUN bracis-28424 33 21 models model NOUN bracis-28424 33 22 which which PRON bracis-28424 33 23 would would AUX bracis-28424 33 24 not not PART bracis-28424 33 25 be be AUX bracis-28424 33 26 suited suit VERB bracis-28424 33 27 for for ADP bracis-28424 33 28 source source NOUN bracis-28424 33 29 identification identification NOUN bracis-28424 33 30 , , PUNCT bracis-28424 33 31 since since SCONJ bracis-28424 33 32 neighbors neighbor NOUN bracis-28424 33 33 of of ADP bracis-28424 33 34 the the DET bracis-28424 33 35 source source NOUN bracis-28424 33 36 node node NOUN bracis-28424 33 37 are be AUX bracis-28424 33 38 often often ADV bracis-28424 33 39 not not PART bracis-28424 33 40 a a DET bracis-28424 33 41 source source NOUN bracis-28424 33 42 ( ( PUNCT bracis-28424 33 43 depending depend VERB bracis-28424 33 44 on on ADP bracis-28424 33 45 how how SCONJ bracis-28424 33 46 source source NOUN bracis-28424 33 47 nodes node NOUN bracis-28424 33 48 are be AUX bracis-28424 33 49 chosen choose VERB bracis-28424 33 50 ) ) PUNCT bracis-28424 33 51 . . PUNCT bracis-28424 34 1 in in ADP bracis-28424 34 2 order order NOUN bracis-28424 34 3 to to PART bracis-28424 34 4 tackle tackle VERB bracis-28424 34 5 this this DET bracis-28424 34 6 issue issue NOUN bracis-28424 34 7 , , PUNCT bracis-28424 34 8 this this DET bracis-28424 34 9 work work NOUN bracis-28424 34 10 leverages leverage VERB bracis-28424 34 11 the the DET bracis-28424 34 12 epidemic epidemic NOUN bracis-28424 34 13 information information NOUN bracis-28424 34 14 within within ADP bracis-28424 34 15 the the DET bracis-28424 34 16 k k ADJ bracis-28424 34 17 - - PUNCT bracis-28424 34 18 hop hop ADJ bracis-28424 34 19 neighborhood neighborhood NOUN bracis-28424 34 20 of of ADP bracis-28424 34 21 the the DET bracis-28424 34 22 node node NOUN bracis-28424 34 23 . . PUNCT bracis-28424 35 1 two two NUM bracis-28424 35 2 metrics metric NOUN bracis-28424 35 3 are be AUX bracis-28424 35 4 proposed propose VERB bracis-28424 35 5 : : PUNCT bracis-28424 35 6 the the DET bracis-28424 35 7 fraction fraction NOUN bracis-28424 35 8 of of ADP bracis-28424 35 9 nodes node NOUN bracis-28424 35 10 infected infect VERB bracis-28424 35 11 at at ADP bracis-28424 35 12 the the DET bracis-28424 35 13 k k PROPN bracis-28424 35 14 - - PUNCT bracis-28424 35 15 hop hop ADJ bracis-28424 35 16 neighborhood neighborhood NOUN bracis-28424 35 17 and and CCONJ bracis-28424 35 18 the the DET bracis-28424 35 19 average average ADJ bracis-28424 35 20 infection infection NOUN bracis-28424 35 21 rate rate NOUN bracis-28424 35 22 at at ADP bracis-28424 35 23 the the DET bracis-28424 35 24 k k ADJ bracis-28424 35 25 - - PUNCT bracis-28424 35 26 hop hop ADJ bracis-28424 35 27 neighborhood neighborhood NOUN bracis-28424 35 28 ( ( PUNCT bracis-28424 35 29 to to PART bracis-28424 35 30 be be AUX bracis-28424 35 31 discussed discuss VERB bracis-28424 35 32 in in ADP bracis-28424 35 33 detail detail NOUN bracis-28424 35 34 ) ) PUNCT bracis-28424 35 35 . . PUNCT bracis-28424 36 1 these these DET bracis-28424 36 2 metrics metric NOUN bracis-28424 36 3 are be AUX bracis-28424 36 4 a a DET bracis-28424 36 5 function function NOUN bracis-28424 36 6 of of ADP bracis-28424 36 7 the the DET bracis-28424 36 8 epidemic epidemic NOUN bracis-28424 36 9 snapshot snapshot NOUN bracis-28424 36 10 and and CCONJ bracis-28424 36 11 are be AUX bracis-28424 36 12 computed compute VERB bracis-28424 36 13 for for SCONJ bracis-28424 36 14 every every DET bracis-28424 36 15 network network NOUN bracis-28424 36 16 node node NOUN bracis-28424 36 17 efficiently efficiently ADV bracis-28424 36 18 . . PUNCT bracis-28424 37 1 the the DET bracis-28424 37 2 information information NOUN bracis-28424 37 3 , , PUNCT bracis-28424 37 4 i.e. i.e. X bracis-28424 37 5 , , PUNCT bracis-28424 37 6 vector vector NOUN bracis-28424 37 7 of of ADP bracis-28424 37 8 rational rational ADJ bracis-28424 37 9 numbers number NOUN bracis-28424 37 10 for for ADP bracis-28424 37 11 each each DET bracis-28424 37 12 metric metric NOUN bracis-28424 37 13 , , PUNCT bracis-28424 37 14 is be AUX bracis-28424 37 15 taken take VERB bracis-28424 37 16 as as ADP bracis-28424 37 17 node node NOUN bracis-28424 37 18 attribute attribute NOUN bracis-28424 37 19 , , PUNCT bracis-28424 37 20 distinguishing distinguish VERB bracis-28424 37 21 neighboring neighboring NOUN bracis-28424 37 22 nodes node NOUN bracis-28424 37 23 much much ADJ bracis-28424 37 24 beyond beyond ADP bracis-28424 37 25 their their PRON bracis-28424 37 26 epidemic epidemic NOUN bracis-28424 37 27 state state NOUN bracis-28424 37 28 and and CCONJ bracis-28424 37 29 hence hence ADV bracis-28424 37 30 providing provide VERB bracis-28424 37 31 better well ADJ bracis-28424 37 32 inputs input NOUN bracis-28424 37 33 to to ADP bracis-28424 37 34 the the DET bracis-28424 37 35 gnn gnn PROPN bracis-28424 37 36 model model NOUN bracis-28424 37 37 . . PUNCT bracis-28424 38 1 the the DET bracis-28424 38 2 remainder remainder NOUN bracis-28424 38 3 of of ADP bracis-28424 38 4 this this DET bracis-28424 38 5 paper paper NOUN bracis-28424 38 6 is be AUX bracis-28424 38 7 organized organize VERB bracis-28424 38 8 as as SCONJ bracis-28424 38 9 follows follow VERB bracis-28424 38 10 . . PUNCT bracis-28424 39 1 in in ADP bracis-28424 39 2 sect sect NOUN bracis-28424 39 3 . . PUNCT bracis-28424 39 4     SPACE bracis-28424 39 5 2 2 NUM bracis-28424 39 6 , , PUNCT bracis-28424 39 7 network network NOUN bracis-28424 39 8 epidemic epidemic NOUN bracis-28424 39 9 and and CCONJ bracis-28424 39 10 multiple multiple ADJ bracis-28424 39 11 source source NOUN bracis-28424 39 12 detection detection NOUN bracis-28424 39 13 problem problem NOUN bracis-28424 39 14 are be AUX bracis-28424 39 15 introduced introduce VERB bracis-28424 39 16 . . PUNCT bracis-28424 40 1 a a DET bracis-28424 40 2 brief brief ADJ bracis-28424 40 3 discussion discussion NOUN bracis-28424 40 4 of of ADP bracis-28424 40 5 the the DET bracis-28424 40 6 related relate VERB bracis-28424 40 7 work work NOUN bracis-28424 40 8 is be AUX bracis-28424 40 9 presented present VERB bracis-28424 40 10 in in ADP bracis-28424 40 11 sect sect NOUN bracis-28424 40 12 . . PUNCT bracis-28424 40 13     SPACE bracis-28424 41 1 3 3 X bracis-28424 41 2 . . PUNCT bracis-28424 41 3 in in ADP bracis-28424 41 4 sect sect NOUN bracis-28424 41 5 . . PUNCT bracis-28424 41 6     SPACE bracis-28424 42 1 4 4 NUM bracis-28424 42 2 , , PUNCT bracis-28424 42 3 the the DET bracis-28424 42 4 proposed propose VERB bracis-28424 42 5 framework framework NOUN bracis-28424 42 6 is be AUX bracis-28424 42 7 presented present VERB bracis-28424 42 8 . . PUNCT bracis-28424 43 1 the the DET bracis-28424 43 2 evaluation evaluation NOUN bracis-28424 43 3 of of ADP bracis-28424 43 4 the the DET bracis-28424 43 5 proposed propose VERB bracis-28424 43 6 framework framework NOUN bracis-28424 43 7 under under ADP bracis-28424 43 8 different different ADJ bracis-28424 43 9 scenarios scenario NOUN bracis-28424 43 10 is be AUX bracis-28424 43 11 shown show VERB bracis-28424 43 12 in in ADP bracis-28424 43 13 sect sect NOUN bracis-28424 43 14 . . PUNCT bracis-28424 43 15     SPACE bracis-28424 44 1 5 5 NUM bracis-28424 44 2 . . PUNCT bracis-28424 45 1 finally finally ADV bracis-28424 45 2 , , PUNCT bracis-28424 45 3 sect sect NOUN bracis-28424 45 4 . . PUNCT bracis-28424 45 5     SPACE bracis-28424 45 6 6 6 NUM bracis-28424 45 7 presents present VERB bracis-28424 45 8 a a DET bracis-28424 45 9 brief brief ADJ bracis-28424 45 10 conclusion conclusion NOUN bracis-28424 45 11 for for ADP bracis-28424 45 12 the the DET bracis-28424 45 13 paper paper NOUN bracis-28424 45 14 . . PUNCT bracis-28424 46 1 2 2 NUM bracis-28424 46 2 network network NOUN bracis-28424 46 3 epidemics epidemic NOUN bracis-28424 46 4 and and CCONJ bracis-28424 46 5     SPACE bracis-28424 46 6 problem problem NOUN bracis-28424 46 7 statement statement NOUN bracis-28424 46 8 network network NOUN bracis-28424 46 9 epidemics epidemic NOUN bracis-28424 46 10 reflect reflect VERB bracis-28424 46 11 different different ADJ bracis-28424 46 12 phenomena phenomenon NOUN bracis-28424 46 13 , , PUNCT bracis-28424 46 14 such such ADJ bracis-28424 46 15 as as ADP bracis-28424 46 16 influence influence NOUN bracis-28424 46 17 models model NOUN bracis-28424 46 18 that that PRON bracis-28424 46 19 describe describe VERB bracis-28424 46 20 “ " PUNCT bracis-28424 46 21 social social ADJ bracis-28424 46 22 contagion contagion NOUN bracis-28424 46 23 ” " PUNCT bracis-28424 47 1 [ [ X bracis-28424 47 2 2 2 NUM bracis-28424 47 3 ] ] PUNCT bracis-28424 47 4 among among ADP bracis-28424 47 5 individuals individual NOUN bracis-28424 47 6 of of ADP bracis-28424 47 7 a a DET bracis-28424 47 8 offline offline ADJ bracis-28424 47 9 or or CCONJ bracis-28424 47 10 online online ADJ bracis-28424 47 11 social social ADJ bracis-28424 47 12 network network NOUN bracis-28424 47 13 , , PUNCT bracis-28424 47 14 and and CCONJ bracis-28424 47 15 infection infection NOUN bracis-28424 47 16 models model NOUN bracis-28424 47 17 that that PRON bracis-28424 47 18 describe describe VERB bracis-28424 47 19 the the DET bracis-28424 47 20 contagion contagion NOUN bracis-28424 47 21 of of ADP bracis-28424 47 22 a a DET bracis-28424 47 23 biological biological ADJ bracis-28424 47 24 disease disease NOUN bracis-28424 47 25 among among ADP bracis-28424 47 26 a a DET bracis-28424 47 27 population population NOUN bracis-28424 47 28 . . PUNCT bracis-28424 48 1 while while SCONJ bracis-28424 48 2 social social ADJ bracis-28424 48 3 and and CCONJ bracis-28424 48 4 biological biological ADJ bracis-28424 48 5 epidemics epidemic NOUN bracis-28424 48 6 have have VERB bracis-28424 48 7 fundamentally fundamentally ADV bracis-28424 48 8 different different ADJ bracis-28424 48 9 underlying underlying ADJ bracis-28424 48 10 contagion contagion NOUN bracis-28424 48 11 mechanisms mechanism NOUN bracis-28424 48 12 , , PUNCT bracis-28424 48 13 their their PRON bracis-28424 48 14 essence essence NOUN bracis-28424 48 15 can can AUX bracis-28424 48 16 be be AUX bracis-28424 48 17 represented represent VERB bracis-28424 48 18 by by ADP bracis-28424 48 19 simple simple ADJ bracis-28424 48 20 epidemic epidemic NOUN bracis-28424 48 21 models model NOUN bracis-28424 48 22 . . PUNCT bracis-28424 49 1 the the DET bracis-28424 49 2 simplest simple ADJ bracis-28424 49 3 epidemic epidemic NOUN bracis-28424 49 4 model model NOUN bracis-28424 49 5 is be AUX bracis-28424 49 6 the the DET bracis-28424 49 7 compartmental compartmental ADJ bracis-28424 49 8 model model NOUN bracis-28424 49 9 where where SCONJ bracis-28424 49 10 each each DET bracis-28424 49 11 individual individual NOUN bracis-28424 49 12 is be AUX bracis-28424 49 13 in in ADP bracis-28424 49 14 one one NUM bracis-28424 49 15 of of ADP bracis-28424 49 16 only only ADV bracis-28424 49 17 two two NUM bracis-28424 49 18 possible possible ADJ bracis-28424 49 19 epidemic epidemic NOUN bracis-28424 49 20 states state NOUN bracis-28424 49 21 : : PUNCT bracis-28424 49 22 susceptible susceptible ADJ bracis-28424 49 23 or or CCONJ bracis-28424 49 24 infected infected ADJ bracis-28424 49 25 . . PUNCT bracis-28424 50 1 this this DET bracis-28424 50 2 model model NOUN bracis-28424 50 3 is be AUX bracis-28424 50 4 known know VERB bracis-28424 50 5 as as ADP bracis-28424 50 6 the the DET bracis-28424 50 7 classic classic ADJ bracis-28424 50 8 si si X bracis-28424 50 9 epidemic epidemic NOUN bracis-28424 50 10 model model NOUN bracis-28424 50 11 [ [ X bracis-28424 50 12 12 12 NUM bracis-28424 50 13 ] ] PUNCT bracis-28424 50 14 where where SCONJ bracis-28424 50 15 individuals individual NOUN bracis-28424 50 16 can can AUX bracis-28424 50 17 only only ADV bracis-28424 50 18 change change VERB bracis-28424 50 19 from from ADP bracis-28424 50 20 the the DET bracis-28424 50 21 susceptible susceptible ADJ bracis-28424 50 22 to to ADP bracis-28424 50 23 infected infect VERB bracis-28424 50 24 . . PUNCT bracis-28424 51 1 in in ADP bracis-28424 51 2 the the DET bracis-28424 51 3 context context NOUN bracis-28424 51 4 of of ADP bracis-28424 51 5 networks network NOUN bracis-28424 51 6 , , PUNCT bracis-28424 51 7 individuals individual NOUN bracis-28424 51 8 are be AUX bracis-28424 51 9 represented represent VERB bracis-28424 51 10 by by ADP bracis-28424 51 11 network network NOUN bracis-28424 51 12 nodes node NOUN bracis-28424 51 13 , , PUNCT bracis-28424 51 14 and and CCONJ bracis-28424 51 15 edges edge NOUN bracis-28424 51 16 indicate indicate VERB bracis-28424 51 17 the the DET bracis-28424 51 18 possibility possibility NOUN bracis-28424 51 19 of of ADP bracis-28424 51 20 contagion contagion NOUN bracis-28424 51 21 . . PUNCT bracis-28424 52 1 thus thus ADV bracis-28424 52 2 , , PUNCT bracis-28424 52 3 let let AUX bracis-28424 52 4 \(g=(v \(g=(v NOUN bracis-28424 52 5 , , PUNCT bracis-28424 52 6 e)\ e)\ NUM bracis-28424 52 7 ) ) PUNCT bracis-28424 52 8 denotes denote VERB bracis-28424 52 9 a a DET bracis-28424 52 10 undirected undirected ADJ bracis-28424 52 11 network network NOUN bracis-28424 52 12 ( ( PUNCT bracis-28424 52 13 graph graph NOUN bracis-28424 52 14 ) ) PUNCT bracis-28424 52 15 where where SCONJ bracis-28424 52 16 v v NOUN bracis-28424 52 17 and and CCONJ bracis-28424 52 18 e e NOUN bracis-28424 52 19 denote denote VERB bracis-28424 52 20 the the DET bracis-28424 52 21 set set NOUN bracis-28424 52 22 of of ADP bracis-28424 52 23 nodes node NOUN bracis-28424 52 24 and and CCONJ bracis-28424 52 25 edges edge NOUN bracis-28424 52 26 , , PUNCT bracis-28424 52 27 respectively respectively ADV bracis-28424 52 28 , , PUNCT bracis-28424 52 29 and and CCONJ bracis-28424 52 30 \(n= \(n= NOUN bracis-28424 52 31 |v|\ |v|\ NOUN bracis-28424 52 32 ) ) PUNCT bracis-28424 52 33 denotes denote VERB bracis-28424 52 34 the the DET bracis-28424 52 35 number number NOUN bracis-28424 52 36 of of ADP bracis-28424 52 37 nodes node NOUN bracis-28424 52 38 . . PUNCT bracis-28424 53 1 the the DET bracis-28424 53 2 si si PROPN bracis-28424 53 3 network network NOUN bracis-28424 53 4 epidemic epidemic NOUN bracis-28424 53 5 model model NOUN bracis-28424 53 6 here here ADV bracis-28424 53 7 considered consider VERB bracis-28424 53 8 is be AUX bracis-28424 53 9 a a DET bracis-28424 53 10 discrete discrete ADJ bracis-28424 53 11 time time NOUN bracis-28424 53 12 model model NOUN bracis-28424 53 13 . . PUNCT bracis-28424 54 1 let let AUX bracis-28424 54 2 i(t i(t NOUN bracis-28424 54 3 ) ) PUNCT bracis-28424 54 4 and and CCONJ bracis-28424 54 5 s(t s(t NUM bracis-28424 54 6 ) ) PUNCT bracis-28424 54 7 denote denote VERB bracis-28424 54 8 the the DET bracis-28424 54 9 set set NOUN bracis-28424 54 10 of of ADP bracis-28424 54 11 infected infected ADJ bracis-28424 54 12 and and CCONJ bracis-28424 54 13 susceptible susceptible ADJ bracis-28424 54 14 nodes node NOUN bracis-28424 54 15 at at ADP bracis-28424 54 16 time time NOUN bracis-28424 54 17 t. t. PROPN bracis-28424 54 18 note note VERB bracis-28424 54 19 that that SCONJ bracis-28424 54 20 \(i(t \(i(t NOUN bracis-28424 54 21 ) ) PUNCT bracis-28424 54 22 \bigcup \bigcup PROPN bracis-28424 54 23 s(t s(t PROPN bracis-28424 54 24 ) ) PUNCT bracis-28424 54 25 = = SYM bracis-28424 55 1 v\ v\ NOUN bracis-28424 55 2 ) ) PUNCT bracis-28424 55 3 and and CCONJ bracis-28424 55 4 \(i(t \(i(t PROPN bracis-28424 55 5 ) ) PUNCT bracis-28424 55 6 \bigcap \bigcap PROPN bracis-28424 55 7 s(t s(t PROPN bracis-28424 55 8 ) ) PUNCT bracis-28424 55 9 = = PUNCT bracis-28424 55 10 \emptyset \emptyset VERB bracis-28424 55 11 \ \ NOUN bracis-28424 55 12 ) ) PUNCT bracis-28424 55 13 for for ADP bracis-28424 55 14 all all DET bracis-28424 55 15 \(t=0,1,\ldots \(t=0,1,\ldot NOUN bracis-28424 55 16 \ \ NOUN bracis-28424 55 17 ) ) PUNCT bracis-28424 55 18 . . PUNCT bracis-28424 56 1 let let AUX bracis-28424 56 2 \(i_0 \(i_0 PROPN bracis-28424 56 3 \subset \subset PROPN bracis-28424 56 4 v\ v\ NOUN bracis-28424 56 5 ) ) PUNCT bracis-28424 56 6 denote denote VERB bracis-28424 56 7 the the DET bracis-28424 56 8 set set NOUN bracis-28424 56 9 of of ADP bracis-28424 56 10 epidemic epidemic NOUN bracis-28424 56 11 sources source NOUN bracis-28424 56 12 , , PUNCT bracis-28424 56 13 namely namely ADV bracis-28424 56 14 , , PUNCT bracis-28424 56 15 the the DET bracis-28424 56 16 set set NOUN bracis-28424 56 17 of of ADP bracis-28424 56 18 nodes node NOUN bracis-28424 56 19 that that PRON bracis-28424 56 20 are be AUX bracis-28424 56 21 infected infect VERB bracis-28424 56 22 at at ADP bracis-28424 56 23 time time NOUN bracis-28424 56 24 zero zero NUM bracis-28424 56 25 , , PUNCT bracis-28424 56 26 thus thus ADV bracis-28424 56 27 , , PUNCT bracis-28424 56 28 \(i(0 \(i(0 NOUN bracis-28424 56 29 ) ) PUNCT bracis-28424 56 30 = = PUNCT bracis-28424 56 31 i_0\ i_0\ PROPN bracis-28424 56 32 ) ) PUNCT bracis-28424 56 33 . . PUNCT bracis-28424 57 1 at at ADP bracis-28424 57 2 each each DET bracis-28424 57 3 time time NOUN bracis-28424 57 4 slot slot NOUN bracis-28424 57 5 , , PUNCT bracis-28424 57 6 an an DET bracis-28424 57 7 infected infected ADJ bracis-28424 57 8 node node NOUN bracis-28424 57 9 infects infect VERB bracis-28424 57 10 each each PRON bracis-28424 57 11 of of ADP bracis-28424 57 12 its its PRON bracis-28424 57 13 susceptible susceptible ADJ bracis-28424 57 14 neighbors neighbor NOUN bracis-28424 57 15 with with ADP bracis-28424 57 16 probability probability NOUN bracis-28424 57 17 p. p. NOUN bracis-28424 57 18 note note NOUN bracis-28424 57 19 that that SCONJ bracis-28424 57 20 infection infection NOUN bracis-28424 57 21 fails fail VERB bracis-28424 57 22 with with ADP bracis-28424 57 23 probability probability NOUN bracis-28424 57 24 \(1 \(1 NOUN bracis-28424 57 25 - - PUNCT bracis-28424 57 26 p\ p\ NOUN bracis-28424 57 27 ) ) PUNCT bracis-28424 57 28 , , PUNCT bracis-28424 57 29 but but CCONJ bracis-28424 57 30 the the DET bracis-28424 57 31 infected infected ADJ bracis-28424 57 32 node node NOUN bracis-28424 57 33 is be AUX bracis-28424 57 34 able able ADJ bracis-28424 57 35 to to PART bracis-28424 57 36 infect infect VERB bracis-28424 57 37 the the DET bracis-28424 57 38 same same ADJ bracis-28424 57 39 susceptible susceptible ADJ bracis-28424 57 40 neighbor neighbor NOUN bracis-28424 57 41 with with ADP bracis-28424 57 42 probability probability NOUN bracis-28424 57 43 p p NOUN bracis-28424 57 44 on on ADP bracis-28424 57 45 subsequent subsequent ADJ bracis-28424 57 46 time time NOUN bracis-28424 57 47 slots slot NOUN bracis-28424 57 48 . . PUNCT bracis-28424 58 1 a a DET bracis-28424 58 2 susceptible susceptible ADJ bracis-28424 58 3 node node NOUN bracis-28424 58 4 that that PRON bracis-28424 58 5 has have VERB bracis-28424 58 6 j j PROPN bracis-28424 58 7 infected infect VERB bracis-28424 58 8 neighbors neighbor NOUN bracis-28424 58 9 in in ADP bracis-28424 58 10 the the DET bracis-28424 58 11 current current ADJ bracis-28424 58 12 time time NOUN bracis-28424 58 13 step step NOUN bracis-28424 58 14 becomes becomes AUX bracis-28424 58 15 infected infect VERB bracis-28424 58 16 in in ADP bracis-28424 58 17 the the DET bracis-28424 58 18 next next ADJ bracis-28424 58 19 time time NOUN bracis-28424 58 20 step step NOUN bracis-28424 58 21 with with ADP bracis-28424 58 22 probability probability NOUN bracis-28424 58 23 \(1-(1 \(1-(1 NOUN bracis-28424 58 24 - - PUNCT bracis-28424 58 25 p)^j\ p)^j\ NOUN bracis-28424 58 26 ) ) PUNCT bracis-28424 58 27 . . PUNCT bracis-28424 59 1 nodes node NOUN bracis-28424 59 2 become become VERB bracis-28424 59 3 infected infected ADJ bracis-28424 59 4 in in ADP bracis-28424 59 5 the the DET bracis-28424 59 6 same same ADJ bracis-28424 59 7 time time NOUN bracis-28424 59 8 slot slot NOUN bracis-28424 59 9 and and CCONJ bracis-28424 59 10 never never ADV bracis-28424 59 11 recover recover VERB bracis-28424 59 12 , , PUNCT bracis-28424 59 13 causing cause VERB bracis-28424 59 14 i(t i(t NOUN bracis-28424 59 15 ) ) PUNCT bracis-28424 59 16 to to PART bracis-28424 59 17 be be AUX bracis-28424 59 18 non non ADJ bracis-28424 59 19 - - ADJ bracis-28424 59 20 decreasing decrease VERB bracis-28424 59 21 with with ADP bracis-28424 59 22 t. t. PROPN bracis-28424 59 23 last last ADJ bracis-28424 59 24 , , PUNCT bracis-28424 59 25 assuming assume VERB bracis-28424 59 26 the the DET bracis-28424 59 27 network network NOUN bracis-28424 59 28 is be AUX bracis-28424 59 29 connected connect VERB bracis-28424 59 30 , , PUNCT bracis-28424 59 31 it it PRON bracis-28424 59 32 can can AUX bracis-28424 59 33 be be AUX bracis-28424 59 34 shown show VERB bracis-28424 59 35 that that SCONJ bracis-28424 59 36 there there PRON bracis-28424 59 37 exists exist VERB bracis-28424 59 38 a a DET bracis-28424 59 39 finite finite NOUN bracis-28424 59 40 large large ADJ bracis-28424 59 41 enough enough ADV bracis-28424 59 42 \(t^*\ \(t^*\ NOUN bracis-28424 59 43 ) ) PUNCT bracis-28424 59 44 such such ADJ bracis-28424 59 45 that that SCONJ bracis-28424 59 46 \(i(t^ \(i(t^ NOUN bracis-28424 59 47 * * PUNCT bracis-28424 59 48 ) ) PUNCT bracis-28424 60 1 = = SYM bracis-28424 60 2 v\ v\ NOUN bracis-28424 60 3 ) ) PUNCT bracis-28424 60 4 with with ADP bracis-28424 60 5 high high ADJ bracis-28424 60 6 probability probability NOUN bracis-28424 60 7 , , PUNCT bracis-28424 60 8 and and CCONJ bracis-28424 60 9 thus thus ADV bracis-28424 60 10 all all DET bracis-28424 60 11 nodes node NOUN bracis-28424 60 12 are be AUX bracis-28424 60 13 infected infect VERB bracis-28424 60 14 . . PUNCT bracis-28424 61 1 as as ADP bracis-28424 61 2 \(i_0\ \(i_0\ NOUN bracis-28424 61 3 ) ) PUNCT bracis-28424 61 4 are be AUX bracis-28424 61 5 the the DET bracis-28424 61 6 nodes node NOUN bracis-28424 61 7 chosen choose VERB bracis-28424 61 8 uniformly uniformly ADV bracis-28424 61 9 at at ADP bracis-28424 61 10 random random ADJ bracis-28424 61 11 when when SCONJ bracis-28424 61 12 the the DET bracis-28424 61 13 epidemic epidemic NOUN bracis-28424 61 14 starts start VERB bracis-28424 61 15 , , PUNCT bracis-28424 61 16 \(s \(s PROPN bracis-28424 61 17 = = SYM bracis-28424 61 18 |i_0|\ |i_0|\ PROPN bracis-28424 61 19 ) ) PUNCT bracis-28424 61 20 is be AUX bracis-28424 61 21 the the DET bracis-28424 61 22 parameter parameter NOUN bracis-28424 61 23 that that PRON bracis-28424 61 24 determines determine VERB bracis-28424 61 25 the the DET bracis-28424 61 26 number number NOUN bracis-28424 61 27 of of ADP bracis-28424 61 28 epidemic epidemic NOUN bracis-28424 61 29 sources source NOUN bracis-28424 61 30 . . PUNCT bracis-28424 62 1 2.1 2.1 NUM bracis-28424 62 2 epidemic epidemic NOUN bracis-28424 62 3 observation observation NOUN bracis-28424 62 4 the the DET bracis-28424 62 5 snapshot snapshot NOUN bracis-28424 62 6 observation observation NOUN bracis-28424 62 7 model model NOUN bracis-28424 62 8 which which PRON bracis-28424 62 9 reveals reveal VERB bracis-28424 62 10 the the DET bracis-28424 62 11 sets set NOUN bracis-28424 62 12 \(i(t_o)\ \(i(t_o)\ NOUN bracis-28424 62 13 ) ) PUNCT bracis-28424 62 14 and and CCONJ bracis-28424 62 15 \(s(t_o)\ \(s(t_o)\ NOUN bracis-28424 62 16 ) ) PUNCT bracis-28424 62 17 is be AUX bracis-28424 62 18 the the DET bracis-28424 62 19 network network NOUN bracis-28424 62 20 observation observation NOUN bracis-28424 62 21 at at ADP bracis-28424 62 22 a a DET bracis-28424 62 23 given give VERB bracis-28424 62 24 time time NOUN bracis-28424 62 25 \(t_o\ \(t_o\ PROPN bracis-28424 62 26 ) ) PUNCT bracis-28424 62 27 . . PUNCT bracis-28424 63 1 note note VERB bracis-28424 63 2 that that SCONJ bracis-28424 63 3 g g PROPN bracis-28424 63 4 ( ( PUNCT bracis-28424 63 5 the the DET bracis-28424 63 6 network network NOUN bracis-28424 63 7 ) ) PUNCT bracis-28424 63 8 is be AUX bracis-28424 63 9 also also ADV bracis-28424 63 10 assumed assume VERB bracis-28424 63 11 to to PART bracis-28424 63 12 be be AUX bracis-28424 63 13 known know VERB bracis-28424 63 14 , , PUNCT bracis-28424 63 15 and and CCONJ bracis-28424 63 16 it it PRON bracis-28424 63 17 is be AUX bracis-28424 63 18 sufficient sufficient ADJ bracis-28424 63 19 to to PART bracis-28424 63 20 observe observe VERB bracis-28424 63 21 i(t i(t NOUN bracis-28424 63 22 ) ) PUNCT bracis-28424 63 23 , , PUNCT bracis-28424 63 24 since since SCONJ bracis-28424 63 25 \(s(t \(s(t PROPN bracis-28424 63 26 ) ) PUNCT bracis-28424 63 27 = = SYM bracis-28424 63 28 v v ADP bracis-28424 63 29 \setminus \setminus PROPN bracis-28424 63 30 i(t)\ i(t)\ NUM bracis-28424 63 31 ) ) PUNCT bracis-28424 63 32 . . PUNCT bracis-28424 64 1 the the DET bracis-28424 64 2 epidemic epidemic NOUN bracis-28424 64 3 snapshot snapshot NOUN bracis-28424 64 4 is be AUX bracis-28424 64 5 taken take VERB bracis-28424 64 6 when when SCONJ bracis-28424 64 7 a a DET bracis-28424 64 8 predefined predefine VERB bracis-28424 64 9 number number NOUN bracis-28424 64 10 of of ADP bracis-28424 64 11 nodes node NOUN bracis-28424 64 12 have have AUX bracis-28424 64 13 been be AUX bracis-28424 64 14 infected infect VERB bracis-28424 64 15 . . PUNCT bracis-28424 65 1 let let AUX bracis-28424 65 2 \(f_o\ \(f_o\ VERB bracis-28424 65 3 ) ) PUNCT bracis-28424 65 4 denote denote VERB bracis-28424 65 5 that that DET bracis-28424 65 6 fraction fraction NOUN bracis-28424 65 7 of of ADP bracis-28424 65 8 infected infect VERB bracis-28424 65 9 the the DET bracis-28424 65 10 nodes node NOUN bracis-28424 65 11 : : PUNCT bracis-28424 65 12 the the DET bracis-28424 65 13 epidemic epidemic NOUN bracis-28424 65 14 snapshot snapshot NOUN bracis-28424 65 15 takes take VERB bracis-28424 65 16 place place NOUN bracis-28424 65 17 the the DET bracis-28424 65 18 first first ADJ bracis-28424 65 19 time time NOUN bracis-28424 65 20 when when SCONJ bracis-28424 65 21 \(i(t)/n \(i(t)/n ADJ bracis-28424 65 22 \ge \ge PROPN bracis-28424 65 23 f_o\ f_o\ NOUN bracis-28424 65 24 ) ) PUNCT bracis-28424 65 25 . . PUNCT bracis-28424 66 1 more more ADV bracis-28424 66 2 precisely precisely ADV bracis-28424 66 3 , , PUNCT bracis-28424 66 4 \(t_o \(t_o NOUN bracis-28424 66 5 = = SYM bracis-28424 66 6 \min \min PROPN bracis-28424 66 7 _ _ PUNCT bracis-28424 66 8 t t PROPN bracis-28424 66 9 \ \ PROPN bracis-28424 66 10 { { PUNCT bracis-28424 66 11 t t NOUN bracis-28424 66 12 | | ADV bracis-28424 66 13 i(t)/n i(t)/n PROPN bracis-28424 66 14 \ge \ge PROPN bracis-28424 66 15 f_o\}\ f_o\}\ NOUN bracis-28424 66 16 ) ) PUNCT bracis-28424 66 17 . . PUNCT bracis-28424 67 1 in in ADP bracis-28424 67 2 what what PRON bracis-28424 67 3 follows follow VERB bracis-28424 67 4 , , PUNCT bracis-28424 67 5 \(f_o\ \(f_o\ VERB bracis-28424 67 6 ) ) PUNCT bracis-28424 67 7 will will AUX bracis-28424 67 8 be be AUX bracis-28424 67 9 used use VERB bracis-28424 67 10 to to PART bracis-28424 67 11 determine determine VERB bracis-28424 67 12 when when SCONJ bracis-28424 67 13 the the DET bracis-28424 67 14 snapshot snapshot NOUN bracis-28424 67 15 is be AUX bracis-28424 67 16 taken take VERB bracis-28424 67 17 . . PUNCT bracis-28424 68 1 2.2 2.2 NUM bracis-28424 68 2 problem problem NOUN bracis-28424 68 3 statement statement NOUN bracis-28424 68 4 consider consider VERB bracis-28424 68 5 a a DET bracis-28424 68 6 si si X bracis-28424 68 7 network network NOUN bracis-28424 68 8 epidemic epidemic NOUN bracis-28424 68 9 with with ADP bracis-28424 68 10 parameter parameter NOUN bracis-28424 68 11 p p PROPN bracis-28424 68 12 on on ADP bracis-28424 68 13 the the DET bracis-28424 68 14 network network NOUN bracis-28424 68 15 \(g=(v \(g=(v VERB bracis-28424 68 16 , , PUNCT bracis-28424 68 17 e)\ e)\ NOUN bracis-28424 68 18 ) ) PUNCT bracis-28424 68 19 having having AUX bracis-28424 68 20 started start VERB bracis-28424 68 21 with with ADP bracis-28424 68 22 the the DET bracis-28424 68 23 epidemic epidemic NOUN bracis-28424 68 24 sources source NOUN bracis-28424 68 25 \(i_0\ \(i_0\ PROPN bracis-28424 68 26 ) ) PUNCT bracis-28424 68 27 . . PUNCT bracis-28424 69 1 a a DET bracis-28424 69 2 single single ADJ bracis-28424 69 3 epidemic epidemic NOUN bracis-28424 69 4 snapshot snapshot NOUN bracis-28424 69 5 is be AUX bracis-28424 69 6 taken take VERB bracis-28424 69 7 when when SCONJ bracis-28424 69 8 a a DET bracis-28424 69 9 fraction fraction NOUN bracis-28424 69 10 of of ADP bracis-28424 69 11 nodes node NOUN bracis-28424 69 12 infected infect VERB bracis-28424 69 13 is be AUX bracis-28424 69 14 \(f_o\ \(f_o\ NOUN bracis-28424 69 15 ) ) PUNCT bracis-28424 69 16 . . PUNCT bracis-28424 70 1 design design VERB bracis-28424 70 2 a a DET bracis-28424 70 3 model model NOUN bracis-28424 70 4 m m VERB bracis-28424 70 5 that that PRON bracis-28424 70 6 classifies classify VERB bracis-28424 70 7 nodes node NOUN bracis-28424 70 8 in in ADP bracis-28424 70 9 \(i(t_o)\ \(i(t_o)\ NOUN bracis-28424 70 10 ) ) PUNCT bracis-28424 70 11 as as ADP bracis-28424 70 12 epidemic epidemic NOUN bracis-28424 70 13 sources source NOUN bracis-28424 70 14 , , PUNCT bracis-28424 70 15 taking take VERB bracis-28424 70 16 as as ADP bracis-28424 70 17 input input NOUN bracis-28424 70 18 g g NOUN bracis-28424 70 19 and and CCONJ bracis-28424 70 20 \(i(t_o)\ \(i(t_o)\ ADJ bracis-28424 70 21 ) ) PUNCT bracis-28424 70 22 . . PUNCT bracis-28424 71 1 ideally ideally ADV bracis-28424 71 2 , , PUNCT bracis-28424 71 3 the the DET bracis-28424 71 4 model model NOUN bracis-28424 71 5 should should AUX bracis-28424 71 6 recover recover VERB bracis-28424 71 7 \(i_0\ \(i_0\ PROPN bracis-28424 71 8 ) ) PUNCT bracis-28424 71 9 , , PUNCT bracis-28424 71 10 namely namely ADV bracis-28424 71 11 $ $ SYM bracis-28424 71 12 $ $ SYM bracis-28424 71 13 \begin{aligned \begin{aligne VERB bracis-28424 71 14 } } PUNCT bracis-28424 71 15 m_{g m_{g ADJ bracis-28424 71 16 , , PUNCT bracis-28424 71 17 i(t_o)}(v i(t_o)}(v NOUN bracis-28424 71 18 ) ) PUNCT bracis-28424 72 1 = = PRON bracis-28424 72 2 { { PUNCT bracis-28424 72 3 \left\ \left\ PROPN bracis-28424 72 4 { { PUNCT bracis-28424 72 5 \begin{array}{ll \begin{array}{ll PROPN bracis-28424 72 6 } } PUNCT bracis-28424 72 7 1 1 NUM bracis-28424 72 8 \text \text NOUN bracis-28424 72 9 { { PUNCT bracis-28424 