Homepage > PHYSICS, DYNAMIC SYSTEMS THEORY

QUANTUM DYNAMICS

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. Featuring Quantum information theorem and Qbit information systems.

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. Bloch waves and Floquet theorem to assess high- and low- brain frequencies.

Tozzi A, Ahmad MZ, Peters JF. 2021. Neural computing in four spatial dimensions. Cognitive Neurodynamics, 15:349-357. https://doi.org/10.1007/s11571-020-09598-2. How to build a 4D computer through the Quantum Hall effect.

Tozzi A. 2022. Informational Approaches Lead to Formulations of Quantum Mechanics on Poincaré Disks. Proceedings, 81(1), 20; https://doi.org/10.3390/proceedings2022081020. When Averroe’s Single Intellect meets information and quantum dynamics.

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. Topological approaches to the slit experiment and to exceptional points in non-Hermitian networks.

Tozzi A, Peters JF, Navarro J, Marijuán PC. 2017. Heidegger’s being and quantum vacuum. Progress in biophysics and molecular biology. https://doi.org/10.1016/j.pbiomolbio.2017.07.009. Quantum vacuum, virtual particles and vacuum trapping.

Tozzi, A., Peters, J.F. A Topological Approach to Infinity in Physics and Biophysics. Found Sci 26, 245–255 (2021). https://doi.org/10.1007/s10699-020-09674-0. Quantum jump, Mandelstamm-Tamm inequality

Peters JF, Alfano R, Smith P, Tozzi A, Vergili T. 2023. Geometric realizations of homotopic paths over curved surfaces. Filomat 38(3):793-802. A generalization of the Borsuk-Ulam theorem, useful in quantum dynamics.

Tozzi A, Peters JF. 2019. Entropy balance in the expanding universe: a novel perspective. Entropy, 21(4), 406. https://doi.org/10.3390/e21040406. Relational quantum dynamics to assess cosmic expansion and entropy.

Tozzi A. 2020. Are Borders Inside or Outside? Found Sci. https://doi.org/10.1007/s10699-020-09708-7. Relational quantum mechanics, superposition and entanglement.

Tozzi A. Ramanujan-derived Hypergeometric Functions Describe Hidden Coupled Dynamics in Physical and Biological Systems. viXra:2405.0059. A new math (possibly) subtending quantum entanglement.

RELATIVITY

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, https://doi.org/10.1016/j.plrev.2018.01.009. Einstein’s special relativity and thoughts: why an imagined object is squeezed in jour mind.

PARTICLES

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 also quantum mechanics’ dictates.

Tozzi A. 2024. Approaching Electroencephalographic Pathological Spikes in Terms of Solitons. Signals, 5, 281-295. https://doi.org/10.3390/signals5020015. Traveling solitary waves that do not waste energy.

Peters JF, Tozzi A. 2016. String-Based Borsuk-Ulam Theorem. arXiv:1606.04031. Topology for cosmological strings.

Tozzi A, Peters JF. 2019. Topology of Black Holes’ Horizons. Emerging Science Journal, 3(2):58-63. DOI: 10.28991/esj-2019-01169. Towards… a negative mass?

Tozzi A, Peters JF. 2017. The multidimensional world. Lambert Academic Publishing, Saarbrücken, Germany. ISBN-13: 978-3-330-03530-0. General mathematical principles for a multidimensional world. Gravitational lensing, Donut-like structures, Bosons, Pauli principle, computation.

GAUGE THEORY

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, 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.

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. Gauge theory: the role of virtual displacement.

ASTRONOMY, ASTROPHYSICS

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 symmetry-based pre-Big Bang scenario of symmetry break including J-function, Leech lattice, sporadic groups, Fisher-Griess Monster Group, Monstrous moonshine, Lie groups, string theories, CFT/AdS correspondence.

