Functioning of Declarative Memory: Intersection between Neuropsychology and Mathematics Elementa Intersections between Philosophy, Epistemology and Empirical Perspectives 1 (2021) 1-2 Pierpaolo Limone Editorial 7 First Section Slavoj Žižek The Vagaries of the Superego 13 Ricardo Espinoza Lolas Nature and Pandemic 33 Paolo Ponzio Mask and Otherness between Recognition and Concealment: 47 Notes on the Self and the You Daniela Savino “Liquid” Identity and Otherness in the Phenomenon 61 of Religious Alienation: The Loss of Critical Thinking and the “Barter” of the Self in the System of Communion Francesca R. Recchia Luciani The Sexistential Vulnerability of Bodies in Contact 85 in the Philosophy of Jean-Luc Nancy Elementa. Intersections between Philosophy, Epistemology and Empirical Perspectives – 1 (2021) 1-2 https://www.ledonline.it/elementa 5 https://www.ledonline.it/elementa Elementa. Intersections between Philosophy, Epistemology and Empirical Perspectives Second Section Martina Rossi Universal Design for Learning and Inclusive Teaching: 103 Future Perspectives Marco Ceccarelli A Historical Account on Italian Mechanism Models 115 Giusi Antonia Toto - Alessia Scarinci Cyberfeminism: A Relationship between Cyberspace, 135 Technology, and the Internet Luigi Traetta - Federica Doronzo Super-Ego after Freud: A Lesson not to Be Forgotten 153 Federica Doronzo - Gianvito Calabrese Functioning of Declarative Memory: Intersection 163 between Neuropsychology and Mathematics Giuliana Nardacchione - Guendalina Peconio Peer Tutoring and Scaffolding Principle for Inclusive Teaching 181 Elementa. Intersections between Philosophy, Epistemology and Empirical Perspectives – 1 (2021) 1-2 https://www.ledonline.it/elementa 6 https://www.ledonline.it/elementa Elementa. Intersections between Philosophy, Epistemology and Empirical Perspectives – 1 (2021) 1-2 https://www.ledonline.it/elementa 163 Functioning of Declarative Memory: Intersection between Neuropsychology and Mathematics 1 Federica Doronzo 1 - Gianvito Calabrese 2 1 Learning Science hub, Università degli Studi di Foggia (Italy) 2 Yield Engineer on Semiconductor doi: https://dx.doi.org/10.7358/elem-2021-0102-doca federica.doronzo@unifg.it g.calabrese.296@gmail.com Abstract The understanding of memory has been a constant challenge for scientific research for centuries. The mnemonic processes, which determine the identity of the human being, have been investigated through multiple points of view, such as the psychological, neuro- physiological and physical ones. The result is complex and multifaceted visions that should be integrated to provide a unitary and complete interpretation. A survey of the most recent scientific literature is carried out on the functioning of declarative memory, to analyse the relationship between real information coming from the outside world, the encoded event and the recovered memory. The aim of the essay is to investigate the neural correlates, which regulate the cognitive system in question, through a dual neuropsycho- logical-mathematical interpretation. Neuropsychology sheds light on the anatomical, physiological and psychic mechanisms of memory while Mathematics associates the corresponding mathematical configurations to neural networks. The reunification process between the two disciplines is achieved through neuromorphic computational simulation that emulates mind uploading. The assembly of artificial neurons has the potential to clarify in detail the memory processes, the functioning of neural correlates and to carry out the mapping of the biological brain. We hope that the results obtained will provide new knowledge on mnestic mechanisms to contribute to the evolution of disciplines such as General Psychology, Forensic Neuroscience, Cognitive Rehabilitation and Awake Surgery. 1 For the purposes of academic recognition, contributions are attributed as follows: introduction and paragraph 1 to Federica Doronzo; paragraph 2 to Gianvito Calabrese; and the conclusion is the result of a shared work. https://www.ledonline.it/elementa https://dx.doi.org/10.7358/elem-2021-0102-doca Federica Doronzo - Gianvito Calabrese Elementa. Intersections between Philosophy, Epistemology and Empirical Perspectives – 1 (2021) 1-2 https://www.ledonline.it/elementa 164 Keywords: declarative memory; mathematical configurations; neuromorphic computation; neuropsychology. Introduction Memory is the cognitive domain that mediates a series of processes to acquire and store information over time, the aim is to guide behavior and plan future actions for survival. This function is fundamental for the human being as long-lasting memories form the basis of identity that is a self/ hetero perception of oneself and of the relationship between the self and the world. In particular, declarative memory is involved in the integration of individual experiences with the socio-cultural knowledge of the world. The