Arturo Tozzi

University of North Texas | UNT · Department of Physics

Brain activity takes place in three spatial-plus time dimensions. This rather obvious claim has been questioned by novel papers that, taking into account the big data outburst and the recently introduced computational tools, are starting to unveil a more intricate state of affairs. Indeed, various brain activities and their correlated mental functi...

Set theory faces two difficulties: formal definitions of sets/subsets are incapable of assessing biophysical issues; formal axiomatic systems are complete/inconsistent or incomplete/consistent. To overtake these problems reminiscent of the old-fashioned principle of individuation, we provide formal treatment/validation/operationalization of a metho...

The massive amount of available neurodata suggests the existence of a mathematical backbone underlying neuronal oscillatory activities. For example, geometric constraints are powerful enough to define cellular distribution and drive the embryonal development of the central nervous system. We aim to elucidate whether underrated notions from geometry...

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...

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...

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...

Intestinal gases are usually discarded as physiologically inert, useless sub-products of colonic fermentation that must be expelled to prevent discomfort and meteorism. Starting from the observation that many living beings use exogenous and/or endogenous gases to attain evolutionary benefits, we question whether intestinal gases in healthy humans c...

Intestinal gases are usually discarded as physiologically inert, useless sub-products of colonic fermentation that must be expelled to prevent discomfort and meteorism. Starting from the observation that many living beings use exogenous and/or endogenous gases to attain evolutionary benefits, we question whether intestinal gases in healthy humans c...

COMMENT TO A NEJM 2022 paper: Low-Dose Subcutaneous or Intravenous Monoclonal Antibody to Prevent Malaria. ----------------------- Most of the Plasmodium-carrying Anopheles spp. (henceforward mosquitoes) increase in individuals’ number during the wet season and decrease during the dry season. It has been demonstrated that female pregnant mosquito...

This paper introduces geometric realizations of homotopic paths over simply-connected surfaces with non-zero curvature as 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 Borsuk Ulam Theorem. All realizations of homotopic paths resi...

[Journal of Topology, London Mathematical Society]. This paper introduces discrete and continuous paths over simply-connected surfaces with non-zero curvature as 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 Borsuk Ulam Theorem....

Turbulence is a fluid dynamic problem refractory to mathematical treatment. 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 water form a fluctuating branched polymer in whic...

When a boat disappears over the horizon, does a distant observer detect the last moment in which the boat is visible, or the first moment in which the boat is not visible? This apparently ludicrous way of reasoning, heritage of long-lasting medieval debates on decision limit problems, paves the way to sophisticated contemporary debates concerning t...

Mechanical properties such as shape, volume and size affect the dynamics of biological systems. Most of the current methodological approaches are inclined to remove the existence of holes and impurities from systems' description, regarding them as routes toward mechanical failure. On the contrary, we suggest that the occurrence of holes might be of...

Mechanical properties such as shape, volume and size affect the dynamics of biological systems. Most of the current methodological approaches are inclined to remove the existence of holes and impurities from systems’ description, regarding them as routes toward mechanical failure. On the contrary, we suggest that the occurrence of holes might be of...

Novel methodological approaches to assess topological mappings and projections between biophysical phase spaces have been recently introduced in neuroscience. In this brief survey of our published manuscripts, we discuss how the "unreasonable power" of algebraic topology permits an experimentally testable top-down inquiry of the brain activity.

A novel methodological approach requires the observer to investigate the information accessible outside the object under scrutiny. The object becomes an “hole” devoid of information, surrounded by a container that is no longer a passive structure. We use this container-framed attitude for a mathematical attempt to take a step towards the unexploite...

Instead of the conventional 0 and 1 values, bipolar reasoning uses-1, 0, +1 to describe double-sided judgements in which neutral elements are halfway between positive and negative evaluations (e.g., "uncertain" lies between "impossible" and "totally sure"). We discuss the state-of-the-art in bipolar logics and recall two medieval forerunners, i.e.,...

One of the criteria to a strong principle in natural sciences is simplicity. The conventional view holds that the world is provided with natural laws that must be simple. This common-sense approach is a modern rewording of the medieval philosophical/theological concept of the Multiple arising from (and generated by) the One. Humans need to pursue u...

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...

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...

When it's right, it's right.

The massive amount of available neurodata suggests the existence of a mathematical backbone underlying the intricate oscillatory activity of the brain. Hidden, unexpected multidisciplinary relationships can be found when mathematics copes with neural phenomena, leading to novel answers for everlasting neuroscientific questions. We elucidate how and...

