Published papers



Tozzi A. 2014. Evolution: Networks and Energy Count.  Nature 515: 343. doi:10.1038/515343c. Dynamic systems theory and evolution.  




Tozzi A. 2015.  Neural code & power laws.  SCTPLS Newsletter, April 7-10.  Weird nervous relationships between information entropies and power laws.

Tozzi A. 2015.  Information Processing in the CNS: A Supramolecular Chemistry?  Cognitive Neurodynamics 9 (5): 463–477.  Supramolecular phrenology: not just spikes! 

Tozzi A. 2015.   How to Turn an Oscillation in a Pink One. Journal of Theoretical Biology 377, 117–18. doi:10.1016/j.jtbi.2015.04.018.  Building fractal oscillations from noise.   

Tozzi A. 2015. Oral Propranolol for Infantile Hemangioma. The New England Journal of Medicine 373 (3): 284–85. doi:10.1056/NEJMc1505699.  Back to pediatrics.




Sengupta B, Tozzi A, Coray GK, Douglas PK, Friston KJ. 2016.  Towards a Neuronal Gauge Theory.  PLOS Biology 14 (3): e1002400. doi:10.1371/journal.pbio.1002400.  The brain from above: a gauge theory of nervous activity.  Feat. Karl Friston and Biswa Sengupta. 

Tozzi A, Zare M, Benasich AA.  2016.  New Perspectives on Spontaneous Brain Activity: Dynamic Networks and Energy Matter.  Front Hum Neurosci. 10:247. doi: 10.3389/fnhum.2016.00247.  The spontaneous activity of the brain displays lower information entropy than task-related activities. 

Tozzi A, Peters JF. 2016.  Towards a Fourth Spatial Dimension of Brain Activity.  Cognitive Neurodynamics 10 (3): 189–199. doi:10.1007/s11571-016-9379-z.  The fourth dimension of the brain activity: the first clue towards the occurrence of a hypersphere in the brain. 

Tozzi A. 2016.  Borsuk-Ulam Theorem Extended to Hyperbolic Spaces.  In Computational Proximity. Excursions in the Topology of Digital Images, edited by J F Peters, 169–171. doi:10.1007/978-3-319-30262-1.  Borsuk-Ulam theorem on concave manifolds.

Peters JF, Tozzi A. 2016.  Quantum Entanglement on a Hypersphere.  Int J Theoret Phys, 1–8. doi:10.1007/s10773-016-2998-7.  Quantum entanglement can be solved in four spatial dimensions. 

Tozzi A, Peters JF. 2016.  A Topological Approach Unveils System Invariances and Broken Symmetries in the Brain.  Journal of Neuroscience Research 94 (5): 351–65. doi:10.1002/jnr.23720.  Hidden symmetries (and symmetry breaks) in the brain: entering the Borsuk-Ulam theorem in the study of nervous issues. 

Peters JF, Tozzi A. Ramanna S. 2016.  Brain Tissue Tessellation Shows Absence of Canonical Microcircuits.  Neuroscience Letters 626: 99–105. doi:10.1016/j.neulet.2016.03.052.  Voronoi tessellations in histological brain tissues: every neuron is different from another. 

Tozzi A, Fla Tor, Peters JF. 2016. Building a minimum frustration framework for brain functions in long timescales. J Neurosci Res. 94(8): 702–716.   Minimum frustration principle and nervous networks: when evolution dictates our thoughts.

Tozzi A, Peters JF, James III C, Deli E.  2016.  Multidimensional chaotic dynamics and entropies.  Archives of Information Science and Technology, 1(1): 10-19. 

Tozzi A, Peters JF.  2016.  Symmetries, Information and Monster Groups before and after the Big Bang. Information 7(4), 73; doi:10.3390/info7040073.  A multidimensional Monster in a pre-big bang scenario: when the Multiple precedes the One in a Spinozian pre-Big Bang.  




Tozzi A, Peters JF. 2017.  A Symmetric Approach Elucidates Multisensory Information Integration.  Information 8,1.  doi: 10.3390/info8010004.  Multisensory integration & Borsuk-Ulam theorem: a Machian melting visual and auditory cues. 

Tozzi A, Peters JF, Ori O.  2017.  Fullerenic-topological tools for honeycomb nanomechanics.  Towards a fullerenic approach to brain functions.  Fullerenes, Nanotubes and Carbon nanostructures.25 (4): 282-288. and why the microcolumn resembles a fullerenic structure and gives rise to a barcode.