four fundamental processes of memory are: coding, consoli- dation, storage and retrieval. Coding is the processing of information (sensory analysis and attribution of meaning), the consolidation allows the generation of a representation, the storage consists in the recording of data in the storage-memory and the recovery phase is the recall mechanism of the memory. Recently Dudai (2012) confirmed the existence of another process, such as reconsolidation which is an extension of the phenomenon of memory consolidation. When a memory is recovered or reactivated it must be consolidated again, increasing the possibility that the reconsoli- dated memory may include new information not present in the original version of the event. The multi-warehouse model, which evolved from James’ first theo- rization in 1890, is the most accredited paradigm in the literature and provides for the subdivision of memory into hierarchically organized modules. A fundamental distinction concerns the component of temporal retention which determines the following subdivision: working memory, sensory memory and long-term memory. The latter can be classified into declarative (explicit), that is, conscious memory of events and facts, and non-declarative (implicit) which consists of memories expressed through the execution of actions regardless of awareness. The most recent model is the MNESIS model, i.e. Memory Neo- Structural Inter-Systemic, in which the memory consists of interconnected sub-systems (Eustache, Viard, & Desgranges, 2016). The three modules of long-term representation (perceptual memory, semantic memory, episodic memory) interact with each other through the processes of consolidation 2 2 Phenomenon of reliving experiences: a still faint trace is converted into a perma- nent or enhanced form. https://www.ledonline.it/elementa Functioning of Declarative Memory: Intersection between Neuropsychology and Mathematics Elementa. Intersections between Philosophy, Epistemology and Empirical Perspectives – 1 (2021) 1-2 https://www.ledonline.it/elementa 165 and semantization 3; the episodic buffer 4 acts as an intermediary between working memory, procedural memory and long-term memory, and the latter two systems in turn have direct links. The structure demonstrates that memories have a dynamic and reconstructive nature and memory operates through a distributed set of brain areas that are, interconnected neural networks (Fig. 1). Figure 1. – MNESIS. Fonte: Eustache, Viard, & Desgranges, 2016, p. 100. Computational Science is contributing to the understanding of brain functioning by designing artificial brain networks. The modeling of the biological brain has the potential to photograph and reproduce the neural configurations during the different memory processes, distinguishing brain activity for coding, consolidation and information retrieval. The key issues of the reflection in question are: • Are past events faithfully reproduced or does the memory function induce constructive activities by distorting the original information? • Is neuromorphic computing  5 a feasible project? What repercussions would it have with respect to the understanding of the Central Nervous System? 3 Passage from episodic memory to semantic memory due to the passage of time which induces the loss of episodic details of memories. 4 In 2000, Baddeley added episodic buffer to his short-term memory model. This third sub-component acts as an intermediary between systems having different codes, and combines them into unitary, meaningful and coherent representations. 5 New paradigm that essentially consists in assembling artificial neurons so that they function according to the principles of the human brain. https://www.ledonline.it/elementa Federica Doronzo - Gianvito Calabrese Elementa. Intersections between Philosophy, Epistemology and Empirical Perspectives – 1 (2021) 1-2 https://www.ledonline.it/elementa 166 The above themes are investigated with a dual point of view, neuropsy- chological and mathematical, in order to integrate the results and increase knowledge with respect to the cognitive domain of memory. Understanding the psycho-physiological mechanisms associated with memory processes, mapping the human brain and mathematically representing neural config- urations, would allow us to answer the aforementioned questions. These goals would generate innumerable implications: Forensic Neuroscience and Cognitive Rehabilitation would implement assessments and interventions calibrated on the specific functioning of the memory process and brain activity. Furthermore, a transdisciplinary understanding of the construct would enrich the theories and open questions of General Psychology (such as reconstruction and alteration of memories) and would help to ensure greater safety of Awake Surgery: the facilitation of intraop- erative mapping would precisely determine the dedicated areas of the brain to fundamental neurological activities and their functioning. 