In this brief note, we propose a novel mechanism that might contribute to the visual ability of depth perception. We suggest a mathematical approach based on the Monge's theorem which allows the perception of the object's distance from the observer's eye and its three-dimensional features.

In this brief note, we cast doubts on the death of the great Hittite king Muwatalli II. Going through the prayer CTH 383 in which the king's impiety against the priestess of the Sun-goddness of Arinna is emphasized and condemned, we argue that Muwatalli II was dismissed and killed: "he paid for it with his head".

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 divergent branches. The discrete branching of ultrametric trees permits the measurement of distances between pairs of individuals that are proportional to their divergence time. Here we ove...

Neuroscientists are able to detect physical changes in information entropy in the available neurodata. However, the information paradigm is inadequate to describe fully nervous dynamics and mental activities such as perception. This paper suggests explanations to neural dynamics that provide an alternative to thermodynamic and information accounts....

Instead of the conventional 0 and 1 values, bipolar reasoning uses-1, 0, +1 to describe double-sided judgements in which neutral elements are halfway between positive and negative evaluations (e.g., "uncertain" lies between "impossible" and "totally sure"). We discuss the state-of-the-art in bipolar logics and recall two medieval forerunners, i.e.,...

Instead of the conventional 0 and 1 values, bipolar reasoning uses -1, 0, +1 to describe double-sided judgements in which neutral elements are halfway between positive and negative evaluations (e.g., “uncertain” lies between “impossible” and “totally sure”). We discuss the state-of-the-art in bipolar logics and recall two medieval forerunners, i.e....

This paper introduces quaternionic views of multi-level brain activation region intensities in resting-state functional magnetic resonance imaging (rs-fMRI) videos. Quaternions make it possible to explore rs-fMRI brain activation regions in a 4D space in which there are varying brain activation intensities in spiralling activation cycles (each with...

Ramsey's economic theory of saving (RTS) estimates how much of its commodities a nation should save to safeguard the well-being of future generations. Since RTS retains many attractive qualities such as simplicity, strength, breadth and generality, here we ask if it would be useful to investigate biophysical issues. Specifically, we focus on a biol...

Ramsey's economic theory of saving (RTS) estimates how much of its commodities a nation should save to safeguard the well-being of future generations. Since RTS retains many attractive qualities such as simplicity, strength, breadth and generality, here we ask if it would be useful to investigate biophysical issues. Specifically, we focus on a biol...

Ramsey’s economic theory of saving (RTS) estimates how much of its commodities a nation should save to safeguard the well-being of future generations. Since RTS retains many attractive qualities such as simplicity, strength, breadth and generality, here we ask if it would be useful to investigate biophysical issues. Specifically, we focus on a biol...

Whenever one attempts to comb a hairy ball flat, there will always be at least one tuft of hair at one point on the ball. This seemingly worthless sentence is an informal description of the hairy ball theorem, an invaluable mathematical weapon that has been proven useful to describe a variety of physical/biological processes/phenomena in terms of t...

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...

When an edge is removed, a cycle graph Cn becomes a n-1 tree graph. This observation from extremal set theory leads us to the realm of set theory, in which a topological manifold of genus-1 turns out to be of genus-0. Starting from these premises, we prove a theorem suggesting that a manifold with disjoint points must be of genus-0, while a manifol...

Tozzi A. 2021. To know them, remove their information: an outer methodological approach to biophysics and humanities. (INTERNATIONAL SOCIETY FOR THE STUDY OF INFORMATION) IS4SI Summit 2021. Theoretical and Foundational Problems in Information Studies. Session 3: Information in Natural Sciences. https://tfpis.com/session-3-information-in-natural-...

The methodological/operational virtues of stochastic approaches allow us to assess biophysical phenomena in terms of random walks, Brownian motions, Markov chains, etc. We argue that these approaches are not profitable when stochastic paths occur in high-dimensional phase spaces. Indeed, contrary to the two-dimensional random walks, the higher-dime...

How do we perceive a visual image? Some authors suggest that we have topological perceptions of visual objects. Here we show that the human mind does not perceive topological findings of visual images, rather it uses a fully different (and still unknown) mechanism.

The unexploited unification of general relativity and quantum mechanics (QM) prevents the proper understanding of the micro- and macroscopic world. Here we put forward a mathematical approach that introduces the problem in terms of negative curvature manifolds. We suggest that the oscillatory dynamics described by wave functions might take place on...