Peters JF, Ramanna S, Tozzi A, İnan E.  2017.  Bold-Independent Computational Entropy Assesses Functional Donut-Like Structures in Brain fMRI Images.  Front Hum Neurosci. 2017 Feb 1;11:38. doi: 10.3389/fnhum.2017.00038. eCollection 2017.  Further proofs of further nervous dimensions.  Introducing 4D maximal nucleus cluster from algebraic topology of digital images.

Tozzi A, Peters JF.  2017.  Towards Topological Mechanisms Underlying Experience Acquisition and Transmission in the Human Brain.  Integr Psychol Behav Sci. 51(2), 303–323.  doi: 10.1007/s12124-017-9380-z.  A topologically framed multidimensional theory of knowledge.  Starring: Richard Avenarius, Ernst Mach and their phenomenal account of the brain activity.

Tozzi A, Peters JF, Ori O.  2017.  Cracking the barcode of fullerene-like cortical microcolumns.  Neurosci Letters, 644, 100–106. and how the microcolumn resembles a fullerenic structure and gives rise to a barcode.


Tozzi A, Peters JF.  2017.  From abstract topology to real thermodynamic brain activity.  Cognitive Neurodynamics, 11(3) 283–292. Doi:10.1007/s11571-017-9431-7.  Neural thermodynamics, entropies, information: a topological account via the Borsuk-Ulam Theorem. 

Peters JF, Tozzi A, Ramanna S, Inan E.  2017. The human brain from above: an increase in complexity from environmental stimuli to abstractions.  Cognitive Neurodynamics,11(4), 391–394.  DOI: 10.1007/s11571-0­17-9428-2.  The brain increases the complexity of sensations: the cat you are watching is three-dimensional in the environment, multi-dimensional in your mind. 

Koczkodaj WW, Magnot J-P, Mazurek J, Peters JF, Rakhshani H, Soltys M, Strzałka D, Szybowski J, Tozzi A.  2017.  On normalization of inconsistency indicators in pairwise comparisons.  International Journal of Approximate Reasoning.86, 73–79. comparison and the infinity problem: no continuum between three apples and three bananas. 

Tozzi A, Peters JF, Jausovec N.  2016.  A repetitive modular oscillation underlies human brain electric activity.  Neurosci Lett, 653, 234-238.  10.1016/j.neulet.2017.05.051.  The unexpected occurrence of J-functions & complex functions in the brain. 


Tozzi A, Peters JF, Navarro J, Kun W, Lin B, Marijuán PC.  2017.   Cellular Gauge Symmetry and the Li Organization Principle.  Progress in Biophysics and Molecular Biology. life from above: a gauge theory of cellular activity. 

Yurkin A, Tozzi A, Peters JF, Marijuan PC.  2017.  Quantifying Energetic Dynamics in Physical and Biological Systems Through a Simple Geometric Tool and Geodetic Curves.  Addendum to: Cellular Gauge Symmetry and the Li Organization Principle.  Progress in Biophysics and Molecular Biology.  Geometric curves underlying physical and biological dynamics. 

Tozzi A, Peters JF.  2017.  The multidimensional world.  Lambert Academic Publishing, Saarbrücken, Germany.  ISBN-13: 978-3-330-03530-0.  The Borsuk-Ulam theorem as a general principle for a multidimensional world. 

Tozzi A, Peters JF, Fingelkurts AA, Fingelkurts AA, Marijuán PC.  2017.  Topodynamics of metastable brains.  Physics of Life Reviews, 21, 1-20. of metastable brains: a survey of the applications of the Borsuk-Ulam theorem to nervous nonlinear paths. 

Tozzi A, Peters JF, Fingelkurts AA, Fingelkurts AA, Marijuán PC.  2017.  Brain projective reality: novel clothes for the emperor.  Reply to comments on “Topodynamics of metastable brains”by Tozzi et al.  Physics of Life Reviews, 21, 46-55. & brain manifolds: the philosophy beyond our approach. 

Tozzi A, Peters JF, Navarro J, Marijuán PC.  2017.   Heidegger’s being and quantum vacuum.  Progress in biophysics and molecular biology.’s Being & quantum vacuum: Being, Essence, Existence and their physical counterparts. 

Tozzi A, Sengupta B, Peters JF, Friston KJ. 2017. Gauge Fields in the Central Nervous System.193-212.  In: The Physics of the Mind and Brain Disorders: Integrated Neural Circuits Supporting the Emergence of Mind, edited by Opris J and Casanova MF. New York, Springer; Series in Cognitive and Neural Systems.Pages 193-212.  ISBN: 978-3-319-29674-6.  DOI10.1007/978-3-319-29674-6_9.   Neural Gauge theory: novel insights in a book chapter (Springer). 