72 10 , , PUNCT bracis-28424 72 11 } } PUNCT bracis-28424 72 12 \text \text NOUN bracis-28424 72 13 { { PUNCT bracis-28424 72 14 if if SCONJ bracis-28424 72 15 } } PUNCT bracis-28424 72 16 v v ADP bracis-28424 72 17 \in \in ADJ bracis-28424 72 18 i_0 i_0 NOUN bracis-28424 72 19 \\ \\ NOUN bracis-28424 72 20 0 0 PUNCT bracis-28424 73 1 \text \text NOUN bracis-28424 73 2 { { PUNCT bracis-28424 73 3 , , PUNCT bracis-28424 73 4 } } PUNCT bracis-28424 73 5 \text \text ADV bracis-28424 73 6 { { PUNCT bracis-28424 73 7 otherwise otherwise ADV bracis-28424 73 8 } } PUNCT bracis-28424 73 9 \end{array}\right \end{array}\right PROPN bracis-28424 73 10 . . PUNCT bracis-28424 73 11 } } PUNCT bracis-28424 73 12 \end{aligned}$$ \end{aligned}$$ X bracis-28424 73 13 ( ( PUNCT bracis-28424 73 14 1 1 X bracis-28424 73 15 ) ) PUNCT bracis-28424 73 16 note note NOUN bracis-28424 73 17 that that SCONJ bracis-28424 73 18 the the DET bracis-28424 73 19 model model NOUN bracis-28424 73 20 m m VERB bracis-28424 73 21 has have VERB bracis-28424 73 22 no no DET bracis-28424 73 23 prior prior ADJ bracis-28424 73 24 information information NOUN bracis-28424 73 25 about about ADP bracis-28424 73 26 p p PRON bracis-28424 73 27 , , PUNCT bracis-28424 73 28 the the DET bracis-28424 73 29 parameter parameter NOUN bracis-28424 73 30 for for ADP bracis-28424 73 31 the the DET bracis-28424 73 32 si si PROPN bracis-28424 73 33 epidemic epidemic NOUN bracis-28424 73 34 . . PUNCT bracis-28424 74 1 m m PROPN bracis-28424 74 2 is be AUX bracis-28424 74 3 trained train VERB bracis-28424 74 4 on on ADP bracis-28424 74 5 different different ADJ bracis-28424 74 6 networks network NOUN bracis-28424 74 7 and and CCONJ bracis-28424 74 8 epidemics epidemic NOUN bracis-28424 74 9 and and CCONJ bracis-28424 74 10 it it PRON bracis-28424 74 11 should should AUX bracis-28424 74 12 classify classify VERB bracis-28424 74 13 nodes node NOUN bracis-28424 74 14 for for ADP bracis-28424 74 15 networks network NOUN bracis-28424 74 16 and and CCONJ bracis-28424 74 17 epidemics epidemic NOUN bracis-28424 74 18 never never ADV bracis-28424 74 19 seen see VERB bracis-28424 74 20 before before ADV bracis-28424 74 21 . . PUNCT bracis-28424 75 1 in in ADP bracis-28424 75 2 fact fact NOUN bracis-28424 75 3 , , PUNCT bracis-28424 75 4 obtaining obtain VERB bracis-28424 75 5 such such ADJ bracis-28424 75 6 generalization generalization NOUN bracis-28424 75 7 is be AUX bracis-28424 75 8 the the DET bracis-28424 75 9 main main ADJ bracis-28424 75 10 challenge challenge NOUN bracis-28424 75 11 in in ADP bracis-28424 75 12 this this DET bracis-28424 75 13 problem problem NOUN bracis-28424 75 14 . . PUNCT bracis-28424 76 1 in in ADP bracis-28424 76 2 addition addition NOUN bracis-28424 76 3 , , PUNCT bracis-28424 76 4 in in ADP bracis-28424 76 5 most most ADJ bracis-28424 76 6 scenarios scenario NOUN bracis-28424 76 7 the the DET bracis-28424 76 8 number number NOUN bracis-28424 76 9 of of ADP bracis-28424 76 10 epidemic epidemic NOUN bracis-28424 76 11 sources source NOUN bracis-28424 76 12 is be AUX bracis-28424 76 13 very very ADV bracis-28424 76 14 small small ADJ bracis-28424 76 15 with with ADP bracis-28424 76 16 respect respect NOUN bracis-28424 76 17 to to ADP bracis-28424 76 18 the the DET bracis-28424 76 19 number number NOUN bracis-28424 76 20 of of ADP bracis-28424 76 21 nodes node NOUN bracis-28424 76 22 infected infect VERB bracis-28424 76 23 in in ADP bracis-28424 76 24 the the DET bracis-28424 76 25 snapshot snapshot NOUN bracis-28424 76 26 , , PUNCT bracis-28424 76 27 often often ADV bracis-28424 76 28 by by ADP bracis-28424 76 29 a a DET bracis-28424 76 30 factor factor NOUN bracis-28424 76 31 of of ADP bracis-28424 76 32 one one NUM bracis-28424 76 33 hundred hundred NUM bracis-28424 76 34 or or CCONJ bracis-28424 76 35 more more ADJ bracis-28424 76 36 , , PUNCT bracis-28424 76 37 hence hence ADV bracis-28424 76 38 , , PUNCT bracis-28424 76 39 this this DET bracis-28424 76 40 classification classification NOUN bracis-28424 76 41 task task NOUN bracis-28424 76 42 deals deal NOUN bracis-28424 76 43 with with ADP bracis-28424 76 44 very very ADV bracis-28424 76 45 imbalanced imbalanced ADJ bracis-28424 76 46 classes class NOUN bracis-28424 76 47 . . PUNCT bracis-28424 77 1 3 3 NUM bracis-28424 77 2 related relate VERB bracis-28424 77 3 work work NOUN bracis-28424 77 4 for for ADP bracis-28424 77 5 over over ADP bracis-28424 77 6 a a PRON bracis-28424 77 7 decade decade NOUN bracis-28424 77 8 , , PUNCT bracis-28424 77 9 efforts effort NOUN bracis-28424 77 10 have have AUX bracis-28424 77 11 been be AUX bracis-28424 77 12 made make VERB bracis-28424 77 13 to to PART bracis-28424 77 14 address address VERB bracis-28424 77 15 the the DET bracis-28424 77 16 problem problem NOUN bracis-28424 77 17 of of ADP bracis-28424 77 18 identifying identify VERB bracis-28424 77 19 the the DET bracis-28424 77 20 source source NOUN bracis-28424 77 21 of of ADP bracis-28424 77 22 a a DET bracis-28424 77 23 network network NOUN bracis-28424 77 24 epidemic epidemic NOUN bracis-28424 78 1 [ [ X bracis-28424 78 2 11 11 NUM bracis-28424 78 3 , , PUNCT bracis-28424 78 4 20 20 NUM bracis-28424 78 5 ] ] PUNCT bracis-28424 78 6 . . PUNCT bracis-28424 79 1 the the DET bracis-28424 79 2 pioneering pioneering ADJ bracis-28424 79 3 methods method NOUN bracis-28424 79 4 considered consider VERB bracis-28424 79 5 single single ADJ bracis-28424 79 6 source source NOUN bracis-28424 79 7 epidemics epidemic NOUN bracis-28424 79 8 and and CCONJ bracis-28424 79 9 simple simple ADJ bracis-28424 79 10 networks network NOUN bracis-28424 79 11 while while SCONJ bracis-28424 79 12 providing provide VERB bracis-28424 79 13 efficient efficient ADJ bracis-28424 79 14 algorithms algorithm NOUN bracis-28424 79 15 to to PART bracis-28424 79 16 identify identify VERB bracis-28424 79 17 the the DET bracis-28424 79 18 source source NOUN bracis-28424 79 19 [ [ X bracis-28424 79 20 19 19 NUM bracis-28424 79 21 ] ] PUNCT bracis-28424 79 22 . . PUNCT bracis-28424 80 1 these these DET bracis-28424 80 2 approaches approach NOUN bracis-28424 80 3 were be AUX bracis-28424 80 4 based base VERB bracis-28424 80 5 on on ADP bracis-28424 80 6 simple simple ADJ bracis-28424 80 7 probabilistic probabilistic ADJ bracis-28424 80 8 epidemic epidemic NOUN bracis-28424 80 9 models model NOUN bracis-28424 80 10 and and CCONJ bracis-28424 80 11 likelihood likelihood NOUN bracis-28424 80 12 functions function NOUN bracis-28424 80 13 given give VERB bracis-28424 80 14 the the DET bracis-28424 80 15 observation observation NOUN bracis-28424 80 16 [ [ X bracis-28424 80 17 5 5 NUM bracis-28424 80 18 , , PUNCT bracis-28424 80 19 10 10 NUM bracis-28424 80 20 , , PUNCT bracis-28424 80 21 23 23 NUM bracis-28424 80 22 ] ] PUNCT bracis-28424 80 23 . . PUNCT bracis-28424 81 1 the the DET bracis-28424 81 2 rumor rumor NOUN bracis-28424 81 3 centrality centrality NOUN bracis-28424 81 4 algorithm algorithm NOUN bracis-28424 81 5 proposed propose VERB bracis-28424 81 6 by by ADP bracis-28424 81 7 shah shah PROPN bracis-28424 81 8 and and CCONJ bracis-28424 81 9 zaman zaman NOUN bracis-28424 81 10 is be AUX bracis-28424 81 11 a a DET bracis-28424 81 12 prominent prominent ADJ bracis-28424 81 13 example example NOUN bracis-28424 81 14 that that PRON bracis-28424 81 15 has have AUX bracis-28424 81 16 been be AUX bracis-28424 81 17 widely widely ADV bracis-28424 81 18 explored explore VERB bracis-28424 81 19 and and CCONJ bracis-28424 81 20 extended extend VERB bracis-28424 81 21 [ [ PUNCT bracis-28424 81 22 18 18 NUM bracis-28424 81 23 , , PUNCT bracis-28424 81 24 19 19 NUM bracis-28424 81 25 ] ] PUNCT bracis-28424 81 26 . . PUNCT bracis-28424 82 1 more more ADJ bracis-28424 82 2 recent recent ADJ bracis-28424 82 3 works work NOUN bracis-28424 82 4 have have AUX bracis-28424 82 5 tackled tackle VERB bracis-28424 82 6 the the DET bracis-28424 82 7 multiple multiple ADJ bracis-28424 82 8 source source NOUN bracis-28424 82 9 detection detection NOUN bracis-28424 82 10 ( ( PUNCT bracis-28424 82 11 msd msd NOUN bracis-28424 82 12 ) ) PUNCT bracis-28424 82 13 problem problem NOUN bracis-28424 82 14 , , PUNCT bracis-28424 82 15 where where SCONJ bracis-28424 82 16 the the DET bracis-28424 82 17 epidemic epidemic NOUN bracis-28424 82 18 simultaneously simultaneously ADV bracis-28424 82 19 starts start VERB bracis-28424 82 20 in in ADP bracis-28424 82 21 different different ADJ bracis-28424 82 22 network network NOUN bracis-28424 82 23 nodes node NOUN bracis-28424 82 24 motivated motivate VERB bracis-28424 82 25 by by ADP bracis-28424 82 26 applications application NOUN bracis-28424 82 27 where where SCONJ bracis-28424 82 28 the the DET bracis-28424 82 29 diffusion diffusion NOUN bracis-28424 82 30 process process NOUN bracis-28424 82 31 starts start VERB bracis-28424 82 32 in in ADP bracis-28424 82 33 various various ADJ bracis-28424 82 34 nodes node NOUN bracis-28424 82 35 , , PUNCT bracis-28424 82 36 e.g. e.g. ADV bracis-28424 82 37 , , PUNCT bracis-28424 82 38 information information NOUN bracis-28424 82 39 in in ADP bracis-28424 82 40 an an DET bracis-28424 82 41 online online ADJ bracis-28424 82 42 social social ADJ bracis-28424 82 43 network network NOUN bracis-28424 82 44 , , PUNCT bracis-28424 82 45 [ [ X bracis-28424 82 46 3 3 NUM bracis-28424 82 47 , , PUNCT bracis-28424 82 48 17 17 NUM bracis-28424 82 49 , , PUNCT bracis-28424 82 50 21 21 NUM bracis-28424 82 51 , , PUNCT bracis-28424 82 52 24 24 NUM bracis-28424 82 53 ] ] PUNCT bracis-28424 82 54 . . PUNCT bracis-28424 83 1 netsleuth netsleuth PROPN bracis-28424 84 1 [ [ X bracis-28424 84 2 17 17 NUM bracis-28424 84 3 ] ] PUNCT bracis-28424 84 4 is be AUX bracis-28424 84 5 an an DET bracis-28424 84 6 approach approach NOUN bracis-28424 84 7 to to PART bracis-28424 84 8 infer infer VERB bracis-28424 84 9 the the DET bracis-28424 84 10 multiple multiple ADJ bracis-28424 84 11 epidemic epidemic NOUN bracis-28424 84 12 sources source NOUN bracis-28424 84 13 in in ADP bracis-28424 84 14 the the DET bracis-28424 84 15 probabilistic probabilistic ADJ bracis-28424 84 16 si si PROPN bracis-28424 84 17 infection infection NOUN bracis-28424 84 18 model model NOUN bracis-28424 84 19 using use VERB bracis-28424 84 20 a a DET bracis-28424 84 21 likelihood likelihood NOUN bracis-28424 84 22 function function NOUN bracis-28424 84 23 approach approach NOUN bracis-28424 84 24 and and CCONJ bracis-28424 84 25 minimum minimum NOUN bracis-28424 84 26 description description NOUN bracis-28424 84 27 length length NOUN bracis-28424 84 28 ( ( PUNCT bracis-28424 84 29 mdl mdl NOUN bracis-28424 84 30 ) ) PUNCT bracis-28424 84 31 scores score NOUN bracis-28424 84 32 . . PUNCT bracis-28424 85 1 netsleuth netsleuth PROPN bracis-28424 85 2 requires require VERB bracis-28424 85 3 prior prior ADJ bracis-28424 85 4 knowledge knowledge NOUN bracis-28424 85 5 of of ADP bracis-28424 85 6 the the DET bracis-28424 85 7 number number NOUN bracis-28424 85 8 of of ADP bracis-28424 85 9 epidemic epidemic NOUN bracis-28424 85 10 sources source NOUN bracis-28424 85 11 . . PUNCT bracis-28424 86 1 another another DET bracis-28424 86 2 approach approach NOUN bracis-28424 86 3 is be AUX bracis-28424 86 4 lpsi lpsi ADJ bracis-28424 86 5 ( ( PUNCT bracis-28424 86 6 label label NOUN bracis-28424 86 7 propagation propagation NOUN bracis-28424 86 8 based base VERB bracis-28424 86 9 source source NOUN bracis-28424 86 10 identification identification NOUN bracis-28424 86 11 ) ) PUNCT bracis-28424 87 1 [ [ X bracis-28424 87 2 21 21 NUM bracis-28424 87 3 ] ] PUNCT bracis-28424 87 4 where where SCONJ bracis-28424 87 5 labels label NOUN bracis-28424 87 6 assigned assign VERB bracis-28424 87 7 to to ADP bracis-28424 87 8 nodes node NOUN bracis-28424 87 9 are be AUX bracis-28424 87 10 propagated propagate VERB bracis-28424 87 11 in in ADP bracis-28424 87 12 iterations iteration NOUN bracis-28424 87 13 to to PART bracis-28424 87 14 build build VERB bracis-28424 87 15 a a DET bracis-28424 87 16 weight weight NOUN bracis-28424 87 17 matrix matrix NOUN bracis-28424 87 18 that that PRON bracis-28424 87 19 is be AUX bracis-28424 87 20 used use VERB bracis-28424 87 21 to to PART bracis-28424 87 22 identify identify VERB bracis-28424 87 23 the the DET bracis-28424 87 24 multiple multiple ADJ bracis-28424 87 25 epidemic epidemic NOUN bracis-28424 87 26 sources source NOUN bracis-28424 87 27 ( ( PUNCT bracis-28424 87 28 the the DET bracis-28424 87 29 top top ADJ bracis-28424 87 30 ranked rank VERB bracis-28424 87 31 nodes node NOUN bracis-28424 87 32 according accord VERB bracis-28424 87 33 to to ADP bracis-28424 87 34 a a DET bracis-28424 87 35 metric metric NOUN bracis-28424 87 36 ) ) PUNCT bracis-28424 87 37 . . PUNCT bracis-28424 88 1 the the DET bracis-28424 88 2 work work NOUN bracis-28424 88 3 of of ADP bracis-28424 88 4 zang zang PROPN bracis-28424 88 5 et et PROPN bracis-28424 88 6 . . PUNCT bracis-28424 89 1 al al PROPN bracis-28424 90 1 [ [ X bracis-28424 90 2 24 24 NUM bracis-28424 90 3 ] ] PUNCT bracis-28424 90 4 considers consider VERB bracis-28424 90 5 sir sir NOUN bracis-28424 90 6 ( ( PUNCT bracis-28424 90 7 susceptible susceptible ADJ bracis-28424 90 8 - - PUNCT bracis-28424 90 9 infected infect VERB bracis-28424 90 10 - - PUNCT bracis-28424 90 11 recovered recover VERB bracis-28424 90 12 ) ) PUNCT bracis-28424 90 13 epidemics epidemic NOUN bracis-28424 90 14 and and CCONJ bracis-28424 90 15 a a DET bracis-28424 90 16 limited limited ADJ bracis-28424 90 17 observation observation NOUN bracis-28424 90 18 model model NOUN bracis-28424 90 19 by by ADP bracis-28424 90 20 building build VERB bracis-28424 90 21 “ " PUNCT bracis-28424 90 22 extended extend VERB bracis-28424 90 23 infected infect VERB bracis-28424 90 24 node node NOUN bracis-28424 90 25 sets set NOUN bracis-28424 90 26 ” " PUNCT bracis-28424 90 27 upon upon SCONJ bracis-28424 90 28 lpsi lpsi PROPN bracis-28424 90 29 that that PRON bracis-28424 90 30 are be AUX bracis-28424 90 31 partitioned partition VERB bracis-28424 90 32 and and CCONJ bracis-28424 90 33 ranked rank VERB bracis-28424 90 34 using use VERB bracis-28424 90 35 a a DET bracis-28424 90 36 network network NOUN bracis-28424 90 37 centrality centrality NOUN bracis-28424 90 38 metric metric NOUN bracis-28424 90 39 . . PUNCT bracis-28424 91 1 different different ADJ bracis-28424 91 2 number number NOUN bracis-28424 91 3 of of ADP bracis-28424 91 4 epidemic epidemic NOUN bracis-28424 91 5 sources source NOUN bracis-28424 91 6 are be AUX bracis-28424 91 7 considered consider VERB bracis-28424 91 8 independently independently ADV bracis-28424 91 9 in in ADP bracis-28424 91 10 order order NOUN bracis-28424 91 11 to to PART bracis-28424 91 12 determine determine VERB bracis-28424 91 13 the the DET bracis-28424 91 14 actual actual ADJ bracis-28424 91 15 number number NOUN bracis-28424 91 16 of of ADP bracis-28424 91 17 sources source NOUN bracis-28424 91 18 . . PUNCT bracis-28424 92 1 while while SCONJ bracis-28424 92 2 the the DET bracis-28424 92 3 above above ADJ bracis-28424 92 4 approaches approach NOUN bracis-28424 92 5 are be AUX bracis-28424 92 6 based base VERB bracis-28424 92 7 on on ADP bracis-28424 92 8 likelihood likelihood NOUN bracis-28424 92 9 functions function NOUN bracis-28424 92 10 and and CCONJ bracis-28424 92 11 label label NOUN bracis-28424 92 12 propagation propagation NOUN bracis-28424 92 13 , , PUNCT bracis-28424 92 14 learning learning NOUN bracis-28424 92 15 - - PUNCT bracis-28424 92 16 based base VERB bracis-28424 92 17 approaches approach NOUN bracis-28424 92 18 have have AUX bracis-28424 92 19 been be AUX bracis-28424 92 20 recently recently ADV bracis-28424 92 21 proposed propose VERB bracis-28424 92 22 to to PART bracis-28424 92 23 tackle tackle VERB bracis-28424 92 24 the the DET bracis-28424 92 25 msd msd NOUN bracis-28424 92 26 problem problem NOUN bracis-28424 92 27 . . PUNCT bracis-28424 93 1 a a DET bracis-28424 93 2 prominent prominent ADJ bracis-28424 93 3 example example NOUN bracis-28424 93 4 is be AUX bracis-28424 93 5 graph graph VERB bracis-28424 93 6 convolutional convolutional ADJ bracis-28424 93 7 networks network NOUN bracis-28424 93 8 based base VERB bracis-28424 93 9 source source NOUN bracis-28424 93 10 identification identification NOUN bracis-28424 93 11 ( ( PUNCT bracis-28424 93 12 gcnsi gcnsi NOUN bracis-28424 93 13 ) ) PUNCT bracis-28424 94 1 [ [ X bracis-28424 94 2 3 3 X bracis-28424 94 3 ] ] PUNCT bracis-28424 94 4 where where SCONJ bracis-28424 94 5 a a DET bracis-28424 94 6 gcn gcn NOUN bracis-28424 94 7 model model NOUN bracis-28424 94 8 is be AUX bracis-28424 94 9 trained train VERB bracis-28424 94 10 with with ADP bracis-28424 94 11 supervision supervision NOUN bracis-28424 94 12 to to PART bracis-28424 94 13 generate generate VERB bracis-28424 94 14 node node ADJ bracis-28424 94 15 representations representation NOUN bracis-28424 94 16 . . PUNCT bracis-28424 95 1 the the DET bracis-28424 95 2 approach approach NOUN bracis-28424 95 3 uses use VERB bracis-28424 95 4 lpsi lpsi PROPN bracis-28424 95 5 as as ADP bracis-28424 95 6 part part NOUN bracis-28424 95 7 of of ADP bracis-28424 95 8 the the DET bracis-28424 95 9 node node NOUN bracis-28424 95 10 attributes attribute NOUN bracis-28424 95 11 and and CCONJ bracis-28424 95 12 considers consider VERB bracis-28424 95 13 different different ADJ bracis-28424 95 14 epidemic epidemic NOUN bracis-28424 95 15 models model NOUN bracis-28424 95 16 beyond beyond ADP bracis-28424 95 17 si si X bracis-28424 95 18 ( ( PUNCT bracis-28424 95 19 susceptible susceptible ADJ bracis-28424 95 20 - - PUNCT bracis-28424 95 21 infected infect VERB bracis-28424 95 22 ) ) PUNCT bracis-28424 95 23 , , PUNCT bracis-28424 95 24 such such ADJ bracis-28424 95 25 as as ADP bracis-28424 95 26 ic ic PROPN bracis-28424 95 27 ( ( PUNCT bracis-28424 95 28 independent independent ADJ bracis-28424 95 29 cascade cascade NOUN bracis-28424 95 30 ) ) PUNCT bracis-28424 95 31 and and CCONJ bracis-28424 95 32 sir sir PROPN bracis-28424 95 33 . . PUNCT bracis-28424 96 1 however however ADV bracis-28424 96 2 , , PUNCT bracis-28424 96 3 different different ADJ bracis-28424 96 4 configurations configuration NOUN bracis-28424 96 5 of of ADP bracis-28424 96 6 gcn gcn NOUN bracis-28424 96 7 need need VERB bracis-28424 96 8 to to PART bracis-28424 96 9 be be AUX bracis-28424 96 10 trained train VERB bracis-28424 96 11 for for ADP bracis-28424 96 12 different different ADJ bracis-28424 96 13 networks network NOUN bracis-28424 96 14 . . PUNCT bracis-28424 97 1 gcnsi gcnsi NOUN bracis-28424 97 2 is be AUX bracis-28424 97 3 the the DET bracis-28424 97 4 closest close ADJ bracis-28424 97 5 approach approach NOUN bracis-28424 97 6 to to ADP bracis-28424 97 7 the the DET bracis-28424 97 8 framework framework NOUN bracis-28424 97 9 designed design VERB bracis-28424 97 10 in in ADP bracis-28424 97 11 this this DET bracis-28424 97 12 paper paper NOUN bracis-28424 97 13 , , PUNCT bracis-28424 97 14 and and CCONJ bracis-28424 97 15 results result NOUN bracis-28424 97 16 will will AUX bracis-28424 97 17 be be AUX bracis-28424 97 18 compared compare VERB bracis-28424 97 19 directly directly ADV bracis-28424 97 20 for for ADP bracis-28424 97 21 scenarios scenario NOUN bracis-28424 97 22 that that PRON bracis-28424 97 23 are be AUX bracis-28424 97 24 available available ADJ bracis-28424 97 25 ( ( PUNCT bracis-28424 97 26 see see VERB bracis-28424 97 27 sect sect NOUN bracis-28424 97 28 . . PUNCT bracis-28424 97 29     SPACE bracis-28424 98 1 5 5 NUM bracis-28424 98 2 ) ) PUNCT bracis-28424 98 3 . . PUNCT bracis-28424 99 1 4 4 NUM bracis-28424 99 2 proposed propose VERB bracis-28424 99 3 framework framework NOUN bracis-28424 99 4 recall recall VERB bracis-28424 99 5 that that SCONJ bracis-28424 99 6 , , PUNCT bracis-28424 99 7 in in ADP bracis-28424 99 8 graph graph NOUN bracis-28424 99 9 neural neural ADJ bracis-28424 99 10 networks network NOUN bracis-28424 99 11 , , PUNCT bracis-28424 99 12 node node NOUN bracis-28424 99 13 attributes attribute NOUN bracis-28424 99 14 serve serve VERB bracis-28424 99 15 as as ADP bracis-28424 99 16 the the DET bracis-28424 99 17 initial initial ADJ bracis-28424 99 18 representation representation NOUN bracis-28424 99 19 ( ( PUNCT bracis-28424 99 20 input input NOUN bracis-28424 99 21 ) ) PUNCT bracis-28424 99 22 to to ADP bracis-28424 99 23 the the DET bracis-28424 99 24 neural neural ADJ bracis-28424 99 25 network network NOUN bracis-28424 99 26 that that PRON bracis-28424 99 27 generates generate VERB bracis-28424 99 28 the the DET bracis-28424 99 29 node node ADJ bracis-28424 99 30 representation representation NOUN bracis-28424 99 31 . . PUNCT bracis-28424 100 1 while while SCONJ bracis-28424 100 2 the the DET bracis-28424 100 3 epidemic epidemic NOUN bracis-28424 100 4 state state NOUN bracis-28424 100 5 of of ADP bracis-28424 100 6 the the DET bracis-28424 100 7 node node NOUN bracis-28424 100 8 is be AUX bracis-28424 100 9 the the DET bracis-28424 100 10 main main ADJ bracis-28424 100 11 node node NOUN bracis-28424 100 12 attribute attribute NOUN bracis-28424 100 13 , , PUNCT bracis-28424 100 14 it it PRON bracis-28424 100 15 is be AUX bracis-28424 100 16 insufficient insufficient ADJ bracis-28424 100 17 information information NOUN bracis-28424 100 18 to to PART bracis-28424 100 19 adequately adequately ADV bracis-28424 100 20 distinguish distinguish VERB bracis-28424 100 21 nodes node NOUN bracis-28424 100 22 when when SCONJ bracis-28424 100 23 it it PRON bracis-28424 100 24 comes come VERB bracis-28424 100 25 to to ADP bracis-28424 100 26 latent latent NOUN bracis-28424 100 27 representation representation NOUN bracis-28424 100 28 generation generation NOUN bracis-28424 100 29 , , PUNCT bracis-28424 100 30 whereas whereas SCONJ bracis-28424 100 31 sources source NOUN bracis-28424 100 32 representation representation NOUN bracis-28424 100 33 should should AUX bracis-28424 100 34 strongly strongly ADV bracis-28424 100 35 distinguish distinguish VERB bracis-28424 100 36 from from ADP bracis-28424 100 37 the the DET bracis-28424 100 38 other other ADJ bracis-28424 100 39 nodes node NOUN bracis-28424 100 40 . . PUNCT bracis-28424 101 1 the the DET bracis-28424 101 2 framework framework NOUN bracis-28424 101 3 here here ADV bracis-28424 101 4 proposed propose VERB bracis-28424 101 5 as as ADV bracis-28424 101 6 well well ADV bracis-28424 101 7 as as ADP bracis-28424 101 8 the the DET bracis-28424 101 9 evaluation evaluation NOUN bracis-28424 101 10 scenarios scenario NOUN bracis-28424 101 11 are be AUX bracis-28424 101 12 publicly publicly ADV bracis-28424 101 13 availablefootnote availablefootnote VERB bracis-28424 101 14 1 1 NUM bracis-28424 101 15 4.1 4.1 NUM bracis-28424 101 16 metrics metric NOUN bracis-28424 101 17 and and CCONJ bracis-28424 101 18     SPACE bracis-28424 101 19 attributes attribute VERB bracis-28424 101 20 the the DET bracis-28424 101 21 idea idea NOUN bracis-28424 101 22 behind behind ADP bracis-28424 101 23 the the DET bracis-28424 101 24 proposed propose VERB bracis-28424 101 25 attributes attribute NOUN bracis-28424 101 26 is be AUX bracis-28424 101 27 to to PART bracis-28424 101 28 reflect reflect VERB bracis-28424 101 29 the the DET bracis-28424 101 30 epidemic epidemic NOUN bracis-28424 101 31 state state NOUN bracis-28424 101 32 around around ADP bracis-28424 101 33 the the DET bracis-28424 101 34 node node NOUN bracis-28424 101 35 in in ADP bracis-28424 101 36 their their PRON bracis-28424 101 37 k k ADJ bracis-28424 101 38 - - ADJ bracis-28424 101 39 hop hop ADJ bracis-28424 101 40 neighborhood neighborhood NOUN bracis-28424 101 41 . . PUNCT bracis-28424 102 1 intuitively intuitively ADV bracis-28424 102 2 , , PUNCT bracis-28424 102 3 the the DET bracis-28424 102 4 epidemic epidemic NOUN bracis-28424 102 5 state state NOUN bracis-28424 102 6 of of ADP bracis-28424 102 7 the the DET bracis-28424 102 8 k k PROPN bracis-28424 102 9 - - PUNCT bracis-28424 102 10 hop hop ADJ bracis-28424 102 11 neighborhoods neighborhood NOUN bracis-28424 102 12 of of ADP bracis-28424 102 13 source source NOUN bracis-28424 102 14 nodes node NOUN bracis-28424 102 15 should should AUX bracis-28424 102 16 be be AUX bracis-28424 102 17 similar similar ADJ bracis-28424 102 18 but but CCONJ bracis-28424 102 19 different different ADJ bracis-28424 102 20 from from ADP bracis-28424 102 21 the the DET bracis-28424 102 22 epidemic epidemic NOUN bracis-28424 102 23 state state NOUN bracis-28424 102 24 of of ADP bracis-28424 102 25 k k PROPN bracis-28424 102 26 - - PUNCT bracis-28424 102 27 hop hop ADJ bracis-28424 102 28 neighborhoods neighborhood NOUN bracis-28424 102 29 of of ADP bracis-28424 102 30 nodes node NOUN bracis-28424 102 31 infected infect VERB bracis-28424 102 32 late late ADV bracis-28424 102 33 during during ADP bracis-28424 102 34 the the DET bracis-28424 102 35 epidemic epidemic NOUN bracis-28424 102 36 . . PUNCT bracis-28424 103 1 therefore therefore ADV bracis-28424 103 2 , , PUNCT bracis-28424 103 3 two two NUM bracis-28424 103 4 metrics metric NOUN bracis-28424 103 5 are be AUX bracis-28424 103 6 proposed propose VERB bracis-28424 103 7 to to PART bracis-28424 103 8 capture capture VERB bracis-28424 103 9 the the DET bracis-28424 103 10 epidemic epidemic NOUN bracis-28424 103 11 state state NOUN bracis-28424 103 12 of of ADP bracis-28424 103 13 k k PROPN bracis-28424 103 14 - - PUNCT bracis-28424 103 15 hop hop ADJ bracis-28424 103 16 neighborhoods neighborhood NOUN bracis-28424 103 17 : : PUNCT bracis-28424 103 18 ring ring NOUN bracis-28424 103 19 infection infection NOUN bracis-28424 103 20 ( ( PUNCT bracis-28424 103 21 ri ri NOUN bracis-28424 103 22 ) ) PUNCT bracis-28424 103 23 and and CCONJ bracis-28424 103 24 depth depth NOUN bracis-28424 103 25 ring ring NOUN bracis-28424 103 26 infection infection NOUN bracis-28424 103 27 ( ( PUNCT bracis-28424 103 28 dri dri PROPN bracis-28424 103 29 ) ) PUNCT bracis-28424 103 30 . . PUNCT bracis-28424 104 1 the the DET bracis-28424 104 2 former former ADJ bracis-28424 104 3 leverages leverage NOUN bracis-28424 104 4 the the DET bracis-28424 104 5 average average ADJ bracis-28424 104 6 epidemic epidemic NOUN bracis-28424 104 7 state state NOUN bracis-28424 104 8 of of ADP bracis-28424 104 9 nodes node NOUN bracis-28424 104 10 at at ADP bracis-28424 104 11 distance distance NOUN bracis-28424 104 12 k k NOUN bracis-28424 104 13 , , PUNCT bracis-28424 104 14 while while SCONJ bracis-28424 104 15 the the DET bracis-28424 104 16 latter latter ADJ bracis-28424 104 17 leverages leverage VERB bracis-28424 104 18 the the DET bracis-28424 104 19 average average ADJ bracis-28424 104 20 neighboring neighboring ADJ bracis-28424 104 21 epidemic epidemic NOUN bracis-28424 104 22 state state NOUN bracis-28424 104 23 of of ADP bracis-28424 104 24 nodes node NOUN bracis-28424 104 25 at at ADP bracis-28424 104 26 distance distance NOUN bracis-28424 104 27 k. k. PROPN bracis-28424 104 28 given give VERB bracis-28424 104 29 the the DET bracis-28424 104 30 snapshot snapshot ADJ bracis-28424 104 31 \(i(t_o)\ \(i(t_o)\ NOUN bracis-28424 104 32 ) ) PUNCT bracis-28424 104 33 and and CCONJ bracis-28424 104 34 considering consider VERB bracis-28424 104 35 a a DET bracis-28424 104 36 node node PROPN bracis-28424 104 37 u u NOUN bracis-28424 104 38 , , PUNCT bracis-28424 104 39 the the DET bracis-28424 104 40 ri ri PROPN bracis-28424 104 41 metric metric NOUN bracis-28424 104 42 is be AUX bracis-28424 104 43 given give VERB bracis-28424 104 44 by by ADP bracis-28424 104 45 : : PUNCT bracis-28424 104 46 $ $ SYM bracis-28424 104 47 $ $ SYM bracis-28424 104 48 \begin{aligned \begin{aligne VERB bracis-28424 104 49 } } PUNCT bracis-28424 104 50 \alpha \alpha ADJ bracis-28424 104 51 ^u_k=\frac{\sum ^u_k=\frac{\sum NOUN bracis-28424 104 52 _ _ PRON bracis-28424 104 53 { { PUNCT bracis-28424 104 54 v v ADP bracis-28424 104 55 \in \in PROPN bracis-28424 104 56 n_k(u n_k(u PART bracis-28424 104 57 ) ) PUNCT bracis-28424 104 58 } } PUNCT bracis-28424 104 59 i_{v}}{|n_k(u)| i_{v}}{|n_k(u)| PROPN bracis-28424 104 60 } } PUNCT bracis-28424 104 61 , , PUNCT bracis-28424 104 62 \text \text NOUN bracis-28424 104 63 { { PUNCT bracis-28424 104 64 for for ADP bracis-28424 104 65 } } PUNCT bracis-28424 104 66 k=0,\ldots k=0,\ldot NOUN bracis-28424 104 67 , , PUNCT bracis-28424 104 68 k k PROPN bracis-28424 104 69 , , PUNCT bracis-28424 104 70 \end{aligned}$$ \end{aligned}$$ PROPN bracis-28424 104 71 ( ( PUNCT bracis-28424 104 72 2 2 X bracis-28424 104 73 ) ) PUNCT bracis-28424 104 74 \(n_k(u)\ \(n_k(u)\ NUM bracis-28424 104 75 ) ) PUNCT bracis-28424 104 76 denotes denote VERB bracis-28424 104 77 the the DET bracis-28424 104 78 k k ADJ bracis-28424 104 79 - - PUNCT bracis-28424 104 80 hop hop ADJ bracis-28424 104 81 neighborhood neighborhood NOUN bracis-28424 104 82 of of ADP bracis-28424 104 83 node node PROPN bracis-28424 104 84 u u PROPN bracis-28424 104 85 , , PUNCT bracis-28424 104 86 or or CCONJ bracis-28424 104 87 equivalently equivalently ADV bracis-28424 104 88 , , PUNCT bracis-28424 104 89 the the DET bracis-28424 104 90 set set NOUN bracis-28424 104 91 of of ADP bracis-28424 104 92 nodes node NOUN bracis-28424 104 93 at at ADP bracis-28424 104 94 distance distance NOUN bracis-28424 104 95 k k PROPN bracis-28424 104 96 from from ADP bracis-28424 104 97 node node PROPN bracis-28424 104 98 u u PROPN bracis-28424 104 99 , , PUNCT bracis-28424 104 100 and and CCONJ bracis-28424 104 101 \(i_v\ \(i_v\ PROPN bracis-28424 104 102 ) ) PUNCT bracis-28424 104 103 the the DET bracis-28424 104 104 epidemic epidemic NOUN bracis-28424 104 105 state state NOUN bracis-28424 104 106 of of ADP bracis-28424 104 107 node node PROPN bracis-28424 104 108 v v NOUN bracis-28424 104 109 in in ADP bracis-28424 104 110 the the DET bracis-28424 104 111 snapshot snapshot ADJ bracis-28424 104 112 \(i(t_o)\ \(i(t_o)\ NOUN bracis-28424 104 113 ) ) PUNCT bracis-28424 104 114 . . PUNCT bracis-28424 105 1 in in ADP bracis-28424 105 2 particular particular ADJ bracis-28424 105 3 , , PUNCT bracis-28424 105 4 $ $ SYM bracis-28424 105 5 $ $ SYM bracis-28424 105 6 \begin{aligned \begin{aligne VERB bracis-28424 105 7 } } PUNCT bracis-28424 105 8 i_v i_v PUNCT bracis-28424 105 9 = = PROPN bracis-28424 105 10 { { PUNCT bracis-28424 105 11 \left\ \left\ PROPN bracis-28424 105 12 { { PUNCT bracis-28424 105 13 \begin{array}{ll \begin{array}{ll PROPN bracis-28424 105 14 } } PUNCT bracis-28424 105 15 1 1 NUM bracis-28424 105 16 \text \text NOUN bracis-28424 105 17 { { PUNCT bracis-28424 105 18 , , PUNCT bracis-28424 105 19 } } PUNCT bracis-28424 105 20 \text \text NOUN bracis-28424 105 21 { { PUNCT bracis-28424 105 22 if if SCONJ bracis-28424 105 23 } } PUNCT bracis-28424 105 24 v v ADP bracis-28424 105 25 \in \in PROPN bracis-28424 105 26 i(t_o i(t_o PROPN bracis-28424 105 27 ) ) PUNCT bracis-28424 105 28 \\ \\ NOUN bracis-28424 105 29 0 0 PUNCT bracis-28424 106 1 \text \text NOUN bracis-28424 106 2 { { PUNCT bracis-28424 106 3 , , PUNCT bracis-28424 106 4 } } PUNCT bracis-28424 106 5 \text \text ADV bracis-28424 106 6 { { PUNCT bracis-28424 106 7 otherwise otherwise ADV bracis-28424 106 8 } } PUNCT bracis-28424 106 9 \end{array}\right \end{array}\right PROPN bracis-28424 106 10 . . PUNCT bracis-28424 106 11 } } PUNCT bracis-28424 106 12 \end{aligned}$$ \end{aligned}$$ X bracis-28424 106 13 ( ( PUNCT bracis-28424 106 14 3 3 X bracis-28424 106 15 ) ) PUNCT bracis-28424 106 16 note note NOUN bracis-28424 106 17 that that SCONJ bracis-28424 106 18 \(\alpha \(\alpha VERB bracis-28424 106 19 ^u_0 ^u_0 NUM bracis-28424 106 20 = = SYM bracis-28424 106 21 i_u\ i_u\ PROPN bracis-28424 106 22 ) ) PUNCT bracis-28424 106 23 is be AUX bracis-28424 106 24 simply simply ADV bracis-28424 106 25 the the DET bracis-28424 106 26 epidemic epidemic NOUN bracis-28424 106 27 state state NOUN bracis-28424 106 28 of of ADP bracis-28424 106 29 node node PROPN bracis-28424 106 30 u. u. PROPN bracis-28424 107 1 also also ADV bracis-28424 107 2 , , PUNCT bracis-28424 107 3 k k PROPN bracis-28424 107 4 is be AUX bracis-28424 107 5 the the DET bracis-28424 107 6 parameter parameter NOUN bracis-28424 107 7 that that PRON bracis-28424 107 8 determines determine VERB bracis-28424 107 9 the the DET bracis-28424 107 10 maximum maximum ADJ bracis-28424 107 11 distance distance NOUN bracis-28424 107 12 to to PART bracis-28424 107 13 be be AUX bracis-28424 107 14 considered consider VERB bracis-28424 107 15 in in ADP bracis-28424 107 16 the the DET bracis-28424 107 17 attribute attribute NOUN bracis-28424 107 18 generation generation NOUN bracis-28424 107 19 . . PUNCT bracis-28424 108 1 the the DET bracis-28424 108 2 dri dri PROPN bracis-28424 108 3 metric metric NOUN bracis-28424 108 4 depends depend VERB bracis-28424 108 5 on on ADP bracis-28424 108 6 the the DET bracis-28424 108 7 epidemic epidemic NOUN bracis-28424 108 8 state state NOUN bracis-28424 108 9 of of ADP bracis-28424 108 10 the the DET bracis-28424 108 11 neighbors neighbor NOUN bracis-28424 108 12 of of ADP bracis-28424 108 13 nodes node NOUN bracis-28424 108 14 that that PRON bracis-28424 108 15 are be AUX bracis-28424 108 16 at at ADP bracis-28424 108 17 distance distance NOUN bracis-28424 108 18 k k PROPN bracis-28424 108 19 from from ADP bracis-28424 108 20 node node PROPN bracis-28424 108 21 u u PROPN bracis-28424 108 22 ( ( PUNCT bracis-28424 108 23 and and CCONJ bracis-28424 108 24 not not PART bracis-28424 108 25 just just ADV bracis-28424 108 26 the the DET bracis-28424 108 27 epidemic epidemic NOUN bracis-28424 108 28 state state NOUN bracis-28424 108 29 of of ADP bracis-28424 108 30 the the DET bracis-28424 108 31 node node NOUN bracis-28424 108 32 ) ) PUNCT bracis-28424 108 33 . . PUNCT bracis-28424 109 1 in in ADP bracis-28424 109 2 particular particular ADJ bracis-28424 109 3 , , PUNCT bracis-28424 109 4 dri dri PROPN bracis-28424 109 5 is be AUX bracis-28424 109 6 the the DET bracis-28424 109 7 average average NOUN bracis-28424 109 8 of of ADP bracis-28424 109 9 ri ri NOUN bracis-28424 109 10 at at ADP bracis-28424 109 11 distance distance NOUN bracis-28424 109 12 1 1 NUM bracis-28424 109 13 among among ADP bracis-28424 109 14 the the DET bracis-28424 109 15 nodes node NOUN bracis-28424 109 16 that that PRON bracis-28424 109 17 are be AUX bracis-28424 109 18 at at ADP bracis-28424 109 19 distance distance NOUN bracis-28424 109 20 k k PROPN bracis-28424 109 21 from from ADP bracis-28424 109 22 node node PROPN bracis-28424 109 23 u. u. PROPN bracis-28424 109 24 dri dri PROPN bracis-28424 109 25 is be AUX bracis-28424 109 26 given give VERB bracis-28424 109 27 by by ADP bracis-28424 109 28 : : PUNCT bracis-28424 109 29 $ $ SYM bracis-28424 109 30 $ $ SYM bracis-28424 109 31 \begin{aligned \begin{aligne VERB bracis-28424 109 32 } } PUNCT bracis-28424 109 33 \beta \beta NOUN bracis-28424 109 34 ^u_k=\frac{\sum ^u_k=\frac{\sum NOUN bracis-28424 109 35 _ _ PRON bracis-28424 109 36 { { PUNCT bracis-28424 109 37 v v ADP bracis-28424 109 38 \in \in PROPN bracis-28424 109 39 n_k(v n_k(v NOUN bracis-28424 109 40 ) ) PUNCT bracis-28424 109 41 } } PUNCT bracis-28424 109 42 \alpha \alpha SCONJ bracis-28424 109 43 _ _ NOUN bracis-28424 109 44 1^u}{|n_k(u)| 1^u}{|n_k(u)| NUM bracis-28424 109 45 } } PUNCT bracis-28424 109 46 , , PUNCT bracis-28424 109 47 \text \text NOUN bracis-28424 109 48 { { PUNCT bracis-28424 109 49 for for ADP bracis-28424 109 50 } } PUNCT bracis-28424 109 51 k=1,\ldots k=1,\ldot NOUN bracis-28424 109 52 , , PUNCT bracis-28424 109 53 k. k. PROPN bracis-28424 109 54 \end{aligned}$$ \end{aligned}$$ X bracis-28424 109 55 ( ( PUNCT bracis-28424 109 56 4 4 X bracis-28424 109 57 ) ) PUNCT bracis-28424 109 58 a a DET bracis-28424 109 59 single single ADJ bracis-28424 109 60 node node NOUN bracis-28424 109 61 can can AUX bracis-28424 109 62 be be AUX bracis-28424 109 63 counted count VERB bracis-28424 109 64 multiple multiple ADJ bracis-28424 109 65 times time NOUN bracis-28424 109 66 in in ADP bracis-28424 109 67 this this DET bracis-28424 109 68 metric metric NOUN bracis-28424 109 69 , , PUNCT bracis-28424 109 70 since since SCONJ bracis-28424 109 71 it it PRON bracis-28424 109 72 can can AUX bracis-28424 109 73 be be AUX bracis-28424 109 74 neighbor neighbor NOUN bracis-28424 109 75 of of ADP bracis-28424 109 76 many many ADJ bracis-28424 109 77 nodes node NOUN bracis-28424 109 78 at at ADP bracis-28424 109 79 distance distance NOUN bracis-28424 109 80 k k PROPN bracis-28424 109 81 from from ADP bracis-28424 109 82 u. u. PROPN bracis-28424 109 83 thus thus ADV bracis-28424 109 84 , , PUNCT bracis-28424 109 85 dri dri PROPN bracis-28424 109 86 provides provide VERB bracis-28424 109 87 information information NOUN bracis-28424 109 88 that that PRON bracis-28424 109 89 is be AUX bracis-28424 109 90 significantly significantly ADV bracis-28424 109 91 different different ADJ bracis-28424 109 92 from from ADP bracis-28424 109 93 ri ri PROPN bracis-28424 109 94 . . PUNCT bracis-28424 110 1 the the DET bracis-28424 110 2 calculations calculation NOUN bracis-28424 110 3 of of ADP bracis-28424 110 4 ri ri PROPN bracis-28424 110 5 and and CCONJ bracis-28424 110 6 dri dri PROPN bracis-28424 110 7 require require VERB bracis-28424 110 8 determining determine VERB bracis-28424 110 9 the the DET bracis-28424 110 10 k k ADJ bracis-28424 110 11 - - PUNCT bracis-28424 110 12 hop hop ADJ bracis-28424 110 13 neighborhoods neighborhood NOUN bracis-28424 110 14 of of ADP bracis-28424 110 15 all all DET bracis-28424 110 16 nodes node NOUN bracis-28424 110 17 in in ADP bracis-28424 110 18 the the DET bracis-28424 110 19 network network NOUN bracis-28424 110 20 . . PUNCT bracis-28424 111 1 for for ADP bracis-28424 111 2 a a DET bracis-28424 111 3 given give VERB bracis-28424 111 4 node node PROPN bracis-28424 111 5 u u PROPN bracis-28424 111 6 , , PUNCT bracis-28424 111 7 a a DET bracis-28424 111 8 breadth breadth NOUN bracis-28424 111 9 first first ADJ bracis-28424 111 10 search search NOUN bracis-28424 111 11 ( ( PUNCT bracis-28424 111 12 bfs bfs NOUN bracis-28424 111 13 ) ) PUNCT bracis-28424 111 14 starting start VERB bracis-28424 111 15 on on ADP bracis-28424 111 16 u u NOUN bracis-28424 111 17 can can AUX bracis-28424 111 18 efficiently efficiently ADV bracis-28424 111 19 determine determine VERB bracis-28424 111 20 the the DET bracis-28424 111 21 k k ADJ bracis-28424 111 22 - - PUNCT bracis-28424 111 23 hop hop ADJ bracis-28424 111 24 neighborhoods neighborhood NOUN bracis-28424 111 25 , , PUNCT bracis-28424 111 26 in in ADP bracis-28424 111 27 linear linear ADJ bracis-28424 111 28 time time NOUN bracis-28424 111 29 \(o(|v|+|e|)\ \(o(|v|+|e|)\ NUM bracis-28424 111 30 ) ) PUNCT bracis-28424 111 31 . . PUNCT bracis-28424 112 1 since since SCONJ bracis-28424 112 2 k k PROPN bracis-28424 112 3 is be AUX bracis-28424 112 4 often often ADV bracis-28424 112 5 small small ADJ bracis-28424 112 6 when when SCONJ bracis-28424 112 7 compared compare VERB bracis-28424 112 8 to to ADP bracis-28424 112 9 the the DET bracis-28424 112 10 network network NOUN bracis-28424 112 11 diameter diameter NOUN bracis-28424 112 12 , , PUNCT bracis-28424 112 13 the the DET bracis-28424 112 14 bfs bfs NOUN bracis-28424 112 15 stops stop VERB bracis-28424 112 16 before before ADP bracis-28424 112 17 reaching reach VERB bracis-28424 112 18 all all DET bracis-28424 112 19 network network NOUN bracis-28424 112 20 nodes node NOUN bracis-28424 112 21 . . PUNCT bracis-28424 113 1 ri ri PROPN bracis-28424 113 2 and and CCONJ bracis-28424 113 3 dri dri PROPN bracis-28424 113 4 for for ADP bracis-28424 113 5 different different ADJ bracis-28424 113 6 nodes node NOUN bracis-28424 113 7 are be AUX bracis-28424 113 8 computed compute VERB bracis-28424 113 9 fully fully ADV bracis-28424 113 10 in in ADP bracis-28424 113 11 parallel parallel NOUN bracis-28424 113 12 , , PUNCT bracis-28424 113 13 as as SCONJ bracis-28424 113 14 there there PRON bracis-28424 113 15 are be VERB bracis-28424 113 16 no no DET bracis-28424 113 17 dependencies dependency NOUN bracis-28424 113 18 . . PUNCT bracis-28424 114 1 this this PRON bracis-28424 114 2 allows allow VERB bracis-28424 114 3 for for ADP bracis-28424 114 4 both both DET bracis-28424 114 5 time time NOUN bracis-28424 114 6 and and CCONJ bracis-28424 114 7 memory memory NOUN bracis-28424 114 8 efficient efficient ADJ bracis-28424 114 9 calculation calculation NOUN bracis-28424 114 10 . . PUNCT bracis-28424 115 1 finally finally ADV bracis-28424 115 2 , , PUNCT bracis-28424 115 3 ri ri PROPN bracis-28424 115 4 and and CCONJ bracis-28424 115 5 dri dri PROPN bracis-28424 115 6 are be AUX bracis-28424 115 7 used use VERB bracis-28424 115 8 to to PART bracis-28424 115 9 determine determine VERB bracis-28424 115 10 the the DET bracis-28424 115 11 attribute attribute NOUN bracis-28424 115 12 vector vector NOUN bracis-28424 115 13 for for ADP bracis-28424 115 14 each each DET bracis-28424 115 15 node node NOUN bracis-28424 115 16 . . PUNCT bracis-28424 116 1 in in ADP bracis-28424 116 2 particular particular ADJ bracis-28424 116 3 , , PUNCT bracis-28424 116 4 node node NOUN bracis-28424 116 5 u u NOUN bracis-28424 116 6 has have VERB bracis-28424 116 7 an an DET bracis-28424 116 8 attribute attribute NOUN bracis-28424 116 9 vector vector NOUN bracis-28424 116 10 that that PRON bracis-28424 116 11 is be AUX bracis-28424 116 12 the the DET bracis-28424 116 13 concatenation concatenation NOUN bracis-28424 116 14 of of ADP bracis-28424 116 15 \(\alpha \(\alpha NOUN bracis-28424 116 16 _ _ PUNCT bracis-28424 116 17 u\ u\ PUNCT bracis-28424 116 18 ) ) PUNCT bracis-28424 116 19 and and CCONJ bracis-28424 116 20 \(\beta \(\beta X bracis-28424 116 21 _ _ PUNCT bracis-28424 116 22 u\ u\ PROPN bracis-28424 116 23 ) ) PUNCT bracis-28424 116 24 for for ADP bracis-28424 116 25 all all DET bracis-28424 116 26 k k NOUN bracis-28424 116 27 whose whose DET bracis-28424 116 28 dimension dimension NOUN bracis-28424 116 29 is be AUX bracis-28424 116 30 \(2k \(2k PROPN bracis-28424 116 31 + + PROPN bracis-28424 116 32 1\ 1\ NUM bracis-28424 116 33 ) ) PUNCT bracis-28424 116 34 ( ( PUNCT bracis-28424 116 35 since since SCONJ bracis-28424 116 36 \(\alpha \(\alpha NUM bracis-28424 116 37 _ _ PUNCT bracis-28424 116 38 u\ u\ PUNCT bracis-28424 116 39 ) ) PUNCT bracis-28424 116 40 has have AUX bracis-28424 116 41 \(k \(k NOUN bracis-28424 116 42 + + CCONJ bracis-28424 116 43 1\ 1\ NUM bracis-28424 116 44 ) ) PUNCT bracis-28424 116 45 values value NOUN bracis-28424 116 46 and and CCONJ bracis-28424 116 47 \(\beta \(\beta NOUN bracis-28424 116 48 _ _ PUNCT bracis-28424 116 49 u\ u\ PROPN bracis-28424 116 50 ) ) PUNCT bracis-28424 116 51 has have VERB bracis-28424 116 52 k k ADJ bracis-28424 116 53 values value NOUN bracis-28424 116 54 ) ) PUNCT bracis-28424 116 55 . . PUNCT bracis-28424 117 1 this this PRON bracis-28424 117 2 is be AUX bracis-28424 117 3 the the DET bracis-28424 117 4 initial initial ADJ bracis-28424 117 5 representation representation NOUN bracis-28424 117 6 ( ( PUNCT bracis-28424 117 7 input input NOUN bracis-28424 117 8 ) ) PUNCT bracis-28424 117 9 to to ADP bracis-28424 117 10 the the DET bracis-28424 117 11 gnn gnn PROPN bracis-28424 117 12 model model NOUN bracis-28424 117 13 . . PUNCT bracis-28424 118 1 4.2 4.2 NUM bracis-28424 118 2 graph graph NOUN bracis-28424 118 3 neural neural ADJ bracis-28424 118 4 network network NOUN bracis-28424 118 5 model model NOUN bracis-28424 118 6 graph graph NOUN bracis-28424 118 7 neural neural ADJ bracis-28424 118 8 networks network NOUN bracis-28424 118 9 ( ( PUNCT bracis-28424 118 10 gnns gnns NOUN bracis-28424 118 11 ) ) PUNCT bracis-28424 118 12 integrate integrate VERB bracis-28424 118 13 structural structural ADJ bracis-28424 118 14 information information NOUN bracis-28424 118 15 with with ADP bracis-28424 118 16 attribute attribute NOUN bracis-28424 118 17 information information NOUN bracis-28424 118 18 ( ( PUNCT bracis-28424 118 19 node node NOUN bracis-28424 118 20 labels label NOUN bracis-28424 118 21 ) ) PUNCT bracis-28424 118 22 in in ADP bracis-28424 118 23 order order NOUN bracis-28424 118 24 to to PART bracis-28424 118 25 generate generate VERB bracis-28424 118 26 representations representation NOUN bracis-28424 118 27 for for ADP bracis-28424 118 28 network network NOUN bracis-28424 118 29 nodes node NOUN bracis-28424 118 30 . . PUNCT bracis-28424 119 1 the the DET bracis-28424 119 2 gnn gnn PROPN bracis-28424 119 3 is be AUX bracis-28424 119 4 a a DET bracis-28424 119 5 stack stack NOUN bracis-28424 119 6 of of ADP bracis-28424 119 7 neural neural ADJ bracis-28424 119 8 network network NOUN bracis-28424 119 9 layers layer NOUN bracis-28424 119 10 whose whose DET bracis-28424 119 11 input input NOUN bracis-28424 119 12 is be AUX bracis-28424 119 13 the the DET bracis-28424 119 14 node node ADJ bracis-28424 119 15 representation representation NOUN bracis-28424 119 16 along along ADP bracis-28424 119 17 with with ADP bracis-28424 119 18 an an DET bracis-28424 119 19 aggregated aggregate VERB bracis-28424 119 20 representation representation NOUN bracis-28424 119 21 of of ADP bracis-28424 119 22 its its PRON bracis-28424 119 23 neighbors neighbor NOUN bracis-28424 119 24 , , PUNCT bracis-28424 119 25 that that PRON bracis-28424 119 26 can can AUX bracis-28424 119 27 take take VERB bracis-28424 119 28 several several ADJ bracis-28424 119 29 forms form NOUN bracis-28424 119 30 such such ADJ bracis-28424 119 31 as as ADP bracis-28424 119 32 averaging average VERB bracis-28424 119 33 . . PUNCT bracis-28424 120 1 in in ADP bracis-28424 120 2 practice practice NOUN bracis-28424 120 3 , , PUNCT bracis-28424 120 4 the the DET bracis-28424 120 5 input input NOUN bracis-28424 120 6 to to ADP bracis-28424 120 7 the the DET bracis-28424 120 8 first first ADJ bracis-28424 120 9 layer layer NOUN bracis-28424 120 10 corresponds correspond VERB bracis-28424 120 11 to to ADP bracis-28424 120 12 node node NOUN bracis-28424 120 13 attributes attribute NOUN bracis-28424 120 14 , , PUNCT bracis-28424 120 15 while while SCONJ bracis-28424 120 16 the the DET bracis-28424 120 17 output output NOUN bracis-28424 120 18 of of ADP bracis-28424 120 19 the the DET bracis-28424 120 20 last last ADJ bracis-28424 120 21 layer layer NOUN bracis-28424 120 22 corresponds correspond VERB bracis-28424 120 23 to to ADP bracis-28424 120 24 the the DET bracis-28424 120 25 node node ADJ bracis-28424 120 26 representation representation NOUN bracis-28424 120 27 . . PUNCT bracis-28424 121 1 the the DET bracis-28424 121 2 implementation implementation NOUN bracis-28424 121 3 discussed discuss VERB bracis-28424 121 4 here here ADV bracis-28424 121 5 adopts adopt VERB bracis-28424 121 6 a a DET bracis-28424 121 7 small small ADJ bracis-28424 121 8 number number NOUN bracis-28424 121 9 of of ADP bracis-28424 121 10 layers layer NOUN bracis-28424 121 11 , , PUNCT bracis-28424 121 12 e.g. e.g. ADV bracis-28424 121 13 , , PUNCT bracis-28424 121 14 three three NUM bracis-28424 121 15 layers layer NOUN bracis-28424 121 16 , , PUNCT bracis-28424 121 17 to to PART bracis-28424 121 18 avoid avoid VERB bracis-28424 121 19 diluting dilute VERB bracis-28424 121 20 the the DET bracis-28424 121 21 signal signal NOUN bracis-28424 121 22 of of ADP bracis-28424 121 23 the the DET bracis-28424 121 24 node node NOUN bracis-28424 121 25 ’s ’s PART bracis-28424 121 26 neighborhood neighborhood NOUN bracis-28424 121 27 . . PUNCT bracis-28424 122 1 while while SCONJ bracis-28424 122 2 being be AUX bracis-28424 122 3 possible possible ADJ bracis-28424 122 4 to to PART bracis-28424 122 5 make make VERB bracis-28424 122 6 gnn gnn NOUN bracis-28424 122 7 models model NOUN bracis-28424 122 8 learn learn VERB bracis-28424 122 9 representations representation NOUN bracis-28424 122 10 without without ADP bracis-28424 122 11 supervision supervision NOUN bracis-28424 122 12 , , PUNCT bracis-28424 122 13 gnns gnns PROPN bracis-28424 122 14 may may AUX bracis-28424 122 15 also also ADV bracis-28424 122 16 be be AUX bracis-28424 122 17 trained train VERB bracis-28424 122 18 in in ADP bracis-28424 122 19 a a DET bracis-28424 122 20 supervised supervised ADJ bracis-28424 122 21 fashion fashion NOUN bracis-28424 122 22 . . PUNCT bracis-28424 123 1 in in ADP bracis-28424 123 2 this this DET bracis-28424 123 3 case case NOUN bracis-28424 123 4 , , PUNCT bracis-28424 123 5 the the DET bracis-28424 123 6 output output NOUN bracis-28424 123 7 of of ADP bracis-28424 123 8 the the DET bracis-28424 123 9 last last ADJ bracis-28424 123 10 layer layer NOUN bracis-28424 123 11 is be AUX bracis-28424 123 12 used use VERB bracis-28424 123 13 to to PART bracis-28424 123 14 compute compute VERB bracis-28424 123 15 a a DET bracis-28424 123 16 loss loss NOUN bracis-28424 123 17 function function NOUN bracis-28424 123 18 that that PRON bracis-28424 123 19 then then ADV bracis-28424 123 20 drives drive VERB bracis-28424 123 21 the the DET bracis-28424 123 22 training training NOUN bracis-28424 123 23 of of ADP bracis-28424 123 24 the the DET bracis-28424 123 25 model model NOUN bracis-28424 123 26 parameters parameter NOUN bracis-28424 123 27 . . PUNCT bracis-28424 124 1 this this DET bracis-28424 124 2 work work NOUN bracis-28424 124 3 uses use VERB bracis-28424 124 4 gnn gnn PROPN bracis-28424 124 5 in in ADP bracis-28424 124 6 a a DET bracis-28424 124 7 classification classification NOUN bracis-28424 124 8 task task NOUN bracis-28424 124 9 whose whose DET bracis-28424 124 10 final final ADJ bracis-28424 124 11 goal goal NOUN bracis-28424 124 12 is be AUX bracis-28424 124 13 to to PART bracis-28424 124 14 classify classify VERB bracis-28424 124 15 an an DET bracis-28424 124 16 epidemic epidemic NOUN bracis-28424 124 17 network network NOUN bracis-28424 124 18 node node NOUN bracis-28424 124 19 as as ADP bracis-28424 124 20 being be AUX bracis-28424 124 21 an an DET bracis-28424 124 22 epidemic epidemic NOUN bracis-28424 124 23 source source NOUN bracis-28424 124 24 . . PUNCT bracis-28424 125 1 therefore therefore ADV bracis-28424 125 2 , , PUNCT bracis-28424 125 3 a a DET bracis-28424 125 4 sigmoid sigmoid NOUN bracis-28424 125 5 function function NOUN bracis-28424 125 6 is be AUX bracis-28424 125 7 applied apply VERB bracis-28424 125 8 to to ADP bracis-28424 125 9 the the DET bracis-28424 125 10 output output NOUN bracis-28424 125 11 of of ADP bracis-28424 125 12 the the DET bracis-28424 125 13 last last ADJ bracis-28424 125 14 ( ( PUNCT bracis-28424 125 15 third third ADJ bracis-28424 125 16 ) ) PUNCT bracis-28424 125 17 layer layer NOUN bracis-28424 125 18 in in ADP bracis-28424 125 19 order order NOUN bracis-28424 125 20 to to PART bracis-28424 125 21 generate generate VERB bracis-28424 125 22 values value NOUN bracis-28424 125 23 between between ADP bracis-28424 125 24 0 0 NUM bracis-28424 125 25 and and CCONJ bracis-28424 125 26 1 1 NUM bracis-28424 125 27 . . PUNCT bracis-28424 126 1 the the DET bracis-28424 126 2 first first ADJ bracis-28424 126 3 and and CCONJ bracis-28424 126 4 second second ADJ bracis-28424 126 5 layers layer NOUN bracis-28424 126 6 use use VERB bracis-28424 126 7 the the DET bracis-28424 126 8 relu relu NOUN bracis-28424 126 9 as as SCONJ bracis-28424 126 10 activation activation NOUN bracis-28424 126 11 function function VERB bracis-28424 126 12 together together ADV bracis-28424 126 13 with with ADP bracis-28424 126 14 a a DET bracis-28424 126 15 dropout dropout NOUN bracis-28424 126 16 layer layer NOUN bracis-28424 126 17 to to PART bracis-28424 126 18 help help VERB bracis-28424 126 19 avoid avoid VERB bracis-28424 126 20 overfitting overfitte VERB bracis-28424 126 21 . . PUNCT bracis-28424 127 1 the the DET bracis-28424 127 2 layers layer NOUN bracis-28424 127 3 adopted adopt VERB bracis-28424 127 4 are be AUX bracis-28424 127 5 sage sage NOUN bracis-28424 127 6 layers layer NOUN bracis-28424 127 7 proposed propose VERB bracis-28424 127 8 by by ADP bracis-28424 127 9 graphsage graphsage NOUN bracis-28424 127 10 , , PUNCT bracis-28424 127 11 given give VERB bracis-28424 127 12 its its PRON bracis-28424 127 13 wide wide ADJ bracis-28424 127 14 applicability applicability NOUN bracis-28424 127 15 and and CCONJ bracis-28424 127 16 efficiency efficiency NOUN bracis-28424 127 17 [ [ X bracis-28424 127 18 9 9 NUM bracis-28424 127 19 ] ] PUNCT bracis-28424 127 20 . . PUNCT bracis-28424 128 1 4.3 4.3 NUM bracis-28424 128 2 loss loss NOUN bracis-28424 128 3 function function NOUN bracis-28424 128 4 since since SCONJ bracis-28424 128 5 the the DET bracis-28424 128 6 problem problem NOUN bracis-28424 128 7 consists consist VERB bracis-28424 128 8 of of ADP bracis-28424 128 9 binary binary ADJ bracis-28424 128 10 classification classification NOUN bracis-28424 128 11 , , PUNCT bracis-28424 128 12 the the DET bracis-28424 128 13 binary binary PROPN bracis-28424 128 14 cross cross PROPN bracis-28424 128 15 entropy entropy PROPN bracis-28424 128 16 function function PROPN bracis-28424 128 17 was be AUX bracis-28424 128 18 adopted adopt VERB bracis-28424 128 19 as as ADP bracis-28424 128 20 the the DET bracis-28424 128 21 loss loss NOUN bracis-28424 128 22 function function NOUN bracis-28424 128 23 . . PUNCT bracis-28424 129 1 in in ADP bracis-28424 129 2 particular particular ADJ bracis-28424 129 3 , , PUNCT bracis-28424 129 4 for for ADP bracis-28424 129 5 each each DET bracis-28424 129 6 node node PROPN bracis-28424 129 7 u u NOUN bracis-28424 129 8 , , PUNCT bracis-28424 129 9 it it PRON bracis-28424 129 10 follows follow VERB bracis-28424 129 11 : : PUNCT bracis-28424 129 12 $ $ SYM bracis-28424 129 13 $ $ SYM bracis-28424 129 14 \begin{aligned \begin{aligne VERB bracis-28424 129 15 } } PUNCT bracis-28424 129 16 \ell \ell PROPN bracis-28424 129 17 _ _ X bracis-28424 129 18 u(i_0 u(i_0 X bracis-28424 129 19 ) ) PUNCT bracis-28424 129 20 = = SYM bracis-28424 129 21 c_u c_u PUNCT bracis-28424 130 1 \log \log PROPN bracis-28424 130 2 \sigma \sigma PROPN bracis-28424 130 3 \left \left PROPN bracis-28424 130 4 ( ( PUNCT bracis-28424 130 5 y_u\right y_u\right NOUN bracis-28424 130 6 ) ) PUNCT bracis-28424 131 1 + + NOUN bracis-28424 131 2 \left \left PROPN bracis-28424 131 3 ( ( PUNCT bracis-28424 131 4 1 1 NUM bracis-28424 131 5 - - PUNCT bracis-28424 131 6 c_u\right c_u\right NOUN bracis-28424 131 7 ) ) PUNCT bracis-28424 131 8 \log \log PROPN bracis-28424 131 9 \left \left PROPN bracis-28424 131 10 ( ( PUNCT bracis-28424 131 11 1-\sigma 1-\sigma NUM bracis-28424 131 12 \left \left PROPN bracis-28424 131 13 ( ( PUNCT bracis-28424 131 14 y_u\right y_u\right NOUN bracis-28424 131 15 ) ) PUNCT bracis-28424 131 16 \right \right NOUN bracis-28424 131 17 ) ) PUNCT bracis-28424 131 18 , , PUNCT bracis-28424 131 19 \end{aligned}$$ \end{aligned}$$ X bracis-28424 131 20 ( ( PUNCT bracis-28424 131 21 5 5 NUM bracis-28424 131 22 ) ) PUNCT bracis-28424 131 23 where where SCONJ bracis-28424 131 24 \(c_u\ \(c_u\ NOUN bracis-28424 131 25 ) ) PUNCT bracis-28424 131 26 indicates indicate VERB bracis-28424 131 27 if if SCONJ bracis-28424 131 28 node node NOUN bracis-28424 131 29 u u NOUN bracis-28424 131 30 is be AUX bracis-28424 131 31 an an DET bracis-28424 131 32 epidemic epidemic NOUN bracis-28424 131 33 source source NOUN bracis-28424 131 34 ( ( PUNCT bracis-28424 131 35 \(u \(u PROPN bracis-28424 131 36 \in \in PROPN bracis-28424 131 37 i_0\ i_0\ PROPN bracis-28424 131 38 ) ) PUNCT bracis-28424 131 39 , , PUNCT bracis-28424 131 40 the the DET bracis-28424 131 41 ground ground NOUN bracis-28424 131 42 truth truth NOUN bracis-28424 131 43 ) ) PUNCT bracis-28424 131 44 , , PUNCT bracis-28424 131 45 \(y_u\ \(y_u\ NOUN bracis-28424 131 46 ) ) PUNCT bracis-28424 131 47 is be AUX bracis-28424 131 48 the the DET bracis-28424 131 49 output output NOUN bracis-28424 131 50 of of ADP bracis-28424 131 51 the the DET bracis-28424 131 52 neural neural ADJ bracis-28424 131 53 network network NOUN bracis-28424 131 54 for for ADP bracis-28424 131 55 node node NOUN bracis-28424 131 56 u u NOUN bracis-28424 131 57 , , PUNCT bracis-28424 131 58 and and CCONJ bracis-28424 131 59 \(\sigma \(\sigma NOUN bracis-28424 131 60 \ \ NOUN bracis-28424 131 61 ) ) PUNCT bracis-28424 131 62 is be AUX bracis-28424 131 63 the the DET bracis-28424 131 64 sigmoid sigmoid NOUN bracis-28424 131 65 function function NOUN bracis-28424 131 66 applied apply VERB bracis-28424 131 67 to to ADP bracis-28424 131 68 the the DET bracis-28424 131 69 output output NOUN bracis-28424 131 70 of of ADP bracis-28424 131 71 the the DET bracis-28424 131 72 neural neural ADJ bracis-28424 131 73 network network NOUN bracis-28424 131 74 . . PUNCT bracis-28424 132 1 the the DET bracis-28424 132 2 average average ADJ bracis-28424 132 3 loss loss NOUN bracis-28424 132 4 function function NOUN bracis-28424 132 5 across across ADP bracis-28424 132 6 all all DET bracis-28424 132 7 nodes node NOUN bracis-28424 132 8 must must AUX bracis-28424 132 9 consider consider VERB bracis-28424 132 10 the the DET bracis-28424 132 11 fact fact NOUN bracis-28424 132 12 that that SCONJ bracis-28424 132 13 classes class NOUN bracis-28424 132 14 are be AUX bracis-28424 132 15 very very ADV bracis-28424 132 16 imbalanced imbalanced ADJ bracis-28424 132 17 in in ADP bracis-28424 132 18 this this DET bracis-28424 132 19 problem problem NOUN bracis-28424 132 20 . . PUNCT bracis-28424 133 1 for for ADP bracis-28424 133 2 that that DET bracis-28424 133 3 matter matter NOUN bracis-28424 133 4 , , PUNCT bracis-28424 133 5 a a DET bracis-28424 133 6 weighted weight VERB bracis-28424 133 7 average average NOUN bracis-28424 133 8 is be AUX bracis-28424 133 9 considered consider VERB bracis-28424 133 10 where where SCONJ bracis-28424 133 11 \(w_0\ \(w_0\ NOUN bracis-28424 133 12 ) ) PUNCT bracis-28424 133 13 and and CCONJ bracis-28424 133 14 \(w_1\ \(w_1\ PROPN bracis-28424 133 15 ) ) PUNCT bracis-28424 133 16 denote denote VERB bracis-28424 133 17 the the DET bracis-28424 133 18 weights weight NOUN bracis-28424 133 19 for for ADP bracis-28424 133 20 each each DET bracis-28424 133 21 class class NOUN bracis-28424 133 22 . . PUNCT bracis-28424 134 1 the the DET bracis-28424 134 2 weights weight NOUN bracis-28424 134 3 must must AUX bracis-28424 134 4 consider consider VERB bracis-28424 134 5 the the DET bracis-28424 134 6 number number NOUN bracis-28424 134 7 of of ADP bracis-28424 134 8 nodes node NOUN bracis-28424 134 9 in in ADP bracis-28424 134 10 each each DET bracis-28424 134 11 class class NOUN bracis-28424 134 12 ; ; PUNCT bracis-28424 134 13 \(w_0 \(w_0 PROPN bracis-28424 134 14 = = SYM bracis-28424 134 15 r_0/(1 r_0/(1 NOUN bracis-28424 134 16 |i_0|/n)\ |i_0|/n)\ NUM bracis-28424 134 17 ) ) PUNCT bracis-28424 134 18 and and CCONJ bracis-28424 134 19 \(w_1 \(w_1 NUM bracis-28424 134 20 = = SYM bracis-28424 134 21 r_1/(|i_0|/n)\ r_1/(|i_0|/n)\ PROPN bracis-28424 134 22 ) ) PUNCT bracis-28424 134 23 where where SCONJ bracis-28424 134 24 \(r_0\ \(r_0\ NOUN bracis-28424 134 25 ) ) PUNCT bracis-28424 134 26 and and CCONJ bracis-28424 134 27 \(r_1\ \(r_1\ NOUN bracis-28424 134 28 ) ) PUNCT bracis-28424 134 29 are be AUX bracis-28424 134 30 constants constant NOUN bracis-28424 134 31 used use VERB bracis-28424 134 32 to to PART bracis-28424 134 33 increase increase VERB bracis-28424 134 34 the the DET bracis-28424 134 35 class class NOUN bracis-28424 134 36 weight weight NOUN bracis-28424 134 37 beyond beyond ADP bracis-28424 134 38 the the DET bracis-28424 134 39 class class NOUN bracis-28424 134 40 balance balance NOUN bracis-28424 134 41 ratio ratio NOUN bracis-28424 134 42 , , PUNCT bracis-28424 134 43 and and CCONJ bracis-28424 134 44 , , PUNCT bracis-28424 134 45 in in ADP bracis-28424 134 46 this this DET bracis-28424 134 47 work work NOUN bracis-28424 134 48 , , PUNCT bracis-28424 134 49 \(r_0=1\ \(r_0=1\ NOUN bracis-28424 134 50 ) ) PUNCT bracis-28424 134 51 and and CCONJ bracis-28424 134 52 \(r_1=100\ \(r_1=100\ NOUN bracis-28424 134 53 ) ) PUNCT bracis-28424 134 54 ( ( PUNCT bracis-28424 134 55 chosen choose VERB bracis-28424 134 56 experimentally experimentally ADV bracis-28424 134 57 ) ) PUNCT bracis-28424 134 58 . . PUNCT bracis-28424 135 1 this this PRON bracis-28424 135 2 indicates indicate VERB bracis-28424 135 3 to to ADP bracis-28424 135 4 the the DET bracis-28424 135 5 model model NOUN bracis-28424 135 6 the the DET bracis-28424 135 7 importance importance NOUN bracis-28424 135 8 of of ADP bracis-28424 135 9 correctly correctly ADV bracis-28424 135 10 classifying classify VERB bracis-28424 135 11 the the DET bracis-28424 135 12 epidemic epidemic NOUN bracis-28424 135 13 source source NOUN bracis-28424 135 14 node node NOUN bracis-28424 135 15 . . PUNCT bracis-28424 136 1 the the DET bracis-28424 136 2 average average ADJ bracis-28424 136 3 loss loss NOUN bracis-28424 136 4 function function NOUN bracis-28424 136 5 is be AUX bracis-28424 136 6 given give VERB bracis-28424 136 7 by by ADP bracis-28424 136 8 : : PUNCT bracis-28424 136 9 $ $ SYM bracis-28424 136 10 $ $ SYM bracis-28424 136 11 \begin{aligned \begin{aligne VERB bracis-28424 136 12 } } PUNCT bracis-28424 136 13 \ell \ell PROPN bracis-28424 136 14 ( ( PUNCT bracis-28424 136 15 i_0)= i_0)= PROPN bracis-28424 136 16 \frac{w_0 \frac{w_0 X bracis-28424 136 17 \sum \sum PROPN bracis-28424 136 18 _ _ PUNCT bracis-28424 136 19 { { PUNCT bracis-28424 136 20 u u NOUN bracis-28424 136 21 \not \not ADV bracis-28424 136 22 \in \in ADJ bracis-28424 136 23 i_0 i_0 NOUN bracis-28424 136 24 } } PUNCT bracis-28424 136 25 \ell \ell PROPN bracis-28424 136 26 _ _ X bracis-28424 136 27 u(i_0 u(i_0 PROPN bracis-28424 136 28 ) ) PUNCT bracis-28424 137 1 + + CCONJ bracis-28424 137 2 w_1 w_1 PROPN bracis-28424 137 3 \sum \sum NOUN bracis-28424 137 4 _ _ PUNCT bracis-28424 137 5 { { PUNCT bracis-28424 137 6 u u NOUN bracis-28424 137 7 \in \in PROPN bracis-28424 137 8 i_0 i_0 PROPN bracis-28424 137 9 } } PUNCT bracis-28424 137 10 \ell \ell PROPN bracis-28424 137 11 _ _ PUNCT bracis-28424 138 1 u(i_0)}{(n u(i_0)}{(n PROPN bracis-28424 138 2 |i_0|)w_0 |i_0|)w_0 PROPN bracis-28424 138 3 + + CCONJ bracis-28424 138 4 |i_0|w_1 |i_0|w_1 VERB bracis-28424 138 5 } } PUNCT bracis-28424 138 6 \end{aligned}$$ \end{aligned}$$ X bracis-28424 138 7 ( ( PUNCT bracis-28424 138 8 6 6 NUM bracis-28424 138 9 ) ) PUNCT bracis-28424 138 10 4.4 4.4 NUM bracis-28424 138 11 datasets dataset NOUN bracis-28424 138 12 and and CCONJ bracis-28424 138 13     SPACE bracis-28424 138 14 training train VERB bracis-28424 138 15 an an DET bracis-28424 138 16 arbitrary arbitrary ADJ bracis-28424 138 17 large large ADJ bracis-28424 138 18 and and CCONJ bracis-28424 138 19 diverse diverse ADJ bracis-28424 138 20 dataset dataset NOUN bracis-28424 138 21 with with ADP bracis-28424 138 22 ground ground NOUN bracis-28424 138 23 truth truth NOUN bracis-28424 138 24 concerning concern VERB bracis-28424 138 25 epidemic epidemic NOUN bracis-28424 138 26 sources source NOUN bracis-28424 138 27 is be AUX bracis-28424 138 28 generated generate VERB bracis-28424 138 29 for for ADP bracis-28424 138 30 this this DET bracis-28424 138 31 problem problem NOUN bracis-28424 138 32 . . PUNCT bracis-28424 139 1 for for ADP bracis-28424 139 2 each each DET bracis-28424 139 3 sampled sample VERB bracis-28424 139 4 network network NOUN bracis-28424 139 5 , , PUNCT bracis-28424 139 6 the the DET bracis-28424 139 7 set set NOUN bracis-28424 139 8 \(i_0\ \(i_0\ PROPN bracis-28424 139 9 ) ) PUNCT bracis-28424 139 10 ( ( PUNCT bracis-28424 139 11 epidemic epidemic NOUN bracis-28424 139 12 sources source NOUN bracis-28424 139 13 ) ) PUNCT bracis-28424 139 14 is be AUX bracis-28424 139 15 chosen choose VERB bracis-28424 139 16 uniformly uniformly ADV bracis-28424 139 17 random random ADJ bracis-28424 139 18 , , PUNCT bracis-28424 139 19 and and CCONJ bracis-28424 139 20 a a DET bracis-28424 139 21 si si NOUN bracis-28424 139 22 epidemic epidemic NOUN bracis-28424 139 23 is be AUX bracis-28424 139 24 simulated simulate VERB bracis-28424 139 25 until until SCONJ bracis-28424 139 26 a a DET bracis-28424 139 27 fraction fraction NOUN bracis-28424 139 28 of of ADP bracis-28424 139 29 nodes node NOUN bracis-28424 139 30 \(f_o\ \(f_o\ VERB bracis-28424 139 31 ) ) PUNCT bracis-28424 139 32 is be AUX bracis-28424 139 33 infected infect VERB bracis-28424 139 34 , , PUNCT bracis-28424 139 35 giving give VERB bracis-28424 139 36 rise rise NOUN bracis-28424 139 37 to to ADP bracis-28424 139 38 one one NUM bracis-28424 139 39 epidemic epidemic NOUN bracis-28424 139 40 network network NOUN bracis-28424 139 41 sample sample NOUN bracis-28424 139 42 . . PUNCT bracis-28424 140 1 this this DET bracis-28424 140 2 entire entire ADJ bracis-28424 140 3 process process NOUN bracis-28424 140 4 is be AUX bracis-28424 140 5 repeated repeat VERB bracis-28424 140 6 to to PART bracis-28424 140 7 generate generate VERB bracis-28424 140 8 independent independent ADJ bracis-28424 140 9 samples sample NOUN bracis-28424 140 10 of of ADP bracis-28424 140 11 network network NOUN bracis-28424 140 12 epidemics epidemic NOUN bracis-28424 140 13 . . PUNCT bracis-28424 141 1 real real ADJ bracis-28424 141 2 networks network NOUN bracis-28424 141 3 are be AUX bracis-28424 141 4 also also ADV bracis-28424 141 5 covered cover VERB bracis-28424 141 6 by by ADP bracis-28424 141 7 the the DET bracis-28424 141 8 dataset dataset NOUN bracis-28424 141 9 , , PUNCT bracis-28424 141 10 and and CCONJ bracis-28424 141 11 in in ADP bracis-28424 141 12 this this DET bracis-28424 141 13 case case NOUN bracis-28424 141 14 the the DET bracis-28424 141 15 network network NOUN bracis-28424 141 16 is be AUX bracis-28424 141 17 always always ADV bracis-28424 141 18 the the DET bracis-28424 141 19 same same ADJ bracis-28424 141 20 ( ( PUNCT bracis-28424 141 21 but but CCONJ bracis-28424 141 22 not not PART bracis-28424 141 23 \(i_0\ \(i_0\ PROPN bracis-28424 141 24 ) ) PUNCT bracis-28424 141 25 nor nor CCONJ bracis-28424 141 26 the the DET bracis-28424 141 27 epidemic epidemic NOUN bracis-28424 141 28 network network NOUN bracis-28424 141 29 ) ) PUNCT bracis-28424 141 30 . . PUNCT bracis-28424 142 1 the the DET bracis-28424 142 2 dataset dataset NOUN bracis-28424 142 3 is be AUX bracis-28424 142 4 then then ADV bracis-28424 142 5 split split VERB bracis-28424 142 6 for for ADP bracis-28424 142 7 training training NOUN bracis-28424 142 8 , , PUNCT bracis-28424 142 9 validation validation NOUN bracis-28424 142 10 and and CCONJ bracis-28424 142 11 testing testing NOUN bracis-28424 142 12 . . PUNCT bracis-28424 143 1 this this DET bracis-28424 143 2 work work NOUN bracis-28424 143 3 made make VERB bracis-28424 143 4 use use NOUN bracis-28424 143 5 of of ADP bracis-28424 143 6 pytorch pytorch NOUN bracis-28424 143 7 geometric geometric ADJ bracis-28424 144 1 [ [ X bracis-28424 144 2 6 6 NUM bracis-28424 144 3 ] ] PUNCT bracis-28424 144 4 , , PUNCT bracis-28424 144 5 which which PRON bracis-28424 144 6 employs employ VERB bracis-28424 144 7 pytorch pytorch NOUN bracis-28424 144 8 [ [ X bracis-28424 144 9 16 16 NUM bracis-28424 144 10 ] ] PUNCT bracis-28424 144 11 and and CCONJ bracis-28424 144 12 provides provide VERB bracis-28424 144 13 a a DET bracis-28424 144 14 number number NOUN bracis-28424 144 15 of of ADP bracis-28424 144 16 gnn gnn NOUN bracis-28424 144 17 layers layer NOUN bracis-28424 144 18 . . PUNCT bracis-28424 145 1 the the DET bracis-28424 145 2 adam adam PROPN bracis-28424 145 3 optimizer optimizer NOUN bracis-28424 145 4 was be AUX bracis-28424 145 5 used use VERB bracis-28424 145 6 with with ADP bracis-28424 145 7 a a DET bracis-28424 145 8 low low ADJ bracis-28424 145 9 learning learning NOUN bracis-28424 145 10 rate rate NOUN bracis-28424 145 11 of of ADP bracis-28424 145 12 0.001 0.001 NUM bracis-28424 145 13 and and CCONJ bracis-28424 145 14 all all DET bracis-28424 145 15 network network NOUN bracis-28424 145 16 nodes node NOUN bracis-28424 145 17 were be AUX bracis-28424 145 18 considered consider VERB bracis-28424 145 19 as as ADP bracis-28424 145 20 a a DET bracis-28424 145 21 single single ADJ bracis-28424 145 22 batch batch NOUN bracis-28424 145 23 at at ADP bracis-28424 145 24 each each DET bracis-28424 145 25 learning learn VERB bracis-28424 145 26 epoch epoch NOUN bracis-28424 145 27 . . PUNCT bracis-28424 146 1 as as ADP bracis-28424 146 2 for for ADP bracis-28424 146 3 sampling sample VERB bracis-28424 146 4 neighboring neighboring NOUN bracis-28424 146 5 nodes node NOUN bracis-28424 146 6 for for ADP bracis-28424 146 7 gnn gnn NOUN bracis-28424 146 8 training training NOUN bracis-28424 146 9 , , PUNCT bracis-28424 146 10 all all DET bracis-28424 146 11 nodes node NOUN bracis-28424 146 12 within within ADP bracis-28424 146 13 a a DET bracis-28424 146 14 distance distance NOUN bracis-28424 146 15 of of ADP bracis-28424 146 16 3 3 NUM bracis-28424 146 17 from from ADP bracis-28424 146 18 the the DET bracis-28424 146 19 target target NOUN bracis-28424 146 20 node node NOUN bracis-28424 146 21 were be AUX bracis-28424 146 22 considered consider VERB bracis-28424 146 23 . . PUNCT bracis-28424 147 1 this this DET bracis-28424 147 2 sampling sample VERB bracis-28424 147 3 strategy strategy NOUN bracis-28424 147 4 is be AUX bracis-28424 147 5 used use VERB bracis-28424 147 6 to to PART bracis-28424 147 7 balance balance VERB bracis-28424 147 8 computational computational ADJ bracis-28424 147 9 cost cost NOUN bracis-28424 147 10 and and CCONJ bracis-28424 147 11 network network NOUN bracis-28424 147 12 coverage coverage NOUN bracis-28424 147 13 as as SCONJ bracis-28424 147 14 nodes node NOUN bracis-28424 147 15 closer close ADJ bracis-28424 147 16 to to ADP bracis-28424 147 17 the the DET bracis-28424 147 18 target target NOUN bracis-28424 147 19 carry carry VERB bracis-28424 147 20 more more ADV bracis-28424 147 21 important important ADJ bracis-28424 147 22 information information NOUN bracis-28424 147 23 . . PUNCT bracis-28424 148 1 the the DET bracis-28424 148 2 model model NOUN bracis-28424 148 3 was be AUX bracis-28424 148 4 trained train VERB bracis-28424 148 5 on on ADP bracis-28424 148 6 500 500 NUM bracis-28424 148 7 epochs epoch NOUN bracis-28424 148 8 and and CCONJ bracis-28424 148 9 an an DET bracis-28424 148 10 early early ADJ bracis-28424 148 11 stopping stopping NOUN bracis-28424 148 12 criteria criterion NOUN bracis-28424 148 13 is be AUX bracis-28424 148 14 adopted adopt VERB bracis-28424 148 15 such such ADJ bracis-28424 148 16 that that SCONJ bracis-28424 148 17 if if SCONJ bracis-28424 148 18 no no DET bracis-28424 148 19 improvements improvement NOUN bracis-28424 148 20 in in ADP bracis-28424 148 21 the the DET bracis-28424 148 22 loss loss NOUN bracis-28424 148 23 function function NOUN bracis-28424 148 24 are be AUX bracis-28424 148 25 observed observe VERB bracis-28424 148 26 in in ADP bracis-28424 148 27 the the DET bracis-28424 148 28 validation validation NOUN bracis-28424 148 29 network network NOUN bracis-28424 148 30 for for ADP bracis-28424 148 31 75 75 NUM bracis-28424 148 32 consecutive consecutive ADJ bracis-28424 148 33 epochs epoch NOUN bracis-28424 148 34 , , PUNCT bracis-28424 148 35 the the DET bracis-28424 148 36 training training NOUN bracis-28424 148 37 with with ADP bracis-28424 148 38 the the DET bracis-28424 148 39 input input NOUN bracis-28424 148 40 network network NOUN bracis-28424 148 41 stops stop VERB bracis-28424 148 42 in in ADP bracis-28424 148 43 order order NOUN bracis-28424 148 44 to to PART bracis-28424 148 45 avoid avoid VERB bracis-28424 148 46 overfitting overfitte VERB bracis-28424 148 47 . . PUNCT bracis-28424 149 1 the the DET bracis-28424 149 2 experiments experiment NOUN bracis-28424 149 3 were be AUX bracis-28424 149 4 carried carry VERB bracis-28424 149 5 on on ADP bracis-28424 149 6 a a DET bracis-28424 149 7 computer computer NOUN bracis-28424 149 8 with with ADP bracis-28424 149 9 an an DET bracis-28424 149 10 intel intel PROPN bracis-28424 149 11 core core NOUN bracis-28424 149 12 i7 i7 NOUN bracis-28424 149 13 - - PUNCT bracis-28424 149 14 11800h 11800h NUM bracis-28424 149 15 , , PUNCT bracis-28424 149 16 gpu gpu PROPN bracis-28424 149 17 nvidia nvidia PROPN bracis-28424 149 18 geforce geforce NOUN bracis-28424 149 19 3070 3070 NUM bracis-28424 149 20 8 8 NUM bracis-28424 149 21     SPACE bracis-28424 149 22 gb gb NOUN bracis-28424 149 23 and and CCONJ bracis-28424 149 24 16 16 NUM bracis-28424 149 25     SPACE bracis-28424 149 26 gb gb NOUN bracis-28424 149 27 ram ram NOUN bracis-28424 149 28 . . PUNCT bracis-28424 150 1 5 5 NUM bracis-28424 150 2 evaluation evaluation NOUN bracis-28424 150 3 the the DET bracis-28424 150 4 performance performance NOUN bracis-28424 150 5 of of ADP bracis-28424 150 6 different different ADJ bracis-28424 150 7 approaches approach NOUN bracis-28424 150 8 to to PART bracis-28424 150 9 identify identify VERB bracis-28424 150 10 epidemic epidemic NOUN bracis-28424 150 11 sources source NOUN bracis-28424 150 12 depends depend VERB bracis-28424 150 13 on on ADP bracis-28424 150 14 various various ADJ bracis-28424 150 15 factors factor NOUN bracis-28424 150 16 , , PUNCT bracis-28424 150 17 including include VERB bracis-28424 150 18 network network NOUN bracis-28424 150 19 structure structure NOUN bracis-28424 150 20 . . PUNCT bracis-28424 151 1 in in ADP bracis-28424 151 2 order order NOUN bracis-28424 151 3 to to PART bracis-28424 151 4 better well ADV bracis-28424 151 5 assess assess VERB bracis-28424 151 6 the the DET bracis-28424 151 7 proposed propose VERB bracis-28424 151 8 framework framework NOUN bracis-28424 151 9 , , PUNCT bracis-28424 151 10 two two NUM bracis-28424 151 11 random random ADJ bracis-28424 151 12 graph graph NOUN bracis-28424 151 13 models model NOUN bracis-28424 151 14 and and CCONJ bracis-28424 151 15 two two NUM bracis-28424 151 16 real real ADJ bracis-28424 151 17 networks network NOUN bracis-28424 151 18 are be AUX bracis-28424 151 19 considered consider VERB bracis-28424 151 20 . . PUNCT bracis-28424 152 1 the the DET bracis-28424 152 2 performance performance NOUN bracis-28424 152 3 of of ADP bracis-28424 152 4 the the DET bracis-28424 152 5 proposed propose VERB bracis-28424 152 6 approach approach NOUN bracis-28424 152 7 will will AUX bracis-28424 152 8 be be AUX bracis-28424 152 9 characterized characterize VERB bracis-28424 152 10 using use VERB bracis-28424 152 11 two two NUM bracis-28424 152 12 different different ADJ bracis-28424 152 13 criteria criterion NOUN bracis-28424 152 14 : : PUNCT bracis-28424 152 15 identifying identify VERB bracis-28424 152 16 epidemic epidemic NOUN bracis-28424 152 17 source source NOUN bracis-28424 152 18 nodes node NOUN bracis-28424 152 19 and and CCONJ bracis-28424 152 20 identifying identify VERB bracis-28424 152 21 neighbors neighbor NOUN bracis-28424 152 22 of of ADP bracis-28424 152 23 source source NOUN bracis-28424 152 24 nodes node NOUN bracis-28424 152 25 . . PUNCT bracis-28424 153 1 5.1 5.1 NUM bracis-28424 153 2 network network NOUN bracis-28424 153 3 models model NOUN bracis-28424 153 4 and and CCONJ bracis-28424 153 5     SPACE bracis-28424 153 6 real real ADJ bracis-28424 153 7 networks network NOUN bracis-28424 153 8 the the DET bracis-28424 153 9 erdős erdős NOUN bracis-28424 153 10 - - PUNCT bracis-28424 153 11 rényi rényi NOUN bracis-28424 153 12 ( ( PUNCT bracis-28424 153 13 er er INTJ bracis-28424 153 14 ) ) PUNCT bracis-28424 153 15 random random ADJ bracis-28424 153 16 graph graph NOUN bracis-28424 153 17 model model NOUN bracis-28424 153 18 , , PUNCT bracis-28424 153 19 also also ADV bracis-28424 153 20 known know VERB bracis-28424 153 21 as as ADP bracis-28424 153 22 g(n g(n PROPN bracis-28424 153 23 , , PUNCT bracis-28424 153 24     SPACE bracis-28424 153 25 p p NOUN bracis-28424 153 26 ) ) PUNCT bracis-28424 153 27 , , PUNCT bracis-28424 153 28 is be AUX bracis-28424 153 29 a a DET bracis-28424 153 30 classic classic ADJ bracis-28424 153 31 model model NOUN bracis-28424 153 32 that that PRON bracis-28424 153 33 has have AUX bracis-28424 153 34 been be AUX bracis-28424 153 35 widely widely ADV bracis-28424 153 36 studied study VERB bracis-28424 153 37 [ [ PUNCT bracis-28424 153 38 8 8 NUM bracis-28424 153 39 ] ] PUNCT bracis-28424 153 40 . . PUNCT bracis-28424 154 1 the the DET bracis-28424 154 2 model model NOUN bracis-28424 154 3 yields yield VERB bracis-28424 154 4 a a DET bracis-28424 154 5 very very ADV bracis-28424 154 6 homogeneous homogeneous ADJ bracis-28424 154 7 graph graph NOUN bracis-28424 154 8 , , PUNCT bracis-28424 154 9 with with ADP bracis-28424 154 10 no no DET bracis-28424 154 11 special special ADJ bracis-28424 154 12 structure structure NOUN bracis-28424 154 13 , , PUNCT bracis-28424 154 14 in in ADP bracis-28424 154 15 which which PRON bracis-28424 154 16 each each DET bracis-28424 154 17 possible possible ADJ bracis-28424 154 18 edge edge NOUN bracis-28424 154 19 is be AUX bracis-28424 154 20 present present ADJ bracis-28424 154 21 in in ADP bracis-28424 154 22 the the DET bracis-28424 154 23 n n ADV bracis-28424 154 24 node node NOUN bracis-28424 154 25 graph graph NOUN bracis-28424 154 26 with with ADP bracis-28424 154 27 probability probability NOUN bracis-28424 154 28 p. p. NOUN bracis-28424 154 29 in in ADP bracis-28424 154 30 contrast contrast NOUN bracis-28424 154 31 , , PUNCT bracis-28424 154 32 the the DET bracis-28424 154 33 barabási barabási NOUN bracis-28424 154 34 - - PUNCT bracis-28424 154 35 albert albert PROPN bracis-28424 154 36 ( ( PUNCT bracis-28424 154 37 ba ba PROPN bracis-28424 154 38 ) ) PUNCT bracis-28424 154 39 model model NOUN bracis-28424 154 40 follows follow VERB bracis-28424 154 41 a a DET bracis-28424 154 42 iterative iterative NOUN bracis-28424 154 43 process process NOUN bracis-28424 154 44 driven drive VERB bracis-28424 154 45 by by ADP bracis-28424 154 46 preferential preferential ADJ bracis-28424 154 47 attachment attachment NOUN bracis-28424 154 48 and and CCONJ bracis-28424 154 49 generates generate VERB bracis-28424 154 50 a a DET bracis-28424 154 51 scale scale NOUN bracis-28424 154 52 free free ADJ bracis-28424 154 53 network network NOUN bracis-28424 154 54 , , PUNCT bracis-28424 154 55 better well ADV bracis-28424 154 56 representing represent VERB bracis-28424 154 57 real real ADJ bracis-28424 154 58 networks network NOUN bracis-28424 154 59 such such ADJ bracis-28424 154 60 as as ADP bracis-28424 154 61 the the DET bracis-28424 154 62 web web NOUN bracis-28424 154 63 and and CCONJ bracis-28424 154 64 the the PRON bracis-28424 154 65 as as ADP bracis-28424 154 66 graph graph NOUN bracis-28424 154 67 [ [ X bracis-28424 154 68 1 1 NUM bracis-28424 154 69 ] ] PUNCT bracis-28424 154 70 . . PUNCT bracis-28424 155 1 networks network NOUN bracis-28424 155 2 generated generate VERB bracis-28424 155 3 by by ADP bracis-28424 155 4 these these DET bracis-28424 155 5 two two NUM bracis-28424 155 6 models model NOUN bracis-28424 155 7 are be AUX bracis-28424 155 8 strikingly strikingly ADV bracis-28424 155 9 different different ADJ bracis-28424 155 10 and and CCONJ bracis-28424 155 11 both both PRON bracis-28424 155 12 will will AUX bracis-28424 155 13 be be AUX bracis-28424 155 14 used use VERB bracis-28424 155 15 in in ADP bracis-28424 155 16 the the DET bracis-28424 155 17 evaluation evaluation NOUN bracis-28424 155 18 . . PUNCT bracis-28424 156 1 to to PART bracis-28424 156 2 allow allow VERB bracis-28424 156 3 for for ADP bracis-28424 156 4 a a DET bracis-28424 156 5 direct direct ADJ bracis-28424 156 6 comparison comparison NOUN bracis-28424 156 7 , , PUNCT bracis-28424 156 8 the the DET bracis-28424 156 9 parameters parameter NOUN bracis-28424 156 10 of of ADP bracis-28424 156 11 the the DET bracis-28424 156 12 two two NUM bracis-28424 156 13 random random ADJ bracis-28424 156 14 graph graph NOUN bracis-28424 156 15 models model NOUN bracis-28424 156 16 are be AUX bracis-28424 156 17 chosen choose VERB bracis-28424 156 18 such such ADJ bracis-28424 156 19 that that SCONJ bracis-28424 156 20 the the DET bracis-28424 156 21 generated generate VERB bracis-28424 156 22 networks network NOUN bracis-28424 156 23 are be AUX bracis-28424 156 24 connected connect VERB bracis-28424 156 25 and and CCONJ bracis-28424 156 26 have have VERB bracis-28424 156 27 the the DET bracis-28424 156 28 same same ADJ bracis-28424 156 29 number number NOUN bracis-28424 156 30 of of ADP bracis-28424 156 31 nodes node NOUN bracis-28424 156 32 and and CCONJ bracis-28424 156 33 edges edge NOUN bracis-28424 156 34 , , PUNCT bracis-28424 156 35 on on ADP bracis-28424 156 36 average average ADJ bracis-28424 156 37 . . PUNCT bracis-28424 157 1 as as ADP bracis-28424 157 2 for for ADP bracis-28424 157 3 networks network NOUN bracis-28424 157 4 modeled model VERB bracis-28424 157 5 after after ADP bracis-28424 157 6 real real ADJ bracis-28424 157 7 life life NOUN bracis-28424 157 8 data datum NOUN bracis-28424 157 9 , , PUNCT bracis-28424 157 10 the the DET bracis-28424 157 11 facebook facebook NOUN bracis-28424 157 12 ego ego NOUN bracis-28424 157 13 network network NOUN bracis-28424 157 14 is be AUX bracis-28424 157 15 a a DET bracis-28424 157 16 social social ADJ bracis-28424 157 17 network network NOUN bracis-28424 157 18 consisting consist VERB bracis-28424 157 19 of of ADP bracis-28424 157 20 the the DET bracis-28424 157 21 ego ego NOUN bracis-28424 157 22 - - PUNCT bracis-28424 157 23 networks network NOUN bracis-28424 157 24 of of ADP bracis-28424 157 25 ten ten NUM bracis-28424 157 26 facebook facebook NOUN bracis-28424 157 27 users user NOUN bracis-28424 157 28 [ [ X bracis-28424 157 29 13 13 NUM bracis-28424 157 30 ] ] PUNCT bracis-28424 157 31 . . PUNCT bracis-28424 158 1 the the DET bracis-28424 158 2 power power NOUN bracis-28424 158 3 grid grid NOUN bracis-28424 158 4 network network NOUN bracis-28424 158 5 represents represent VERB bracis-28424 158 6 the the DET bracis-28424 158 7 electrical electrical ADJ bracis-28424 158 8 power power NOUN bracis-28424 158 9 grid grid NOUN bracis-28424 158 10 of of ADP bracis-28424 158 11 the the DET bracis-28424 158 12 western western ADJ bracis-28424 158 13 united united PROPN bracis-28424 158 14 states states PROPN bracis-28424 158 15 with with ADP bracis-28424 158 16 generators generator NOUN bracis-28424 158 17 , , PUNCT bracis-28424 158 18 transformers transformer NOUN bracis-28424 158 19 and and CCONJ bracis-28424 158 20 substation substation NOUN bracis-28424 158 21 acting act VERB bracis-28424 158 22 as as ADP bracis-28424 158 23 network network NOUN bracis-28424 158 24 nodes node NOUN bracis-28424 158 25 [ [ X bracis-28424 158 26 22 22 NUM bracis-28424 158 27 ] ] PUNCT bracis-28424 158 28 . . PUNCT bracis-28424 159 1 these these DET bracis-28424 159 2 two two NUM bracis-28424 159 3 real real ADJ bracis-28424 159 4 networks network NOUN bracis-28424 159 5 are be AUX bracis-28424 159 6 also also ADV bracis-28424 159 7 very very ADV bracis-28424 159 8 different different ADJ bracis-28424 159 9 in in ADP bracis-28424 159 10 terms term NOUN bracis-28424 159 11 of of ADP bracis-28424 159 12 node node NOUN bracis-28424 159 13 degree degree NOUN bracis-28424 159 14 and and CCONJ bracis-28424 159 15 distances distance NOUN bracis-28424 159 16 . . PUNCT bracis-28424 160 1 table table NOUN bracis-28424 160 2     SPACE bracis-28424 160 3 1 1 NUM bracis-28424 160 4 summarizes summarize NOUN bracis-28424 160 5 some some DET bracis-28424 160 6 details detail NOUN bracis-28424 160 7 on on ADP bracis-28424 160 8 the the DET bracis-28424 160 9 networks network NOUN bracis-28424 160 10 considered consider VERB bracis-28424 160 11 . . PUNCT bracis-28424 161 1 table table NOUN bracis-28424 161 2 1 1 NUM bracis-28424 161 3 . . PUNCT bracis-28424 162 1 network network NOUN bracis-28424 162 2 information information NOUN bracis-28424 162 3 ( ( PUNCT bracis-28424 162 4 \(^*\ \(^*\ ADV bracis-28424 162 5 ) ) PUNCT bracis-28424 162 6 indicates indicate VERB bracis-28424 162 7 average average ADJ bracis-28424 162 8 values).full values).full NOUN bracis-28424 162 9 size size NOUN bracis-28424 162 10 table table NOUN bracis-28424 162 11 for for ADP bracis-28424 162 12 each each DET bracis-28424 162 13 random random ADJ bracis-28424 162 14 graph graph NOUN bracis-28424 162 15 model model NOUN bracis-28424 162 16 and and CCONJ bracis-28424 162 17 parameters parameter NOUN bracis-28424 162 18 determining determine VERB bracis-28424 162 19 a a DET bracis-28424 162 20 scenario scenario NOUN bracis-28424 162 21 ( ( PUNCT bracis-28424 162 22 such such ADJ bracis-28424 162 23 as as ADP bracis-28424 162 24 number number NOUN bracis-28424 162 25 of of ADP bracis-28424 162 26 epidemic epidemic NOUN bracis-28424 162 27 sources source NOUN bracis-28424 162 28 and and CCONJ bracis-28424 162 29 infection infection NOUN bracis-28424 162 30 ratio ratio NOUN bracis-28424 162 31 ) ) PUNCT bracis-28424 162 32 , , PUNCT bracis-28424 162 33 30 30 NUM bracis-28424 162 34 independent independent ADJ bracis-28424 162 35 epidemic epidemic NOUN bracis-28424 162 36 networks network NOUN bracis-28424 162 37 are be AUX bracis-28424 162 38 generated generate VERB bracis-28424 162 39 and and CCONJ bracis-28424 162 40 split split VERB bracis-28424 162 41 equally equally ADV bracis-28424 162 42 into into ADP bracis-28424 162 43 training training NOUN bracis-28424 162 44 , , PUNCT bracis-28424 162 45 validation validation NOUN bracis-28424 162 46 and and CCONJ bracis-28424 162 47 testing testing NOUN bracis-28424 162 48 sets set NOUN bracis-28424 162 49 . . PUNCT bracis-28424 163 1 when when SCONJ bracis-28424 163 2 considering consider VERB bracis-28424 163 3 real real ADJ bracis-28424 163 4 networks network NOUN bracis-28424 163 5 , , PUNCT bracis-28424 163 6 50 50 NUM bracis-28424 163 7 independent independent ADJ bracis-28424 163 8 epidemic epidemic NOUN bracis-28424 163 9 networks network NOUN bracis-28424 163 10 are be AUX bracis-28424 163 11 generated generate VERB bracis-28424 163 12 , , PUNCT bracis-28424 163 13 from from ADP bracis-28424 163 14 which which PRON bracis-28424 163 15 1/5 1/5 NUM bracis-28424 163 16 is be AUX bracis-28424 163 17 used use VERB bracis-28424 163 18 for for ADP bracis-28424 163 19 training training NOUN bracis-28424 163 20 , , PUNCT bracis-28424 163 21 1/5 1/5 NUM bracis-28424 163 22 for for ADP bracis-28424 163 23 validation validation NOUN bracis-28424 163 24 and and CCONJ bracis-28424 163 25 3/5 3/5 NUM bracis-28424 163 26 used use VERB bracis-28424 163 27 for for ADP bracis-28424 163 28 testing testing NOUN bracis-28424 163 29 . . PUNCT bracis-28424 164 1 the the DET bracis-28424 164 2 testing testing NOUN bracis-28424 164 3 dataset dataset NOUN bracis-28424 164 4 is be AUX bracis-28424 164 5 larger large ADJ bracis-28424 164 6 to to PART bracis-28424 164 7 ensure ensure VERB bracis-28424 164 8 a a DET bracis-28424 164 9 better well ADJ bracis-28424 164 10 estimation estimation NOUN bracis-28424 164 11 of of ADP bracis-28424 164 12 the the DET bracis-28424 164 13 average average ADJ bracis-28424 164 14 performance performance NOUN bracis-28424 164 15 and and CCONJ bracis-28424 164 16 allow allow VERB bracis-28424 164 17 a a DET bracis-28424 164 18 better well ADJ bracis-28424 164 19 comparison comparison NOUN bracis-28424 164 20 with with ADP bracis-28424 164 21 prior prior ADJ bracis-28424 164 22 works work NOUN bracis-28424 164 23 . . PUNCT bracis-28424 165 1 5.2 5.2 NUM bracis-28424 165 2 evaluation evaluation NOUN bracis-28424 165 3 metrics metric NOUN bracis-28424 165 4 accuracy accuracy NOUN bracis-28424 165 5 is be AUX bracis-28424 165 6 not not PART bracis-28424 165 7 an an DET bracis-28424 165 8 adequate adequate ADJ bracis-28424 165 9 metric metric NOUN bracis-28424 165 10 to to PART bracis-28424 165 11 capture capture VERB bracis-28424 165 12 the the DET bracis-28424 165 13 performance performance NOUN bracis-28424 165 14 of of ADP bracis-28424 165 15 the the DET bracis-28424 165 16 framework framework NOUN bracis-28424 165 17 , , PUNCT bracis-28424 165 18 since since SCONJ bracis-28424 165 19 there there PRON bracis-28424 165 20 are be VERB bracis-28424 165 21 very very ADV bracis-28424 165 22 few few ADJ bracis-28424 165 23 epidemic epidemic NOUN bracis-28424 165 24 sources source NOUN bracis-28424 165 25 ( ( PUNCT bracis-28424 165 26 less less ADJ bracis-28424 165 27 than than ADP bracis-28424 165 28 \(0.3\%\ \(0.3\%\ NOUN bracis-28424 165 29 ) ) PUNCT bracis-28424 165 30 ) ) PUNCT bracis-28424 165 31 and and CCONJ bracis-28424 165 32 thus thus ADV bracis-28424 165 33 a a DET bracis-28424 165 34 very very ADV bracis-28424 165 35 unbalanced unbalanced ADJ bracis-28424 165 36 dataset dataset NOUN bracis-28424 165 37 . . PUNCT bracis-28424 166 1 metrics metric NOUN bracis-28424 166 2 that that PRON bracis-28424 166 3 capture capture VERB bracis-28424 166 4 the the DET bracis-28424 166 5 ability ability NOUN bracis-28424 166 6 of of ADP bracis-28424 166 7 correctly correctly ADV bracis-28424 166 8 identifying identify VERB bracis-28424 166 9 the the DET bracis-28424 166 10 sources source NOUN bracis-28424 166 11 are be AUX bracis-28424 166 12 more more ADV bracis-28424 166 13 adequate adequate ADJ bracis-28424 166 14 , , PUNCT bracis-28424 166 15 hence hence ADV bracis-28424 166 16 taking take VERB bracis-28424 166 17 into into ADP bracis-28424 166 18 account account NOUN bracis-28424 166 19 true true ADJ bracis-28424 166 20 positives positive NOUN bracis-28424 166 21 , , PUNCT bracis-28424 166 22 false false ADJ bracis-28424 166 23 positives positive NOUN bracis-28424 166 24 and and CCONJ bracis-28424 166 25 false false ADJ bracis-28424 166 26 negatives negative NOUN bracis-28424 166 27 . . PUNCT bracis-28424 167 1 recollect recollect VERB bracis-28424 167 2 that that SCONJ bracis-28424 167 3 the the DET bracis-28424 167 4 proposed propose VERB bracis-28424 167 5 model model NOUN bracis-28424 167 6 outputs output VERB bracis-28424 167 7 the the DET bracis-28424 167 8 probability probability NOUN bracis-28424 167 9 that that SCONJ bracis-28424 167 10 a a DET bracis-28424 167 11 node node NOUN bracis-28424 167 12 is be AUX bracis-28424 167 13 an an DET bracis-28424 167 14 epidemic epidemic NOUN bracis-28424 167 15 source source