1. Neuropsychological perspective Neuropsychology has provided a significant contribution to the knowledge on the functioning of declarative memory through the study of both the healthy subject and that affected by diseases of the Central Nervous System. The transdisciplinary nature provides it with an added value, this paragraph investigates the studies and empirical evidences that clarify the declarative mnestic mechanisms from a psychic and physiological point of view. 1.1. Construction and reconstruction of declarative memories To understand how memory works, it starts by examining its character- izing process: learning. This process, which mediates the consolidation of the traces, is determined by changes involving the synapses for both short- term memory (greater neurotransmitter release) and long-term memory (formation of new synapses). Any experience that results in remembering produces physical changes in the Central Nervous System (CNS). The brain circuits that support the formation, storage and retrieval of declara- tive memory converge in a hippocampus-dependent system  6. In 1937 6 Eichenbaum (2000) demonstrated that rats with hippocampal and parahip- pocampal lesions lose the ability to retrieve previously acquired memories (specifically spatial ones). https://www.ledonline.it/elementa Functioning of Declarative Memory: Intersection between Neuropsychology and Mathematics Elementa. Intersections between Philosophy, Epistemology and Empirical Perspectives – 1 (2021) 1-2 https://www.ledonline.it/elementa 167 Papez was among the first to identify the circuit involved in the forma- tion of long-term memories, known as the Papez circuit, consisting of the projections from the hippocampal formation to the mammillary bodies and from the mammillary bodies to the anterior thalamus. Squire (2015) most recently identified the main areas of the circuit: medial temporal lobe, hippocampus and primary, secondary and associative cortex. The hippocampus and the diencephalic structures are of crucial importance for the formation and consolidation of memories which are subsequently stored throughout the brain. Here are four theories that differently describe how episodic memory works. Squire, in 2004, developed the Standard consolidation theory according to which the hippocampus acts as an “index” of access to recent memories for their spatial localization, for example visual elements are stored in the visual cortices, the sounds of words in language areas, etc. Subsequently, the consolidation period allows direct connection to the cortical traces of memories, and the hippocampus is no longer essential for the retrieval of information. Nadel and Moscovitch (1997) with the Multiple trace theory argue that episodic memories, more or less consolidated, are always dependent on the hippocampus. The temporal gradient is not associated with the transfer to the cortex but with the number of traces stored in the hippocampus: every time a memory is reactivated, a new memory trace is stored in the hippocampus. As a result, remote memories are encoded by multiple tracks and become more resistant to hippocampal damage. The recall can therefore alter the memory as a photograph of what really happened is not constructed, but rather a reconstruction of what is remem- bered the last time one thought about the memory takes place. In 2013 Maguire and Mullally advanced the Scene construction theory, according to which the hippocampus is able to reconstruct the past experience in the absence of the original trace. During the re-enactment of a recent event, the hippocampus constructs a series of coherent scenes with event through neocortical-hippocampal interactions. These scenes quickly fade from the hippocampus as the representations consolidate into adjacent cortical areas. Schacter and Addis (2007), with the Episodic simulation of future events, argue that the memory of the past and the imagination of the future draw on similar information stored in episodic memory, which therefore also supports the construction of future events by extracting and recom- bining the information stored in a simulation of a new event. Bartlett provides another element in support of the distorted nature of memory by proposing a constructive vision of memory as early as the https://www.ledonline.it/elementa Federica Doronzo - Gianvito Calabrese Elementa. Intersections between Philosophy, Epistemology and Empirical Perspectives – 1 (2021) 1-2 https://www.ledonline.it/elementa 168 first half of the 1900s. Cognition would not allow a duplicative process of reality as it is impossible to separate memory from other higher func- tions such as thought and imagination. Memory therefore plays a role of active transformation of memories by integrating perception and subjec- tive experience. This phenomenon is due to the presence