Arturo Tozzi

• former Adjunct Assistant Professor dept. Physics University of North Texas
• Pediatrician at Azienda Sanitaria Locale Napoli 1

We propose a framework for artificial intelligence design grounded in Immanuel Kant's transcendental philosophy, particularly his theory of cognition as presented in the Critique of Pure Reason. We argue that Kant's model of the mind-structured by a priori forms of intuition and categories of understanding-provides a valuable conceptual foundation...

Computing hardware approaches face challenges related to spatial efficiency, thermal regulation, signal latency and manufacturing complexity. We evaluated the potential of Plücker conoid-inspired geometry (PCIG) as a wave modulation strategy for wave-based systems like optical/acoustic computing platforms. We propose optical transistors in which gu...

Time crystals are a class of non-equilibrium phases of motion characterized by spontaneous temporal symmetry breaking. We describe a time-crystal-inspired microdevice (TCIM) structured around a hexagonal shell encapsulating a central triangular motif. The geometry is derived from the Fukuta-Cerin theorem, where the centroid of each triangle aligns...

Water is central to biological processes not only as a solvent, but also as an agent shaping macromolecular behavior. Insights into water micro assemblies (WMA), defined by transient regions of low-density water (LDW) and high-density water (HDW), have highlighted their potential impact on biological phenomena. LDW, with its structured hydrogen bon...

Cerebrospinal fluid (CSF) flows play a main role in maintaining brain homeostasis, supporting waste clearance, nutrient delivery and interstitial solute exchange. Although current models emphasize mechanical drivers such as cardiac pulsation, respiration and ciliary motion, these mechanisms alone fall short of explaining the nuanced spatiotemporal...

T cell activation results from the integration of multiple concurrent signals, including antigen engagement through the T cell receptor (TCR), co-stimulatory cues and inhibitory modulation. While traditional computational models often rely on Boolean logic to describe immune decision-making, these binary representations oversimplify the nuanced, re...

A wide range of biological and evolutionary processes is determined not merely by the occurrence of specific events, but by the exact order in which those events unfold. Gene regulation, developmental pathways, metabolic cascades and genetic evolution often display non-commutative behaviour, in which reversing the sequence of events results in func...

T cell activation results from the integration of multiple concurrent signals, including antigen engagement through the T cell receptor (TCR), co-stimulatory cues and inhibitory modulation. While traditional computational models often rely on Boolean logic to describe immune decision-making, these binary representations oversimplify the nuanced, re...

A wide range of biological and evolutionary processes is determined not merely by the occurrence of specific events, but by the exact order in which those events unfold. Gene regulation, developmental pathways, metabolic cascades and genetic evolution often display non-commutative behaviour, in which reversing the sequence of events results in func...

Nonlinear dynamical systems resist global analysis when approached through classical linearization techniques which rely on differential equations and local approximations. In seeking approaches to structurally reduce nonlinear dynamics to linear components, we propose interpreting the evolution of a nonlinear system as a sequence of non-commuting...

A theoretical framework bridging General Relativity (GR) and Quantum Dynamics (QD) is introduced through the application of Kripke semantics and linear logic. While conventional unification efforts often rely on structural or geometrical formulations, we instead treat causality, energy and information as finite, non-replicable resources constrainin...

Nonlinear dynamical systems resist global analysis when approached through classical linearization techniques which rely on differential equations and local approximations. In seeking approaches to structurally reduce nonlinear dynamics to linear components, we propose interpreting the evolution of a nonlinear system as a sequence of non-commuting...

The origin of life is a complex scientific problem demanding interdisciplinary approaches. We propose a Linear Logic (LL)-based computational framework to formally evaluate the feasibility of early biochemical pathways across competing abiogenesis scenarios. Unlike classical logic, LL explicitly tracks resource consumption and transformation. This...

The origin of life is a complex scientific problem demanding interdisciplinary approaches. We propose a Linear Logic (LL)-based computational framework to formally evaluate the feasibility of early biochemical pathways across competing abiogenesis scenarios. Unlike classical logic, LL explicitly tracks resource consumption and transformation. This...

