How topological projections describe physical and biological observables



Arturo Tozzi (MD, Pediatrician, PhD, former Adjunct Assistant Professor in Physics)


ASL Napoli 2 Nord, Distretto 45, Via Santa Chiara, 80023, Caivano, Naples, Italy

Computational Intelligence Laboratory, University of Manitoba, Winnipeg, Canada 

Former Center for Nonlinear Science, Department of Physics, University of North Texas, Denton, Texas





This is my story, the story of a family pediatrician and amateur neuroscientist/physicist.  As an “outsider”, I publish in some of the major scientific journals (also nuts in Nature and NEJM) and collaborate with worldwide universities and renewed scientists.  My scientific field? Difficult to say, because I do not like at all to be on focus.  Not regarding myself as a proper scientist, I feel free to (try to) publish in rather different disciplines (medicine, biology, physics, math, philosophy and, above all, neuroscience).  Working locked in my room in Naples without vis-à-vis contacts with real scientists, my favoured methodological approach is necessarily a “testable rationalism”: sharp experimental previsions arising from top-down, deductive mathematical approaches.  Joining together concepts from far-flung fields, I pursue the application of mathematic and physical theory to biology, especially to neural systems.





The Borsuk-Ulam theorem and its novel variants.  We investigated the Borsuk-Ulam theorem (BUT) from algebraic topology, which states that a single point on a circumference maps to two points on a sphere[11].  In more technical terms, a point embedded in lower dimensions gives rise to two points with matching description in higher dimensions.  The BUT is not simply a metaphor, rather a real computational tool standing for a universal principle for physical and biological systems.  Indeed, the BUT perspective allows a feature (e.g., a shape, a trajectory or an energy) located in the environment to be translated to abstract spaces of different dimensions.  Achieving a map from one system to another enables researchers to assess and elucidate a wide range of phenomena.  We provided either demonstrations or testable hypotheses related to the BUT framework in far-flung disciplines, such as neuroscience, theoretical physics, nanomaterials, computational topology, applied algebraic topology, philosophy of the mind, chaotic systems, group theory and cosmology. 

We provided many BUT variants and generalizations[28, 44] that enlarge the possible applications of the theorem.  For a survey, watch our brief movie (just one minute) on YouTube[24].  Instead of points, the novel BUT variants allow the assessment (from one dimension to another) of shapes, regions[31], trajectories, strings[32, 52], mathematical functions, vectors and tensors[38], information, activities such as entropies and energies [28, 43].  BUT variants hold not just for convex structures such as the circumferences and spheres described by the classical BUT, but also for flat, concave[15] or more complicated manifolds[54], such as the complex trajectories that can be detected in many physical systems’ dynamics.  Further, the dimensions described by BUT do not stand just for spatial dimensions (as in the case of a circle and a sphere), but also for abstract dimensions (such as for example, biological complexity, fractional quantities, fractal measurements, nonlinear bifurcations, different time-frames[16]).  We also showed how physical and biological activities can be described in terms of trajectories taking place on donut-like structures (tori) [32, 52]., and also on Mobius strips[62].  The crucial issue is that matching descriptions allow commensurability between entities of different dimensions.  We also assessed an important question: what does it mean matching description? Does it stand for equality, or sameness, or closeness, or belonging together[48]?


Projectionism.  We realized that the BUT is a universal principle for physical and biological activities, including the elusive brain functions[38, 44].  Systems operations become projections among different levels, giving rise to apparently emergent properties in higher dimensions[44, 57].  Therefore, we proposed a novel paradigm, which also provides a fresh philosophical approach to the world and the topology[35, 38]: the “projectionism”.  Projectionism stands for a form of top-down, deductive rationalism: the abstract math underlies the issues of mind and matter[54].  Nevertheless, in order keep ourselves firmly grounded in the realm of the true science, we took care to demonstrate our abstract deductions through scientific tools or, at least, to provide fully testable and falsifiable scientific hypotheses.  Therefore, we are in front of a “testable rationalism”, based on mappings and projections (and not on cause/effect relationships!) among different activity levels.  A complete description of a phenomenon can be reached just by looking at its higher levels, where the differences are more easily detectable and assessable.  