of patterns, e.g. knowledge that everyone has about objects or events, which guide the memory processes. From these theories it emerges that declarative memory is still the subject of controversial studies and appears to be the result of complex constructive and reconstructive mechanisms dependent on extended brain circuits. The doubt about the reliability of memories arises from the first mnestic process of information processing. Constructivism argues that knowledge is necessarily dependent on the knowing subject as an active construction process. Objectivity is therefore an illusion: the subject intro- duces his own order and meaning to what he experiences. The same event is meaning and remembered differently on the basis of one’s psycho-physical state (depending on the moment in which it is known), past experiences (which build the representations, defined by the Bowlby theory IWM  7), and the common sense 8 determined by the place of belonging and the inter- actions subsequent to the occurrence of the event. Below we present some theories that analyze the processes that affect the reliability of memories. The emotion-memory interactions occur in several phases from the construction to recovery of the memory trace by modifying the original data. The amygdala modulates, according to emotions, both the encoding and the memorization of memories dependent on the hippocampus, this in turn generates episodic representations of the emotional meaning and interpretation of events, influencing the response of the amyg- dala when stimuli are encountered emotional. Although the amygdala and hippocampus are independent, they act in concert (Phelps, 2004): emotions regulate memory and vice versa. The association between mood disorders and memory impairment is due to the fact that dysfunctional emotional alterations reduce the amount of cognitive resources available for the memory domain (Dalgleish & Power, 2004). 7 Individuals, through interaction with the environment and in particular with the caregiver, build Internal Working Models from childhood, that is, representations of them- selves and the world. These mental structures regulate the perception and interpretation of events, allowing you to make predictions and create expectations about the events of your relational life. 8 Pre-conceptual sense, implicitly shared by the members of a cultural context, which allows people to be in tune with what is common (Stanghellini, 2008). https://www.ledonline.it/elementa Functioning of Declarative Memory: Intersection between Neuropsychology and Mathematics Elementa. Intersections between Philosophy, Epistemology and Empirical Perspectives – 1 (2021) 1-2 https://www.ledonline.it/elementa 169 The Self Memory System  9 (Conway & Pleydell-Pearce, 2000) intro- duces another dynamic influencing memory such as the self-concept. This framework considers memory as a “motivated process” that is guided by the self-goals. Autobiographical knowledge limits what the self is, has been and can be, in turn the self modulates access to long-term knowledge: in the event of changes in the self, memory stores are radically reorganized (Conway, 2005). The self and memory can therefore operate indepen- dently and influence each other. It is also necessary to consider that memories also interact with each other changing them self. This interrelation is called interference, and it is both the tendency of new memories to compromise the recovery of past memories (retroactive) and vice versa the tendency of pre-existing informa- tion to influence new events (proactive). As a demonstration of this, it is observed that the mastery of a task can facilitate or hinder the learning or execution of a new task. At the end of this path, the contribution that Schacter, one of the most famous researcher of memory, has provided to the theme, is exhibited. The scientist argues that memory plays fundamental functions in everyday life, but that it is also vulnerable to error and delusion. He theorized the existence of seven sins (imperfections) by assigning to memory a construc- tive and adaptive nature (functional to survival). Sins are divided into three types of phenomena: oblivion phenomena (transience, absent-mindedness, blocking), distortion phenomena (misattribution, suggestibility, bias) and pathological phenomena (persistence). Considering the evidence showing the pervasiveness of memory errors, Schather concludes that memory is a faulty process that has serious repercussions on the legal system, especially in the context of the accuracy of the testimony. In fact, research has shown that post-event suggestion can contaminate a person’s memory by inducing false memories. This discussion has presented the pitfalls to which the memory is exposed. What emerged has implications not only for police investiga- tions and criminal judgments but also for other disciplinary sectors such as Psychotherapy which has long debated the veracity of memories. The novelty proposed is that Mathematics is trying to combine psychological phenomena with neural correlates explained in terms of mathematical models, to scientifically corroborate what has been observed at a behavioral level. 