The challenge of the vacuum catastrophe arises from the vast discrepancy between quantum field theoretical predictions and observed vacuum energy density. Using analytic continuation techniques and asymptotic analysis to ensure physical consistency, we explored the Mittag-Leffler function (MLF), a generalized exponential function widely applied in...

The challenge of the vacuum catastrophe arises from the vast discrepancy between quantum field theoretical predictions and observed vacuum energy density. Using analytic continuation techniques and asymptotic analysis to ensure physical consistency, we explored the Mittag-Leffler function (MLF), a generalized exponential function widely applied in...

Raynaud’s Phenomenon (RP), characterized by episodic reductions in peripheral blood flow, leads to significant discomfort and functional impairment. Existing therapeutic strategies focus on pharmacological treatments, external heat supplementation and exercise-based rehabilitation, but fail to address biomechanical contributions to vascular dysfunc...

Optimal transport models may provide a robust framework for quantifying gas movement from the intestinal lumen into the gut layers in pneumatosis intestinalis (PI), a condition characterized by abnormal gas accumulation within the intestinal wall. We develop a mathematical approach that integrates circular gas diffusion from the lumen with the subs...

Raynaud's Phenomenon (RP), characterized by episodic reductions in peripheral blood flow, leads to significant discomfort and functional impairment. Existing therapeutic strategies focus on pharmacological treatments, external heat supplementation and exercise-based rehabilitation, but fail to address biomechanical contributions to vascular dysfunc...

Optimal transport models may provide a robust framework for quantifying gas movement from the intestinal lumen into the gut layers in pneumatosis intestinalis (PI), a condition characterized by abnormal gas accumulation within the intestinal wall. We develop a mathematical approach that integrates circular gas diffusion from the lumen with the subs...

Wolfram's Elementary Cellular Automata (ECA) serve as fundamental models for studying discrete dynamical systems, yet their classification remains challenging under traditional statistical and heuristic methods. By leveraging tools from algebraic topology, homotopy theory and differential geometry, we establish a formal connection between topologic...

Wolfram’s Elementary Cellular Automata (ECA) serve as fundamental models for studying discrete dynamical systems, yet their classification remains challenging under traditional statistical and heuristic methods. By leveraging tools from algebraic topology, homotopy theory and differential geometry, we establish a formal connection between topologic...

Understanding intelligence-related variations in electroencephalographic (EEG) activity requires advanced mathematical approaches capable of capturing geometric transformations and long-range dependencies in neural dynamics. These approaches may provide methodological advantages over conventional spectral and connectivity-based techniques by offeri...

Understanding intelligence-related variations in electroencephalographic (EEG) activity requires advanced mathematical approaches capable of capturing geometric transformations and long-range dependencies in neural dynamics. These approaches may provide methodological advantages over conventional spectral and connectivity-based techniques by offeri...

The intersection of mathematics and philosophy has been extensively explored through logic and set theory, but the application of topological and algebraic tools to the analysis of philosophical arguments and conceptual structures has received less attention. By integrating key concepts from algebraic topology, homotopy theory and probability theor...

The intersection of mathematics and philosophy has been extensively explored through logic and set theory, but the application of topological and algebraic tools to the analysis of philosophical arguments and conceptual structures has received less attention. By integrating key concepts from algebraic topology, homotopy theory and probability theor...

The application of topological methods to cerebral angiography may provide a robust mathematical framework for analyzing cerebrovascular structures at multiple scales. In this proof-of concept study, we explored the use of algebraic and differential topology to characterize structural integrity, connectivity, flow dynamics and hierarchical organiza...

Medical decision-making relies on scientific data to ensure accurate diagnoses and effective treatments. However, in many real-world scenarios, medical data may be incomplete, unreliable or conflicting, leaving clinicians with significant uncertainty. We propose a pragmatic and structured approach to medical judgment when sufficient empirical evide...

Topological approaches to biological systems provide insights into their growth patterns, network connectivity and spatial organization. This perspective explores how biological structures self-organize, maintain stability and adapt to environmental constraints, revealing fundamental principles of efficiency, robustness, resilience and functional o...

The application of topological methods to cerebral angiography may provide a robust mathematical framework for analyzing cerebrovascular structures at multiple scales. In this proof-of concept study, we explored the use of algebraic and differential topology to characterize structural integrity, connectivity, flow dynamics and hierarchical organiza...