The brain is multidimensional.  Our first application of the BUT and its variants was in neuroscience.  We moved from the observation that our brain exhibits the unique ability to connect past, present and future events in a single, coherent picture, as if we were allowed to watch the three screens of past-present-future glued together in a mental kaleidoscope.  We conjectured that the brain activity takes place on a multidimensional donut-like torus, so that our thoughts follow a donut-like trajectory in brain[11].  Despite recent, as well as older, literature display countless clues indirectly confirming  our claims[54], we looked also for more direct proofs.  By using fully novel topological techniques of computational proximity, we provided the first clue of the presence a brain four-dimensional moving hypersphere, located insight the very structure of the connectome[34].   In other words, a ceaseless, functional four-dimensional cap surrounds our brain.  In subsequent papers, we showed how the entropy in primary sensory areas is lower than in associative ones: this corroborates our claim that the brain activity lies in higher dimensions than the three-dimensional (plus time) environment[45].  Rather that concentrate the message coming from the external world, our brain dilutes the incoming input and enriches it with novel meanings, in higher functional dimensions.  This means that a cat in the world displays less information than the idea of cat in our mind: indeed, when we think to a cat that we have seen, we take into account also emotional (“what a nice cat!”), rational (“it is a feline”) issues, and so on.  We also, with the help of one of the Mirzakhani’s theorems, described how brain electric activity can be described in terms of paths taking place on hyperbolic, positive-curved manifolds, rather than three-dimensional (plus time) classical spaces[59]


Brain symmetries are correlated with cortical entropies.  We noticed that symmetries stand for two features with matching description lying in higher dimensions, while symmetry breaks for a single point lying one dimension lower.  Such symmetries described in terms of BUT can be correlated with neural thermodynamic activity[16,60].  At first, we evaluated the general role of symmetries and broken symmetries in the brain[16]; then, we assessed energy requirements and constraints during spontaneous and evoked brain activity[14].  By introducing novel topological tools that analyze enthalpy, free-energy and entropy in fMRI brain studies, we provided a testable approach to proceed from abstract topology to real thermodynamic nervous activity[43].  We also proposed a link between power laws and spike frequency in brain[3, 36], via the Rényi entropy, that is a generalization of the Shannon informational entropy: this correlation might be useful in order to modify the external oscillations used by transcranial stimulation[3].  We also assessed the probabilistic virtues of the temperature in the Bayesian brain[7, 43] and proposed a link between time-reversal asymmetry and the vanishing of memories[8].   Looking for biologically plausible nervous phase spaces, we found a feasible framework, characterized by a double behavior: mental trajectories might be embedded into strange attractors during perception, and into torus-like structures during mind wandering and spontaneous activity of the brain[241


Novel insights in the microscopic brain.  Based on the recent literature, we noticed that peripheral receptors perform cognitive computations previously thought to be exclusive to the cortex[4].  We proposed a model of “supramolecular phrenology”, in which every neuron (or group of neurons) perform a different activity via the non-covalent links among macromolecular intracellular assemblies[4].  In touch with the old claims of Mosso[57], the neural code and brain information might not be endowed just in electric spikes[54].  We developed a novel computational method able to assess slight differences in histological samples of cortical neurons[17].  In particular, we showed how tessellation of Primate cortical slices reveals micro-areas of higher functional brain activity[17] and increased entropy[34].  We also tackled the issue of the controversial location of the neural code, suggesting that it might be encompassed in fullerene-like cortical microcolumns, were a sort of brain “barcode” might be endowed[30, 37].  We also proposed that collective brain dynamics might be explained by using modifications of the Vlasov equations for plasma movements: they might give rise to collisionless movements that stand for long-range correlations among far cortical areas [25].