9 The SMS is a paradigm made up of two main components, the working self (complex set of active goals and associated self-images) and the knowledge of autobiograph- ical memory. These components intertwine to form memories and self-representations. https://www.ledonline.it/elementa Federica Doronzo - Gianvito Calabrese Elementa. Intersections between Philosophy, Epistemology and Empirical Perspectives – 1 (2021) 1-2 https://www.ledonline.it/elementa 170 1.2. The engram: from the biochemical perspective to the mathematical model Neuropsychology clarifies the brain psychic and neurophysiological pro- cesses regulating memory but does not precisely delineate the activation configurations of neurons in the various mnestic phases. The innovative connectionist model implements a computational approach of the mind: it attempts to simulate biological intelligence, reproducible on a computer, through artificial neural networks. Mathematical models can help provide a detailed representation of neural activity during the different memory processes to photograph the neural correlates of coding, consolidation, reconsolidation and recovery of memories. Emerging changing configurations in support of the constructive and reconstructive nature theorized by neuropsychological research. Below we describe the functioning of the learning process, at the basis of mathematical modelling, starting from the concept of engram. The engram is structured through a biochemical process by which neurons, which once functioned independently, begin to work together as a network. Daniel Hebb was the first, in 1949, to hypothesize that memories are stored in the brain in the form of networks of neurons. Hebb’s postulate states that axonic terminations, strengthened thanks to corelated activity, form new branches, while terminations weakened by unrelated activity lose their grip on the post-synaptic cell. Bills and Lomo, in 1973, discovered that by administering a train of high frequency electrical stimuli (at the hippocampus) the action potentials produced by subsequent stimuli were increased but only in that neural path (the electric current strengthened the synaptic connections along that away for hours or weeks). This is the long-term potentiation (LTP): a persistent increase in synaptic efficacy that mediates the forma- tion of memory. This phenomenon occurs only in the presence of a close temporal correspondence between the paired activities of pre-synaptic and post-synaptic cells. The neural activity model gradually changes with training to become consistent: the synchrony index of the triggered neurons is low at the beginning but increases with training cycles (Zhou et al., 2020). The change in the dynamics of neurons from irregularity to synchronization coincides with the appearance of learned behaviors (e.g., mouse freezing for fear conditioning). Synaptic plasticity is the generative mechanism of memorization, the LTP with the formation of new synapses regulates the consolidation of memories. https://www.ledonline.it/elementa Functioning of Declarative Memory: Intersection between Neuropsychology and Mathematics Elementa. Intersections between Philosophy, Epistemology and Empirical Perspectives – 1 (2021) 1-2 https://www.ledonline.it/elementa 171 The neuronal dynamics, which determine the memorization, can be described through mathematical models based on measurements of the voltage and time dependence of the currents that cross the membrane. The memorization process is interpreted as a return of the brain to the neuronal configuration equal to the one it had at the time of the stimulus; and the brain network is studied as a mathematical system having dynamic configurations (Luccioli, 2005). The neuronal network can be represented as a system of N units (neurons) that interact with each other at instant t. At each instant the network is characterized by a configuration determined by the values of the electrical potentials assumed by the neurons. The information is then represented by specific configurations where the first neuron is active and the second quiescent and so on. The potential that the i-th neuron receives from the others is defined by the sum of the potentials that the neurons send to the i-th neuron. A neuron will be active if the sum of the electrical potentials, it receives from the other neurons, exceeds its threshold value in analogy to what happens biologically. On the basis of the mathematically defined configuration it is possible to identify the recognition of a stimulus and compare the configurations at different instants, differentiating the processes of coding and retrieving informa- tion (Doria, 1994). What has been discovered, biologically and mathematically, coded potentially makes it possible to carefully evaluate the admissibility limits of testimonial evidence, the memory impairments in the medical field and the mapping of neural networks as a function of neurosurgical interven- tions. 