NOUN bracis-28424 167 16 . . PUNCT bracis-28424 168 1 therefore therefore ADV bracis-28424 168 2 , , PUNCT bracis-28424 168 3 given give VERB bracis-28424 168 4 an an DET bracis-28424 168 5 epidemic epidemic NOUN bracis-28424 168 6 network network NOUN bracis-28424 168 7 , , PUNCT bracis-28424 168 8 each each DET bracis-28424 168 9 node node NOUN bracis-28424 168 10 is be AUX bracis-28424 168 11 used use VERB bracis-28424 168 12 as as ADP bracis-28424 168 13 input input NOUN bracis-28424 168 14 to to ADP bracis-28424 168 15 the the DET bracis-28424 168 16 trained train VERB bracis-28424 168 17 model model NOUN bracis-28424 168 18 and and CCONJ bracis-28424 168 19 ranked rank VERB bracis-28424 168 20 according accord VERB bracis-28424 168 21 to to ADP bracis-28424 168 22 their their PRON bracis-28424 168 23 probability probability NOUN bracis-28424 168 24 in in ADP bracis-28424 168 25 decreasing decrease VERB bracis-28424 168 26 order order NOUN bracis-28424 168 27 ( ( PUNCT bracis-28424 168 28 most most ADV bracis-28424 168 29 probable probable ADJ bracis-28424 168 30 first first ADV bracis-28424 168 31 ) ) PUNCT bracis-28424 168 32 . . PUNCT bracis-28424 169 1 from from ADP bracis-28424 169 2 this this DET bracis-28424 169 3 list list NOUN bracis-28424 169 4 , , PUNCT bracis-28424 169 5 the the DET bracis-28424 169 6 top top ADJ bracis-28424 169 7 - - PUNCT bracis-28424 169 8 k k NOUN bracis-28424 169 9 nodes node NOUN bracis-28424 169 10 are be AUX bracis-28424 169 11 taken take VERB bracis-28424 169 12 as as ADP bracis-28424 169 13 epidemic epidemic NOUN bracis-28424 169 14 sources source NOUN bracis-28424 169 15 , , PUNCT bracis-28424 169 16 where where SCONJ bracis-28424 169 17 k k PROPN bracis-28424 169 18 is be AUX bracis-28424 169 19 parameter parameter NOUN bracis-28424 169 20 of of ADP bracis-28424 169 21 the the DET bracis-28424 169 22 evaluation evaluation NOUN bracis-28424 169 23 methodology methodology NOUN bracis-28424 169 24 . . PUNCT bracis-28424 170 1 using use VERB bracis-28424 170 2 this this DET bracis-28424 170 3 methodology methodology NOUN bracis-28424 170 4 , , PUNCT bracis-28424 170 5 the the DET bracis-28424 170 6 precision precision NOUN bracis-28424 170 7 and and CCONJ bracis-28424 170 8 recall recall NOUN bracis-28424 170 9 values value NOUN bracis-28424 170 10 for for ADP bracis-28424 170 11 the the DET bracis-28424 170 12 top top ADJ bracis-28424 170 13 - - PUNCT bracis-28424 170 14 k k NOUN bracis-28424 170 15 are be AUX bracis-28424 170 16 computed compute VERB bracis-28424 170 17 , , PUNCT bracis-28424 170 18 and and CCONJ bracis-28424 170 19 consequently consequently ADV bracis-28424 170 20 the the DET bracis-28424 170 21 f f ADJ bracis-28424 170 22 - - PUNCT bracis-28424 170 23 score score NOUN bracis-28424 170 24 metric metric NOUN bracis-28424 170 25 . . PUNCT bracis-28424 171 1 note note VERB bracis-28424 171 2 that that SCONJ bracis-28424 171 3 k k PROPN bracis-28424 171 4 should should AUX bracis-28424 171 5 be be AUX bracis-28424 171 6 a a DET bracis-28424 171 7 function function NOUN bracis-28424 171 8 of of ADP bracis-28424 171 9 the the DET bracis-28424 171 10 number number NOUN bracis-28424 171 11 of of ADP bracis-28424 171 12 epidemic epidemic NOUN bracis-28424 171 13 sources source NOUN bracis-28424 171 14 , , PUNCT bracis-28424 171 15 which which PRON bracis-28424 171 16 is be AUX bracis-28424 171 17 given give VERB bracis-28424 171 18 by by ADP bracis-28424 171 19 \(s \( NOUN bracis-28424 171 20 = = SYM bracis-28424 171 21 |i_0|\ |i_0|\ PROPN bracis-28424 171 22 ) ) PUNCT bracis-28424 171 23 . . PUNCT bracis-28424 172 1 two two NUM bracis-28424 172 2 different different ADJ bracis-28424 172 3 sets set NOUN bracis-28424 172 4 are be AUX bracis-28424 172 5 considered consider VERB bracis-28424 172 6 as as ADP bracis-28424 172 7 true true ADJ bracis-28424 172 8 positives positive NOUN bracis-28424 172 9 when when SCONJ bracis-28424 172 10 assessing assess VERB bracis-28424 172 11 the the DET bracis-28424 172 12 performance performance NOUN bracis-28424 172 13 of of ADP bracis-28424 172 14 the the DET bracis-28424 172 15 framework framework NOUN bracis-28424 172 16 : : PUNCT bracis-28424 172 17 i i NOUN bracis-28424 172 18 ) ) PUNCT bracis-28424 172 19 the the DET bracis-28424 172 20 set set PROPN bracis-28424 172 21 \(i_0\ \(i_0\ PROPN bracis-28424 172 22 ) ) PUNCT bracis-28424 172 23 , , PUNCT bracis-28424 172 24 namely namely ADV bracis-28424 172 25 the the DET bracis-28424 172 26 epidemic epidemic NOUN bracis-28424 172 27 source source NOUN bracis-28424 172 28 nodes node NOUN bracis-28424 172 29 ; ; PUNCT bracis-28424 173 1 ii ii X bracis-28424 173 2 ) ) PUNCT bracis-28424 173 3 the the DET bracis-28424 173 4 set set NOUN bracis-28424 173 5 \(o \(o PRON bracis-28424 173 6 = = SYM bracis-28424 173 7 \ \ ADJ bracis-28424 173 8 { { PUNCT bracis-28424 173 9 v v NOUN bracis-28424 173 10 | | ADV bracis-28424 173 11 v v ADP bracis-28424 173 12 \in \in PROPN bracis-28424 173 13 i_0 i_0 PROPN bracis-28424 173 14 \vee \vee PROPN bracis-28424 173 15 v v ADP bracis-28424 173 16 \in \in PROPN bracis-28424 173 17 n_1(u n_1(u NOUN bracis-28424 173 18 ) ) PUNCT bracis-28424 173 19 , , PUNCT bracis-28424 173 20 u u PROPN bracis-28424 173 21 \in \in PROPN bracis-28424 173 22 i_0\}\ i_0\}\ NOUN bracis-28424 173 23 ) ) PUNCT bracis-28424 173 24 , , PUNCT bracis-28424 173 25 namely namely ADV bracis-28424 173 26 the the DET bracis-28424 173 27 epidemic epidemic NOUN bracis-28424 173 28 sources source NOUN bracis-28424 173 29 and and CCONJ bracis-28424 173 30 the the DET bracis-28424 173 31 neighbors neighbor NOUN bracis-28424 173 32 of of ADP bracis-28424 173 33 the the DET bracis-28424 173 34 epidemic epidemic NOUN bracis-28424 173 35 sources source NOUN bracis-28424 173 36 ( ( PUNCT bracis-28424 173 37 \(n_1(u)\ \(n_1(u)\ NOUN bracis-28424 173 38 ) ) PUNCT bracis-28424 173 39 denotes denote VERB bracis-28424 173 40 the the DET bracis-28424 173 41 neighbors neighbor NOUN bracis-28424 173 42 of of ADP bracis-28424 173 43 node node PROPN bracis-28424 173 44 u u NOUN bracis-28424 173 45 ) ) PUNCT bracis-28424 173 46 . . PUNCT bracis-28424 174 1 note note VERB bracis-28424 174 2 that that SCONJ bracis-28424 174 3 o o NOUN bracis-28424 174 4 considers consider VERB bracis-28424 174 5 the the DET bracis-28424 174 6 neighbors neighbor NOUN bracis-28424 174 7 of of ADP bracis-28424 174 8 the the DET bracis-28424 174 9 epidemic epidemic NOUN bracis-28424 174 10 source source NOUN bracis-28424 174 11 nodes node NOUN bracis-28424 174 12 as as ADP bracis-28424 174 13 nodes node NOUN bracis-28424 174 14 classified classify VERB bracis-28424 174 15 correctly correctly ADV bracis-28424 174 16 by by ADP bracis-28424 174 17 the the DET bracis-28424 174 18 framework framework NOUN bracis-28424 174 19 . . PUNCT bracis-28424 175 1 obviously obviously ADV bracis-28424 175 2 , , PUNCT bracis-28424 175 3 identifying identify VERB bracis-28424 175 4 nodes node NOUN bracis-28424 175 5 that that PRON bracis-28424 175 6 are be AUX bracis-28424 175 7 neighbors neighbor NOUN bracis-28424 175 8 of of ADP bracis-28424 175 9 the the DET bracis-28424 175 10 epidemic epidemic NOUN bracis-28424 175 11 source source NOUN bracis-28424 175 12 has have VERB bracis-28424 175 13 much much ADV bracis-28424 175 14 more more ADJ bracis-28424 175 15 value value NOUN bracis-28424 175 16 than than ADP bracis-28424 175 17 nodes node NOUN bracis-28424 175 18 that that PRON bracis-28424 175 19 are be AUX bracis-28424 175 20 not not PART bracis-28424 175 21 neighbors neighbor NOUN bracis-28424 175 22 . . PUNCT bracis-28424 176 1 5.3 5.3 NUM bracis-28424 176 2 results result VERB bracis-28424 176 3 fig fig NOUN bracis-28424 176 4 . . PUNCT bracis-28424 177 1 1 1 NUM bracis-28424 177 2 . . X bracis-28424 177 3 f f X bracis-28424 177 4 - - PUNCT bracis-28424 177 5 score score NOUN bracis-28424 177 6 for for ADP bracis-28424 177 7 all all DET bracis-28424 177 8 four four NUM bracis-28424 177 9 networks network NOUN bracis-28424 177 10 for for ADP bracis-28424 177 11 both both DET bracis-28424 177 12 evaluation evaluation NOUN bracis-28424 177 13 scenarios scenario NOUN bracis-28424 177 14 ( ( PUNCT bracis-28424 177 15 w/ w/ NOUN bracis-28424 177 16 and and CCONJ bracis-28424 177 17 w/o w/o ADP bracis-28424 177 18 neighbors neighbor NOUN bracis-28424 177 19 ) ) PUNCT bracis-28424 177 20 for for ADP bracis-28424 177 21 different different ADJ bracis-28424 177 22 number number NOUN bracis-28424 177 23 of of ADP bracis-28424 177 24 epidemic epidemic NOUN bracis-28424 177 25 sources source NOUN bracis-28424 177 26 ( ( PUNCT bracis-28424 177 27 \(s \(s VERB bracis-28424 177 28 \in \in PROPN bracis-28424 177 29 \{3 \{3 NOUN bracis-28424 177 30 , , PUNCT bracis-28424 177 31 5 5 NUM bracis-28424 177 32 , , PUNCT bracis-28424 177 33 10 10 NUM bracis-28424 177 34 , , PUNCT bracis-28424 177 35 15\}\ 15\}\ NUM bracis-28424 177 36 ) ) PUNCT bracis-28424 177 37 ) ) PUNCT bracis-28424 177 38 and and CCONJ bracis-28424 177 39 different different ADJ bracis-28424 177 40 top top ADJ bracis-28424 177 41 - - PUNCT bracis-28424 177 42 k k NOUN bracis-28424 177 43 values value NOUN bracis-28424 177 44 ( ( PUNCT bracis-28424 177 45 as as ADP bracis-28424 177 46 a a DET bracis-28424 177 47 function function NOUN bracis-28424 177 48 of of ADP bracis-28424 177 49 s s NOUN bracis-28424 177 50 ) ) PUNCT bracis-28424 177 51 . . PUNCT bracis-28424 178 1 in in ADP bracis-28424 178 2 all all DET bracis-28424 178 3 scenarios scenario NOUN bracis-28424 178 4 , , PUNCT bracis-28424 178 5 \(f_0=\ \(f_0=\ NOUN bracis-28424 178 6 ) ) PUNCT bracis-28424 178 7 20 20 NUM bracis-28424 178 8 % % NOUN bracis-28424 178 9 . . PUNCT bracis-28424 179 1 full full ADJ bracis-28424 179 2 size size NOUN bracis-28424 179 3 image image NOUN bracis-28424 179 4 figure figure NOUN bracis-28424 179 5     SPACE bracis-28424 179 6 1 1 NUM bracis-28424 179 7 shows show VERB bracis-28424 179 8 the the DET bracis-28424 179 9 performance performance NOUN bracis-28424 179 10 of of ADP bracis-28424 179 11 the the DET bracis-28424 179 12 proposed propose VERB bracis-28424 179 13 framework framework NOUN bracis-28424 179 14 on on ADP bracis-28424 179 15 all all DET bracis-28424 179 16 four four NUM bracis-28424 179 17 networks network NOUN bracis-28424 179 18 ( ( PUNCT bracis-28424 179 19 one one NUM bracis-28424 179 20 network network NOUN bracis-28424 179 21 for for ADP bracis-28424 179 22 each each DET bracis-28424 179 23 subfigure subfigure NOUN bracis-28424 179 24 ) ) PUNCT bracis-28424 179 25 . . PUNCT bracis-28424 180 1 each each DET bracis-28424 180 2 graph graph NOUN bracis-28424 180 3 shows show VERB bracis-28424 180 4 the the DET bracis-28424 180 5 f f NOUN bracis-28424 180 6 - - PUNCT bracis-28424 180 7 score score NOUN bracis-28424 180 8 for for ADP bracis-28424 180 9 the the DET bracis-28424 180 10 two two NUM bracis-28424 180 11 scenarios scenario NOUN bracis-28424 180 12 , , PUNCT bracis-28424 180 13 considering consider VERB bracis-28424 180 14 just just ADV bracis-28424 180 15 the the DET bracis-28424 180 16 epidemic epidemic NOUN bracis-28424 180 17 sources source NOUN bracis-28424 180 18 ( ( PUNCT bracis-28424 180 19 set set VERB bracis-28424 180 20 \(i_0\ \(i_0\ PROPN bracis-28424 180 21 ) ) PUNCT bracis-28424 180 22 , , PUNCT bracis-28424 180 23 w/o w/o ADP bracis-28424 180 24 neighbors neighbor NOUN bracis-28424 180 25 ) ) PUNCT bracis-28424 180 26 and and CCONJ bracis-28424 180 27 epidemic epidemic NOUN bracis-28424 180 28 sources source NOUN bracis-28424 180 29 and and CCONJ bracis-28424 180 30 their their PRON bracis-28424 180 31 neighbors neighbor NOUN bracis-28424 180 32 ( ( PUNCT bracis-28424 180 33 set set NOUN bracis-28424 180 34 o o NOUN bracis-28424 180 35 , , PUNCT bracis-28424 180 36 w/ w/ NOUN bracis-28424 180 37 neighbors neighbor NOUN bracis-28424 180 38 ) ) PUNCT bracis-28424 180 39 . . PUNCT bracis-28424 181 1 each each DET bracis-28424 181 2 curve curve NOUN bracis-28424 181 3 corresponds correspond VERB bracis-28424 181 4 to to ADP bracis-28424 181 5 a a DET bracis-28424 181 6 different different ADJ bracis-28424 181 7 number number NOUN bracis-28424 181 8 of of ADP bracis-28424 181 9 sources source NOUN bracis-28424 181 10 , , PUNCT bracis-28424 181 11 \(s \( NOUN bracis-28424 181 12 = = SYM bracis-28424 181 13 |i_0|\ |i_0|\ PROPN bracis-28424 181 14 ) ) PUNCT bracis-28424 181 15 and and CCONJ bracis-28424 181 16 the the DET bracis-28424 181 17 x x NOUN bracis-28424 181 18 - - NOUN bracis-28424 181 19 axis axis NOUN bracis-28424 181 20 is be AUX bracis-28424 181 21 the the DET bracis-28424 181 22 value value NOUN bracis-28424 181 23 for for ADP bracis-28424 181 24 k k PROPN bracis-28424 181 25 in in ADP bracis-28424 181 26 the the DET bracis-28424 181 27 k k NOUN bracis-28424 181 28 - - ADJ bracis-28424 181 29 top top ADJ bracis-28424 181 30 nodes node NOUN bracis-28424 181 31 , , PUNCT bracis-28424 181 32 as as ADP bracis-28424 181 33 a a DET bracis-28424 181 34 multiple multiple NOUN bracis-28424 181 35 of of ADP bracis-28424 181 36 s. s. PROPN bracis-28424 181 37 in in ADP bracis-28424 181 38 all all DET bracis-28424 181 39 scenarios scenario NOUN bracis-28424 181 40 , , PUNCT bracis-28424 181 41 \(f_o \(f_o NOUN bracis-28424 181 42 = = SYM bracis-28424 181 43 \ \ NOUN bracis-28424 181 44 ) ) PUNCT bracis-28424 181 45 20 20 NUM bracis-28424 181 46 % % NOUN bracis-28424 181 47 . . PUNCT bracis-28424 182 1 it it PRON bracis-28424 182 2 also also ADV bracis-28424 182 3 shows show VERB bracis-28424 182 4 that that SCONJ bracis-28424 182 5 increasing increase VERB bracis-28424 182 6 k k PROPN bracis-28424 182 7 improves improve VERB bracis-28424 182 8 performance performance NOUN bracis-28424 182 9 on on ADP bracis-28424 182 10 all all DET bracis-28424 182 11 networks network NOUN bracis-28424 182 12 on on ADP bracis-28424 182 13 the the DET bracis-28424 182 14 w/ w/ NOUN bracis-28424 182 15 neighbors neighbor NOUN bracis-28424 182 16 evaluation evaluation NOUN bracis-28424 182 17 scenario scenario NOUN bracis-28424 182 18 in in ADP bracis-28424 182 19 most most ADJ bracis-28424 182 20 cases case NOUN bracis-28424 182 21 . . PUNCT bracis-28424 183 1 one one NUM bracis-28424 183 2 exception exception NOUN bracis-28424 183 3 being be AUX bracis-28424 183 4 facebook facebook NOUN bracis-28424 183 5 ego ego NOUN bracis-28424 183 6 , , PUNCT bracis-28424 183 7 where where SCONJ bracis-28424 183 8 the the DET bracis-28424 183 9 performance performance NOUN bracis-28424 183 10 decreases decrease VERB bracis-28424 183 11 when when SCONJ bracis-28424 183 12 s s NOUN bracis-28424 183 13 is be AUX bracis-28424 183 14 5 5 NUM bracis-28424 183 15 or or CCONJ bracis-28424 183 16 10 10 NUM bracis-28424 183 17 . . PUNCT bracis-28424 184 1 additionally additionally ADV bracis-28424 184 2 , , PUNCT bracis-28424 184 3 increasing increase VERB bracis-28424 184 4 the the DET bracis-28424 184 5 number number NOUN bracis-28424 184 6 of of ADP bracis-28424 184 7 epidemic epidemic NOUN bracis-28424 184 8 sources source NOUN bracis-28424 184 9 also also ADV bracis-28424 184 10 improves improve VERB bracis-28424 184 11 performance performance NOUN bracis-28424 184 12 on on ADP bracis-28424 184 13 all all DET bracis-28424 184 14 networks network NOUN bracis-28424 184 15 on on ADP bracis-28424 184 16 both both DET bracis-28424 184 17 scenarios scenario NOUN bracis-28424 184 18 , , PUNCT bracis-28424 184 19 with with ADP bracis-28424 184 20 the the DET bracis-28424 184 21 exception exception NOUN bracis-28424 184 22 of of ADP bracis-28424 184 23 ba ba PROPN bracis-28424 184 24 networks network NOUN bracis-28424 184 25 . . PUNCT bracis-28424 185 1 note note VERB bracis-28424 185 2 that that SCONJ bracis-28424 185 3 for for ADP bracis-28424 185 4 er er INTJ bracis-28424 185 5 networks network NOUN bracis-28424 185 6 , , PUNCT bracis-28424 185 7 performance performance NOUN bracis-28424 185 8 clearly clearly ADV bracis-28424 185 9 improves improve VERB bracis-28424 185 10 as as ADP bracis-28424 185 11 s s PART bracis-28424 185 12 increases increase NOUN bracis-28424 185 13 . . PUNCT bracis-28424 186 1 in in ADP bracis-28424 186 2 ba ba PROPN bracis-28424 186 3 networks network NOUN bracis-28424 186 4 , , PUNCT bracis-28424 186 5 having have VERB bracis-28424 186 6 less less ADJ bracis-28424 186 7 epidemic epidemic NOUN bracis-28424 186 8 sources source NOUN bracis-28424 186 9 yields yield VERB bracis-28424 186 10 better well ADJ bracis-28424 186 11 performance performance NOUN bracis-28424 186 12 when when SCONJ bracis-28424 186 13 considering consider VERB bracis-28424 186 14 w/o w/o ADP bracis-28424 186 15 neighbors neighbor NOUN bracis-28424 186 16 scenario scenario PROPN bracis-28424 186 17 . . PUNCT bracis-28424 187 1 this this PRON bracis-28424 187 2 occurs occur VERB bracis-28424 187 3 possibly possibly ADV bracis-28424 187 4 because because SCONJ bracis-28424 187 5 of of ADP bracis-28424 187 6 the the DET bracis-28424 187 7 distinctive distinctive ADJ bracis-28424 187 8 network network NOUN bracis-28424 187 9 topology topology NOUN bracis-28424 187 10 where where SCONJ bracis-28424 187 11 having have VERB bracis-28424 187 12 a a DET bracis-28424 187 13 few few ADJ bracis-28424 187 14 epidemic epidemic NOUN bracis-28424 187 15 sources source NOUN bracis-28424 187 16 allows allow VERB bracis-28424 187 17 for for ADP bracis-28424 187 18 easier easy ADJ bracis-28424 187 19 identification identification NOUN bracis-28424 187 20 . . PUNCT bracis-28424 188 1 fig fig NOUN bracis-28424 188 2 . . PUNCT bracis-28424 189 1 2 2 X bracis-28424 189 2 . . X bracis-28424 189 3 precision precision NOUN bracis-28424 189 4 for for ADP bracis-28424 189 5 all all DET bracis-28424 189 6 four four NUM bracis-28424 189 7 networks network NOUN bracis-28424 189 8 for for ADP bracis-28424 189 9 both both DET bracis-28424 189 10 evaluation evaluation NOUN bracis-28424 189 11 scenarios scenario NOUN bracis-28424 189 12 ( ( PUNCT bracis-28424 189 13 w/ w/ NOUN bracis-28424 189 14 and and CCONJ bracis-28424 189 15 w/o w/o ADP bracis-28424 189 16 neighbors neighbor NOUN bracis-28424 189 17 ) ) PUNCT bracis-28424 189 18 for for ADP bracis-28424 189 19 different different ADJ bracis-28424 189 20 number number NOUN bracis-28424 189 21 of of ADP bracis-28424 189 22 epidemic epidemic NOUN bracis-28424 189 23 sources source NOUN bracis-28424 189 24 ( ( PUNCT bracis-28424 189 25 \(s \(s VERB bracis-28424 189 26 \in \in PROPN bracis-28424 189 27 \{3 \{3 NOUN bracis-28424 189 28 , , PUNCT bracis-28424 189 29 5 5 NUM bracis-28424 189 30 , , PUNCT bracis-28424 189 31 10 10 NUM bracis-28424 189 32 , , PUNCT bracis-28424 189 33 15\}\ 15\}\ NUM bracis-28424 189 34 ) ) PUNCT bracis-28424 189 35 ) ) PUNCT bracis-28424 189 36 and and CCONJ bracis-28424 189 37 different different ADJ bracis-28424 189 38 top top ADJ bracis-28424 189 39 - - PUNCT bracis-28424 189 40 k k NOUN bracis-28424 189 41 values value NOUN bracis-28424 189 42 . . PUNCT bracis-28424 190 1 in in ADP bracis-28424 190 2 all all DET bracis-28424 190 3 scenarios scenario NOUN bracis-28424 190 4 , , PUNCT bracis-28424 190 5 \(f_0=\ \(f_0=\ NOUN bracis-28424 190 6 ) ) PUNCT bracis-28424 190 7 20 20 NUM bracis-28424 190 8 % % NOUN bracis-28424 190 9 . . PUNCT bracis-28424 191 1 full full ADJ bracis-28424 191 2 size size NOUN bracis-28424 191 3 image image NOUN bracis-28424 191 4 interestingly interestingly ADV bracis-28424 191 5 , , PUNCT bracis-28424 191 6 fig fig NOUN bracis-28424 191 7 . . PUNCT bracis-28424 191 8     SPACE bracis-28424 191 9 1 1 NUM bracis-28424 191 10 shows show VERB bracis-28424 191 11 that that SCONJ bracis-28424 191 12 it it PRON bracis-28424 191 13 is be AUX bracis-28424 191 14 not not PART bracis-28424 191 15 always always ADV bracis-28424 191 16 the the DET bracis-28424 191 17 case case NOUN bracis-28424 191 18 that that SCONJ bracis-28424 191 19 performance performance NOUN bracis-28424 191 20 is be AUX bracis-28424 191 21 better well ADJ bracis-28424 191 22 in in ADP bracis-28424 191 23 w/ w/ PROPN bracis-28424 191 24 neighbors neighbor NOUN bracis-28424 191 25 scenario scenario PROPN bracis-28424 191 26 . . PUNCT bracis-28424 192 1 on on ADP bracis-28424 192 2 the the DET bracis-28424 192 3 power power NOUN bracis-28424 192 4 grid grid NOUN bracis-28424 192 5 network network NOUN bracis-28424 192 6 , , PUNCT bracis-28424 192 7 leveraging leverage VERB bracis-28424 192 8 neighbors neighbor NOUN bracis-28424 192 9 clearly clearly ADV bracis-28424 192 10 improves improve VERB bracis-28424 192 11 performance performance NOUN bracis-28424 192 12 , , PUNCT bracis-28424 192 13 while while SCONJ bracis-28424 192 14 for for SCONJ bracis-28424 192 15 ba ba PROPN bracis-28424 192 16 network network NOUN bracis-28424 192 17 the the DET bracis-28424 192 18 opposite opposite NOUN bracis-28424 192 19 is be AUX bracis-28424 192 20 observed observe VERB bracis-28424 192 21 , , PUNCT bracis-28424 192 22 and and CCONJ bracis-28424 192 23 for for SCONJ bracis-28424 192 24 er er INTJ bracis-28424 192 25 networks network NOUN bracis-28424 192 26 results result NOUN bracis-28424 192 27 are be AUX bracis-28424 192 28 mixed mixed ADJ bracis-28424 192 29 . . PUNCT bracis-28424 193 1 therefore therefore ADV bracis-28424 193 2 , , PUNCT bracis-28424 193 3 w/ w/ NOUN bracis-28424 193 4 neighbors neighbor NOUN bracis-28424 193 5 has have VERB bracis-28424 193 6 greater great ADJ bracis-28424 193 7 precision precision NOUN bracis-28424 193 8 but but CCONJ bracis-28424 193 9 potentially potentially ADV bracis-28424 193 10 smaller small ADJ bracis-28424 193 11 recall recall NOUN bracis-28424 193 12 values value NOUN bracis-28424 193 13 , , PUNCT bracis-28424 193 14 as as SCONJ bracis-28424 193 15 the the DET bracis-28424 193 16 set set NOUN bracis-28424 193 17 of of ADP bracis-28424 193 18 true true ADJ bracis-28424 193 19 positives positive NOUN bracis-28424 193 20 has have AUX bracis-28424 193 21 increased increase VERB bracis-28424 193 22 significantly significantly ADV bracis-28424 193 23 . . PUNCT bracis-28424 194 1 this this DET bracis-28424 194 2 intuition intuition NOUN bracis-28424 194 3 is be AUX bracis-28424 194 4 verified verify VERB bracis-28424 194 5 in in ADP bracis-28424 194 6 fig fig NOUN bracis-28424 194 7 . . PUNCT bracis-28424 194 8     SPACE bracis-28424 195 1 2 2 NUM bracis-28424 195 2 . . X bracis-28424 195 3 figure figure NOUN bracis-28424 195 4     SPACE bracis-28424 195 5 2 2 NUM bracis-28424 195 6 shows show VERB bracis-28424 195 7 precision precision NOUN bracis-28424 195 8 values value NOUN bracis-28424 195 9 for for ADP bracis-28424 195 10 the the DET bracis-28424 195 11 same same ADJ bracis-28424 195 12 scenarios scenario NOUN bracis-28424 195 13 as as ADP bracis-28424 195 14 fig fig NOUN bracis-28424 195 15 . . PUNCT bracis-28424 195 16     SPACE bracis-28424 196 1 1 1 X bracis-28424 196 2 . . X bracis-28424 196 3 note note VERB bracis-28424 196 4 that that SCONJ bracis-28424 196 5 in in ADP bracis-28424 196 6 all all DET bracis-28424 196 7 networks network NOUN bracis-28424 196 8 , , PUNCT bracis-28424 196 9 precision precision NOUN bracis-28424 196 10 for for ADP bracis-28424 196 11 a a DET bracis-28424 196 12 fixed fix VERB bracis-28424 196 13 number number NOUN bracis-28424 196 14 of of ADP bracis-28424 196 15 sources source NOUN bracis-28424 196 16 is be AUX bracis-28424 196 17 always always ADV bracis-28424 196 18 higher high ADJ bracis-28424 196 19 when when SCONJ bracis-28424 196 20 considering consider VERB bracis-28424 196 21 the the DET bracis-28424 196 22 set set ADJ bracis-28424 196 23 o o X bracis-28424 196 24 ( ( PUNCT bracis-28424 196 25 w/ w/ NOUN bracis-28424 196 26 neighbors neighbor NOUN bracis-28424 196 27 ) ) PUNCT bracis-28424 196 28 in in ADP bracis-28424 196 29 comparison comparison NOUN bracis-28424 196 30 to to ADP bracis-28424 196 31 the the DET bracis-28424 196 32 set set ADJ bracis-28424 196 33 \(i_0\ \(i_0\ PROPN bracis-28424 196 34 ) ) PUNCT bracis-28424 196 35 ( ( PUNCT bracis-28424 196 36 w/o w/o ADP bracis-28424 196 37 neighbors neighbor NOUN bracis-28424 196 38 ) ) PUNCT bracis-28424 196 39 . . PUNCT bracis-28424 197 1 moreover moreover ADV bracis-28424 197 2 , , PUNCT bracis-28424 197 3 for for ADP bracis-28424 197 4 er er INTJ bracis-28424 197 5 , , PUNCT bracis-28424 197 6 facebook facebook NOUN bracis-28424 197 7 and and CCONJ bracis-28424 197 8 power power NOUN bracis-28424 197 9 grid grid NOUN bracis-28424 197 10 networks network NOUN bracis-28424 197 11 , , PUNCT bracis-28424 197 12 having have VERB bracis-28424 197 13 more more ADJ bracis-28424 197 14 epidemic epidemic NOUN bracis-28424 197 15 sources source NOUN bracis-28424 197 16 improves improve VERB bracis-28424 197 17 precision precision NOUN bracis-28424 197 18 for for ADP bracis-28424 197 19 the the DET bracis-28424 197 20 o o NOUN bracis-28424 197 21 set set NOUN bracis-28424 197 22 in in ADP bracis-28424 197 23 all all DET bracis-28424 197 24 scenarios scenario NOUN bracis-28424 197 25 . . PUNCT bracis-28424 198 1 when when SCONJ bracis-28424 198 2 considering consider VERB bracis-28424 198 3 \(s=15\ \(s=15\ PROPN bracis-28424 198 4 ) ) PUNCT bracis-28424 198 5 , , PUNCT bracis-28424 198 6 precision precision NOUN bracis-28424 198 7 for for ADP bracis-28424 198 8 er er INTJ bracis-28424 198 9 and and CCONJ bracis-28424 198 10 facebook facebook PROPN bracis-28424 198 11 network network NOUN bracis-28424 198 12 are be AUX bracis-28424 198 13 above above ADP bracis-28424 198 14 20 20 NUM bracis-28424 198 15 % % NOUN bracis-28424 198 16 and and CCONJ bracis-28424 198 17 45 45 NUM bracis-28424 198 18 % % NOUN bracis-28424 198 19 for for ADP bracis-28424 198 20 all all DET bracis-28424 198 21 top top ADJ bracis-28424 198 22 - - PUNCT bracis-28424 198 23 k k NOUN bracis-28424 198 24 values value NOUN bracis-28424 198 25 considered consider VERB bracis-28424 198 26 , , PUNCT bracis-28424 198 27 respectively respectively ADV bracis-28424 198 28 , , PUNCT bracis-28424 198 29 while while SCONJ bracis-28424 198 30 for for ADP bracis-28424 198 31 the the DET bracis-28424 198 32 power power NOUN bracis-28424 198 33 grid grid NOUN bracis-28424 198 34 precision precision NOUN bracis-28424 198 35 is be AUX bracis-28424 198 36 always always ADV bracis-28424 198 37 below below ADP bracis-28424 198 38 8 8 NUM bracis-28424 198 39 % % NOUN bracis-28424 198 40 . . PUNCT bracis-28424 199 1 this this PRON bracis-28424 199 2 indicates indicate VERB bracis-28424 199 3 the the DET bracis-28424 199 4 importance importance NOUN bracis-28424 199 5 of of ADP bracis-28424 199 6 the the DET bracis-28424 199 7 network network NOUN bracis-28424 199 8 structure structure NOUN bracis-28424 199 9 on on ADP bracis-28424 199 10 identifying identify VERB bracis-28424 199 11 epidemic epidemic NOUN bracis-28424 199 12 sources source NOUN bracis-28424 199 13 . . PUNCT bracis-28424 200 1 5.4 5.4 NUM bracis-28424 200 2 results result NOUN bracis-28424 200 3 with with ADP bracis-28424 200 4     SPACE bracis-28424 200 5 mixed mixed ADJ bracis-28424 200 6 datasets dataset NOUN bracis-28424 200 7 the the DET bracis-28424 200 8 previous previous ADJ bracis-28424 200 9 results result NOUN bracis-28424 200 10 considered consider VERB bracis-28424 200 11 specialized specialized ADJ bracis-28424 200 12 datasets dataset NOUN bracis-28424 200 13 where where SCONJ bracis-28424 200 14 all all DET bracis-28424 200 15 samples sample NOUN bracis-28424 200 16 were be AUX bracis-28424 200 17 independent independent ADJ bracis-28424 200 18 and and CCONJ bracis-28424 200 19 identically identically ADV bracis-28424 200 20 distributed distribute VERB bracis-28424 200 21 , , PUNCT bracis-28424 200 22 all all PRON bracis-28424 200 23 having have VERB bracis-28424 200 24 the the DET bracis-28424 200 25 same same ADJ bracis-28424 200 26 parameters parameter NOUN bracis-28424 200 27 . . PUNCT bracis-28424 201 1 such such ADJ bracis-28424 201 2 samples sample NOUN bracis-28424 201 3 were be AUX bracis-28424 201 4 used use VERB bracis-28424 201 5 for for ADP bracis-28424 201 6 training training NOUN bracis-28424 201 7 , , PUNCT bracis-28424 201 8 validation validation NOUN bracis-28424 201 9 , , PUNCT bracis-28424 201 10 and and CCONJ bracis-28424 201 11 testing testing NOUN bracis-28424 201 12 . . PUNCT bracis-28424 202 1 however however ADV bracis-28424 202 2 , , PUNCT bracis-28424 202 3 it it PRON bracis-28424 202 4 is be AUX bracis-28424 202 5 also also ADV bracis-28424 202 6 important important ADJ bracis-28424 202 7 to to PART bracis-28424 202 8 consider consider VERB bracis-28424 202 9 the the DET bracis-28424 202 10 performance performance NOUN bracis-28424 202 11 of of ADP bracis-28424 202 12 the the DET bracis-28424 202 13 framework framework NOUN bracis-28424 202 14 when when SCONJ bracis-28424 202 15 the the DET bracis-28424 202 16 datasets dataset NOUN bracis-28424 202 17 are be AUX bracis-28424 202 18 more more ADV bracis-28424 202 19 diverse diverse ADJ bracis-28424 202 20 and and CCONJ bracis-28424 202 21 not not PART bracis-28424 202 22 composed compose VERB bracis-28424 202 23 by by ADP bracis-28424 202 24 identically identically ADV bracis-28424 202 25 distributed distribute VERB bracis-28424 202 26 samples sample NOUN bracis-28424 202 27 . . PUNCT bracis-28424 203 1 a a DET bracis-28424 203 2 heterogeneous heterogeneous ADJ bracis-28424 203 3 dataset dataset NOUN bracis-28424 203 4 was be AUX bracis-28424 203 5 generated generate VERB bracis-28424 203 6 for for ADP bracis-28424 203 7 each each DET bracis-28424 203 8 network network NOUN bracis-28424 203 9 model model NOUN bracis-28424 203 10 . . PUNCT bracis-28424 204 1 the the DET bracis-28424 204 2 samples sample NOUN bracis-28424 204 3 in in ADP bracis-28424 204 4 each each DET bracis-28424 204 5 dataset dataset NOUN bracis-28424 204 6 have have VERB bracis-28424 204 7 different different ADJ bracis-28424 204 8 networks network NOUN bracis-28424 204 9 ( ( PUNCT bracis-28424 204 10 from from ADP bracis-28424 204 11 the the DET bracis-28424 204 