Deli E. Tozzi A, Peters JF.  2017.  Relationships between short and fast brain timescales.  Cognitive Neurodynamics, 11(6), 539-552.DOI: 10.1007/s11571-017-9450-4.  The Bloch theorem correlates high- and low- brain frequencies. 

Tozzi A. Peters JF.  2017.  Critique of pure free energy principle: Comment on “Answering Schrödinger's question: A free-energy formulation” by Maxwell James Désormeau Ramstead et al. Physics of Life Reviews.DOI: 10.1016/j.plrev.2017.10.003.  Time-reversal entropy: an underrated actor. 

Peters JF, Tozzi A, Deli E.  2017.  Towards Equations for Brain Dynamics and the Concept of Extended Connectome. SF J Neuro Sci 1:1.   Sprott’s equations in the brain: a single equation describes linear and nonlinear nervous dynamics.




Tozzi A, Peters JF, Deli E.  2018.  Towards plasma-like collisionless trajectories in the brain.  Neurosci Lett.662:105-109. collisionless nervous trajectories: long-range correlations in the brain. 

Tozzi A, Peters JF. 2018.  What it is like to be “the same”? Progress in Biophysics and Molecular Biology.  133, 30-35.“The same” in biology.  The principle of identity reloaded: When A=A turns out A≠A.

Tozzi A. 2018.  Einstein and the physics of the mind: Comment on “Physics of mind: experimental confirmations of theoretical predictions” by Felix Schoeller et al.Phys Life Rev,  Einstein’s special relativity and thoughts: why an imagined object is squeezed in jour mind. 


Tozzi A, Peters JF, Chafin C, De Falco D, Today J.  2018.  A timeless biology.  Progr Biophys Mol Biol. 134, 38-43.  doi: 10.1016/j.pbiomolbio.2017.12.002.  A gauge theory for timeless biology: when time does not count. 


Deli E, Peters JF, Tozzi A.  2018.  The Thermodynamic Analysis of Neural Computation. J Neurosci Clin Res 3:1.


Tozzi A, Peters JF.  2018.  Multidimensional brain activity dictated by winner-take-all mechanisms.  Neuroscience Letters, 678 (21):83-89.   Evolutional architecture of multidimensional sensations: the winner takes all also in nervous hidden dimensions.  


Tozzi A, Peters JF, Fingelkurts A, Fingelkurts A, Perlovsky L.  2018. Syntax meets semantics during brain logical computations.  ProgrBiophys Mol Biol, 140: 133-141.  A neuroscientific account of lower-dimensional syntax and higher-dimensional semantics says that the Wittgenstein’s Tractatus was right.  


Tozzi A, Peters JF, Cankaya MN.  2018. The informational entropy endowed in cortical oscillations.  Cognitive Neurodynamics, 12(5), 501-507.  DOI: 10.1007/s11571-018-9491-3.  Weird nervous relationships between information entropies and power laws: when a two-dimensional shadow encompasses more information that the corresponding three-dimensional object. 


Tozzi A, Peters JF, Jaušovec N.  2018.  EEG dynamics on hyperbolic manifolds.  Neurosci Lett, 683: 138-143.  Mirzakhani’s hyperbolic spaces are also in the brain. 

Tozzi, A.   2018.  Richard Avenarius’ “Kritik Der Reinen Erfahrung” (Critique of Pure Experience): An English Summary. Preprints, 2018090403.  doi: 10.20944/preprints201809.0403.v1.  Richard Avenarius’ Kritik: an English summary. 

Yurkin A, Peters JF, Tozzi A.  2018.  A novel belt model of the atom, compatible with quantum dynamics.  Journal of Scientific and Engineering Research, 2018, 5(7):413-419.  ISSN: 2394-2630.   An atomic geometric model encompassing quantum mechanics' dictates too.  




Tozzi A, Peters JF.  2019.  The common features of different brain activities.  Neurosci Lett, 692 (23): 41-46. duality of the brain functions: towards a single nervous activity encompassing all the mental faculties.

Tozzi A.  2019.  The multidimensional brain.  Physics of Life Reviews, 31: 86-103. doi: brain activity takes place in higher dimensions: not just a figure of speech! 

Tozzi A, Peters JF. 2019.  Topology of Human Perception.  Preprints, 2019030235.  Gibson 4.0:  the topological horizons of the ecological theory of vision. 

Tozzi A, Peters JF.  2019. Topology of Black Holes’ Horizons.  Emerging Science Journal, 3(2):58-63.  DOI: 10.28991/esj-2019-01169.  Black holes horizons: an unnoticed correlation with the Borsuk-Ulam theorem and the Mobius strip.