2. Mathematical perspective The difference in scale between the biological phenomena (neural activi- ties) and the behavioral expressions (mnestic processes) creates room for multiple discipline to be hosted in and, in this scenario, mathematics has taken its role as special guest. The mathematical modelling allows to simu- late the association between specific neural configurations and the various cognitive operations laying the foundation for the data neuromorphic processing. In the current paragraph the most important milestones, success (and perplexities) along the artifical neural networks conceptualization roadpath are presented. https://www.ledonline.it/elementa Federica Doronzo - Gianvito Calabrese Elementa. Intersections between Philosophy, Epistemology and Empirical Perspectives – 1 (2021) 1-2 https://www.ledonline.it/elementa 172 2.1. The technological keys of the mind The difficulties involing a neuromorphic processor realization are multiple. In the classical computational system based on the von Neumann archi- tecture (hardware architecture for programmable digital machines which shares the instructions and the data in the same memory area) the control processing units (CPUs) are physically separetad from the memory block, instead in the neural networks, processing and memorization co-exist inside the same synaptic structure. The increase of the completed opera- tions by time unit (i.e. increasing clock frequency), could affect the micro- electronic fabrication process. Considering that forcing the boundaries of the solid state physics is not always a chance some strategitcal workaround and smart tricks are needed to support the continuos improvement of the computer performance. First of all the multi core parallel computing and the hierarical organization of cache memory. For the special case of paral- lelism, Amdahl law state that if F is the fraction of a processing which can be done in parallel, and (1 − F ) is the part which has to be done in serial, then the best achievable speedup 10 (S) using a N core machine is: S = 1 (1 − F ) + F N (2.1) Looking at the future of computation virtually means to reimage it: the brain organization is one of the most promising and ispiring technolog- ical architecture in the roadmap of the computer evolution. The field of application of the neuromorphic computing are wide, as it is extensive the number of solution proposed to reach the final accomplishment. The new neuromorphic technological platform could be the most natural interface between human body and cybernetic prostheses. This can open a new window on the way to approach the nervous system diseas, as quadriplegia and also more complex clinical picture (Collinger et al., 2013). For the moment this looks like more the (happy) ending of the story. The input processing capacity a biological system can accept (104) and the fan-in 11, nominal or effective, of the computation machines are order of magnitude different (102). Beyond the scale issue it’s the spike-timing design to be a deep conceptual difference in the information treatment 10 Computational acceleration of partially divisible algorithm due to the insertion of N processors in parallel. 11 Number of acceptable input from a circuit logic operator. https://www.ledonline.it/elementa Functioning of Declarative Memory: Intersection between Neuropsychology and Mathematics Elementa. Intersections between Philosophy, Epistemology and Empirical Perspectives – 1 (2021) 1-2 https://www.ledonline.it/elementa 173 when comparent to the current standard. The SpiNNaker project (Spiking Neural Network Architecture) try to jump over the fence by a multi-core architecture based on the paradigm of the brain functioning (Mead, 1990). Its billions of computation units are able to reinforce their interconnection thanks to the STDP mechanism constituing an high parallel degree artifi- cial platform. If compared to the biological systems it is not more than the 1% of the human brain, of if it sounds more encouraging, it is equivalent to ten times a mouse brain (Fig. 2). The basic block of the SpiNNaker is the SpiNNaker multicore System- on-Chip. The chip is a Globally Asynchronous Locally Synchronous (GALS) system 12 whee the nodes are represented by 18 ARM968 processors working in synchronized regime, grafted in a circuital infrastracture based on the Address-Event-Representation (AER)  13 communication protocol, which allows large fan-in and fan-out. The AER protocol is optimized for the real time housing of a great number of mini-packets able to emulate the