12 same same ADJ bracis-28424 204 13 model model NOUN bracis-28424 204 14 ) ) PUNCT bracis-28424 204 15 , , PUNCT bracis-28424 204 16 different different ADJ bracis-28424 204 17 number number NOUN bracis-28424 204 18 of of ADP bracis-28424 204 19 sources source NOUN bracis-28424 204 20 ( ( PUNCT bracis-28424 204 21 \(s \(s VERB bracis-28424 204 22 \in \in PROPN bracis-28424 204 23 \{3 \{3 NOUN bracis-28424 204 24 , , PUNCT bracis-28424 204 25 5 5 NUM bracis-28424 204 26 , , PUNCT bracis-28424 204 27 10 10 NUM bracis-28424 204 28 , , PUNCT bracis-28424 204 29 15\}\ 15\}\ NUM bracis-28424 204 30 ) ) PUNCT bracis-28424 204 31 ) ) PUNCT bracis-28424 204 32 and and CCONJ bracis-28424 204 33 different different ADJ bracis-28424 204 34 infection infection NOUN bracis-28424 204 35 rates rate NOUN bracis-28424 204 36 ( ( PUNCT bracis-28424 204 37 \(f_o \(f_o NOUN bracis-28424 204 38 \in \in PROPN bracis-28424 204 39 \ \ PROPN bracis-28424 204 40 { { PUNCT bracis-28424 204 41 0.1 0.1 NUM bracis-28424 204 42 , , PUNCT bracis-28424 204 43 0.2 0.2 NUM bracis-28424 204 44 , , PUNCT bracis-28424 204 45 0.3 0.3 NUM bracis-28424 204 46 \}\ \}\ NOUN bracis-28424 204 47 ) ) PUNCT bracis-28424 204 48 ) ) PUNCT bracis-28424 204 49 . . PUNCT bracis-28424 205 1 the the DET bracis-28424 205 2 exception exception NOUN bracis-28424 205 3 are be AUX bracis-28424 205 4 real real ADJ bracis-28424 205 5 networks network NOUN bracis-28424 205 6 where where SCONJ bracis-28424 205 7 the the DET bracis-28424 205 8 network network NOUN bracis-28424 205 9 is be AUX bracis-28424 205 10 always always ADV bracis-28424 205 11 the the DET bracis-28424 205 12 same same ADJ bracis-28424 205 13 ( ( PUNCT bracis-28424 205 14 but but CCONJ bracis-28424 205 15 all all DET bracis-28424 205 16 else else ADV bracis-28424 205 17 is be AUX bracis-28424 205 18 simulated simulate VERB bracis-28424 205 19 to to PART bracis-28424 205 20 generate generate VERB bracis-28424 205 21 an an DET bracis-28424 205 22 epidemic epidemic NOUN bracis-28424 205 23 network network NOUN bracis-28424 205 24 ) ) PUNCT bracis-28424 205 25 . . PUNCT bracis-28424 206 1 this this DET bracis-28424 206 2 heterogeneous heterogeneous ADJ bracis-28424 206 3 dataset dataset NOUN bracis-28424 206 4 is be AUX bracis-28424 206 5 used use VERB bracis-28424 206 6 for for ADP bracis-28424 206 7 training training NOUN bracis-28424 206 8 , , PUNCT bracis-28424 206 9 validation validation NOUN bracis-28424 206 10 and and CCONJ bracis-28424 206 11 testing test VERB bracis-28424 206 12 a a DET bracis-28424 206 13 general general ADJ bracis-28424 206 14 model model NOUN bracis-28424 206 15 . . PUNCT bracis-28424 207 1 results result NOUN bracis-28424 207 2 comparing compare VERB bracis-28424 207 3 the the DET bracis-28424 207 4 performance performance NOUN bracis-28424 207 5 of of ADP bracis-28424 207 6 the the DET bracis-28424 207 7 framework framework NOUN bracis-28424 207 8 on on ADP bracis-28424 207 9 the the DET bracis-28424 207 10 homogeneous homogeneous ADJ bracis-28424 207 11 and and CCONJ bracis-28424 207 12 heterogeneous heterogeneous ADJ bracis-28424 207 13 datasets dataset NOUN bracis-28424 207 14 are be AUX bracis-28424 207 15 shown show VERB bracis-28424 207 16 in in ADP bracis-28424 207 17 fig fig NOUN bracis-28424 207 18 . . PUNCT bracis-28424 207 19     SPACE bracis-28424 208 1 3 3 X bracis-28424 208 2 . . PUNCT bracis-28424 209 1 each each DET bracis-28424 209 2 subfigure subfigure NOUN bracis-28424 209 3 shows show VERB bracis-28424 209 4 a a DET bracis-28424 209 5 different different ADJ bracis-28424 209 6 infection infection NOUN bracis-28424 209 7 rate rate NOUN bracis-28424 209 8 , , PUNCT bracis-28424 209 9 \(f_o\ \(f_o\ VERB bracis-28424 209 10 ) ) PUNCT bracis-28424 209 11 and and CCONJ bracis-28424 209 12 each each DET bracis-28424 209 13 couple couple NOUN bracis-28424 209 14 of of ADP bracis-28424 209 15 bars bar NOUN bracis-28424 209 16 correspond correspond VERB bracis-28424 209 17 to to ADP bracis-28424 209 18 different different ADJ bracis-28424 209 19 number number NOUN bracis-28424 209 20 of of ADP bracis-28424 209 21 sources source NOUN bracis-28424 209 22 , , PUNCT bracis-28424 209 23 s. s. PROPN bracis-28424 209 24 performance performance NOUN bracis-28424 209 25 on on ADP bracis-28424 209 26 the the DET bracis-28424 209 27 homogeneous homogeneous ADJ bracis-28424 209 28 ( ( PUNCT bracis-28424 209 29 specialized specialized ADJ bracis-28424 209 30 ) ) PUNCT bracis-28424 209 31 dataset dataset NOUN bracis-28424 209 32 is be AUX bracis-28424 209 33 almost almost ADV bracis-28424 209 34 always always ADV bracis-28424 209 35 superior superior ADJ bracis-28424 209 36 than than ADP bracis-28424 209 37 performance performance NOUN bracis-28424 209 38 on on ADP bracis-28424 209 39 heterogeneous heterogeneous ADJ bracis-28424 209 40 dataset dataset NOUN bracis-28424 209 41 . . PUNCT bracis-28424 210 1 however however ADV bracis-28424 210 2 , , PUNCT bracis-28424 210 3 when when SCONJ bracis-28424 210 4 the the DET bracis-28424 210 5 infection infection NOUN bracis-28424 210 6 rate rate NOUN bracis-28424 210 7 is be AUX bracis-28424 210 8 small small ADJ bracis-28424 210 9 , , PUNCT bracis-28424 210 10 e.g. e.g. ADV bracis-28424 210 11 , , PUNCT bracis-28424 210 12 \(f_o \(f_o NOUN bracis-28424 210 13 = = SYM bracis-28424 210 14 0.1\ 0.1\ PROPN bracis-28424 210 15 ) ) PUNCT bracis-28424 210 16 , , PUNCT bracis-28424 210 17 the the DET bracis-28424 210 18 performance performance NOUN bracis-28424 210 19 of of ADP bracis-28424 210 20 the the DET bracis-28424 210 21 models model NOUN bracis-28424 210 22 are be AUX bracis-28424 210 23 comparable comparable ADJ bracis-28424 210 24 for for ADP bracis-28424 210 25 both both DET bracis-28424 210 26 er er INTJ bracis-28424 210 27 and and CCONJ bracis-28424 210 28 ba ba PROPN bracis-28424 210 29 networks network NOUN bracis-28424 210 30 for for ADP bracis-28424 210 31 different different ADJ bracis-28424 210 32 number number NOUN bracis-28424 210 33 of of ADP bracis-28424 210 34 sources source NOUN bracis-28424 210 35 . . PUNCT bracis-28424 211 1 this this PRON bracis-28424 211 2 indicates indicate VERB bracis-28424 211 3 that that SCONJ bracis-28424 211 4 the the DET bracis-28424 211 5 framework framework NOUN bracis-28424 211 6 can can AUX bracis-28424 211 7 be be AUX bracis-28424 211 8 effectively effectively ADV bracis-28424 211 9 trained train VERB bracis-28424 211 10 on on ADP bracis-28424 211 11 a a DET bracis-28424 211 12 more more ADV bracis-28424 211 13 general general ADJ bracis-28424 211 14 dataset dataset NOUN bracis-28424 211 15 when when SCONJ bracis-28424 211 16 the the DET bracis-28424 211 17 infection infection NOUN bracis-28424 211 18 rate rate NOUN bracis-28424 211 19 is be AUX bracis-28424 211 20 small small ADJ bracis-28424 211 21 . . PUNCT bracis-28424 212 1 indeed indeed ADV bracis-28424 212 2 , , PUNCT bracis-28424 212 3 when when SCONJ bracis-28424 212 4 the the DET bracis-28424 212 5 infection infection NOUN bracis-28424 212 6 rate rate NOUN bracis-28424 212 7 is be AUX bracis-28424 212 8 small small ADJ bracis-28424 212 9 , , PUNCT bracis-28424 212 10 increasing increase VERB bracis-28424 212 11 the the DET bracis-28424 212 12 number number NOUN bracis-28424 212 13 of of ADP bracis-28424 212 14 sources source NOUN bracis-28424 212 15 will will AUX bracis-28424 212 16 still still ADV bracis-28424 212 17 allow allow VERB bracis-28424 212 18 them they PRON bracis-28424 212 19 to to PART bracis-28424 212 20 have have VERB bracis-28424 212 21 a a DET bracis-28424 212 22 distinctive distinctive ADJ bracis-28424 212 23 signature signature NOUN bracis-28424 212 24 in in ADP bracis-28424 212 25 the the DET bracis-28424 212 26 epidemic epidemic NOUN bracis-28424 212 27 network network NOUN bracis-28424 212 28 . . PUNCT bracis-28424 213 1 fig fig NOUN bracis-28424 213 2 . . PUNCT bracis-28424 214 1 3 3 X bracis-28424 214 2 . . X bracis-28424 214 3 performance performance NOUN bracis-28424 214 4 of of ADP bracis-28424 214 5 network network NOUN bracis-28424 214 6 models model NOUN bracis-28424 214 7 using use VERB bracis-28424 214 8 specialized specialized ADJ bracis-28424 214 9 / / SYM bracis-28424 214 10 homogeneous homogeneous ADJ bracis-28424 214 11 dataset dataset NOUN bracis-28424 214 12 ( ( PUNCT bracis-28424 214 13 individual individual ADJ bracis-28424 214 14 ) ) PUNCT bracis-28424 214 15 and and CCONJ bracis-28424 214 16 generalized generalize VERB bracis-28424 214 17 / / SYM bracis-28424 214 18 heterogeneous heterogeneous ADJ bracis-28424 214 19 datasets dataset NOUN bracis-28424 214 20 ( ( PUNCT bracis-28424 214 21 general general ADJ bracis-28424 214 22 ) ) PUNCT bracis-28424 214 23 for for ADP bracis-28424 214 24 different different ADJ bracis-28424 214 25 number number NOUN bracis-28424 214 26 of of ADP bracis-28424 214 27 sources source NOUN bracis-28424 214 28 ( ( PUNCT bracis-28424 214 29 s s NOUN bracis-28424 214 30 ) ) PUNCT bracis-28424 214 31 and and CCONJ bracis-28424 214 32 different different ADJ bracis-28424 214 33 infection infection NOUN bracis-28424 214 34 rates rate NOUN bracis-28424 214 35 ( ( PUNCT bracis-28424 214 36 \(f_o\ \(f_o\ NOUN bracis-28424 214 37 ) ) PUNCT bracis-28424 214 38 ) ) PUNCT bracis-28424 214 39 . . PUNCT bracis-28424 215 1 full full ADJ bracis-28424 215 2 size size NOUN bracis-28424 215 3 image image NOUN bracis-28424 215 4 figure figure NOUN bracis-28424 215 5     SPACE bracis-28424 215 6 3 3 NUM bracis-28424 215 7 also also ADV bracis-28424 215 8 shows show VERB bracis-28424 215 9 that that SCONJ bracis-28424 215 10 as as ADP bracis-28424 215 11 the the DET bracis-28424 215 12 infection infection NOUN bracis-28424 215 13 rate rate NOUN bracis-28424 215 14 increases increase NOUN bracis-28424 215 15 , , PUNCT bracis-28424 215 16 performance performance NOUN bracis-28424 215 17 degrades degrade VERB bracis-28424 215 18 for for ADP bracis-28424 215 19 both both CCONJ bracis-28424 215 20 homogeneous homogeneous ADJ bracis-28424 215 21 and and CCONJ bracis-28424 215 22 heterogeneous heterogeneous ADJ bracis-28424 215 23 datasets dataset NOUN bracis-28424 215 24 , , PUNCT bracis-28424 215 25 but but CCONJ bracis-28424 215 26 falls fall VERB bracis-28424 215 27 faster fast ADV bracis-28424 215 28 for for ADP bracis-28424 215 29 the the DET bracis-28424 215 30 heterogeneous heterogeneous ADJ bracis-28424 215 31 . . PUNCT bracis-28424 216 1 in in ADP bracis-28424 216 2 fact fact NOUN bracis-28424 216 3 , , PUNCT bracis-28424 216 4 performance performance NOUN bracis-28424 216 5 is be AUX bracis-28424 216 6 zero zero NUM bracis-28424 216 7 for for ADP bracis-28424 216 8 \(f_o \(f_o PROPN bracis-28424 216 9 = = SYM bracis-28424 216 10 0.3\ 0.3\ NUM bracis-28424 216 11 ) ) PUNCT bracis-28424 216 12 and and CCONJ bracis-28424 216 13 \(s \(s VERB bracis-28424 216 14 \in \in PROPN bracis-28424 216 15 \{3,5\})\ \{3,5\})\ NOUN bracis-28424 216 16 ) ) PUNCT bracis-28424 216 17 for for ADP bracis-28424 216 18 er er INTJ bracis-28424 216 19 networks network NOUN bracis-28424 216 20 , , PUNCT bracis-28424 216 21 showing show VERB bracis-28424 216 22 that that DET bracis-28424 216 23 heterogeneous heterogeneous ADJ bracis-28424 216 24 dataset dataset NOUN bracis-28424 216 25 trained train VERB bracis-28424 216 26 model model NOUN bracis-28424 216 27 can can AUX bracis-28424 216 28 not not PART bracis-28424 216 29 adequately adequately ADV bracis-28424 216 30 identify identify VERB bracis-28424 216 31 source source NOUN bracis-28424 216 32 nodes node NOUN bracis-28424 216 33 in in ADP bracis-28424 216 34 more more ADV bracis-28424 216 35 difficult difficult ADJ bracis-28424 216 36 scenarios scenario NOUN bracis-28424 216 37 . . PUNCT bracis-28424 217 1 a a DET bracis-28424 217 2 curious curious ADJ bracis-28424 217 3 exception exception NOUN bracis-28424 217 4 was be AUX bracis-28424 217 5 ba ba PROPN bracis-28424 217 6 for for ADP bracis-28424 217 7 \(f_o \(f_o PROPN bracis-28424 217 8 = = SYM bracis-28424 217 9 0.2\ 0.2\ ADJ bracis-28424 217 10 ) ) PUNCT bracis-28424 217 11 where where SCONJ bracis-28424 217 12 performance performance NOUN bracis-28424 217 13 for for ADP bracis-28424 217 14 the the DET bracis-28424 217 15 heterogeneous heterogeneous ADJ bracis-28424 217 16 dataset dataset NOUN bracis-28424 217 17 was be AUX bracis-28424 217 18 in in ADP bracis-28424 217 19 some some DET bracis-28424 217 20 cases case NOUN bracis-28424 217 21 higher high ADJ bracis-28424 217 22 , , PUNCT bracis-28424 217 23 \(s \(s ADP bracis-28424 217 24 \in \in PROPN bracis-28424 217 25 \{3,5\}\ \{3,5\}\ PROPN bracis-28424 217 26 ) ) PUNCT bracis-28424 217 27 . . PUNCT bracis-28424 218 1 figure figure NOUN bracis-28424 218 2     SPACE bracis-28424 218 3 4 4 NUM bracis-28424 218 4 shows show VERB bracis-28424 218 5 the the DET bracis-28424 218 6 performance performance NOUN bracis-28424 218 7 of of ADP bracis-28424 218 8 using use VERB bracis-28424 218 9 the the DET bracis-28424 218 10 homogeneous homogeneous ADJ bracis-28424 218 11 and and CCONJ bracis-28424 218 12 heterogeneous heterogeneous ADJ bracis-28424 218 13 datasets dataset NOUN bracis-28424 218 14 when when SCONJ bracis-28424 218 15 considering consider VERB bracis-28424 218 16 the the DET bracis-28424 218 17 two two NUM bracis-28424 218 18 real real ADJ bracis-28424 218 19 networks network NOUN bracis-28424 218 20 . . PUNCT bracis-28424 219 1 results result NOUN bracis-28424 219 2 clearly clearly ADV bracis-28424 219 3 indicate indicate VERB bracis-28424 219 4 that that SCONJ bracis-28424 219 5 using use VERB bracis-28424 219 6 a a DET bracis-28424 219 7 heterogeneous heterogeneous ADJ bracis-28424 219 8 dataset dataset NOUN bracis-28424 219 9 is be AUX bracis-28424 219 10 significantly significantly ADV bracis-28424 219 11 worst bad ADJ bracis-28424 219 12 than than ADP bracis-28424 219 13 using use VERB bracis-28424 219 14 a a DET bracis-28424 219 15 homogeneous homogeneous ADJ bracis-28424 219 16 dataset dataset NOUN bracis-28424 219 17 , , PUNCT bracis-28424 219 18 even even ADV bracis-28424 219 19 in in ADP bracis-28424 219 20 the the DET bracis-28424 219 21 case case NOUN bracis-28424 219 22 \(f_o \(f_o NOUN bracis-28424 219 23 = = SYM bracis-28424 219 24 0.1\ 0.1\ PROPN bracis-28424 219 25 ) ) PUNCT bracis-28424 219 26 . . PUNCT bracis-28424 220 1 results result NOUN bracis-28424 220 2 also also ADV bracis-28424 220 3 corroborate corroborate VERB bracis-28424 220 4 that that SCONJ bracis-28424 220 5 for for ADP bracis-28424 220 6 a a DET bracis-28424 220 7 given give VERB bracis-28424 220 8 infection infection NOUN bracis-28424 220 9 rate rate NOUN bracis-28424 220 10 , , PUNCT bracis-28424 220 11 increasing increase VERB bracis-28424 220 12 the the DET bracis-28424 220 13 number number NOUN bracis-28424 220 14 of of ADP bracis-28424 220 15 sources source NOUN bracis-28424 220 16 improves improve VERB bracis-28424 220 17 performance performance NOUN bracis-28424 220 18 , , PUNCT bracis-28424 220 19 for for ADP bracis-28424 220 20 both both CCONJ bracis-28424 220 21 homogeneous homogeneous ADJ bracis-28424 220 22 and and CCONJ bracis-28424 220 23 heterogeneous heterogeneous ADJ bracis-28424 220 24 datasets dataset NOUN bracis-28424 220 25 . . PUNCT bracis-28424 221 1 moreover moreover ADV bracis-28424 221 2 , , PUNCT bracis-28424 221 3 results result NOUN bracis-28424 221 4 also also ADV bracis-28424 221 5 corroborate corroborate VERB bracis-28424 221 6 that that SCONJ bracis-28424 221 7 increasing increase VERB bracis-28424 221 8 the the DET bracis-28424 221 9 infection infection NOUN bracis-28424 221 10 rate rate NOUN bracis-28424 221 11 reduces reduce VERB bracis-28424 221 12 the the DET bracis-28424 221 13 performance performance NOUN bracis-28424 221 14 , , PUNCT bracis-28424 221 15 and and CCONJ bracis-28424 221 16 again again ADV bracis-28424 221 17 for for ADP bracis-28424 221 18 both both DET bracis-28424 221 19 datasets dataset NOUN bracis-28424 221 20 . . PUNCT bracis-28424 222 1 note note VERB bracis-28424 222 2 that that SCONJ bracis-28424 222 3 performance performance NOUN bracis-28424 222 4 under under ADP bracis-28424 222 5 the the DET bracis-28424 222 6 homogeneous homogeneous ADJ bracis-28424 222 7 dataset dataset NOUN bracis-28424 222 8 is be AUX bracis-28424 222 9 in in ADP bracis-28424 222 10 some some DET bracis-28424 222 11 cases case NOUN bracis-28424 222 12 twice twice ADV bracis-28424 222 13 larger large ADJ bracis-28424 222 14 than than ADP bracis-28424 222 15 the the DET bracis-28424 222 16 heterogeneous heterogeneous ADJ bracis-28424 222 17 dataset dataset NOUN bracis-28424 222 18 , , PUNCT bracis-28424 222 19 indicating indicate VERB bracis-28424 222 20 that that SCONJ bracis-28424 222 21 generalization generalization NOUN bracis-28424 222 22 is be AUX bracis-28424 222 23 much much ADV bracis-28424 222 24 harder hard ADJ bracis-28424 222 25 for for ADP bracis-28424 222 26 real real ADJ bracis-28424 222 27 networks network NOUN bracis-28424 222 28 . . PUNCT bracis-28424 223 1 5.5 5.5 NUM bracis-28424 223 2 comparison comparison NOUN bracis-28424 223 3 with with ADP bracis-28424 223 4     SPACE bracis-28424 223 5 baselines baseline NOUN bracis-28424 223 6 only only ADV bracis-28424 223 7 a a DET bracis-28424 223 8 few few ADJ bracis-28424 223 9 prior prior ADJ bracis-28424 223 10 works work NOUN bracis-28424 223 11 have have AUX bracis-28424 223 12 evaluated evaluate VERB bracis-28424 223 13 the the DET bracis-28424 223 14 multiple multiple ADJ bracis-28424 223 15 epidemic epidemic NOUN bracis-28424 223 16 source source NOUN bracis-28424 223 17 detection detection NOUN bracis-28424 223 18 ( ( PUNCT bracis-28424 223 19 msd msd NOUN bracis-28424 223 20 ) ) PUNCT bracis-28424 223 21 problem problem NOUN bracis-28424 223 22 in in ADP bracis-28424 223 23 scenarios scenario NOUN bracis-28424 223 24 that that PRON bracis-28424 223 25 are be AUX bracis-28424 223 26 reproducible reproducible ADJ bracis-28424 223 27 and and CCONJ bracis-28424 223 28 comparable comparable ADJ bracis-28424 223 29 . . PUNCT bracis-28424 224 1 in in ADP bracis-28424 224 2 fact fact NOUN bracis-28424 224 3 , , PUNCT bracis-28424 224 4 a a DET bracis-28424 224 5 contribution contribution NOUN bracis-28424 224 6 of of ADP bracis-28424 224 7 this this DET bracis-28424 224 8 work work NOUN bracis-28424 224 9 is be AUX bracis-28424 224 10 the the DET bracis-28424 224 11 evaluation evaluation NOUN bracis-28424 224 12 of of ADP bracis-28424 224 13 the the DET bracis-28424 224 14 proposed propose VERB bracis-28424 224 15 framework framework NOUN bracis-28424 224 16 under under ADP bracis-28424 224 17 well well ADV bracis-28424 224 18 - - PUNCT bracis-28424 224 19 studied study VERB bracis-28424 224 20 network network NOUN bracis-28424 224 21 models model NOUN bracis-28424 224 22 and and CCONJ bracis-28424 224 23 epidemic epidemic NOUN bracis-28424 224 24 models model NOUN bracis-28424 224 25 that that PRON bracis-28424 224 26 can can AUX bracis-28424 224 27 be be AUX bracis-28424 224 28 easily easily ADV bracis-28424 224 29 reproduced reproduce VERB bracis-28424 224 30 . . PUNCT bracis-28424 225 1 an an DET bracis-28424 225 2 exception exception NOUN bracis-28424 225 3 is be AUX bracis-28424 225 4 gcnsi gcnsi NOUN bracis-28424 225 5 [ [ X bracis-28424 225 6 3 3 X bracis-28424 225 7 ] ] PUNCT bracis-28424 225 8 that that PRON bracis-28424 225 9 performed perform VERB bracis-28424 225 10 numerical numerical ADJ bracis-28424 225 11 evaluations evaluation NOUN bracis-28424 225 12 on on ADP bracis-28424 225 13 real real ADJ bracis-28424 225 14 world world NOUN bracis-28424 225 15 networks network NOUN bracis-28424 225 16 and and CCONJ bracis-28424 225 17 reported report VERB bracis-28424 225 18 their their PRON bracis-28424 225 19 scenario scenario NOUN bracis-28424 225 20 with with ADP bracis-28424 225 21 sufficient sufficient ADJ bracis-28424 225 22 details detail NOUN bracis-28424 225 23 , , PUNCT bracis-28424 225 24 using use VERB bracis-28424 225 25 f f NOUN bracis-28424 225 26 - - PUNCT bracis-28424 225 27 score score NOUN bracis-28424 225 28 metric metric NOUN bracis-28424 225 29 , , PUNCT bracis-28424 225 30 while while SCONJ bracis-28424 225 31 also also ADV bracis-28424 225 32 reporting report VERB bracis-28424 225 33 results result NOUN bracis-28424 225 34 for for ADP bracis-28424 225 35 lpsi lpsi ADJ bracis-28424 225 36 and and CCONJ bracis-28424 225 37 netsleuth netsleuth NOUN bracis-28424 225 38 for for ADP bracis-28424 225 39 the the DET bracis-28424 225 40 same same ADJ bracis-28424 225 41 scenarios scenario NOUN bracis-28424 225 42 . . PUNCT bracis-28424 226 1 table table NOUN bracis-28424 226 2     SPACE bracis-28424 226 3 2 2 NUM bracis-28424 226 4 compares compare VERB bracis-28424 226 5 f f NOUN bracis-28424 226 6 - - PUNCT bracis-28424 226 7 score score NOUN bracis-28424 226 8 results result NOUN bracis-28424 226 9 for for ADP bracis-28424 226 10 3 3 NUM bracis-28424 226 11 , , PUNCT bracis-28424 226 12 5 5 NUM bracis-28424 226 13 and and CCONJ bracis-28424 226 14 10 10 NUM bracis-28424 226 15 epidemic epidemic NOUN bracis-28424 226 16 sources source NOUN bracis-28424 226 17 when when SCONJ bracis-28424 226 18 30 30 NUM bracis-28424 226 19 % % NOUN bracis-28424 226 20 of of ADP bracis-28424 226 21 the the DET bracis-28424 226 22 network network NOUN bracis-28424 226 23 is be AUX bracis-28424 226 24 infected infect VERB bracis-28424 226 25 , , PUNCT bracis-28424 227 1 \(f_o \(f_o ADP bracis-28424 227 2 = = NOUN bracis-28424 227 3 0.3\ 0.3\ NUM bracis-28424 227 4 ) ) PUNCT bracis-28424 227 5 , , PUNCT bracis-28424 227 6 for for ADP bracis-28424 227 7 gcnsi gcnsi NOUN bracis-28424 227 8 , , PUNCT bracis-28424 227 9 lpsi lpsi ADJ bracis-28424 227 10 and and CCONJ bracis-28424 227 11 netsleuth netsleuth NOUN bracis-28424 227 12 approaches approach NOUN bracis-28424 227 13 . . PUNCT bracis-28424 228 1 recall recall VERB bracis-28424 228 2 that that SCONJ bracis-28424 228 3 only only ADV bracis-28424 228 4 gcnsi gcnsi NOUN bracis-28424 228 5 uses use VERB bracis-28424 228 6 graph graph NOUN bracis-28424 228 7 convolution convolution NOUN bracis-28424 228 8 networks network NOUN bracis-28424 228 9 . . PUNCT bracis-28424 229 1 results result NOUN bracis-28424 229 2 for for ADP bracis-28424 229 3 the the DET bracis-28424 229 4 proposed propose VERB bracis-28424 229 5 framework framework NOUN bracis-28424 229 6 are be AUX bracis-28424 229 7 shown show VERB bracis-28424 229 8 in in ADP bracis-28424 229 9 the the DET bracis-28424 229 10 row row NOUN bracis-28424 229 11 sage sage NOUN bracis-28424 229 12 with with ADP bracis-28424 229 13 maximum maximum ADJ bracis-28424 229 14 and and CCONJ bracis-28424 229 15 average average ADJ bracis-28424 229 16 values value NOUN bracis-28424 229 17 across across ADP bracis-28424 229 18 different different ADJ bracis-28424 229 19 values value NOUN bracis-28424 229 20 for for ADP bracis-28424 229 21 k k PROPN bracis-28424 229 22 in in ADP bracis-28424 229 23 the the DET bracis-28424 229 24 top top ADJ bracis-28424 229 25 - - PUNCT bracis-28424 229 26 k k NOUN bracis-28424 229 27 ranking ranking PROPN bracis-28424 229 28 . . PUNCT bracis-28424 230 1 fig fig NOUN bracis-28424 230 2 . . PUNCT bracis-28424 231 1 4 4 X bracis-28424 231 2 . . X bracis-28424 231 3 performance performance NOUN bracis-28424 231 4 of of ADP bracis-28424 231 5 real real ADJ bracis-28424 231 6 networks network NOUN bracis-28424 231 7 using use VERB bracis-28424 231 8 specialized specialized ADJ bracis-28424 231 9 / / SYM bracis-28424 231 10 homogeneous homogeneous ADJ bracis-28424 231 11 dataset dataset NOUN bracis-28424 231 12 ( ( PUNCT bracis-28424 231 13 individual individual ADJ bracis-28424 231 14 ) ) PUNCT bracis-28424 231 15 and and CCONJ bracis-28424 231 16 generalized generalize VERB bracis-28424 231 17 / / SYM bracis-28424 231 18 heterogeneous heterogeneous ADJ bracis-28424 231 19 datasets dataset NOUN bracis-28424 231 20 ( ( PUNCT bracis-28424 231 21 general general ADJ bracis-28424 231 22 ) ) PUNCT bracis-28424 231 23 for for ADP bracis-28424 231 24 different different ADJ bracis-28424 231 25 number number NOUN bracis-28424 231 26 of of ADP bracis-28424 231 27 sources source NOUN bracis-28424 231 28 ( ( PUNCT bracis-28424 231 29 s s NOUN bracis-28424 231 30 ) ) PUNCT bracis-28424 231 31 and and CCONJ bracis-28424 231 32 different different ADJ bracis-28424 231 33 infection infection NOUN bracis-28424 231 34 rates rate NOUN bracis-28424 231 35 ( ( PUNCT bracis-28424 231 36 \(f_o\ \(f_o\ NOUN bracis-28424 231 37 ) ) PUNCT bracis-28424 231 38 ) ) PUNCT bracis-28424 231 39 . . PUNCT bracis-28424 232 1 full full ADJ bracis-28424 232 2 size size NOUN bracis-28424 232 3 image image NOUN bracis-28424 232 4 table table NOUN bracis-28424 232 5 2 2 NUM bracis-28424 232 6 . . PUNCT bracis-28424 233 1 f f X bracis-28424 233 2 - - PUNCT bracis-28424 233 3 score score NOUN bracis-28424 233 4 values value NOUN bracis-28424 233 5 of of ADP bracis-28424 233 6 different different ADJ bracis-28424 233 7 frameworks framework NOUN bracis-28424 233 8 on on ADP bracis-28424 233 9 real real ADJ bracis-28424 233 10 networks network NOUN bracis-28424 233 11 with with ADP bracis-28424 233 12 3 3 NUM bracis-28424 233 13 , , PUNCT bracis-28424 233 14 5 5 NUM bracis-28424 233 15 and and CCONJ bracis-28424 233 16 10 10 NUM bracis-28424 233 17 epidemic epidemic NOUN bracis-28424 233 18 sources source NOUN bracis-28424 233 19 . . PUNCT bracis-28424 234 1 gcnsi gcnsi NOUN bracis-28424 234 2 , , PUNCT bracis-28424 234 3 lpsi lpsi ADJ bracis-28424 234 4 and and CCONJ bracis-28424 234 5 netsleuth netsleuth NOUN bracis-28424 234 6 results result NOUN bracis-28424 234 7 extracted extract VERB bracis-28424 234 8 from from ADP bracis-28424 234 9 [ [ PUNCT bracis-28424 234 10 3].full 3].full NUM bracis-28424 234 11 size size NOUN bracis-28424 234 12 table table NOUN bracis-28424 234 13 note note NOUN bracis-28424 234 14 that that SCONJ bracis-28424 234 15 results result NOUN bracis-28424 234 16 are be AUX bracis-28424 234 17 generally generally ADV bracis-28424 234 18 poor poor ADJ bracis-28424 234 19 across across ADP bracis-28424 234 20 all all DET bracis-28424 234 21 table table NOUN bracis-28424 234 22 entries entry NOUN bracis-28424 234 23 since since SCONJ bracis-28424 234 24 reported report VERB bracis-28424 234 25 f f NUM bracis-28424 234 26 - - PUNCT bracis-28424 234 27 score score NOUN bracis-28424 234 28 values value NOUN bracis-28424 234 29 are be AUX bracis-28424 234 30 much much ADV bracis-28424 234 31 closer close ADJ bracis-28424 234 32 to to ADP bracis-28424 234 33 zero zero NUM bracis-28424 234 34 than than ADP bracis-28424 234 35 to to ADP bracis-28424 234 36 one one NUM bracis-28424 234 37 , , PUNCT bracis-28424 234 38 indicating indicate VERB bracis-28424 234 39 that that SCONJ bracis-28424 234 40 the the DET bracis-28424 234 41 msd msd NOUN bracis-28424 234 42 is be AUX bracis-28424 234 43 rather rather ADV bracis-28424 234 44 a a DET bracis-28424 234 45 difficult difficult ADJ bracis-28424 234 46 problem problem NOUN bracis-28424 234 47 . . PUNCT bracis-28424 235 1 however however ADV bracis-28424 235 2 , , PUNCT bracis-28424 235 3 results result NOUN bracis-28424 235 4 in in ADP bracis-28424 235 5 general general ADJ bracis-28424 235 6 improve improve VERB bracis-28424 235 7 with with ADP bracis-28424 235 8 the the DET bracis-28424 235 9 increasing increase VERB bracis-28424 235 10 number number NOUN bracis-28424 235 11 of of ADP bracis-28424 235 12 epidemic epidemic NOUN bracis-28424 235 13 sources source NOUN bracis-28424 235 14 . . PUNCT bracis-28424 236 1 note note VERB bracis-28424 236 2 that that SCONJ bracis-28424 236 3 sage sage NOUN bracis-28424 236 4 stands stand VERB bracis-28424 236 5 out out ADP bracis-28424 236 6 showing show VERB bracis-28424 236 7 the the DET bracis-28424 236 8 best good ADJ bracis-28424 236 9 performance performance NOUN bracis-28424 236 10 across across ADP bracis-28424 236 11 the the DET bracis-28424 236 12 table table NOUN bracis-28424 236 13 for for ADP bracis-28424 236 14 all all DET bracis-28424 236 15 scenarios scenario NOUN bracis-28424 236 16 , , PUNCT bracis-28424 236 17 for for ADP bracis-28424 236 18 maximum maximum ADJ bracis-28424 236 19 and and CCONJ bracis-28424 236 20 average average ADJ bracis-28424 236 21 performance performance NOUN bracis-28424 236 22 . . PUNCT bracis-28424 237 1 also also ADV bracis-28424 237 2 , , PUNCT bracis-28424 237 3 the the DET bracis-28424 237 4 gap gap NOUN bracis-28424 237 5 between between ADP bracis-28424 237 6 sage sage NOUN bracis-28424 237 7 and and CCONJ bracis-28424 237 8 the the DET bracis-28424 237 9 other other ADJ bracis-28424 237 10 models model NOUN bracis-28424 237 11 increase increase VERB bracis-28424 237 12 along along ADP bracis-28424 237 13 with with ADP bracis-28424 237 14 the the DET bracis-28424 237 15 number number NOUN bracis-28424 237 16 of of ADP bracis-28424 237 17 sources source NOUN bracis-28424 237 18 : : PUNCT bracis-28424 237 19 sage sage VERB bracis-28424 237 20 ’s ’s PART bracis-28424 237 21 f f NOUN bracis-28424 237 22 - - PUNCT bracis-28424 237 23 score score NOUN bracis-28424 237 24 on on ADP bracis-28424 237 25 facebook facebook PROPN bracis-28424 237 26 ego ego NOUN bracis-28424 237 27 with with ADP bracis-28424 237 28 10 10 NUM bracis-28424 237 29 sources source NOUN bracis-28424 237 30 are be AUX bracis-28424 237 31 five five NUM bracis-28424 237 32 times time NOUN bracis-28424 237 33 larger large ADJ bracis-28424 237 34 than than ADP bracis-28424 237 35 the the DET bracis-28424 237 36 second second ADJ bracis-28424 237 37 best good ADJ bracis-28424 237 38 model model NOUN bracis-28424 237 39 . . PUNCT bracis-28424 238 1 6 6 NUM bracis-28424 238 2 conclusion conclusion NOUN bracis-28424 238 3 identifying identify VERB bracis-28424 238 4 multiple multiple ADJ bracis-28424 238 5 epidemics epidemic NOUN bracis-28424 238 6 source source NOUN bracis-28424 238 7 nodes node NOUN bracis-28424 238 8 from from ADP bracis-28424 