Sensations and perceptions.  We proposed a computational model that, in analogy with protein folding, allows the stabilization of our thoughts in long timescales[18]: mental trajectories fall into funnel-like attractors dictated by evolutionary constraints, elucidating phenomena such as visual sensation and pattern recognition[18].  Also, a BUT framework allows to understand how the brain perceives “sharp” objects and is able to solve the Kullback-Leibler perceptual divergence[16].  A model based on neural Darwinism, e.g., a fight among neurons where “the winner takes all”, gave us the possibility to assess a novel variant of Selfridge’s Pandemonium in topological terms[50, 54].  In sum, during the mental activities of sensation and perception, our brain, rather that joining together environmental objects’ features, recognizes topological invariants and global patterns at the very first, performing a sort of “topological gestaltic” activity[50, 54].  A symmetric, topological approach (based on Mach’s “phenomenological” “complex of sensations” and Gardenfors’ “cognitive semantics”) is able to elucidate also the puzzling phenomenon of multisensory information integration in the brain[14, 29]


Knowledge and imagination. Based on the Gibson’s ecological approach, we developed a novel topological theory of perception[20, 35].  Taking into account Richard Avenarius’ “Critique of pure experience”, we described a novel theory of knowledge, which encompasses: immediate naïve perception, persistence perception, the Humeian cause/effect relationship, the occurrence of social assemblies[2, 35].  We also asked: how are images and ideas “described” by our mind? We found a possible answer correlated with Einstein’s special relativity and Bekenstein-Hawking formulas for the entropy of black holes[49].  A topological approach to the brain also elucidates syntactic and semantic cortical processing [44], paving the way to build four-dimensional semantic computers.  This means that the second Wittgenstein was wrong: the semantic content of the Tractatus can be computable through fuzzy logic[51].  Hence, the old, “despised” weapons of classical and novel logic (Aristotle, Nicholas of Autrecourt, Wittgenstein, Godel, Hilbert, Łukaszewski) might still be useful in scientific, experimental contexts[27,35].  Also we showed that Euclid’s Geometry is Just in Our Mind, Rather Than Describing the Real World [61].  Our data corroborate the claims that the brain displays a generative, internal model, being equipped with a “Kantian” a priori” activity that takes place in higher functional cortical dimensions[13, 54, 57].  All the different brain activities, such as sensations, perception, mind-wandering, thinking and so on, are dual, i.e., can be described with the same mechanism.  This means that micro-, meso- and macro- levels of neural observation describe the same brain activity, so that and seemingly different neuro-techniques turn out to be equivalent[40].  Therefore, a topological unification of mental functions might be achieved[44, 54].  We also provided practical examples of topology applied to neuroimaging data[44, 54]



Quantum accounts of the brain.  We described a feasible and testable correlation between low- and high- cortical oscillations.  Such relationship can be assessed in terms of the Bloch theorem, from solid-state physics and quantum dynamics[56].  We also proposed a possible biochemical mechanism that might explain the hypothetical occurrence of quantum phenomena in a brain at the edge of the chaos: the so called “dewetting transitions” occurring into the channels of the neuronal receptors[18]







As suggested by several philosophers and scientists[35], the world and its dynamics can be described in terms of mapping and projections.  Every physical and biological structure has a history, and system properties in physical spaces can be translated to abstract mathematical spaces[38].  And vice-versa.


Pre- big bang scenarios.  Starting from the changes in dimensions described by BUT and its variants, we proposed a pre-Big Bang scenario, characterized by the presence of a Monster sporadic group encompassing our Universe[28].  In other words, the physics of sporadic groups points towards our Universe embedded in a Monster Module, standing for a sort of Spinoza’s God[28].  We provided a testable hypothesis: a modular j-function, i.e., a peculiar wave correlated with the Monster Moonshine hypothesis, could be identified in our Universe.  We found this modular j-function correlated with the Monster in the human electric activity[47].  


Quantum physics.  We proposed a model of quantum entanglement on a four-dimensional hypersphere[12].  We found a close, unexpected relationship between the Heidegger’s philosophical concept of the Being and the quantum vacuum from the real physics[55].  Other unpublished manuscripts (under review) assess quantum vacuum (a T-symmetry violation: from quantum vacuum to big bang and vacuum catastrophe)[19], topological unification of cosmological brane theories[33] and Einstein’s relativity (does an observed object shadow encompass more information than the object itself?)[39].  Furthermore, we provided an effort in order to elucidate the long-standing problem of the unification of general relativity and quantum mechanics: we tackled the issue by introducing a groupoid for (macroscopic relativistic) commutative and (microscopic quantum) non-commutative operations [59].   