Physical and biological measurements might display range values extending towards infinite. The occurrence of infinity in equations, such as the black hole singularities, is a troublesome issue that causes many theories to break down when assessing extreme events. Different methods, such as re-normalization, have been proposed to avoid detrimental...

My teachers used to tell me: “Tozzi, be on focus”. But I never liked “to be on focus”: I like a lot to play with hidden, unexpected multidisciplinary relationships. Despite my harsh criticism to current attitudes toward scientific issues, I never take a full sceptic turn: I engage in “pragmaticistic” active outreach, showing how fresh interpretatio...

Neural networks are commonly described in terms of feedforward paths coupled with feedback circuits that guarantee backpropagation and message control. Here we, based on mathematical arguments from algebraic topology, near set theory and category theory, suggest the testable hypothesis that neuronal networks might be equipped with feedback mechanis...

The brain, rather than being homogeneous, displays an almost infinite topological genus, since it is punctured with a high number of “cavities”. We might think to the brain as a sponge equipped with countless, uniformly placed, holes. Here we show how these holes, termed topological vortexes, stand for nesting, non-concentric brain signal cycles re...

According to Shannon, the entropy for continuous stochastic processes has many properties analogous to the entropy for discrete processes. Nevertheless, there are some mathematical and physical problems with Shannon's account. The obstacle arises in chapter 21 (Shannon 1948), when Shannon describes the continuous case of the entropy of ergodic ense...

Background: Gene-environment interactions are relevant for several respiratory diseases. This communication raises the hypothesis that the severity of COVID-19, a complex disease where the individual response to the infection may play a significant role, could partly result from a gene-environment interaction between air-pollution and Alpha-1 Anti...

Set theory faces two difficulties: formal definitions of sets/subsets are incapable of assessing biophysical issues; formal axiomatic systems are complete/inconsistent or incomplete/consistent. To overtake these problems reminiscent of the old-fashioned principle of individuation, we provide formal treatment/validation/operationalization of a metho...

Set theory faces two difficulties: formal definitions of sets/subsets are incapable of assessing biophysical issues; formal axiomatic systems are complete/inconsistent or incomplete/consistent. To overtake these problems reminiscent of the old-fashioned principle of individuation, we provide formal treatment/validation/operationalization of a metho...

The heretic Capuchin Celestino of Verona, one of the harshest opponents of Giordano Bruno, wrote in 1599 to the Roman Inquisition and (anonymously) to the Venetian Inquisitor to inform himself. In a few months, he was burnt alive on the heels of an unusually short Inquisitorial trial. This traditional account, held by the most prominent scholars of...

Relationships among near set theory, shape maps and recent accounts of the Quantum Hall effect pave the way to neural networks computations performed in higher dimensions. We illustrate the operational procedure to build a real or artificial neural network able to detect, assess and quantify a fourth spatial dimension. We show how, starting from tw...

The unexploited unification of general relativity and quantum mechanics (QM) prevents the proper understanding of the micro- and macroscopic world. Here we put forward a mathematical approach that introduces the problem in terms of negative curvature manifolds. We suggest that the oscillatory dynamics described by wave functions might take place on...

We suggest that the 14th century scholar Nicholas of Autrecourt can be regarded as a precursor of the paraconsistent logics developed around 1950. We show how the Sorbonne licentiatus in theology provided in his few extant writings a refutation of both the principle of explosion and the law of non-contradiction, in accordance with the tenets of par...

The dynamical processes of living systems are characterized by the cooperative interaction of many units. This claim enables us to portray the embryo-fetal development of the central and peripheral nervous systems in terms of assemblies of building blocks. We describe how the structure and arrangement of nervous fibers is-at least partially-dictate...

The dynamical processes of living systems are characterized by the cooperative interaction of many units. This claim enables us to portray the embryo-fetal development of the central and peripheral nervous systems in terms of assemblies of building blocks. We describe how the structure and arrangement of nervous fibers is - at least partially - dic...

Quote as: Tozzi A. 2021. XOR: another feasible logcal operation apart from AND, OR, NOT (electronic response to: Lajoie MJ, Boyken SE, Salter AI, Bruffey J, Rajan A. 2021 . Designed protein logic to target cells with precise combinations of surface antigens. Science, 369(6511): 1637-1643. DOI: 10.1126/science.aba6527).

The nervous activity of the brain takes place in higher-dimensional functional spaces. It has been proposed that the brain might be equipped with phase spaces characterized by four spatial dimensions plus time, instead of the classical three plus time. This suggests that global visualization methods for exploiting four-dimensional maps of three-dim...