Tozzi A, Peters JF, Deli E. 2018. Towards plasma-like collisionless trajectories in the brain. Neurosci Lett.662:105-109. https://doi.org/10.1016/j.neulet.2017.10.016 50 Plasma collisionless - Neurosci Lett.pdf (231,2 kB). Plasma-like collisionless nervous trajectories: McKean-Vlasov equations.

Tozzi A, Peters JF. 2019. Topology of Black Holes’ Horizons. Emerging Science Journal, 3(2):58-63. DOI: 10.28991/esj-2019-01169 08 t-Hooft black holes - BUT.pdf (1 MB). Black holes horizons: an unnoticed correlation with the Borsuk-Ulam theorem and the Mobius strip: holographic principle and t’Hooft’-inspired topological mappings on entangled horizons.

Tozzi A, Peters JF. 2019. Entropy balance in the expanding universe: a novel perspective. Entropy, 21(4), 406. https://doi.org/10.3390/e21040406. Local observer’s commoving horizon, cosmic expansion, Bekenstein bound & relational quantum dynamics

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. Topological approaches to gravitational lenses and plasma collisionless interactions.

Tozzi A. 2020. Are Borders Inside or Outside? Found Sci. https://doi.org/10.1007/s10699-020-09708-7. Singularity inside the black hole, wormholes, null singularity at the Cauchy horizon.

MATERIALS

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. https://dx.doi.org/10.1080/1536383X.2017.1283618.

Tozzi A, Peters JF, Ori O. 2017. Cracking the barcode of fullerene-like cortical microcolumns. Neurosci Letters, 644, 100–106. https://dx.doi.org/10.1016/j.neulet.2017.02.064. Why and how the microcolumn resembles a fullerenic structure and gives rise to a barcode. Featuring topological defects and Stone-Whales transformations.

Tozzi A, Mariniello L. 2022. Unusual Mathematical Approaches Untangle Nervous Dynamics. Biomedicines; 10(10):2581 https://doi.org/10.3390/biomedicines10102581. Knots & braids, Frank-Kasper phases, quasicrystals assemblies.

Tozzi A. 2020. Are Borders Inside or Outside? Found Sci. https://doi.org/10.1007/s10699-020-09708-7. Metrology, Statistics of the extreme, optimal random search, unconventional superconductivity.

FLUID DYNAMICS

Tozzi A, Peters J, Mariniello L. 2022. 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.

Tozzi, A., Peters, J.F. A Topological Approach to Infinity in Physics and Biophysics. Found Sci 26, 245–255 (2021). https://doi.org/10.1007/s10699-020-09674-0. Turbulence.

Tozzi A. 2024. Approaching Electroencephalographic Pathological Spikes in Terms of Solitons. Signals, 5, 281-295. https://doi.org/10.3390/signals5020015. The astonishing traveling solitary waves that do not waste energy.

Tozzi A, Bormashenko E, Jausovec N. 2021. Topology of EEG wave fronts. Cognit Neurodyn. https://doi.org/10.1007/s11571-021-09668-z . Wave propagation, antennas, front propagation of electric waves.

Tozzi A. 2020. Towards dewetting monoclonal antibodies for therapeutical purposes. Progress in Biophysics and Molecular Biology, 150:153-159. https://doi.org/10.1016/j.pbiomolbio.2019.09.001. Gas/surface tension, Lifshitz-van Der Wall interactions, Superhydrophobic structures.

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 . How to detect multidimensional flows in physical and biological settings.

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?

Tozzi A. Ramanujan-derived Hypergeometric Functions Describe Hidden Coupled Dynamics in Physical and Biological Systems. viXra:2405.0059. A new math (possibly) subtending Turing patterns and gomboc dynamics.

ENTROPIES, INFORMATION, THERMODYNAMICS

Peters JF, Tozzi A. 2016. Quantum Entanglement on a Hypersphere. Int J Theoret Phys, 1–8. doi:10.1007/s10773-016-2998-7. Hypersphere quantum information theorem.

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.

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. Includes Ohm’s law and Free energy principle.

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 relationships between Rényi entropies and power laws.