The application of topological methods to cerebral angiography may provide a robust mathematical framework for analyzing cerebrovascular structures at multiple scales. In this proof-of concept study, we explored the use of algebraic and differential topology to characterize structural integrity, connectivity, flow dynamics and hierarchical organiza...

Poincaré duality from algebraic topology describes how shapes and spaces interrelate across different dimensions, linking structures of one scale to complementary structures at another. This suggests that densely packed neurons in certain brain areas may correspond to broader connectivity patterns, balancing local processing with global communicati...

Topological approaches to biological systems provide insights into their growth patterns, network connectivity and spatial organization. This perspective explores how biological structures self-organize, maintain stability and adapt to environmental constraints, revealing fundamental principles of efficiency, robustness, resilience and functional o...

Poincaré duality from algebraic topology describes how shapes and spaces interrelate across different dimensions, linking structures of one scale to complementary structures at another. This suggests that densely packed neurons in certain brain areas may correspond to broader connectivity patterns, balancing local processing with global communicati...

Lévy flights (LF), a concept originating in statistical physics, describe random walks in which the step lengths follow a heavy-tailed probability distribution, often a power law. Unlike Brownian motion, where step lengths are constrained within a narrow range, LF are characterized by the coexistence of many short steps interspersed with occasional...

Levy flights (LF), a concept originating in statistical physics, describe random walks in which the step lengths follow a heavy-tailed probability distribution, often a power law. Unlike Brownian motion, where step lengths are constrained within a narrow range, LF are characterized by the coexistence of many short steps interspersed with occasional...

Water is central to biological processes not only as a solvent but also as an agent shaping macromolecular behaviour. Insights into water micro-assemblies (WMA), defined by transient regions of low-density water (LDW) and high-density water (HDW), have highlighted their potential impact on biological phenomena. LDW, with its structured hydrogen bon...

Water is central to biological processes not only as a solvent but also as an agent shaping macromolecular behaviour. Insights into water micro-assemblies (WMA), defined by transient regions of low-density water (LDW) and high-density water (HDW), have highlighted their potential impact on biological phenomena. LDW, with its structured hydrogen bon...

We investigated the application of percolation theory to the Planck's Cosmic Microwave Background (CMB) to analyze the connectivity and statistical properties of temperature anisotropies. Percolation, which describes the emergence of large-scale connectivity, provides a unique framework for interpreting CMB as a statistical realization of cosmic pr...

We explored the nonlinear movement patterns of Anacridium aegyptium during terrestrial locomotion, providing insights into the walking dynamics of this large grasshopper species. Using video recordings, we analysed the trajectory of an insect and quantified key metrics, including curvature, tortuosity and fractal dimension. Curvature analysis revea...

We investigated the application of percolation theory to the Planck’s Cosmic Microwave Background (CMB) to analyze the connectivity and statistical properties of temperature anisotropies. Percolation, which describes the emergence of large-scale connectivity, provides a unique framework for interpreting CMB as a statistical realization of cosmic pr...

Takens' theorem (TT) proves that the behaviour of a dynamical system can be effectively reconstructed within a multidimensional phase space. This offers a comprehensive framework for examining temporal dependencies, dimensional complexity and predictability of time series data. We applied TT to investigate the physiological regional differences in...

Takens' theorem (TT) proves that the behaviour of a dynamical system can be effectively reconstructed within a multidimensional phase space. This offers a comprehensive framework for examining temporal dependencies, dimensional complexity and predictability of time series data. We applied TT to investigate the physiological regional differences in...

We explored the nonlinear movement patterns of Anacridium aegyptium during terrestrial locomotion, providing insights into the walking dynamics of this large grasshopper species. Using video recordings, we analysed the trajectory of an insect and quantified key metrics, including curvature, tortuosity and fractal dimension. Curvature analysis revea...

The traditional Stokes' theorem connects the macroscopic circulation along a closed boundary to the microscopic circulation across the surface it encloses. However, it proves inadequate for addressing complex geometries such as helicoidal paths, non-planar flow patterns and dynamic systems with open boundaries. We introduce an extension of Stokes'...