QUOTE AS: Tozzi A. 2021. Variations in cellular temperature and thermodynamic outcomes (electronic response to: Sotoma S, Zhong C, Kah JCY, Yamashita4 H. Plakhotnik T, et al. 2021. In situ measurements of intracellular thermal conductivity using heater-thermometer hybrid diamond nanosensors. Science Advances. Vol. 7, no. 3, eabd7888, DOI: 10.1126...

Against the critiques against Pfizer and Moderna vaccines raised by BMJ.

The internationals guidelines about food intolerances, allergy and immunity provide for rigorous steps in which ultrasonography is not provided. However there is evidence in literature about an ancillar role of ultrasonography in these conditions. In this report we analyze the main pathologies with allergic or immune pathogenesis. -----------------...

Take a balloon, that is a genus-one manifold. If you break the jointness by piercing its surface, the hole gets lost and the punctured balloon becomes a genus-0 manifold. Starting from this trivial claim, we prove a topological theorem which plainly states that "the ends of a donut can meet, whilst the ends of a kidney pie cannot". In this succinct...

This manuscript has been published. Please quote as: Tozzi A. 2021. Why Should Natural Principles Be Simple? Philosophia. https://doi.org/10.1007/s11406-021-00359-x. -------------------------------------------------------------------One of the criteria to a strong principle in natural sciences is simplicity. The conventional view holds that the wor...

William of Ockham's Mass... and quantum dynamics.

In this brief manuscript, we show how the sensitive ascending nervous fibers connecting peripheral receptors to cortical areas can be described in terms of braid groups. The group structure and generator operations of braids suggest a fresh approach to long-standing questions concerning human sensation and perception.

Physical and biological phenomena are often portrayed in terms of random walks, white noise, Markov paths, stochastic trajectories with subsequent symmetry breaks. Here we show that this approach from dynamical systems theory is not profitable when random walks occur in phase spaces of dimensions higher than two. The more the dimensions, the more t...

Physical and biological phenomena are often portrayed in terms of random walks, white noise, Markov paths, stochastic trajectories with subsequent symmetry breaks. Here we show that this approach from dynamical systems theory is not profitable when random walks occur in phase spaces of dimensions higher than two. The more the dimensions, the more t...

A listof my proposals concerning SARS-Cov-2 pandemics

We suggest that the SARS-Cov-2 particles emerging from the cells of elder or pediatric hosts are phenotypically different, because they are equipped with a slightly different envelope. This might contribute to the well-documented variations of COVID-19 symptoms severity in populations of different ages.

The SARS-Cov-2 virions produced in human children, adults and elder people display slight differences in their makeup.

Neuroscientists draw lines of separation among structures and functions that they judge different, arbitrarily excluding or including issues in our description, to achieve positive demarcations that permits a pragmatic treatment of the nervous activity based on regularity and uniformity. However, uncertainty due to disconnectedness, lack of informa...

When a boat disappears over the horizon, does a distant observer detect the last moment in which the boat is visible, or the first moment in which the boat is not visible? This apparently ludicrous way of reasoning, heritage of long-lasting medieval debates on decision limit problems, paves the way to sophisticated contemporary debates concerning t...

Quote as: Tozzi A. 2020. Measles vaccine: protective against COVID-19? (electronic response to: Mina MJ, Kula T, Leng Y, Li M, de Vries,et al. 2019. Measles virus infection diminishes preexisting antibodies that offer protection from other pathogens. Science, 366(6465):599-606. doi: 10.1126/science.aay6485).

Quote as: Tozzi A. 2020. A deluge of disinfectants and skin lesions during COVID-19 pandemics (electronic response to: Madigan LM, Micheletti RG, Shinkai K. 20202. How Dermatologists Can Learn and Contribute at the Leading Edge of the COVID-19 Global Pandemic. JAMA Dermatol. doi:10.1001/jamadermatol.2020.1438)

Quote as: Tozzi A, D’Amato G. 2020. SARS-CoV-2 viroporin: a behind the scenes therapeutic target (electronic response to: Mahase E. 2020. Covid-19: Remdesivir is helpful but not a wonder drug, say researchers. BMJ 2020;369:m1798).

Here we ask: what if it the claim of simplicity was not true? Why singularity must precede multiplicity? Why there must be unifying laws? Why has an extreme physicalism to be unavoidably the right answer?

In previous years, the role of gastroesophageal (GE) ultrasound as a diagnostic tool in gastroesophageal reflux disease (GERD) has been disputed. Most authors believe that it is difficult to diagnose GERD without correlation studies between esophageal pathology and ultrasonographic signs. Indeed, there are many anatomic descriptions of the normal G...