238 9 the the DET bracis-28424 238 10 observation observation NOUN bracis-28424 238 11 of of ADP bracis-28424 238 12 an an DET bracis-28424 238 13 epidemic epidemic NOUN bracis-28424 238 14 network network NOUN bracis-28424 238 15 is be AUX bracis-28424 238 16 a a DET bracis-28424 238 17 challenging challenging ADJ bracis-28424 238 18 problem problem NOUN bracis-28424 238 19 that that PRON bracis-28424 238 20 has have AUX bracis-28424 238 21 recently recently ADV bracis-28424 238 22 been be AUX bracis-28424 238 23 explored explore VERB bracis-28424 238 24 in in ADP bracis-28424 238 25 the the DET bracis-28424 238 26 literature literature NOUN bracis-28424 238 27 . . PUNCT bracis-28424 239 1 this this DET bracis-28424 239 2 work work NOUN bracis-28424 239 3 proposed propose VERB bracis-28424 239 4 a a DET bracis-28424 239 5 framework framework NOUN bracis-28424 239 6 based base VERB bracis-28424 239 7 graph graph NOUN bracis-28424 239 8 neural neural ADJ bracis-28424 239 9 networks network NOUN bracis-28424 239 10 that that PRON bracis-28424 239 11 starts start VERB bracis-28424 239 12 by by ADP bracis-28424 239 13 generating generate VERB bracis-28424 239 14 features feature NOUN bracis-28424 239 15 for for ADP bracis-28424 239 16 nodes node NOUN bracis-28424 239 17 from from ADP bracis-28424 239 18 the the DET bracis-28424 239 19 observed observe VERB bracis-28424 239 20 epidemic epidemic NOUN bracis-28424 239 21 network network NOUN bracis-28424 239 22 . . PUNCT bracis-28424 240 1 these these DET bracis-28424 240 2 features feature NOUN bracis-28424 240 3 capture capture VERB bracis-28424 240 4 the the DET bracis-28424 240 5 infection infection NOUN bracis-28424 240 6 state state NOUN bracis-28424 240 7 of of ADP bracis-28424 240 8 k k PROPN bracis-28424 240 9 - - PUNCT bracis-28424 240 10 hop hop NOUN bracis-28424 240 11 neighborhoods neighborhood NOUN bracis-28424 240 12 around around ADP bracis-28424 240 13 the the DET bracis-28424 240 14 node node NOUN bracis-28424 240 15 . . PUNCT bracis-28424 241 1 finally finally ADV bracis-28424 241 2 , , PUNCT bracis-28424 241 3 a a DET bracis-28424 241 4 sage sage NOUN bracis-28424 241 5 supervised supervise VERB bracis-28424 241 6 trained train VERB bracis-28424 241 7 model model NOUN bracis-28424 241 8 is be AUX bracis-28424 241 9 used use VERB bracis-28424 241 10 to to PART bracis-28424 241 11 rank rank VERB bracis-28424 241 12 nodes node NOUN bracis-28424 241 13 of of ADP bracis-28424 241 14 a a DET bracis-28424 241 15 ( ( PUNCT bracis-28424 241 16 never never ADV bracis-28424 241 17 before before ADP bracis-28424 241 18 seen see VERB bracis-28424 241 19 ) ) PUNCT bracis-28424 241 20 epidemic epidemic NOUN bracis-28424 241 21 network network NOUN bracis-28424 241 22 with with ADP bracis-28424 241 23 respect respect NOUN bracis-28424 241 24 to to ADP bracis-28424 241 25 their their PRON bracis-28424 241 26 probabilities probability NOUN bracis-28424 241 27 of of ADP bracis-28424 241 28 being be AUX bracis-28424 241 29 an an DET bracis-28424 241 30 epidemic epidemic NOUN bracis-28424 241 31 source source NOUN bracis-28424 241 32 for for ADP bracis-28424 241 33 that that DET bracis-28424 241 34 observation observation NOUN bracis-28424 241 35 . . PUNCT bracis-28424 242 1 the the DET bracis-28424 242 2 proposed propose VERB bracis-28424 242 3 model model NOUN bracis-28424 242 4 is be AUX bracis-28424 242 5 generalizable generalizable ADJ bracis-28424 242 6 and and CCONJ bracis-28424 242 7 can can AUX bracis-28424 242 8 be be AUX bracis-28424 242 9 applied apply VERB bracis-28424 242 10 to to ADP bracis-28424 242 11 any any DET bracis-28424 242 12 network network NOUN bracis-28424 242 13 , , PUNCT bracis-28424 242 14 any any DET bracis-28424 242 15 si si NOUN bracis-28424 242 16 contagion contagion NOUN bracis-28424 242 17 model model NOUN bracis-28424 242 18 , , PUNCT bracis-28424 242 19 and and CCONJ bracis-28424 242 20 any any DET bracis-28424 242 21 number number NOUN bracis-28424 242 22 of of ADP bracis-28424 242 23 epidemic epidemic NOUN bracis-28424 242 24 sources source NOUN bracis-28424 242 25 . . PUNCT bracis-28424 243 1 the the DET bracis-28424 243 2 performance performance NOUN bracis-28424 243 3 of of ADP bracis-28424 243 4 the the DET bracis-28424 243 5 proposed propose VERB bracis-28424 243 6 framework framework NOUN bracis-28424 243 7 was be AUX bracis-28424 243 8 evaluated evaluate VERB bracis-28424 243 9 on on ADP bracis-28424 243 10 two two NUM bracis-28424 243 11 random random ADJ bracis-28424 243 12 network network NOUN bracis-28424 243 13 models model NOUN bracis-28424 243 14 and and CCONJ bracis-28424 243 15 two two NUM bracis-28424 243 16 real real ADJ bracis-28424 243 17 networks network NOUN bracis-28424 243 18 , , PUNCT bracis-28424 243 19 along along ADP bracis-28424 243 20 with with ADP bracis-28424 243 21 two two NUM bracis-28424 243 22 evaluation evaluation NOUN bracis-28424 243 23 scenarios scenario NOUN bracis-28424 243 24 ( ( PUNCT bracis-28424 243 25 source source NOUN bracis-28424 243 26 nodes node NOUN bracis-28424 243 27 and and CCONJ bracis-28424 243 28 source source NOUN bracis-28424 243 29 nodes node NOUN bracis-28424 243 30 with with ADP bracis-28424 243 31 their their PRON bracis-28424 243 32 neighbors neighbor NOUN bracis-28424 243 33 ) ) PUNCT bracis-28424 243 34 . . PUNCT bracis-28424 244 1 results result NOUN bracis-28424 244 2 highlight highlight VERB bracis-28424 244 3 the the DET bracis-28424 244 4 importance importance NOUN bracis-28424 244 5 of of ADP bracis-28424 244 6 the the DET bracis-28424 244 7 network network NOUN bracis-28424 244 8 structure structure NOUN bracis-28424 244 9 on on ADP bracis-28424 244 10 the the DET bracis-28424 244 11 framework framework NOUN bracis-28424 244 12 ’s ’s PART bracis-28424 244 13 performance performance NOUN bracis-28424 244 14 . . PUNCT bracis-28424 245 1 besides besides ADV bracis-28424 245 2 , , PUNCT bracis-28424 245 3 results result NOUN bracis-28424 245 4 indicate indicate VERB bracis-28424 245 5 that that SCONJ bracis-28424 245 6 performance performance NOUN bracis-28424 245 7 improves improve VERB bracis-28424 245 8 when when SCONJ bracis-28424 245 9 the the DET bracis-28424 245 10 number number NOUN bracis-28424 245 11 of of ADP bracis-28424 245 12 sources source NOUN bracis-28424 245 13 is be AUX bracis-28424 245 14 larger large ADJ bracis-28424 245 15 , , PUNCT bracis-28424 245 16 and and CCONJ bracis-28424 245 17 decreases decrease NOUN bracis-28424 245 18 as as SCONJ bracis-28424 245 19 the the DET bracis-28424 245 20 fraction fraction NOUN bracis-28424 245 21 of of ADP bracis-28424 245 22 infected infected ADJ bracis-28424 245 23 nodes node NOUN bracis-28424 245 24 increases increase VERB bracis-28424 245 25 in in ADP bracis-28424 245 26 the the DET bracis-28424 245 27 observation observation NOUN bracis-28424 245 28 . . PUNCT bracis-28424 246 1 results result NOUN bracis-28424 246 2 also also ADV bracis-28424 246 3 indicate indicate VERB bracis-28424 246 4 that that SCONJ bracis-28424 246 5 a a DET bracis-28424 246 6 single single ADJ bracis-28424 246 7 model model NOUN bracis-28424 246 8 does do AUX bracis-28424 246 9 not not PART bracis-28424 246 10 perform perform VERB bracis-28424 246 11 well well ADV bracis-28424 246 12 when when SCONJ bracis-28424 246 13 considering consider VERB bracis-28424 246 14 various various ADJ bracis-28424 246 15 scenarios scenario NOUN bracis-28424 246 16 ( ( PUNCT bracis-28424 246 17 with with ADP bracis-28424 246 18 the the DET bracis-28424 246 19 exception exception NOUN bracis-28424 246 20 of of ADP bracis-28424 246 21 low low ADJ bracis-28424 246 22 infection infection NOUN bracis-28424 246 23 rates rate NOUN bracis-28424 246 24 and and CCONJ bracis-28424 246 25 random random ADJ bracis-28424 246 26 network network NOUN bracis-28424 246 27 models model NOUN bracis-28424 246 28 ) ) PUNCT bracis-28424 246 29 . . PUNCT bracis-28424 247 1 finally finally ADV bracis-28424 247 2 , , PUNCT bracis-28424 247 3 the the DET bracis-28424 247 4 proposed propose VERB bracis-28424 247 5 framework framework NOUN bracis-28424 247 6 significantly significantly ADV bracis-28424 247 7 outperformed outperform VERB bracis-28424 247 8 recent recent ADJ bracis-28424 247 9 prior prior ADJ bracis-28424 247 10 works work NOUN bracis-28424 247 11 in in ADP bracis-28424 247 12 all all DET bracis-28424 247 13 scenarios scenario NOUN bracis-28424 247 14 where where SCONJ bracis-28424 247 15 a a DET bracis-28424 247 16 direct direct ADJ bracis-28424 247 17 comparison comparison NOUN bracis-28424 247 18 was be AUX bracis-28424 247 19 possible possible ADJ bracis-28424 247 20 . . PUNCT bracis-28424 248 1 in in ADP bracis-28424 248 2 general general ADJ bracis-28424 248 3 , , PUNCT bracis-28424 248 4 reported report VERB bracis-28424 248 5 values value NOUN bracis-28424 248 6 for for ADP bracis-28424 248 7 f1 f1 NOUN bracis-28424 248 8 - - PUNCT bracis-28424 248 9 score score NOUN bracis-28424 248 10 and and CCONJ bracis-28424 248 11 other other ADJ bracis-28424 248 12 metrics metric NOUN bracis-28424 248 13 ( ( PUNCT bracis-28424 248 14 precision precision NOUN bracis-28424 248 15 and and CCONJ bracis-28424 248 16 recall recall NOUN bracis-28424 248 17 ) ) PUNCT bracis-28424 248 18 are be AUX bracis-28424 248 19 low low ADJ bracis-28424 248 20 both both CCONJ bracis-28424 248 21 here here ADV bracis-28424 248 22 and and CCONJ bracis-28424 248 23 in in ADP bracis-28424 248 24 prior prior ADJ bracis-28424 248 25 works work NOUN bracis-28424 248 26 , , PUNCT bracis-28424 248 27 but but CCONJ bracis-28424 248 28 this this PRON bracis-28424 248 29 is be AUX bracis-28424 248 30 an an DET bracis-28424 248 31 indication indication NOUN bracis-28424 248 32 that that SCONJ bracis-28424 248 33 detecting detect VERB bracis-28424 248 34 multiple multiple ADJ bracis-28424 248 35 epidemic epidemic NOUN bracis-28424 248 36 sources source NOUN bracis-28424 248 37 is be AUX bracis-28424 248 38 a a DET bracis-28424 248 39 challenging challenging ADJ bracis-28424 248 40 problem problem NOUN bracis-28424 248 41 . . PUNCT bracis-28424 249 1 future future ADJ bracis-28424 249 2 works work NOUN bracis-28424 249 3 can can AUX bracis-28424 249 4 explore explore VERB bracis-28424 249 5 node node ADJ bracis-28424 249 6 features feature NOUN bracis-28424 249 7 and and CCONJ bracis-28424 249 8 classification classification NOUN bracis-28424 249 9 model model NOUN bracis-28424 249 10 in in ADP bracis-28424 249 11 search search NOUN bracis-28424 249 12 of of ADP bracis-28424 249 13 more more ADV bracis-28424 249 14 promising promising ADJ bracis-28424 249 15 approaches approach NOUN bracis-28424 249 16 . . PUNCT bracis-28424 250 1 notes note NOUN bracis-28424 250 2 1.accessible 1.accessible NUM bracis-28424 250 3 on on ADP bracis-28424 250 4 : : PUNCT bracis-28424 250 5 https://github.com/rodrigohaddad/multiple-source-detector-gnn https://github.com/rodrigohaddad/multiple-source-detector-gnn NOUN bracis-28424 250 6 . . PUNCT bracis-28424 251 1 references reference NOUN bracis-28424 251 2 barabási barabási NOUN bracis-28424 251 3 , , PUNCT bracis-28424 251 4 a.l a.l PROPN bracis-28424 251 5 . . PROPN bracis-28424 251 6 , , PUNCT bracis-28424 251 7 pósfai pósfai NOUN bracis-28424 251 8 , , PUNCT bracis-28424 251 9 m. m. NOUN bracis-28424 251 10 : : PUNCT bracis-28424 251 11 network network NOUN bracis-28424 251 12 science science PROPN bracis-28424 251 13 . . PUNCT bracis-28424 252 1 cambridge cambridge PROPN bracis-28424 252 2 university university PROPN bracis-28424 252 3 press press PROPN bracis-28424 252 4 , , PUNCT bracis-28424 252 5 cambridge cambridge PROPN bracis-28424 252 6 ( ( PUNCT bracis-28424 252 7 2016 2016 NUM bracis-28424 252 8 ) ) PUNCT bracis-28424 252 9 google google PROPN bracis-28424 252 10 scholar scholar NOUN bracis-28424 252 11     SPACE bracis-28424 252 12 david david PROPN bracis-28424 252 13 , , PUNCT bracis-28424 252 14 e. e. PROPN bracis-28424 252 15 , , PUNCT bracis-28424 252 16 jon jon PROPN bracis-28424 252 17 , , PUNCT bracis-28424 252 18 k. k. PROPN bracis-28424 252 19 : : PUNCT bracis-28424 252 20 networks network NOUN bracis-28424 252 21 , , PUNCT bracis-28424 252 22 crowds crowd NOUN bracis-28424 252 23 , , PUNCT bracis-28424 252 24 and and CCONJ bracis-28424 252 25 markets market NOUN bracis-28424 252 26 : : PUNCT bracis-28424 252 27 reasoning reason VERB bracis-28424 252 28 about about ADP bracis-28424 252 29 a a DET bracis-28424 252 30 highly highly ADV bracis-28424 252 31 connected connected ADJ bracis-28424 252 32 world world NOUN bracis-28424 252 33 . . PUNCT bracis-28424 253 1 cambridge cambridge PROPN bracis-28424 253 2 university university PROPN bracis-28424 253 3 press press PROPN bracis-28424 253 4 , , PUNCT bracis-28424 253 5 new new PROPN bracis-28424 253 6 york york PROPN bracis-28424 253 7 ( ( PUNCT bracis-28424 253 8 2010 2010 NUM bracis-28424 253 9 ) ) PUNCT bracis-28424 253 10 math math NOUN bracis-28424 253 11     SPACE bracis-28424 253 12 google google PROPN bracis-28424 253 13 scholar scholar NOUN bracis-28424 253 14     SPACE bracis-28424 253 15 dong dong NOUN bracis-28424 253 16 , , PUNCT bracis-28424 253 17 m. m. NOUN bracis-28424 253 18 , , PUNCT bracis-28424 253 19 zheng zheng PROPN bracis-28424 253 20 , , PUNCT bracis-28424 253 21 b. b. PROPN bracis-28424 253 22 , , PUNCT bracis-28424 253 23 quoc quoc PROPN bracis-28424 253 24 viet viet PROPN bracis-28424 253 25 hung hung PROPN bracis-28424 253 26 , , PUNCT bracis-28424 253 27 n. n. PROPN bracis-28424 253 28 , , PUNCT bracis-28424 253 29 su su PROPN bracis-28424 253 30 , , PUNCT bracis-28424 253 31 h. h. PROPN bracis-28424 253 32 , , PUNCT bracis-28424 253 33 li li PROPN bracis-28424 253 34 , , PUNCT bracis-28424 253 35 g. g. PROPN bracis-28424 253 36 : : PUNCT bracis-28424 253 37 multiple multiple ADJ bracis-28424 253 38 rumor rumor NOUN bracis-28424 253 39 source source NOUN bracis-28424 253 40 detection detection NOUN bracis-28424 253 41 with with ADP bracis-28424 253 42 graph graph NOUN bracis-28424 253 43 convolutional convolutional ADJ bracis-28424 253 44 networks network NOUN bracis-28424 253 45 . . PUNCT bracis-28424 254 1 in in ADP bracis-28424 254 2 : : PUNCT bracis-28424 254 3 acm acm PROPN bracis-28424 254 4 international international ADJ bracis-28424 254 5 conference conference NOUN bracis-28424 254 6 on on ADP bracis-28424 254 7 information information NOUN bracis-28424 254 8 and and CCONJ bracis-28424 254 9 knowledge knowledge NOUN bracis-28424 254 10 management management NOUN bracis-28424 254 11 ( ( PUNCT bracis-28424 254 12 cikm cikm NOUN bracis-28424 254 13 ) ) PUNCT bracis-28424 254 14 , , PUNCT bracis-28424 254 15 pp pp ADP bracis-28424 254 16 . . PUNCT bracis-28424 255 1 569–578 569–578 NUM bracis-28424 255 2 ( ( PUNCT bracis-28424 255 3 2019 2019 NUM bracis-28424 255 4 ) ) PUNCT bracis-28424 255 5 google google PROPN bracis-28424 255 6 scholar scholar NOUN bracis-28424 255 7     SPACE bracis-28424 255 8 draief draief NOUN bracis-28424 255 9 , , PUNCT bracis-28424 255 10 m. m. NOUN bracis-28424 255 11 , , PUNCT bracis-28424 255 12 massouli massouli PROPN bracis-28424 255 13 , , PUNCT bracis-28424 255 14 l. l. PROPN bracis-28424 255 15 : : PUNCT bracis-28424 255 16 epidemics epidemic NOUN bracis-28424 255 17 and and CCONJ bracis-28424 255 18 rumours rumour NOUN bracis-28424 255 19 in in ADP bracis-28424 255 20 complex complex ADJ bracis-28424 255 21 networks network NOUN bracis-28424 255 22 . . PUNCT bracis-28424 256 1 cambridge cambridge PROPN bracis-28424 256 2 university university PROPN bracis-28424 256 3 press press PROPN bracis-28424 256 4 , , PUNCT bracis-28424 256 5 cambridge cambridge PROPN bracis-28424 256 6 ( ( PUNCT bracis-28424 256 7 2010 2010 NUM bracis-28424 256 8 ) ) PUNCT bracis-28424 256 9 math math NOUN bracis-28424 256 10     SPACE bracis-28424 256 11 google google PROPN bracis-28424 256 12 scholar scholar NOUN bracis-28424 256 13     SPACE bracis-28424 256 14 feizi feizi NOUN bracis-28424 256 15 , , PUNCT bracis-28424 256 16 s. s. PROPN bracis-28424 256 17 , , PUNCT bracis-28424 256 18 médard médard PROPN bracis-28424 256 19 , , PUNCT bracis-28424 256 20 m. m. NOUN bracis-28424 256 21 , , PUNCT bracis-28424 256 22 quon quon NOUN bracis-28424 256 23 , , PUNCT bracis-28424 256 24 g. g. PROPN bracis-28424 256 25 , , PUNCT bracis-28424 256 26 kellis kellis PROPN bracis-28424 256 27 , , PUNCT bracis-28424 256 28 m. m. NOUN bracis-28424 256 29 , , PUNCT bracis-28424 256 30 duffy duffy PROPN bracis-28424 256 31 , , PUNCT bracis-28424 256 32 k. k. PROPN bracis-28424 256 33 : : PUNCT bracis-28424 256 34 network network NOUN bracis-28424 256 35 infusion infusion NOUN bracis-28424 256 36 to to PART bracis-28424 256 37 infer infer VERB bracis-28424 256 38 information information NOUN bracis-28424 256 39 sources source NOUN bracis-28424 256 40 in in ADP bracis-28424 256 41 networks network NOUN bracis-28424 256 42 . . PUNCT bracis-28424 257 1 ieee ieee PROPN bracis-28424 257 2 trans trans PROPN bracis-28424 257 3 . . PUNCT bracis-28424 258 1 netw netw PROPN bracis-28424 258 2 . . PUNCT bracis-28424 259 1 sci sci PROPN bracis-28424 259 2 . . PUNCT bracis-28424 260 1 eng eng PROPN bracis-28424 260 2 . . PROPN bracis-28424 260 3 6(3 6(3 NUM bracis-28424 260 4 ) ) PUNCT bracis-28424 260 5 , , PUNCT bracis-28424 260 6 402–417 402–417 NUM bracis-28424 260 7 ( ( PUNCT bracis-28424 260 8 2019 2019 NUM bracis-28424 260 9 ) ) PUNCT bracis-28424 260 10 article article NOUN bracis-28424 260 11     SPACE bracis-28424 260 12 mathscinet mathscinet NOUN bracis-28424 260 13     SPACE bracis-28424 260 14 google google PROPN bracis-28424 260 15 scholar scholar NOUN bracis-28424 260 16     SPACE bracis-28424 260 17 fey fey PROPN bracis-28424 260 18 , , PUNCT bracis-28424 260 19 m. m. NOUN bracis-28424 260 20 , , PUNCT bracis-28424 260 21 lenssen lenssen NOUN bracis-28424 260 22 , , PUNCT bracis-28424 260 23 j.e j.e PROPN bracis-28424 260 24 . . PROPN bracis-28424 260 25 : : PUNCT bracis-28424 260 26 fast fast ADJ bracis-28424 260 27 graph graph NOUN bracis-28424 260 28 representation representation NOUN bracis-28424 260 29 learning learn VERB bracis-28424 260 30 with with ADP bracis-28424 260 31 pytorch pytorch NOUN bracis-28424 260 32 geometric geometric ADJ bracis-28424 260 33 . . PUNCT bracis-28424 261 1 in in ADP bracis-28424 261 2 : : PUNCT bracis-28424 261 3 iclr iclr NOUN bracis-28424 261 4 workshop workshop NOUN bracis-28424 261 5 on on ADP bracis-28424 261 6 representation representation NOUN bracis-28424 261 7 learning learn VERB bracis-28424 261 8 on on ADP bracis-28424 261 9 graphs graph NOUN bracis-28424 261 10 and and CCONJ bracis-28424 261 11 manifolds manifold NOUN bracis-28424 261 12 ( ( PUNCT bracis-28424 261 13 2019 2019 NUM bracis-28424 261 14 ) ) PUNCT bracis-28424 261 15 google google PROPN bracis-28424 261 16 scholar scholar NOUN bracis-28424 261 17     SPACE bracis-28424 261 18 firth firth PROPN bracis-28424 261 19 , , PUNCT bracis-28424 261 20 j. j. PROPN bracis-28424 261 21 , , PUNCT bracis-28424 261 22 hellewell hellewell PROPN bracis-28424 261 23 , , PUNCT bracis-28424 261 24 j. j. PROPN bracis-28424 261 25 , , PUNCT bracis-28424 261 26 klepac klepac PROPN bracis-28424 261 27 , , PUNCT bracis-28424 261 28 p. p. NOUN bracis-28424 261 29 , , PUNCT bracis-28424 261 30 kissler kissler PROPN bracis-28424 261 31 , , PUNCT bracis-28424 261 32 s. s. PROPN bracis-28424 261 33 , , PUNCT bracis-28424 261 34 kucharski kucharski PROPN bracis-28424 261 35 , , PUNCT bracis-28424 261 36 a. a. NOUN bracis-28424 261 37 , , PUNCT bracis-28424 261 38 spurgin spurgin NOUN bracis-28424 261 39 , , PUNCT bracis-28424 261 40 l. l. PROPN bracis-28424 261 41 : : PUNCT bracis-28424 261 42 using use VERB bracis-28424 261 43 a a DET bracis-28424 261 44 real real ADJ bracis-28424 261 45 - - PUNCT bracis-28424 261 46 world world NOUN bracis-28424 261 47 network network NOUN bracis-28424 261 48 to to PART bracis-28424 261 49 model model VERB bracis-28424 261 50 localized localize VERB bracis-28424 261 51 covid-19 covid-19 PROPN bracis-28424 261 52 control control NOUN bracis-28424 261 53 strategies strategy NOUN bracis-28424 261 54 . . PUNCT bracis-28424 262 1 nat nat PROPN bracis-28424 262 2 . . PUNCT bracis-28424 263 1 med med PROPN bracis-28424 263 2 . . PROPN bracis-28424 263 3 26 26 NUM bracis-28424 263 4 , , PUNCT bracis-28424 263 5 1616–1622 1616–1622 NUM bracis-28424 263 6 ( ( PUNCT bracis-28424 263 7 2020 2020 NUM bracis-28424 263 8 ) ) PUNCT bracis-28424 263 9 article article NOUN bracis-28424 263 10     SPACE bracis-28424 263 11 google google PROPN bracis-28424 263 12 scholar scholar NOUN bracis-28424 263 13     SPACE bracis-28424 263 14 gilbert gilbert PROPN bracis-28424 263 15 , , PUNCT bracis-28424 263 16 e.n e.n PROPN bracis-28424 263 17 . . PROPN bracis-28424 263 18 : : PUNCT bracis-28424 263 19 random random ADJ bracis-28424 263 20 graphs graph NOUN bracis-28424 263 21 . . PUNCT bracis-28424 264 1 ann ann PROPN bracis-28424 264 2 . . PUNCT bracis-28424 264 3 math math PROPN bracis-28424 264 4 . . PUNCT bracis-28424 265 1 stat stat PROPN bracis-28424 265 2 . . PUNCT bracis-28424 266 1 30(4 30(4 NUM bracis-28424 266 2 ) ) PUNCT bracis-28424 266 3 , , PUNCT bracis-28424 266 4 1141–1144 1141–1144 NUM bracis-28424 266 5 ( ( PUNCT bracis-28424 266 6 1959 1959 NUM bracis-28424 266 7 ) ) PUNCT bracis-28424 266 8 article article NOUN bracis-28424 266 9     SPACE bracis-28424 266 10 math math NOUN bracis-28424 266 11     SPACE bracis-28424 266 12 google google PROPN bracis-28424 266 13 scholar scholar NOUN bracis-28424 266 14     SPACE bracis-28424 266 15 hamilton hamilton PROPN bracis-28424 266 16 , , PUNCT bracis-28424 266 17 w.l w.l PROPN bracis-28424 266 18 . . PROPN bracis-28424 266 19 , , PUNCT bracis-28424 266 20 ying ying PROPN bracis-28424 266 21 , , PUNCT bracis-28424 266 22 r. r. PROPN bracis-28424 266 23 , , PUNCT bracis-28424 266 24 leskovec leskovec PROPN bracis-28424 266 25 , , PUNCT bracis-28424 266 26 j. j. PROPN bracis-28424 266 27 : : PUNCT bracis-28424 266 28 inductive inductive ADJ bracis-28424 266 29 representation representation NOUN bracis-28424 266 30 learning learn VERB bracis-28424 266 31 on on ADP bracis-28424 266 32 large large ADJ bracis-28424 266 33 graphs graph NOUN bracis-28424 266 34 . . PUNCT bracis-28424 267 1 in in ADP bracis-28424 267 2 : : PUNCT bracis-28424 267 3 neurips neurip NOUN bracis-28424 267 4 , , PUNCT bracis-28424 267 5 p. p. NOUN bracis-28424 267 6 1025–1035 1025–1035 NUM bracis-28424 267 7 ( ( PUNCT bracis-28424 267 8 2017 2017 NUM bracis-28424 267 9 ) ) PUNCT bracis-28424 267 10 google google PROPN bracis-28424 267 11 scholar scholar NOUN bracis-28424 267 12     SPACE bracis-28424 267 13 jiang jiang PROPN bracis-28424 267 14 , , PUNCT bracis-28424 267 15 j. j. PROPN bracis-28424 267 16 , , PUNCT bracis-28424 267 17 wen wen PROPN bracis-28424 267 18 , , PUNCT bracis-28424 267 19 s. s. PROPN bracis-28424 267 20 , , PUNCT bracis-28424 267 21 yu yu PROPN bracis-28424 267 22 , , PUNCT bracis-28424 267 23 s. s. PROPN bracis-28424 267 24 , , PUNCT bracis-28424 267 25 xiang xiang PROPN bracis-28424 267 26 , , PUNCT bracis-28424 267 27 y. y. PROPN bracis-28424 267 28 , , PUNCT bracis-28424 267 29 zhou zhou PROPN bracis-28424 267 30 , , PUNCT bracis-28424 267 31 w. w. PROPN bracis-28424 267 32 : : PUNCT bracis-28424 267 33 k k X bracis-28424 267 34 - - PUNCT bracis-28424 267 35 center center NOUN bracis-28424 267 36 : : PUNCT bracis-28424 267 37 an an DET bracis-28424 267 38 approach approach NOUN bracis-28424 267 39 on on ADP bracis-28424 267 40 the the DET bracis-28424 267 41 multi multi ADJ bracis-28424 267 42 - - ADJ bracis-28424 267 43 source source NOUN bracis-28424 267 44 identification identification NOUN bracis-28424 267 45 of of ADP bracis-28424 267 46 information information NOUN bracis-28424 267 47 diffusion diffusion NOUN bracis-28424 267 48 . . PUNCT bracis-28424 268 1 ieee ieee PROPN bracis-28424 268 2 trans trans PROPN bracis-28424 268 3 . . PROPN bracis-28424 268 4 inf inf PROPN bracis-28424 268 5 . . PUNCT bracis-28424 268 6 forensics forensic NOUN bracis-28424 268 7 secur secur PROPN bracis-28424 268 8 . . PUNCT bracis-28424 269 1 10(12 10(12 NUM bracis-28424 269 2 ) ) PUNCT bracis-28424 269 3 , , PUNCT bracis-28424 269 4 2616–2626 2616–2626 NUM bracis-28424 269 5 ( ( PUNCT bracis-28424 269 6 2015 2015 NUM bracis-28424 269 7 ) ) PUNCT bracis-28424 269 8 article article NOUN bracis-28424 269 9     SPACE bracis-28424 269 10 google google PROPN bracis-28424 269 11 scholar scholar NOUN bracis-28424 269 12     SPACE bracis-28424 269 13 jiang jiang PROPN bracis-28424 269 14 , , PUNCT bracis-28424 269 15 j. j. PROPN bracis-28424 269 16 , , PUNCT bracis-28424 269 17 wen wen PROPN bracis-28424 269 18 , , PUNCT bracis-28424 269 19 s. s. PROPN bracis-28424 269 20 , , PUNCT bracis-28424 269 21 yu yu PROPN bracis-28424 269 22 , , PUNCT bracis-28424 269 23 s. s. PROPN bracis-28424 269 24 , , PUNCT bracis-28424 269 25 xiang xiang PROPN bracis-28424 269 26 , , PUNCT bracis-28424 269 27 y. y. PROPN bracis-28424 269 28 , , PUNCT bracis-28424 269 29 zhou zhou PROPN bracis-28424 269 30 , , PUNCT bracis-28424 269 31 w. w. PROPN bracis-28424 269 32 : : PUNCT bracis-28424 269 33 identifying identify VERB bracis-28424 269 34 propagation propagation NOUN bracis-28424 269 35 sources source NOUN bracis-28424 269 36 in in ADP bracis-28424 269 37 networks network NOUN bracis-28424 269 38 : : PUNCT bracis-28424 269 39 state state NOUN bracis-28424 269 40 - - PUNCT bracis-28424 269 41 of of ADP bracis-28424 269 42 - - PUNCT bracis-28424 269 43 the the DET bracis-28424 269 44 - - PUNCT bracis-28424 269 45 art art NOUN bracis-28424 269 46 and and CCONJ bracis-28424 269 47 comparative comparative ADJ bracis-28424 269 48 studies study NOUN bracis-28424 269 49 . . PUNCT bracis-28424 270 1 ieee ieee PROPN bracis-28424 270 2 commun commun PROPN bracis-28424 270 3 . . PUNCT bracis-28424 271 1 surv surv PROPN bracis-28424 271 2 . . PUNCT bracis-28424 272 1 tutor tutor NOUN bracis-28424 272 2 . . PUNCT bracis-28424 273 1 19(1 19(1 NUM bracis-28424 273 2 ) ) PUNCT bracis-28424 273 3 , , PUNCT bracis-28424 273 4 465–481 465–481 NUM bracis-28424 273 5 ( ( PUNCT bracis-28424 273 6 2017 2017 NUM bracis-28424 273 7 ) ) PUNCT bracis-28424 273 8 article article NOUN bracis-28424 273 9     SPACE bracis-28424 273 10 google google PROPN bracis-28424 273 11 scholar scholar NOUN bracis-28424 273 12     SPACE bracis-28424 273 13 kermack kermack NOUN bracis-28424 273 14 , , PUNCT bracis-28424 273 15 w.o w.o PROPN bracis-28424 273 16 . . PROPN bracis-28424 273 17 , , PUNCT bracis-28424 273 18 mckendrick mckendrick PROPN bracis-28424 273 19 , , PUNCT bracis-28424 273 20 a.g a.g PROPN bracis-28424 273 21 . . PROPN bracis-28424 273 22 , , PUNCT bracis-28424 273 23 walker walker PROPN bracis-28424 273 24 , , PUNCT bracis-28424 273 25 g.t g.t PROPN bracis-28424 273 26 . . PROPN bracis-28424 273 27 : : PUNCT bracis-28424 274 1 a a DET bracis-28424 274 2 contribution contribution NOUN bracis-28424 274 3 to to ADP bracis-28424 274 4 the the DET bracis-28424 274 5 mathematical mathematical ADJ bracis-28424 274 6 theory theory NOUN bracis-28424 274 7 of of ADP bracis-28424 274 8 epidemics epidemic NOUN bracis-28424 274 9 . . PUNCT bracis-28424 275 1 roy roy PROPN bracis-28424 275 2 . . PROPN bracis-28424 275 3 soc soc PROPN bracis-28424 275 4 . . PUNCT bracis-28424 276 1 lond lond PROPN bracis-28424 276 2 . . PUNCT bracis-28424 277 1 115(772 115(772 NUM bracis-28424 277 2 ) ) PUNCT bracis-28424 277 3 , , PUNCT bracis-28424 278 1 700–721 700–721 NUM bracis-28424 278 2 ( ( PUNCT bracis-28424 278 3 1927 1927 NUM bracis-28424 278 4 ) ) PUNCT bracis-28424 278 5 math math NOUN bracis-28424 278 6     SPACE bracis-28424 278 7 google google PROPN bracis-28424 278 8 scholar scholar NOUN bracis-28424 278 9     SPACE bracis-28424 278 10 leskovec leskovec NOUN bracis-28424 278 11 , , PUNCT bracis-28424 278 12 j. j. PROPN bracis-28424 278 13 , , PUNCT bracis-28424 278 14 mcauley mcauley PROPN bracis-28424 278 15 , , PUNCT bracis-28424 278 16 j. j. PROPN bracis-28424 278 17 : : PUNCT bracis-28424 278 18 learning learn VERB bracis-28424 278 19 to to PART bracis-28424 278 20 discover discover VERB bracis-28424 278 21 social social ADJ bracis-28424 278 22 circles circle NOUN bracis-28424 278 23 in in ADP bracis-28424 278 24 ego ego ADJ bracis-28424 278 25 networks network NOUN bracis-28424 278 26 . . PUNCT bracis-28424 279 1 in in ADP bracis-28424 279 2 : : PUNCT bracis-28424 279 3 nips nip NOUN bracis-28424 279 4 ( ( PUNCT bracis-28424 279 5 2012 2012 NUM bracis-28424 279 6 ) ) PUNCT bracis-28424 279 7 google google PROPN bracis-28424 279 8 scholar scholar NOUN bracis-28424 279 9     SPACE bracis-28424 279 10 newman newman PROPN bracis-28424 279 11 , , PUNCT bracis-28424 279 12 m.e m.e PROPN bracis-28424 279 13 . . PROPN bracis-28424 279 14 : : PUNCT bracis-28424 279 15 spread spread NOUN bracis-28424 279 16 of of ADP bracis-28424 279 17 epidemic epidemic NOUN bracis-28424 279 18 disease disease NOUN bracis-28424 279 19 on on ADP bracis-28424 279 20 networks network NOUN bracis-28424 279 21 . . PUNCT bracis-28424 280 1 phys phy NOUN bracis-28424 280 2 . . PUNCT bracis-28424 281 1 rev rev PROPN bracis-28424 281 2 . . PUNCT bracis-28424 282 1 e e PROPN bracis-28424 282 2 66(1 66(1 NOUN bracis-28424 282 3 ) ) PUNCT bracis-28424 282 4 , , PUNCT bracis-28424 282 5 016128 016128 NUM bracis-28424 282 6 ( ( PUNCT bracis-28424 282 7 2002 2002 NUM bracis-28424 282 8 ) ) PUNCT bracis-28424 282 9 article article NOUN bracis-28424 282 10     SPACE bracis-28424 282 11 mathscinet mathscinet NOUN bracis-28424 282 12     SPACE bracis-28424 282 13 google google PROPN bracis-28424 282 14 scholar scholar NOUN bracis-28424 282 15     SPACE bracis-28424 282 16 pastor pastor NOUN bracis-28424 282 17 - - PUNCT bracis-28424 282 18 satorras satorra NOUN bracis-28424 282 19 , , PUNCT bracis-28424 282 20 r. r. PROPN bracis-28424 282 21 , , PUNCT bracis-28424 282 22 castellano castellano NOUN bracis-28424 282 23 , , PUNCT bracis-28424 282 24 c. c. PROPN bracis-28424 282 25 , , PUNCT bracis-28424 282 26 van van PROPN bracis-28424 282 27 mieghem mieghem PROPN bracis-28424 282 28 , , PUNCT bracis-28424 282 29 p. p. PROPN bracis-28424 282 30 , , PUNCT bracis-28424 282 31 vespignani vespignani PROPN bracis-28424 282 32 , , PUNCT bracis-28424 282 33 a. a. NOUN bracis-28424 282 34 : : PUNCT bracis-28424 282 35 epidemic epidemic NOUN bracis-28424 282 36 processes process NOUN bracis-28424 282 37 in in ADP bracis-28424 282 38 complex complex ADJ bracis-28424 282 39 networks network NOUN bracis-28424 282 40 . . PUNCT bracis-28424 283 1 rev rev PROPN bracis-28424 283 2 . . PROPN bracis-28424 284 1 mod mod PROPN bracis-28424 284 2 . . PUNCT bracis-28424 285 1 phys phys PROPN bracis-28424 285 2 . . PUNCT bracis-28424 286 1 87(3 87(3 NUM bracis-28424 286 2 ) ) PUNCT bracis-28424 286 3 , , PUNCT bracis-28424 286 4 925 925 NUM bracis-28424 286 5 ( ( PUNCT bracis-28424 286 6 2015 2015 NUM bracis-28424 286 7 ) ) PUNCT bracis-28424 286 8 article article NOUN bracis-28424 286 9     SPACE bracis-28424 286 10 mathscinet mathscinet NOUN bracis-28424 286 11     SPACE bracis-28424 286 12 google google PROPN bracis-28424 286 13 scholar scholar NOUN bracis-28424 286 14     SPACE bracis-28424 286 15 paszke paszke NOUN bracis-28424 286 16 , , PUNCT bracis-28424 286 17 a. a. NOUN bracis-28424 286 18 , , PUNCT bracis-28424 286 19 gross gross ADJ bracis-28424 286 20 , , PUNCT bracis-28424 286 21 s. s. PROPN bracis-28424 286 22 , , PUNCT bracis-28424 286 23 chintala chintala PROPN bracis-28424 286 24 , , PUNCT bracis-28424 286 25 s. s. PROPN bracis-28424 286 26 : : PUNCT bracis-28424 286 27 pytorch pytorch NOUN bracis-28424 286 28 : : PUNCT bracis-28424 286 29 an an DET bracis-28424 286 30 imperative imperative ADJ bracis-28424 286 31 style style NOUN bracis-28424 286 32 , , PUNCT bracis-28424 286 33 high high ADJ bracis-28424 286 34 - - PUNCT bracis-28424 286 35 performance performance NOUN bracis-28424 286 36 deep deep ADJ bracis-28424 286 37 learning learning NOUN bracis-28424 286 38 library library NOUN bracis-28424 286 39 . . PUNCT bracis-28424 287 1 in in ADP bracis-28424 287 2 : : PUNCT bracis-28424 287 3 neurips neurip NOUN bracis-28424 287 4 , , PUNCT bracis-28424 287 5 pp pp ADV bracis-28424 287 6 . . PUNCT bracis-28424 288 1 8024–8035 8024–8035 NUM bracis-28424 288 2 ( ( PUNCT bracis-28424 288 3 2019 2019 NUM bracis-28424 288 4 ) ) PUNCT bracis-28424 288 5 google google PROPN bracis-28424 288 6 scholar scholar NOUN bracis-28424 288 7     SPACE bracis-28424 288 8 prakash prakash PROPN bracis-28424 288 9 , , PUNCT bracis-28424 288 10 b.a b.a PROPN bracis-28424 288 11 . . PROPN bracis-28424 288 12 , , PUNCT bracis-28424 288 13 vreeken vreeken VERB bracis-28424 288 14 , , PUNCT bracis-28424 288 15 j. j. PROPN bracis-28424 288 16 , , PUNCT bracis-28424 288 17 faloutsos faloutsos PROPN bracis-28424 288 18 , , PUNCT bracis-28424 288 19 c. c. NOUN bracis-28424 288 20 : : PUNCT bracis-28424 288 21 spotting spot VERB bracis-28424 288 22 culprits culprit NOUN bracis-28424 288 23 in in ADP bracis-28424 288 24 epidemics epidemic NOUN bracis-28424 288 25 : : PUNCT bracis-28424 288 26 how how SCONJ bracis-28424 288 27 many many ADJ bracis-28424 288 28 and and CCONJ bracis-28424 288 29 which which PRON bracis-28424 288 30 ones one NOUN bracis-28424 288 31 ? ? PUNCT bracis-28424 289 1 in in ADP bracis-28424 289 2 : : PUNCT bracis-28424 289 3 ieee ieee PROPN bracis-28424 289 4 international international ADJ bracis-28424 289 5 conference conference NOUN bracis-28424 289 6 on on ADP bracis-28424 289 7 data datum NOUN bracis-28424 289 8 mining mining NOUN bracis-28424 289 9 ( ( PUNCT bracis-28424 289 10 2012 2012 NUM bracis-28424 289 11 ) ) PUNCT bracis-28424 289 12 google google PROPN bracis-28424 289 13 scholar scholar NOUN bracis-28424 289 14     SPACE bracis-28424 289 15 shah shah NOUN bracis-28424 289 16 , , PUNCT bracis-28424 289 17 d. d. PROPN bracis-28424 289 18 , , PUNCT bracis-28424 289 19 zaman zaman PROPN bracis-28424 289 20 , , PUNCT bracis-28424 289 21 t. t. PROPN bracis-28424 289 22 : : PUNCT bracis-28424 289 23 rumors rumor NOUN bracis-28424 289 24 in in ADP bracis-28424 289 25 a a DET bracis-28424 289 26 network network NOUN bracis-28424 289 27 : : PUNCT bracis-28424 289 28 who who PRON bracis-28424 289 29 ’s ’ VERB bracis-28424 289 30 the the DET bracis-28424 289 31 culprit culprit NOUN bracis-28424 289 32 ? ? PUNCT bracis-28424 290 1 ieee ieee PROPN bracis-28424 290 2 trans trans PROPN bracis-28424 290 3 . . PROPN bracis-28424 290 4 inf inf PROPN bracis-28424 290 5 . . PROPN bracis-28424 290 6 theory theory NOUN bracis-28424 290 7 57(8 57(8 NUM bracis-28424 290 8 ) ) PUNCT bracis-28424 290 9 , , PUNCT bracis-28424 290 10 5163–5181 5163–5181 NUM bracis-28424 290 11 ( ( PUNCT bracis-28424 290 12 2011 2011 NUM bracis-28424 290 13 ) ) PUNCT bracis-28424 290 14 article article NOUN bracis-28424 290 15     SPACE bracis-28424 290 16 mathscinet mathscinet NOUN bracis-28424 290 17     SPACE bracis-28424 290 18 math math NOUN bracis-28424 290 19     SPACE bracis-28424 290 20 google google PROPN bracis-28424 290 21 scholar scholar NOUN bracis-28424 290 22     SPACE bracis-28424 290 23 shah shah NOUN bracis-28424 290 24 , , PUNCT bracis-28424 290 25 d. d. PROPN bracis-28424 290 26 , , PUNCT bracis-28424 290 27 zaman zaman PROPN bracis-28424 290 28 , , PUNCT bracis-28424 290 29 t. t. PROPN bracis-28424 290 30 : : PUNCT bracis-28424 290 31 rumor rumor NOUN bracis-28424 290 32 centrality centrality NOUN bracis-28424 290 33 : : PUNCT bracis-28424 290 34 a a DET bracis-28424 290 35 universal universal ADJ bracis-28424 290 36 source source NOUN bracis-28424 290 37 detector detector NOUN bracis-28424 290 38 . . PUNCT bracis-28424 291 1 in in ADP bracis-28424 291 2 : : PUNCT bracis-28424 291 3 acm acm PROPN bracis-28424 291 4 sigmetrics sigmetric NOUN bracis-28424 291 5 performance performance NOUN bracis-28424 291 6 evaluation evaluation NOUN bracis-28424 291 7 review review NOUN bracis-28424 291 8 , , PUNCT bracis-28424 291 9 vol vol NOUN bracis-28424 291 10 . . PROPN bracis-28424 291 11 40 40 NUM bracis-28424 291 12 , , PUNCT bracis-28424 291 13 pp pp ADJ bracis-28424 291 14 . . PUNCT bracis-28424 292 1 199–210 199–210 NUM bracis-28424 292 2 ( ( PUNCT bracis-28424 292 3 2012 2012 NUM bracis-28424 292 4 ) ) PUNCT bracis-28424 292 5 google google PROPN bracis-28424 292 6 scholar scholar NOUN bracis-28424 292 7     SPACE bracis-28424 292 8 shelke shelke NOUN bracis-28424 292 9 , , PUNCT bracis-28424 292 10 s. s. PROPN bracis-28424 292 11 , , PUNCT bracis-28424 292 12 attar attar PROPN bracis-28424 292 13 , , PUNCT bracis-28424 292 14 v. v. NOUN bracis-28424 292 15 : : PUNCT bracis-28424 292 16 source source NOUN bracis-28424 292 17 detection detection NOUN bracis-28424 292 18 of of ADP bracis-28424 292 19 rumor rumor NOUN bracis-28424 292 20 in in ADP bracis-28424 292 21 social social ADJ bracis-28424 292 22 network network NOUN bracis-28424 292 23 - - PUNCT bracis-28424 292 24 a a DET bracis-28424 292 25 review review NOUN bracis-28424 292 26 . . PUNCT bracis-28424 293 1 online online PROPN bracis-28424 293 2 soc soc PROPN bracis-28424 293 3 . . PUNCT bracis-28424 294 1 netw netw NOUN bracis-28424 294 2 . . PUNCT bracis-28424 295 1 media medium NOUN bracis-28424 295 2 9 9 NUM bracis-28424 295 3 , , PUNCT bracis-28424 295 4 30–42 30–42 NUM bracis-28424 295 5 ( ( PUNCT bracis-28424 295 6 2019 2019 NUM bracis-28424 295 7 ) ) PUNCT bracis-28424 295 8 article article NOUN bracis-28424 295 9     SPACE bracis-28424 295 10 google google PROPN bracis-28424 295 11 scholar scholar NOUN bracis-28424 295 12     SPACE bracis-28424 295 13 wang wang PROPN bracis-28424 295 14 , , PUNCT bracis-28424 295 15 z. z. PROPN bracis-28424 295 16 , , PUNCT bracis-28424 295 17 wang wang PROPN bracis-28424 295 18 , , PUNCT bracis-28424 295 19 c. c. PROPN bracis-28424 295 20 , , PUNCT bracis-28424 295 21 pei pei PROPN bracis-28424 295 22 , , PUNCT bracis-28424 295 23 j. j. PROPN bracis-28424 295 24 , , PUNCT bracis-28424 295 25 ye ye PROPN bracis-28424 295 26 , , PUNCT bracis-28424 295 27 x. x. NOUN bracis-28424 295 28 : : PUNCT bracis-28424 295 29 multiple multiple ADJ bracis-28424 295 30 source source NOUN bracis-28424 295 31 detection detection NOUN bracis-28424 295 32 without without ADP bracis-28424 295 33 knowing know VERB bracis-28424 295 34 the the DET bracis-28424 295 35 underlying underlie VERB bracis-28424 295 36 propagation propagation NOUN bracis-28424 295 37 model model NOUN bracis-28424 295 38 . . PUNCT bracis-28424 296 1 in in ADP bracis-28424 296 2 : : PUNCT bracis-28424 296 3 aaai aaai PROPN bracis-28424 296 4 conference conference PROPN bracis-28424 296 5 on on ADP bracis-28424 296 6 artificial artificial ADJ bracis-28424 296 7 intelligence intelligence NOUN bracis-28424 296 8 ( ( PUNCT bracis-28424 296 9 2017 2017 NUM bracis-28424 296 10 ) ) PUNCT bracis-28424 296 11 google google PROPN bracis-28424 296 12 scholar scholar NOUN bracis-28424 296 13     SPACE bracis-28424 296 14 watts watt NOUN bracis-28424 296 15 , , PUNCT bracis-28424 296 16 d.j d.j PROPN bracis-28424 296 17 . . PROPN bracis-28424 296 18 , , PUNCT bracis-28424 296 19 strogatz strogatz PROPN bracis-28424 296 20 , , PUNCT bracis-28424 296 21 s.h s.h PROPN bracis-28424 296 22 . . PROPN bracis-28424 296 23 : : PUNCT bracis-28424 296 24 collective collective ADJ bracis-28424 296 25 dynamics dynamic NOUN bracis-28424 296 26 of of ADP bracis-28424 296 27 ‘ ' PUNCT bracis-28424 296 28 small small ADJ bracis-28424 296 29 - - PUNCT bracis-28424 296 30 world world NOUN bracis-28424 296 31 ’ ' PUNCT bracis-28424 296 32 networks network NOUN bracis-28424 296 33 . . PUNCT bracis-28424 297 1 nature nature NOUN bracis-28424 297 2 393(6684 393(6684 NUM bracis-28424 297 3 ) ) PUNCT bracis-28424 297 4 , , PUNCT bracis-28424 297 5 440–442 440–442 NUM bracis-28424 297 6 ( ( PUNCT bracis-28424 297 7 1998 1998 NUM bracis-28424 297 8 ) ) PUNCT bracis-28424 297 9 article article NOUN bracis-28424 297 10     SPACE bracis-28424 297 11 math math NOUN bracis-28424 297 12     SPACE bracis-28424 297 13 google google PROPN bracis-28424 297 14 scholar scholar NOUN bracis-28424 297 15     SPACE bracis-28424 297 16 yu yu PROPN bracis-28424 297 17 , , PUNCT bracis-28424 297 18 p.d p.d PROPN bracis-28424 297 19 . . PROPN bracis-28424 297 20 , , PUNCT bracis-28424 297 21 tan tan PROPN bracis-28424 297 22 , , PUNCT bracis-28424 297 23 c.w c.w PROPN bracis-28424 297 24 . . PROPN bracis-28424 297 25 , , PUNCT bracis-28424 297 26 fu fu PROPN bracis-28424 297 27 , , PUNCT bracis-28424 297 28 h.l h.l PROPN bracis-28424 297 29 . . PROPN bracis-28424 297 30 : : PUNCT bracis-28424 297 31 epidemic epidemic NOUN bracis-28424 297 32 source source NOUN bracis-28424 297 33 detection detection NOUN bracis-28424 297 34 in in ADP bracis-28424 297 35 contact contact NOUN bracis-28424 297 36 tracing trace VERB bracis-28424 297 37 networks network NOUN bracis-28424 297 38 : : PUNCT bracis-28424 297 39 epidemic epidemic NOUN bracis-28424 297 40 centrality centrality NOUN bracis-28424 297 41 in in ADP bracis-28424 297 42 graphs graph NOUN bracis-28424 297 43 and and CCONJ bracis-28424 297 44 message message NOUN bracis-28424 297 45 - - PUNCT bracis-28424 297 46 passing pass VERB bracis-28424 297 47 algorithms algorithm NOUN bracis-28424 297 48 . . PUNCT bracis-28424 298 1 ieee ieee PROPN bracis-28424 298 2 j. j. PROPN bracis-28424 298 3 sel sel PROPN bracis-28424 298 4 . . PUNCT bracis-28424 299 1 topics topic NOUN bracis-28424 299 2 signal signal NOUN bracis-28424 299 3 process process NOUN bracis-28424 299 4 . . PUNCT bracis-28424 300 1 16(2 16(2 NUM bracis-28424 300 2 ) ) PUNCT bracis-28424 300 3 , , PUNCT bracis-28424 300 4 234–249 234–249 NUM bracis-28424 300 5 ( ( PUNCT bracis-28424 300 6 2022 2022 NUM bracis-28424 300 7 ) ) PUNCT bracis-28424 300 8 article article NOUN bracis-28424 300 9     SPACE bracis-28424 300 10 google google PROPN bracis-28424 300 11 scholar scholar NOUN bracis-28424 300 12     SPACE bracis-28424 300 13 zang zang PROPN bracis-28424 300 14 , , PUNCT bracis-28424 300 15 w. w. PROPN bracis-28424 300 16 , , PUNCT bracis-28424 300 17 zhang zhang PROPN bracis-28424 300 18 , , PUNCT bracis-28424 300 19 p. p. PROPN bracis-28424 300 20 , , PUNCT bracis-28424 300 21 zhou zhou PROPN bracis-28424 300 22 , , PUNCT bracis-28424 300 23 c. c. PROPN bracis-28424 300 24 , , PUNCT bracis-28424 300 25 guo guo PROPN bracis-28424 300 26 , , PUNCT bracis-28424 300 27 l. l. PROPN bracis-28424 300 28 : : PUNCT bracis-28424 300 29 locating locate VERB bracis-28424 300 30 multiple multiple ADJ bracis-28424 300 31 sources source NOUN bracis-28424 300 32 in in ADP bracis-28424 300 33 social social ADJ bracis-28424 300 34 networks network NOUN bracis-28424 300 35 under under ADP bracis-28424 300 36 the the DET bracis-28424 300 37 sir sir PROPN bracis-28424 300 38 model model NOUN bracis-28424 300 39 : : PUNCT bracis-28424 300 40 a a DET bracis-28424 300 41 divide divide NOUN bracis-28424 300 42 - - PUNCT bracis-28424 300 43 and and CCONJ bracis-28424 300 44 - - PUNCT bracis-28424 300 45 conquer conquer NOUN bracis-28424 300 46 approach approach NOUN bracis-28424 300 47 . . PUNCT bracis-28424 301 1 j. j. PROPN bracis-28424 301 2 comput comput PROPN bracis-28424 301 3 . . PUNCT bracis-28424 302 1 sci sci PROPN bracis-28424 302 2 . . PROPN bracis-28424 302 3 10 10 NUM bracis-28424 302 4 , , PUNCT bracis-28424 302 5 278–287 278–287 NUM bracis-28424 302 6 ( ( PUNCT bracis-28424 302 7 2015 2015 NUM bracis-28424 302 8 ) ) PUNCT bracis-28424 302 9 article article NOUN bracis-28424 302 10     SPACE bracis-28424 302 11 mathscinet mathscinet NOUN bracis-28424 302 12     SPACE bracis-28424 302 13 google google PROPN bracis-28424 302 14 scholar scholar NOUN bracis-28424 302 15     SPACE bracis-28424 302 16 download download NOUN bracis-28424 302 17 references reference NOUN bracis-28424 302 18 author author NOUN bracis-28424 302 19 information information NOUN bracis-28424 302 20 authors author NOUN bracis-28424 302 21 and and CCONJ bracis-28424 302 22 affiliations affiliation NOUN bracis-28424 302 23 system system NOUN bracis-28424 302 24 engineering engineering NOUN bracis-28424 302 25 and and CCONJ bracis-28424 302 26 computer computer NOUN bracis-28424 302 27 science science NOUN bracis-28424 302 28 ( ( PUNCT bracis-28424 302 29 pesc pesc PROPN bracis-28424 302 30 ) ) PUNCT bracis-28424 302 31 , , PUNCT bracis-28424 302 32 federal federal ADJ bracis-28424 302 33 university university PROPN bracis-28424 302 34 of of ADP bracis-28424 302 35 rio rio PROPN bracis-28424 302 36 de de PROPN bracis-28424 302 37 janeiro janeiro PROPN bracis-28424 302 38 ( ( PUNCT bracis-28424 302 39 ufrj ufrj PROPN bracis-28424 302 40 ) ) PUNCT bracis-28424 302 41 , , PUNCT bracis-28424 302 42 rio rio PROPN bracis-28424 302 43 de de PROPN bracis-28424 302 44 janeiro janeiro PROPN bracis-28424 302 45 , , PUNCT bracis-28424 302 46 brazil brazil PROPN bracis-28424 302 47 rodrigo rodrigo PROPN bracis-28424 302 48 gonçalves gonçalves PROPN bracis-28424 302 49 haddad haddad PROPN bracis-28424 302 50     SPACE bracis-28424 302 51 & & CCONJ bracis-28424 302 52     SPACE bracis-28424 302 53 daniel daniel PROPN bracis-28424 302 54 ratton ratton PROPN bracis-28424 302 55 figueiredo figueiredo PROPN bracis-28424 302 56 authors author NOUN bracis-28424 302 57 rodrigo rodrigo PROPN bracis-28424 302 58 gonçalves gonçalves PROPN bracis-28424 302 59 haddadview haddadview PROPN bracis-28424 302 60 author author NOUN bracis-28424 302 61 publications publication NOUN bracis-28424 302 62 search search NOUN bracis-28424 302 63 author author NOUN bracis-28424 302 64 on on ADP bracis-28424 302 65 : : PUNCT bracis-28424 302 66 pubmed pubmed PROPN bracis-28424 302 67     SPACE bracis-28424 302 68 google google PROPN bracis-28424 302 69 scholar scholar PROPN bracis-28424 302 70 daniel daniel PROPN bracis-28424 302 71 ratton ratton PROPN bracis-28424 302 72 figueiredoview figueiredoview PROPN bracis-28424 302 73 author author NOUN bracis-28424 302 74 publications publication VERB bracis-28424 302 75 search search NOUN bracis-28424 302 76 author author NOUN bracis-28424 302 77 on on ADP bracis-28424 302 78 : : PUNCT bracis-28424 302 79 pubmed pubmed PROPN bracis-28424 302 80     SPACE bracis-28424 302 81 google google PROPN bracis-28424 302 82 scholar scholar NOUN bracis-28424 302 83 corresponding correspond VERB bracis-28424 302 84 author author NOUN bracis-28424 302 85 correspondence correspondence NOUN bracis-28424 302 86 to to ADP bracis-28424 302 87 rodrigo rodrigo PROPN bracis-28424 302 88 gonçalves gonçalves PROPN bracis-28424 302 89 haddad haddad PROPN bracis-28424 302 90 . . PUNCT bracis-28424 303 1 editor editor NOUN bracis-28424 303 2 information information NOUN bracis-28424 303 3 editors editor NOUN bracis-28424 303 4 and and CCONJ bracis-28424 303 5 affiliations affiliation NOUN bracis-28424 303 6 federal federal PROPN bracis-28424 303 7 university university PROPN bracis-28424 303 8 of of ADP bracis-28424 303 9 são são PROPN bracis-28424 303 10 carlos carlos PROPN bracis-28424 303 11 , , PUNCT bracis-28424 303 12 são são PROPN bracis-28424 303 13 carlos carlos PROPN bracis-28424 303 14 , , PUNCT bracis-28424 303 15 brazil brazil PROPN bracis-28424 303 16 murilo murilo PROPN bracis-28424 303 17 c. c. PROPN bracis-28424 303 18 naldi naldi PROPN bracis-28424 303 19 centro centro PROPN bracis-28424 303 20 universitario universitario PROPN bracis-28424 303 21 da da PROPN bracis-28424 303 22 fei fei PROPN bracis-28424 303 23 , , PUNCT bracis-28424 303 24 são são PROPN bracis-28424 303 25 bernardo bernardo PROPN bracis-28424 303 26 do do AUX bracis-28424 303 27 campo campo PROPN bracis-28424 303 28 , , PUNCT bracis-28424 303 29 brazil brazil PROPN bracis-28424 303 30 reinaldo reinaldo PROPN bracis-28424 303 31 a. a. PROPN bracis-28424 303 32 c. c. PROPN bracis-28424 303 33 bianchi bianchi PROPN bracis-28424 303 34 rights right NOUN bracis-28424 303 35 and and CCONJ bracis-28424 303 36 permissions permission NOUN bracis-28424 303 37 reprints reprint NOUN bracis-28424 303 38 and and CCONJ bracis-28424 303 39 permissions permission VERB bracis-28424 303 40 copyright copyright NOUN bracis-28424 303 41 information information NOUN bracis-28424 303 42 © © ADP bracis-28424 303 43 2023 2023 NUM bracis-28424 303 44 the the DET bracis-28424 303 45 author(s author(s NOUN bracis-28424 303 46 ) ) PUNCT bracis-28424 303 47 , , PUNCT bracis-28424 303 48 under under ADP bracis-28424 303 49 exclusive exclusive ADJ bracis-28424 303 50 license license NOUN bracis-28424 303 51 to to ADP bracis-28424 303 52 springer springer NOUN bracis-28424 303 53 nature nature PROPN bracis-28424 303 54 switzerland switzerland PROPN bracis-28424 303 55 ag ag PROPN bracis-28424 303 56 about about ADP bracis-28424 303 57 this this DET bracis-28424 303 58 paper paper NOUN bracis-28424 303 59 cite cite VERB bracis-28424 303 60 this this DET bracis-28424 303 61 paper paper NOUN bracis-28424 303 62 haddad haddad PROPN bracis-28424 303 63 , , PUNCT bracis-28424 303 64 r.g r.g PROPN bracis-28424 303 65 . . PROPN bracis-28424 303 66 , , PUNCT bracis-28424 303 67 figueiredo figueiredo PROPN bracis-28424 303 68 , , PUNCT bracis-28424 303 69 d.r d.r PROPN bracis-28424 303 70 . . PROPN bracis-28424 303 71 ( ( PUNCT bracis-28424 303 72 2023 2023 NUM bracis-28424 303 73 ) ) PUNCT bracis-28424 303 74 . . PUNCT bracis-28424 304 1 detecting detect VERB bracis-28424 304 2 multiple multiple ADJ bracis-28424 304 3 epidemic epidemic NOUN bracis-28424 304 4 sources source NOUN bracis-28424 304 5 in in ADP bracis-28424 304 6     SPACE bracis-28424 304 7 network network NOUN bracis-28424 304 8 epidemics epidemic NOUN bracis-28424 304 9 using use VERB bracis-28424 304 10 graph graph NOUN bracis-28424 304 11 neural neural ADJ bracis-28424 304 12 networks network NOUN bracis-28424 304 13 . . PUNCT bracis-28424 305 1 in in ADP bracis-28424 305 2 : : PUNCT bracis-28424 305 3 naldi naldi PROPN bracis-28424 305 4 , , PUNCT bracis-28424 305 5 m.c m.c PROPN bracis-28424 305 6 . . PROPN bracis-28424 305 7 , , PUNCT bracis-28424 305 8 bianchi bianchi PROPN bracis-28424 305 9 , , PUNCT bracis-28424 305 10 r.a.c r.a.c ADP bracis-28424 305 11 . . PUNCT bracis-28424 305 12 ( ( PUNCT bracis-28424 305 13 eds ed NOUN bracis-28424 305 14 ) ) PUNCT bracis-28424 305 15 intelligent intelligent ADJ bracis-28424 305 16 systems system NOUN bracis-28424 305 17 . . PUNCT bracis-28424 306 1 bracis bracis PROPN bracis-28424 306 2 2023 2023 NUM bracis-28424 306 3 . . PUNCT bracis-28424 307 1 lecture lecture NOUN bracis-28424 307 2 notes note NOUN bracis-28424 307 3 in in ADP bracis-28424 307 4 computer computer NOUN bracis-28424 307 5 science science NOUN bracis-28424 307 6 ( ( PUNCT bracis-28424 307 7 ) ) PUNCT bracis-28424 307 8 , , PUNCT bracis-28424 307 9 vol vol NOUN bracis-28424 307 10 14197 14197 NUM bracis-28424 307 11 . . PUNCT bracis-28424 308 1 springer springer NOUN bracis-28424 308 2 , , PUNCT bracis-28424 308 3 cham cham PROPN bracis-28424 308 4 . . PUNCT bracis-28424 309 1 https://doi.org/10.1007/978-3-031-45392-2_22 https://doi.org/10.1007/978-3-031-45392-2_22 PROPN bracis-28424 309 2 download download NOUN bracis-28424 309 3 citation citation NOUN bracis-28424 309 4 .ris .ris PUNCT bracis-28424 310 1 .enw .enw PROPN bracis-28424 310 2 .bib .bib PUNCT bracis-28424 311 1 doi doi PROPN bracis-28424 311 2 : : PUNCT bracis-28424 311 3 https://doi.org/10.1007/978-3-031-45392-2_22 https://doi.org/10.1007/978-3-031-45392-2_22 NOUN bracis-28424 311 4 published publish VERB bracis-28424 311 5 : : PUNCT bracis-28424 311 6 12 12 NUM bracis-28424 311 7 october october PROPN bracis-28424 311 8 2023 2023 NUM bracis-28424 311 9 publisher publisher NOUN bracis-28424 311 10 name name NOUN bracis-28424 311 11 : : PUNCT bracis-28424 311 12 springer springer NOUN bracis-28424 311 13 , , PUNCT bracis-28424 311 14 cham cham PROPN bracis-28424 311 15 print print PROPN bracis-28424 311 16 isbn isbn PROPN bracis-28424 311 17 : : PUNCT bracis-28424 311 18 978 978 NUM bracis-28424 311 19 - - SYM bracis-28424 311 20 3 3 NUM bracis-28424 311 21 - - PUNCT bracis-28424 311 22 031 031 NUM bracis-28424 311 23 - - PUNCT bracis-28424 311 24 45391 45391 NUM bracis-28424 311 25 - - SYM bracis-28424 311 26 5 5 NUM bracis-28424 311 27 online online ADJ bracis-28424 311 28 isbn isbn NOUN bracis-28424 311 29 : : PUNCT bracis-28424 311 30 978 978 NUM bracis-28424 311 31 - - SYM bracis-28424 311 32 3 3 NUM bracis-28424 311 33 - - PUNCT bracis-28424 311 34 031 031 NUM bracis-28424 311 35 - - PUNCT bracis-28424 311 36 45392 45392 NUM bracis-28424 311 37 - - SYM bracis-28424 311 38 2 2 NUM bracis-28424 311 39 ebook ebook NOUN bracis-28424 311 40 packages package NOUN bracis-28424 311 41 : : PUNCT bracis-28424 311 42 computer computer NOUN bracis-28424 311 43 sciencecomputer sciencecomputer NOUN bracis-28424 311 44 science science NOUN bracis-28424 311 45 ( ( PUNCT bracis-28424 311 46 r0 r0 NOUN bracis-28424 311 47 ) ) PUNCT bracis-28424 311 48 share share VERB bracis-28424 311 49 this this DET bracis-28424 311 50 paper paper NOUN bracis-28424 311 51 anyone anyone PRON bracis-28424 311 52 you you PRON bracis-28424 311 53 share share VERB bracis-28424 311 54 the the DET bracis-28424 311 55 following follow VERB bracis-28424 311 56 link link NOUN bracis-28424 311 57 with with ADP bracis-28424 311 58 will will AUX bracis-28424 311 59 be be AUX bracis-28424 311 60 able able ADJ bracis-28424 311 61 to to PART bracis-28424 311 62 read read VERB bracis-28424 311 63 this this DET bracis-28424 311 64 content content NOUN bracis-28424 311 65 : : PUNCT bracis-28424 311 66 get get VERB bracis-28424 311 67 shareable shareable ADJ bracis-28424 311 68 linksorry linksorry NOUN bracis-28424 311 69 , , PUNCT bracis-28424 311 70 a a DET bracis-28424 311 71 shareable shareable ADJ bracis-28424 311 72 link link NOUN bracis-28424 311 73 is be AUX bracis-28424 311 74 not not PART bracis-28424 311 75 currently currently ADV bracis-28424 311 76 available available ADJ bracis-28424 311 77 for for ADP bracis-28424 311 78 this this DET bracis-28424 311 79 article article NOUN bracis-28424 311 80 . . PUNCT bracis-28424 312 1 copy copy VERB bracis-28424 312 2 shareable shareable ADJ bracis-28424 312 3 link link NOUN bracis-28424 312 4 to to PART bracis-28424 312 5 clipboard clipboard NOUN bracis-28424 312 6 provided provide VERB bracis-28424 312 7 by by ADP bracis-28424 312 8 the the DET bracis-28424 312 9 springer springer NOUN bracis-28424 312 10 nature nature PROPN bracis-28424 312 11 sharedit sharedit PROPN bracis-28424 312 12 content content NOUN bracis-28424 312 13 - - PUNCT bracis-28424 312 14 sharing share VERB bracis-28424 312 15 initiative initiative NOUN bracis-28424 312 16 keywords keyword NOUN bracis-28424 312 17 network network NOUN bracis-28424 312 18 epidemic epidemic NOUN bracis-28424 312 19 epidemic epidemic NOUN bracis-28424 312 20 source source NOUN bracis-28424 312 21 identification identification NOUN bracis-28424 312 22 graph graph NOUN bracis-28424 312 23 neural neural ADJ bracis-28424 312 24 network network NOUN bracis-28424 312 25 supervised supervise VERB bracis-28424 312 26 learning learn VERB bracis-28424 312 27 publish publish VERB bracis-28424 312 28 with with ADP bracis-28424 312 29 us us PROPN bracis-28424 312 30 policies policy NOUN bracis-28424 312 31 and and CCONJ bracis-28424 312 32 ethics ethic NOUN bracis-28424 312 33 search search NOUN bracis-28424 312 34 search search NOUN bracis-28424 312 35 by by ADP bracis-28424 312 36 keyword keyword NOUN bracis-28424 312 37 or or CCONJ bracis-28424 312 38 author author NOUN bracis-28424 312 39 search search NOUN bracis-28424 312 40 navigation navigation NOUN bracis-28424 312 41 find find VERB bracis-28424 312 42 a a DET bracis-28424 312 43 journal journal NOUN bracis-28424 312 44 publish publish VERB bracis-28424 312 45 with with ADP bracis-28424 312 46 us we PRON bracis-28424 312 47 track track VERB bracis-28424 312 48 your your PRON bracis-28424 312 49 research research NOUN bracis-28424 312 50 discover discover VERB bracis-28424 312 51 content content NOUN bracis-28424 312 52 journals journal NOUN bracis-28424 312 53 a a DET bracis-28424 312 54 - - PUNCT bracis-28424 312 55 z z NOUN bracis-28424 312 56 books book NOUN bracis-28424 312 57 a a DET bracis-28424 312 58 - - PUNCT bracis-28424 312 59 z z NOUN bracis-28424 312 60 publish publish NOUN bracis-28424 312 61 with with ADP bracis-28424 312 62 us us PROPN bracis-28424 312 63 journal journal PROPN bracis-28424 312 64 finder finder PROPN bracis-28424 312 65 publish publish VERB bracis-28424 312 66 your your PRON bracis-28424 312 67 research research NOUN bracis-28424 312 68 language language NOUN bracis-28424 312 69 editing edit VERB bracis-28424 312 70 open open ADJ bracis-28424 312 71 access access NOUN bracis-28424 312 72 publishing publishing NOUN bracis-28424 312 73 products product NOUN bracis-28424 312 74 and and CCONJ bracis-28424 312 75 services service NOUN bracis-28424 312 76 our our PRON bracis-28424 312 77 products product NOUN bracis-28424 312 78 librarians librarian VERB bracis-28424 312 79 societies society NOUN bracis-28424 312 80 partners partner NOUN bracis-28424 312 81 and and CCONJ bracis-28424 312 82 advertisers advertiser NOUN bracis-28424 312 83 our our PRON bracis-28424 312 84 brands brand NOUN bracis-28424 312 85 springer springer NOUN bracis-28424 312 86 nature nature PROPN bracis-28424 312 87 portfolio portfolio PROPN bracis-28424 312 88 bmc bmc PROPN bracis-28424 312 89 palgrave palgrave PROPN bracis-28424 312 90 macmillan macmillan PROPN bracis-28424 312 91 apress apress PROPN bracis-28424 312 92 discover discover VERB bracis-28424 312 93 your your PRON bracis-28424 312 94 privacy privacy NOUN bracis-28424 312 95 choices choice NOUN bracis-28424 312 96 / / SYM bracis-28424 312 97 manage manage NOUN bracis-28424 312 98 cookies cookie NOUN bracis-28424 312 99 your your PRON bracis-28424 312 100 us us PROPN bracis-28424 313 1 state state NOUN bracis-28424 313 2 privacy privacy NOUN bracis-28424 313 3 rights right NOUN bracis-28424 313 4 accessibility accessibility NOUN bracis-28424 313 5 statement statement NOUN bracis-28424 313 6 terms term NOUN bracis-28424 313 7 and and CCONJ bracis-28424 313 8 conditions condition NOUN bracis-28424 313 9 privacy privacy NOUN bracis-28424 313 10 policy policy NOUN bracis-28424 313 11 help help NOUN bracis-28424 313 12 and and CCONJ bracis-28424 313 13 support support VERB bracis-28424 313 14 legal legal ADJ bracis-28424 313 15 notice notice NOUN bracis-28424 313 16 cancel cancel VERB bracis-28424 313 17 contracts contract NOUN bracis-28424 313 18 here here ADV bracis-28424 313 19 129.74.145.123 129.74.145.123 NUM bracis-28424 313 20 hesburgh hesburgh PROPN bracis-28424 313 21 library library PROPN bracis-28424 313 22 er er INTJ bracis-28424 313 23 unit unit NOUN bracis-28424 313 24 ( ( PUNCT bracis-28424 313 25 3005732405 3005732405 NUM bracis-28424 313 26 ) ) PUNCT bracis-28424 313 27 northeast northeast ADJ bracis-28424 313 28 research research NOUN bracis-28424 313 29 libraries library NOUN bracis-28424 313 30 ( ( PUNCT bracis-28424 313 31 nerl nerl PROPN bracis-28424 313 32 ) ) PUNCT bracis-28424 313 33 ( ( PUNCT bracis-28424 313 34 8200828607 8200828607 NUM bracis-28424 313 35 ) ) PUNCT bracis-28424 313 36 nerl nerl VERB bracis-28424 313 37 ta ta X bracis-28424 313 38 account account NOUN bracis-28424 313 39 ( ( PUNCT bracis-28424 313 40 3006206169 3006206169 NUM bracis-28424 313 41 ) ) PUNCT bracis-28424 313 42 university university NOUN bracis-28424 313 43 of of ADP bracis-28424 313 44 notre notre PROPN bracis-28424 313 45 dame dame PROPN bracis-28424 313 46 hesburgh hesburgh PROPN bracis-28424 313 47 library library NOUN bracis-28424 313 48 ( ( PUNCT bracis-28424 313 49 3000184373 3000184373 NUM bracis-28424 313 50 ) ) PUNCT bracis-28424 314 1 © © ADP bracis-28424 314 2 2025 2025 NUM bracis-28424 314 3 springer springer NOUN bracis-28424 314 4 nature nature NOUN