The traditional Stokes' theorem connects the macroscopic circulation along a closed boundary to the microscopic circulation across the surface it encloses. However, it proves inadequate for addressing complex geometries such as helicoidal paths, non-planar flow patterns and dynamic systems with open boundaries. We introduce an extension of Stokes'...

A Markov chain (MC) is a mathematical model used to describe a system where the probability of moving to the next state depends solely on the current state and not on the sequence of the preceding states. A Markov blanket (MB) for a node includes its parents, children and other parents of its children, capturing the minimal set of nodes required to...

The neural mechanisms underlying individual differences in intelligence are a central focus in neuroscience. We investigated the effectiveness of Monte Carlo simulations in predicting real EEG patterns and uncovering potential neural differences between individuals with high and low intelligence. EEG data were collected from two groups of volunteer...

A Markov chain (MC) is a mathematical model used to describe a system where the probability of moving to the next state depends solely on the current state and not on the sequence of the preceding states. A Markov blanket (MB) for a node includes its parents, children and other parents of its children, capturing the minimal set of nodes required to...

The neural mechanisms underlying individual differences in intelligence are a central focus in neuroscience. We investigated the effectiveness of Monte Carlo simulations in predicting real EEG patterns and uncovering potential neural differences between individuals with high and low intelligence. EEG data were collected from two groups of volunteer...

Envelope viruses infecting human individuals can originate from two sources: either from an intermediary animal that transmits the virus to humans, or from another infected human. During a pandemic such as SARS-CoV-2, identifying the intermediate host or the primary human source presents a significant challenge. This complex task is typically addre...

Envelope viruses infecting human individuals can originate from two sources: either from an intermediary animal that transmits the virus to humans, or from another infected human. During a pandemic such as SARS-CoV-2, identifying the intermediate host or the primary human source presents a significant challenge. This complex task is typically addre...

We are introducing a novel thermodynamic emotion model. In this model, emotions are regarded as deviations from equilibrium, akin to fluctuations in body temperature. This bipolar regulation maintains bodily and psychological homeostasis while spurring mental development. Emotional regulation typically occurs through expanding one's perception of t...

The macroscopic flow along the boundary of a closed curve is equivalent to the cumulative sum of microscopic flows within the enclosed area. Green's theorem formalizes this relationship by connecting the counterclockwise flow within the surface of a two-dimensional manifold to the counterclockwise flow along its boundary. Building on this, Stokes'...

A unified mathematical framework, referred to as Picard-Fuchs Hypergeometric Manifolds (PFHM), is introduced to integrate modular symmetry, coupled dynamics and energy conservation. PFHM are constructed using a synthesis of Ramanujan's real period functions, Picard-Fuchs differential equations and Gaussian hypergeometric functions. We argue that PF...

FReSCo is a recently developed algorithm that generates images and videos starting from point patterns. We suggest a feasible neuroscientific application for FReSCo. As a proof-of concept study, FReSCo could be used to test freely available videos of intermittently firing neurons at different coarse-grained neuronal scales. Interpreting cortical ne...

The Sansevero Chapel displays a well-conceived design, in which Ripa’s iconographic references play an important role. We argue that di Sangro at times distorts Ripa’s iconography to illustrate the difficult path awaiting the Mason apprentice. Decorum, one of the first sculptures the visitor encounters on their left upon entering the Chapel, lacks...

Physical properties such as shape, volume, and size influence the dynamics of biological systems. In this context, we focus on the geometric properties of limb movements and their physiological and biomechanical effects. Using hand grasping as a paradigmatic example, we describe how dynamic changes in geometric configuration can affect the pathophy...

The universe is punctured with a high number of black holes that might stand for topological "holes" or "cavities". Starting from this observation, we discuss the possibility to think over the universe in terms of a manifold of very high genus (henceforward VHGM), rather than an isotropic and homogeneous manifold of genus zero. We argue about the f...

After the introduction of the Christian religion, a traumatic shift took place in the Norse approach to death rituals. Transition went with strains between the ancient era of cremation and the new inhumation period. We argue that the myth of Ragnarök, written after Icelandic Christianization, might refer to the Norse mythical past of funeral pyres...