Tozzi A, Peters JF. 2019.  Entropy balance in the expanding universe: a novel perspective. Entropy, 21(4), 406.’s horizon & relational quantum dynamics: when entropy and information become subjective.   

Tozzi A, Peters JF.  2019.  The Borsuk-Ulam theorem solves the curse of dimensionality: Comment on “the unreasonable effectiveness of small neural ensembles in high-dimensional brain” by Alexander N. Gorban et al. Physics of Life Reviews. 29: 89-92 curse of dimensionality: when the spherical dimension increase… the volume decreases!

Tozzi A, Peters JF.  2019. Points and lines inside our brains.  Cognitive Neurodynamics, 13(5): 417–428.  DOI: 10.1007/s11571-019-09539-8.  When points and lines do not exist, de Cusa’s hyperbolic geometry comes into play: a physical answer to ancient questions about infinity.  




Tozzi A. 2020.  Towards dewetting monoclonal antibodies for therapeutical purposes.  Progress in Biophysics and Molecular Biology, 150:153-159.


Tozzi A, Papo D.  2020.  Projective mechanisms subtending real world phenomena wipe away cause effect relationships.  Progress in Biophysics and Molecular Biology.  151:1-13.  DOI: 10.1016/j.pbiomolbio.2019.12.002.  Induction reloaded: heretic topological approaches to cause/effect relationships. 


Tozzi A, Peters JF.  2020 Removing uncertainty in neural networks. Cognitive Neurodynamics, 14:339–345. fuzzy holes demarcate objects.  How to solve decision limit problems... with holes. 


Don AP, Peters JF, Ramanna S, Tozzi A.  2020.  Topological View of Flows inside the BOLD Spontaneous Activity of the Human Brain.  Front. Comput. Neurosci.  DOI: 10.3389/fncom.2020.00034.  The occurrence of Betti numbers in neurodata. 


Minella R, Minelli R, Rossi E, Cremone G, Tozzi A.  2020.   Gastroesophageal and gastric ultrasound in children: the state of the art.  Journal of Ultrasound.  Online ahead of print. 


Tozzi A.  2020.  Are Borders Inside or Outside? Found Sci. problem of boundaries and borders: from Medieval thinkers to the contemporary physics and biology.





Tozzi, A., Peters, J.F. A Topological Approach to Infinity in Physics and Biophysics. Found Sci 26, 245–255 (2021). When Achilles meets the Alexander horn, he leaves the straight path and overtakes the turtle. 


Tozzi, A., Peters, J.F. 2021.  Information-devoid routes for scale-free neurodynamics. Synthese.  199: 2491-2504. Information Entropies Are Unable to Describe Mental Activities: a mathematical alternative from the Banach–Tarski paradox. 


Tozzi A, Ahmad MZ, Peters JF.  2021.  Neural computing in four spatial dimensions.  Cognitive Neurodynamics, 15:349-357.   How to build a 4D computer, ALIAS how to simulate a multidimensional brain, through the Quantum Hall effect. 


Tozzi A, Bormashenko E, Jausovec N.  2021.  Topology of EEG wave fronts.  Cognit Neurodyn, 15, 887–896 The hairy ball theorem and the electric wave fronts in the brain.  


Tozzi A, Peters JF, Jausovec N, Don APH, Ramanna S, Legchenkova I, Bormashenko E.  2021.  Nervous Activity of the Brain in Five Dimensions. Biophysica; 1(1):38-47. to build a 4D computer, ALIAS how to simulate a multidimensional brain,  through quaternionic networks.


Murgia N, Corsico AG, D’Amato G, Maesano CN, Tozzi A, Annesi Maesano I. 2021. Do gene-environment interactions play a role in COVID-19 distribution? The case of Alpha-1 Antitrypsin, air pollution and COVID-19. Multidis Res Med, Vol. 16.


Tozzi, A. 2022.  Why Should Natural Principles Be Simple? Philosophia 50, 321–335. Against the Ockham's razor.  The Multiple before the One: what if Alain Badiou was right? 


Murgia N, Corsico AG, D’Amato G, Maesano CN, Tozzi A, Annesi Maesano I. 2021. Do gene-environment interactions play a role in COVID-19 distribution? The case of Alpha-1 Antitrypsin, air pollution and COVID-19. Multidis Res Med, Vol. 16.


Tozzi A, Yurkin A, Peters JF.  2021.  A Geometric Milieu Inside the Brain. Found Sci. inhibitory cavities of the brain in the geometric terms of Pascal’s triangles.