neural spikes (Mead, 1990). The strong legacy of the standard management of the computational resources introuduced by the classic ARM processors seems to have been further exceeded by the TrueNorth project by IBM. The struc- ture is made by 4096 cores which fulfil the role on neural network in turn integrated on a single motherboard. Each one of the core raccoglie 256 simil-neural electronic units (approximately the size of a caterpillar’s brain) that allows to program 256 × 256 binary synaptic connections (Indiveri, 2011). The True North is the IBM second largest chip ever made and only consumes 73 mW (a thousand time less than a typical commercial CPU) proving, as expected, a natural inclination toward the challenges coming from the domain of the cognitive responses or, from a more computer science point of view, the target themes of the machine learning alghorithms (Indiveri & Liu, 2015). A quantitative metric of what just discussed can be better defined looking at the image recognition capacity. The TrueNorth is able to categorize 6000 images per watt with respect to a canonical GPU, altought excellent, as the NVIDIA Tesla p4 GPU which can perform the identification of just 160 immagini for the same power unit. This approach seems to be most successful than SpiNNaker in terms of memory distribution grade (Fig. 3). 12 Computational architecture based on secure and robust communication between synchronous islands in a system of independent clock domains. 13 Address Event Representation (AER) is an emerging protocol dedicated to the communication of neuromorphic networks that aims to create a massive interconnection between neural units with a strong real-time focus. https://www.ledonline.it/elementa Figure 2. – Schematic representation of the GALS architecture flanked by an image of the SpiNNaker matrix, with the 18 cores (synchronous islands). Source: http://apt.cs.manchester.ac.uk. Figure 3. – The Neurogrid Layout (to the left) is characterized by a 64 × 64 “neurosynaptic cores”. Each core (to the right) owns 256 neurons and 65,536 synapsis. Surce: IBM Research, CC BY. 174 http://apt.cs.manchester.ac.uk Functioning of Declarative Memory: Intersection between Neuropsychology and Mathematics Elementa. Intersections between Philosophy, Epistemology and Empirical Perspectives – 1 (2021) 1-2 https://www.ledonline.it/elementa 175 One of the main issues is the large size di questo dispositivo, 4.3 cm2, which makes questionable is industrial sustinability in term of die yield. Also assuming to miniaturize the chip consistently with the mass produc- tion CPU size, the processor shows up a lack of plasticity/learning capacity which represent, instead, a choice taken during the development face in order to semplify design and operation. As last study case it is proposed the NeuroGrid which is based on an unusual array of neurons and synapses made by analog electronic circuits assisted by a digital router. This MixedSignal machine is the apotheosis of the real-time concept thought to handle the data on the fly and avoid any kind of machine state storage (Douglas, Mahowald, & Mead, 1995). It appears to be what is closest to the formlization of coincidence of data retainment with the dynamic dialogue of the circuital components. The network pretends to interact realistically with biological systems and is, therefore, calibrated on time constants of tens of milliseconds. It’s a very long time scale if the reference is the digital system performance but for sure, for an analogic VLSI 14 is a very challenging result to reach. Conclusions The studies on memories evolve constantly and the underlying compre- hension is gradually becaming more complex and detailed. In particular all the learning about the memories generation and recall mechanism have quicly expanded. An important item in the field is the trustability of the recalled information. The brain is not a passive storage node instead it covers an adaptive function which can cause the memories alteration. This kind of error introduction serves for survival purpose. The memory builds patterns to expedite and facilitate the world understanding, although these processes cause the distortion of remembered events. The Neuropsychology is helping to clarify the anatomical, physi- ological and psychic correlates of memory in order to understand its functioning. The Neuropsychological studies show that mental activity is distributed through the brain and not categorized into independent modules: the modularization paradigm has been discarded in favor of the connectionist one, proving the existence of interconnected neural networks. 