Real and epistemically justified judgements require individuals' beliefs grounded on empiric inductive experience. Yet, solid scientific evidence is frequently unavailable, unreliable or controversial, preventing individuals to build their own beliefs in real-life events that require clear-cut and fast answers, especially across domains like employ...

Medical judgements require doctor's belief based on the solid scientific evidence provided by empiric inductive experience. Yet, it is not infrequent that scientific data are unavailable, unreliable or controversial, such that the empirical evidence is not solid enough to allow doctors to build their own belief and make a final choice. Here we ask...

Ramanujan’s real period functions plus Picard–Fuchs differential equations and Gaussian hypergeometric functions generate a wide range of simple hypergeometric manifolds (henceforward PFHM) consisting of two-dimensional coupled subsystems combined in a single three-dimensional system with dihedral symmetry. We argue that PFHM could be used to eluci...

Ramanujan's real period functions plus Picard-Fuchs differential equations and Gaussian hypergeometric functions generate a wide range of simple hypergeometric manifolds (henceforward PFHM) consisting of two-dimensional coupled subsystems combined in a single three-dimensional system with dihedral symmetry. We argue that PFHM could be used to eluci...

The great Hittite king Muwatalli II, passed to posterity for taking part in the first ever recorded battle, namely, the battle of Kadesh in 1274 B.C. against Ramesses II, passed away around the year 1272 B.C. We suggest that Muwatalli II didn't die for natural causes as commonly believed, but he was killed. We provide a list of the enemies who want...

A delicate balance between dissipative and nonlinear forces allows traveling waves termed solitons to preserve their shape and energy for long distances without steepening and flattening out. Solitons are so widespread that they can generate both destructive waves on oceans' surfaces and noise-free message propagation in silica optic fibers. They a...

Elliptic curves are fundamental mathematical objects obeying two-variable equations in which the square of one variable relates to the third power of another. Wondering whether elliptic curves might stand for the abstract counterpart of biological activities, we identified a correspondence between the two-dimensional plots of various elliptic curve...

Local interactions between flock members in absence of centralized control generate collective dynamics characterized by coherent large-scale patterns. We investigate whether aggregates of individuals like birds, swarms and fishes behaving in concert with their neighbors may modify the physical properties of the fluid medium in which they are embed...

A delicate balance between dissipative and nonlinear forces allows traveling waves termed solitons to preserve their shape and energy for long distances without steepen and flatten out. Solitons are so widespread that can generate both destructive waves in oceans' surface and noise-free message propagation in silica optic fibers. They are naturally...

Many living beings use exogenous and/or endogenous gases to attain evolutionary benefits. We make a comprehensive assessment of one of the major gaseous reservoirs in the human body, i.e., the bowel, providing extensive data that may serve as reference for future studies. We assess the intestinal gases in healthy humans, including their volume, com...

Turbulence is a widespread phenomenon detectable in physical and biological systems. Examining a theoretical model of liquid water flowing in a cylinder at different Raleigh numbers, we propose a novel approach to elucidate the first stages of turbulent flows. The weakly bonded molecular assemblies of liquid distilled water form a fluctuating branc...

Local interactions between flock members in absence of centralized control generate collective dynamics characterized by coherent large-scale patterns. We investigate whether aggregates of individuals like birds, swarms and fishes behaving in concert with their neighbors may modify the physical properties of the fluid medium in which they are embed...

PREMISE: In 2023, increases in scarlet fever's incidence have been detected throughout Europe. Based on general pediatricians' experience, we hypothesize that a shift has occurred in both group A streptococcus (GAS) clinical findings and age of onset. Therefore, we propose to evaluate whether the well-standardized signs and symptoms leading to GAS...

Physical properties like shape, volume and size affect the dynamics of biological systems. Along these lines, we focus on the topological properties of biological fluids and their biochemical and physiological outcomes. We take as a paradigmatic example the salivary fluid and describe how its topological features may affect the physiopathology of t...

Physical properties like shape, volume and size affect the dynamics of biological systems. Along these lines, we focus on the topological properties of biological fluids and their biochemical and physiological outcomes. We take as a paradigmatic example the salivary fluid and describe how its topological features may affect the physiopathology of t...