Spatio-temporal brain activities with variable delay detectable in resting-state functional magnetic resonance imaging (rs-fMRI) give rise to highly reproducible structures, termed cortical lag threads, that propagate from one brain region to another. Using a computational topology of data approach, we found that persistent, recurring blood oxygen...

Quote as: Tozzi A, D’Amato G, Guarino A. 2020. Rectal swabs for COVID-19 diagnosis (electronic response to: Vetter P, Vu DL, L’Huillier AG, Schibler M, Kaiser L, Jacquerioz F. 2020. Clinical features of covid-19. BMJ 2020; 369 doi: https://doi.org/10.1136/bmj.m1470).

NOTE: chunks of this manuscript have been inserted in another published paper of mine. Therefore, if you want to quote this manuscript's content, please write: Tozzi A. 2021. Why Should Natural Principles Be Simple? Philosophia. https://doi.org/10.1007/s11406-021-00359-x. -----------------------------------------------------------------------------...

We hypothesize that the increased expression of the SUSD1 host gene caused by Coronavirus infection may contribute to the lower respiratory tract cytokine storm that makes severe acute respiratory syndrome a life-threatening disease.

Neuroscientists are able to detect physical changes in information entropy in available neurodata. However, the information paradigm is inadequate to fully describe nervous dynamics and mental activities such as perception. This paper provides an effort to build explanations to neural dynamics alternative to thermodynamic and information accounts....

Quote as: Tozzi A. 2020. Healthy children’s blood for treating COVID-19? (electronic response to: Li Q, Guan X, Wu P, Wang X, Zhou L, et al. 2020. Early Transmission Dynamics in Wuhan, China, of Novel Coronavirus-Infected Pneumonia. N Engl J Med. 2020 Mar 26;382(13):1199-1207. doi: 10.1056/NEJMoa2001316).

Quote as: Tozzi A. 2020. Endoplasmic reticulum-Golgi intermediate compartment: a novel target for SARS-Cov-2 therapies? https://www.bmj.com/content/368/bmj.m1252/rr-2 (electronic response to: Mahase E. 2020. Covid-19: what treatments are being investigated? BMJ. 2020 Mar 26;368:m1252. doi: 10.1136/bmj.m1252).

Quote as: Mitroi-Symeonidis F-C, Anghel I, Tozzi A. 2020. Preventing a covid-19 pandemic flashover (electronic response to: Day M. 2020. Covid-19: identifying and isolating asymptomatic people helped eliminate virus in Italian village. BMJ 2020;368:m1165).

Here we suggest three feasible options that could be useful in COVID-19 medical management.

Quote as: Tozzi A. 2020. Mild COVID-19 Cases: Who Might Be Hospitalized And Who Can Be Quarantined? (electronic response to: Grasselli G, Pesenti A, Cecconi M. 2020. Critical Care Utilization for the COVID-19 Outbreak in Lombardy, Italy. Early Experience and Forecast During an Emergency Response. JAMA, doi:10.1001/jama.2020.4031).

We suggest to look for cross-reactions between SARS-CoV-2 and childhood vaccines. In particular, it could be investigated whether adult patients affected by COVID -19 have been previously vaccinated for MenA. ----------------------------Quote as: Tozzi A, D’Amato G, Guarino A. 2020. Towards cross-reaction between SARS-CoV-2 and childhood vaccines...

The nervous activity of the brain takes place in higher-dimensional functional spaces. Indeed, recent claims advocate that the brain might be equipped with a phase space displaying four spatial dimensions plus time, instead of the classical three plus time. This suggests the possibility to investigate global visualization methods for exploiting fou...

Quote as: Tozzi A. 2020. The microbiome produces biliary acids: therapeutical implications for bile acid diarrhoea? (electronic response to: Quinn RA, Melnik AV, Vrbanac A, Fu T, Patras KA, et al. 2020. Global chemical effects of the microbiome include new bile-acid conjugations. Nature. 2020 Feb 26. doi: 10.1038/s41586-020-2047-9).

Quote as: Tozzi A. 2020. Tunneling nanotubes: towards a transient microconnectome? (electronic response to: Sartori-Rupp A, Cordero Cervantes D, Pepe A, Gousset K, Delage E, et al. 2019. Correlative cryo-electron microscopy reveals the structure of TNTs in neuronal cells. Nat Commun;10(1):342. doi: 10.1038/s41467-018-08178-7).