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, 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. Variational free-energy, Hullback-Leibler divergence.

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.

Tozzi A. 2022. Informational Approaches Lead to Formulations of Quantum Mechanics on Poincaré Disks. Proceedings, 81(1), 20; https://doi.org/10.3390/proceedings2022081020. Wheeler’s total cosmic information in Hilbert spaces.

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. A computational entropy: introducing 4D maximal nucleus cluster from algebraic topology of digital images.

Tozzi, A., Peters, J.F. 2021. Information-devoid routes for scale-free neurodynamics. Synthese. 199: 2491-2504. https://doi.org/10.1007/s11229-020-02895-7. Information Entropies Are Unable to Describe Mental Activities: a mathematical alternative featuring the Banach–Tarski paradox.

Tozzi A, Peters JF. 2019. Entropy balance in the expanding universe: a novel perspective. Entropy, 21(4), 406. https://doi.org/10.3390/e21040406. When entropy and information become subjective.

DYNAMIC SYSTEMS THEORY, INCLUDING NONLINEAR DYNAMICS, CRITICALITY

Tozzi A. 2020. Are Borders Inside or Outside? Found Sci. https://doi.org/10.1007/s10699-020-09708-7. Collective systems, non-equilibrium dynamics, self-organized criticality, logistic map, bifurcation diagrams, gradient/descent apparatuses of Bayesian machines.

Tozzi A, Peters JF, Fingelkurts AA, Fingelkurts AA, Marijuán PC. 2017. Topodynamics of metastable brains. Physics of Life Reviews, 21, 1-20. https://dx.doi.org/10.1016/j.plrev.2017.03.001. A survey of the applications of the Borsuk-Ulam theorem to nervous nonlinear paths.

Tozzi, A., Peters, J.F. A Topological Approach to Infinity in Physics and Biophysics. Found Sci 26, 245–255 (2021). https://doi.org/10.1007/s10699-020-09674-0. The Alexander horned sphere describes nonlinear paths via logistic plots and chaotic flows. Langevin equations, Levi-Civita and Ehresmann connections, Minkowski metric.

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 equation: a single equation describes linear and nonlinear dynamics.

Tozzi A, Yurkin A, Peters JF. 2021. A Geometric Milieu Inside the Brain. Found Sci. https://doi.org/10.1007/s10699-021-09798-x. Geometric models of random walks.

Tozzi A. 2021. Random Walks Are Not So Random, After All. viXra:2010.0002. Random walks, white noise, Markov paths, stochastic trajectories, closed paths, Markov chains, dynamical systems theory, boosting chemistry, tunnelling nanotubes, backward entropy, chaotic attractors.

Tozzi A, Peters JF, Fingelkurts AA, Fingelkurts AA, Marijuán PC. 2017. Topodynamics of metastable brains. Physics of Life Reviews, 21, 1-20. https://dx.doi.org/10.1016/j.plrev.2017.03.001. Kullback-Leibler divergence, ergodicity, Renewal events, metastability.

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. Logistic maps in chaotic dynamics, with Zeeman effect & bifurcation plots.

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

Tozzi A. 2024. Tozzi A. 2024. Flock members experience gas pressures higher than lone individuals. Biosystems, Volume 238, 105192. https://doi.org/10.1016/j.biosystems.2024.105192. Active agents and their relationship with the surrounding phase space.

Tozzi A. Ramanujan-derived Hypergeometric Functions Describe Hidden Coupled Dynamics in Physical and Biological Systems. viXra:2405.0059. A new math (possibly) subtending gomboc dynamics.

LONG-RANGE CORRELATIONS, COLLECTIVE BEHAVIOUR

Tozzi A, Peters JF, Deli E. 2018. Towards plasma-like collisionless trajectories in the brain. Neurosci Lett.662:105-109. https://doi.org/10.1016/j.neulet.2017.10.016. Plasma-like collisionless nervous trajectories: long-range correlations in the brain.