Don APH, Peters JF, Ramanna S, Tozzi A.  2021.  Quaternionic views of rs-fMRI hierarchical brain activation regions. Discovery of multilevel brain activation region intensities in rs-fMRI video frames.  Chaos, Solitons & Fractals. Vol 152, 111351.  Further insights in the dynamics of the four-dimensional brain.




Tozzi A.  2022.  An economic approach to energy budgets: how many resources should living organisms spare? Biosystems.  Volume 211, 104584.  Ramsey’s economic theory of savings may help to quantify the energetic requests of the living cells.

Tozzi A.  2022.  Bipolar reasoning in feedback pathways. Biosystems.  Volumes 215–216, June 2022, 104652 just 1 and 0 in logic: historical survey and future scientific developments, including globular sets in neuroscience.   

Tozzi A.  2022.  Informational Approaches Lead to Formulations of Quantum Mechanics on Poincaré Disks.  Proceedings, 81(1), 20; Averroe’s Single Intellect meets information and quantum dynamics.





Tozzi A.  2019.  Is shape deformation a topological invariant? (electronic response to: Kawabata K, Higashikawa S, Gong Z, Ashida Y, Ueda M.  2019. Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics.   Nature Communications 10: 297).  Deformation is not a topological invariant: a critique to topology. 

Tozzi A.  2020.  Underrated topological approaches, apart from the every-day network connectivity (electronic response to: Flavahan WA, Drier Y, Johnstone SE, Hemming ML, Tarjan DR. et al.  Altered chromosomal topology drives oncogenic programs in SDH-deficient GISTs. Nature, 575, pages229–233).

Zhang Y, Guo S, Sun M, Tozzi A, Zhao X.  2019.  Non-equilibrium Belousov-Zhabotinsky reaction describes the spontaneous activity of the brain.  BioRxiv.  doi: link between travelling waves of neural activity and front waves in chemical reactions. 

Tozzi, A. Biophysics of Nervous Embryo-Fetal Development. Preprints 2021, 2021030111.  doi: 10.20944/preprints202103.0111.v1.  Knots, braids and… anyons in your brain.

Tozzi A. 2021.  To Know Them, Remove Them: An Outer Methodological Approach to Biophysics and Humanities. Preprints. doi: 10.20944/preprints202104.0681.v1.  Investigating objects from outside.

Tozzi A.  2021.  Lack of Disjointness in Genus-1 Surfaces: The Punctured Balloon Theorem.  viXra:2101.0005.  A novel topological theorem.

Tozzi A. 2021. Random Walks Are Not So Random, After All. viXra:2010.0002.  A fully-novel topological theorem. 

Tozzi A.  2021. Troubles with Shannon’s account of the entropy in the continuous case. viXra:2105.0048.  What if Claude Shannon was (partially, of course) wrong? 

Tozzi A.  2021.  Ramsey’s Theory Meets The Human Brain Connectome. Preprints- doi: 10.20944/preprints202109.0412.v1.   Regularities & repeated patterns inside structures equipped with nodes and edges.

Tozzi A, Peters JF.  2022 towards a single parameter for the assessment of EEG oscillations.  MedRxiv.  doi:  The Green’s theorem for flows describes EEG features of intelligence.

Tozzi, A.  2022. Living Cell’s Feeling of Holes: The Mathematics of Cavities in Biophysical Structures. Preprints. doi: 10.20944/preprints202204.0156.v1.  When holes impair the cellular homogeneity and the surface/volume ratio.  

Tozzi, A.; Peters, J.; Mariniello, L. Structural and Dynamical Properties of Liquid Water Increase Turbulent Flows. Preprints 2022, 2022060128 (doi: 10.20944/preprints202206.0128.v1).  Liquid water’s transient micro-assemblies help to generate micro-vortices and subsequent turbulence.

Peters JF, Alfano R, Smith P, Tozzi A. 2022.  Discrete and continuous curved surface antipodal paths. Extensions of the Borsuk-Ulam theorem and application of the Feynman path integral and Wodehouse contour integral. 2022. hal-03698584Another generalization of the Borsuk-Ulam theorem, useful in quantum dynamics.  


Tozzi A. 2022.  Anopheles' peri-equatorial migration via Coriolis forces (electronic response to: Wu RL, Idris AH, Berkowitz NM, Happe M, Gaudinski MR, et al.  2022.  Low-Dose Subcutaneous or Intravenous Monoclonal Antibody to Prevent Malaria.  N Engl J Med 2022; 387:397-407. DOI: 10.1056/NEJMoa2203067). How do mosquitoes survive during the dry African seasons?