14 Very large scale integration (in acronym VLSI) is a denomination that indicates a high integration of transistors within a single chip. Generally it refers to the devices with the highest level of integration based on the technologies of the time. https://www.ledonline.it/elementa Federica Doronzo - Gianvito Calabrese Elementa. Intersections between Philosophy, Epistemology and Empirical Perspectives – 1 (2021) 1-2 https://www.ledonline.it/elementa 176 Mathematics fits into this context by representing complex neural configu- rations through the mathematical models. All the disciplines offer their contribution in the same direction of establishing the neuromorphic computing theory and design the perfect machine for its interpretation. The development of new IT architectures is slowly becoming a reality. In the 2020 the neural chips market counted 1.952 billion dollars, and it is expected to grow to exceed 7 billion ollars by the 2026 with a particular traction from the automotive market (Mordor Intelligence, 2021). The integration of psychological, neuro-physiological knowledge with the mathematical one implies making an improvement for different disciplines and for the quality of life of the human being. The General Psychology will be able to answer unresolved questions about the unreli- ability of memories and their reconstructive nature. The Forensic Neuro- science will have a valid mathematical model that illustrates brain activity during the memorization making the detectives able to easily filter out fake information. Thanks to the Neuroimaging the cerebral images could be directly associated with some computational configuration to support the diagnosis and and the follow-up in in the neurological and psychiatric fields. The Awake Surgery will increase the safety and effectiveness of the interventions throught the systematic mapping by the cerebral network. At the end the Neuropsychological rehabilitation could arrange very precise intervention plan to fix the specific mnestic impairment and better moni- toring the further progresses by the support of the prediction and behav- iour suggested by the mathematical modelling. References Andrews-Hanna, J. R., Saxe, R., & Yarkoni, T. (2014). Contributions of episodic retrieval and mentalizing to autobiographical thought: Evidence from functional neuroimaging, resting-state connectivity, and fMRI meta-anal- yses. Neuroimage, 91, 324-335. Ardito, R., Pellegrino, S., & Adenzato, M. (2018). 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Ne risultano visioni complesse e sfaccettate che andrebbero integrate per fornire un’interpretazione unitaria e completa. Si effettua una ricognizione della letteratura scientifica più recente, sul funzionamento della memoria dichiarativa, per analizzare la relazione tra l’informazione reale proveniente dal mondo esterno, l’evento codificato e il ricordo recuperato. L’obiettivo del saggio è indagare i correlati neurali, che regolano il sistema cognitivo in oggetto, mediante una duplice interpretazione neuropsicologico- matematica. La Neuropsicologia fa luce sui meccanismi anatomici, fisiologici e psichici della memoria mentre la Matematica associa alle reti neurali le corrispondenti configu- razioni matematiche. Il percorso di ricongiungimento, tra le due discipline, si realizza attraverso la simulazione computazionale neuromorfica che emula il “mind uploading”. Copyright (©) 2021 Federica Doronzo, Gianvito Calabrese Editorial format and graphical layout: copyright (©) LED Edizioni Universitarie This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. How to cite this paper: Doronzo, F., & Calabrese, G. (2021). Functioning of declarative memory: Intersection between neuropsychology and mathematics. Elementa. Intersections between Philosophy, Epistemology and Empirical Perspectives, 1(1-2), 163-179. doi: https://dx.doi.org/10.7358/ elem-2021-0102-doca https://www.ledonline.it/elementa https://dx.doi.org/10.7358/elem-2021-0102-doca https://dx.doi.org/10.7358/elem-2021-0102-doca Elementa_1-2021-1-2_00b_Sommario.pdf Editorial Pierpaolo Limone First Section The Vagaries of the Superego Slavoj Žižek Nature and Pandemic Ricardo Espinoza Lolas Mask and Otherness between Recognition and Concealment: Notes on the Self and the You Paolo Ponzio “Liquid” Identity and Otherness in the Phenomenon of Religious Alienation: The Loss of Critical Thinking and the “Barter” of the Self in the System of Communion Daniela Savino The Sexistential Vulnerability of Bodies in Contact in the Philosophy of Jean-Luc Nancy Francesca R. Recchia Luciani Second Section Universal Design for Learning and Inclusive Teaching: Future Perspectives Martina Rossi A Historical Account on Italian Mechanism Models Marco Ceccarelli Cyberfeminism: A Relationship between Cyberspace, Technology, and the Internet Giusi Antonia Toto 1 - Alessia Scarinci 2 Super-Ego after Freud: A Lesson not to Be Forgotten Luigi Traetta 1 - Federica Doronzo 2 Functioning of Declarative Memory: Intersection between Neuropsychology and Mathematics Federica Doronzo 1 - Gianvito Calabrese 2 Peer Tutoring and Scaffolding Principle for Inclusive Teaching Giuliana Nardacchione - Guendalina Peconio