The central dogma of molecular biology dictates that, with only a few exceptions, information proceeds from DNA to protein through an RNA intermediate. Examining the enigmatic steps from prebiotic to biological chemistry, we take another road suggesting that primordial peptides acted as template for the self-assembly of the first nucleic acids poly...

(Communicated by Hari M. SRIVASTAVA on 6 August 2023). This paper introduces geometric realizations of homotopic paths over simply-connected surfaces with non-zero curvature as a means of comparing and measuring paths between antipodes with either a Feynman path integral or Woodhouse contour integral, resulting in a number of extensions of the Bo...

In macro-public finance, the Ramsey rule (RR) concerns variable taxation to maximize social welfare and economic efficiency in a purely competitive monopolistic system. To extract tax revenue with the least loss of utility to the representative individual, RR dictates that optimal, proportionate taxes should be such as to diminish in the same propo...

Tozzi A. 2023. The ubiquitous role of complete graphs: Ramsey’s theorem & electrical synapses in connectomics. 2023. (Electronic Response to Hürkey, S., Niemeyer, N., Schleimer, JH. et al. Gap junctions desynchronize a neural circuit to stabilize insect flight. Nature 618, 118–125 (2023). https://doi.org/10.1038/s41586-023-06099-0).

In macro-public finance, the Ramsey rule (RR) concerns variable taxation to maximize social welfare and economic efficiency in a purely competitive monopolistic system. To extract tax revenue with the least loss of utility to the representative individual, RR dictates that optimal, proportionate taxes should be such as to diminish in the same propo...

In macro-public finance, the Ramsey rule (RR) concerns variable taxation to maximize social welfare and economic efficiency in a purely competitive monopolistic system. To extract tax revenue with the least loss of utility to the representative individual, RR dictates that optimal, proportionate taxes should be such as to diminish in the same propo...

Ultrametric spaces are widely used to depict evolutionary times in phylogenetic trees since they assume that every population/species is located at the tips of bifurcating branches of the same length. The discrete branching of ultrametric trees permits the measurement of distances between pairs of individuals that are proportional to their divergen...

Dogs display vast phenotypic diversity, including differences in height, skull shape, tail, etc. Yet, humans are almost always able to quickly recognize a dog, despite no single feature or group of features are critical to distinguish dogs from other objects/animals. In search of the mental activities leading human individuals to state _“I see a do...

Dogs display vast phenotypic diversity, including differences in height, skull shape, tail, etc. Yet, humans are almost always able to quickly recognize a dog, despite no single feature or group of features are critical to distinguish dogs from other objects/animals. In search of the mental activities leading human individuals to state "I see a dog...

The single macroscopic flow on the boundary of a closed curve equals the sum of the countless microscopic flows in the enclosed area. According to the dictates of the Green’s theorem, the counterclockwise movements on the border of a two-dimensional shape must equal all the counterclockwise movements taking place inside the shape. This mathematical...

Visual imagery (VI) is the mental experience of objects in the absence of their corresponding visual stimuli. Asking whether mental images can be physically quantified, we seek for relationships between visual imagery and special relativity. The Einstein's account states that, by an observer's standpoint, an object traveling at light speed is subje...

The central dogma of molecular biology dictates that, with only a few exceptions, information proceeds from DNA to protein through an RNA intermediate. Examining the enigmatic steps from prebiotic to biological chemistry, we take another road suggesting that primordial peptides acted as template for the self-assembly of the first nucleic acids poly...

The central dogma of molecular biology dictates that, with only a few exceptions, information proceeds from DNA to protein through an RNA intermediate. Examining the enigmatic steps from prebiotic to biological chemistry, we take another road suggesting that primordial peptides acted as template for the self-assembly of the first nucleic acids poly...

Ramsey's theory (RAM) from combinatorics and network theory goes looking for regularities and repeated patterns inside structures equipped with nodes and edges. RAM represents the outcome of a dual methodological commitment: by one side a top-down approach evaluates the possible arrangement of specific subgraphs when the number of graph's vertices...

Travelling waves crossing the nervous networks at mesoscopic/macroscopic scales have been correlated with different brain functions, from long-term memory to visual stimuli. Here we investigate a feasible relationship between wave generation/propagation in recurrent nervous networks and a physical/chemical model, namely the Belousov-Zhabotinsky rea...