Looking for hidden cosmic dimensions.  Our multidimensional framework hypothesizes that further hidden dimensions, either functional or real, micro- or macroscopic, might influence the activity of countless physical and biological systems.  To make an example, the typical change in dimensions described by the BUT might help to elucidate the puzzling phenomenon of quantum entanglement: we proposed a model of quantum entanglement on a hypersphere[12], that requires just a further spatial dimension.  Further, we found a method, based on flow dynamics, able to detect possible macroscopic hidden dimensions [38],


A versatile tool for countless physical activities.  BUT and its variants assess in abstract terms a series of real processes taking place not just in the brain, but also in various inanimate and animate physical systems.  For example, we studied the logistic maps of chaotic activities[11] and demonstrated that nonlinear brain dynamics are linear, after all[44]. Furthermore, we described an unexpected numeric correlation between the Feigenbaum constant and the Zeeman effect[41].

We also found a close relationship between ergodic and non-ergodic systems, so that this classical division does not hold anymore [44].  We showed how the BUT is able to unveil the mystery of fractals[5] and power laws, both in the brain and in other physical and biological systems.  A BUT mechanism allows also the assessment of small world networks[38] and informational entropies[38].  

With a little help by Nicholas de Cusa, we tried to erase infinity from physical teories[61]




Gauge fields in biology.  Starting from recent papers that describe time physical gauge theories applied to the brain activity [13, 57], we proposed a physical approach to biological functions, based on symmetries and symmetry breaks.  We looked for gauge theories for living cells, providing a topological exploration on the deep structure of the complexity endowed in the genetic code[52].  We also proposed, based on purely physical gauge constraints, a “teleological” model for the occurrence of life in the Universe[42].  We also asked: what if time is a gauge field that dictates the evolution of biological systems[9, 57]?


The topological evolution. During evolution, life forms an increase in complexity[52, 58] that stands for an increase of systems’ dimensions. In other worlds, evolution increases the symmetries and the dimensions of the living beings. Still, we provided a biological BUT variant able to explain the overwhelming variety of living species on the Earth[58]. Our account is not just theoretical: we also provided a geometrical grid for the assessment of countless physical and biological activities, including human diseases[53].  





When I was younger and very enthusiast, and still believed in the possibility of an academic career, I wrote a lot of stuff in pediatrics, in particular in gastroenterology and gut nerve plexuses [63-79].  In the very last years, I did not fully loose this attitude towards medical publications: I worked with short gut rats, producing models of post-resected intestine[80].   Further I raised concerns about the worldwide use of propranolol in the treatment of pediatric hemangiomas[81].   







Note: the unpublished manuscripts and the published papers’ unedited drafts are available on ResearchGate and on the website:  https://arturotozzi.webnode.it/

  1. Tozzi A. 2014. Evolution: Networks and Energy Count.Nature 515: 343. doi:10.1038/515343c.
  2. Tozzi A. 2015.  Richard Avenarius’ “Kritik Der Reinen Erfharung”: the English Translation.  viXra:1511.0251.
  3. Tozzi A. 2015. Neural code & power laws.  SCTPLS Newsletter, April, 7-10. 
  4. Tozzi A. 2015.  Information Processing in the CNS: A Supramolecular Chemistry?  Cognitive Neurodynamics 9 (5): 463–477.
  5. 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.
  6. Tozzi A. 2015. Oral Propranolol for Infantile Hemangioma. The New England Journal of Medicine 373 (3): 284–85. doi:10.1056/NEJMc1505699.
  7. 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. 
  8. 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. 
  9. Tozzi A, Peters JF, Chafin C, De Falco D, Today J.  2018.  A timeless biology.  Progr Biophys Mol Biol. doi: 10.1016/j.pbiomolbio.2017.12.002.  In press. 
  10. Tozzi A, Peters JF, Çankaya MN, Korbel J, Zare M, Papo D.  2016.  Energetic Link Between Spike Frequencies and Brain Fractal Dimensions.   viXra:1609.0105.
  11. 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.
  12. Peters JF, Tozzi A. 2016.  Quantum Entanglement on a Hypersphere.  Int J Theoret Phys, 1–8. doi:10.1007/s10773-016-2998-7.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. 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. 
  19. Tozzi A, Peters JF, Chafin C, De Falco D.  2016.  Time Symmetry Breaking in Pre-Big Bang Vacuum State.  viXra:1609.0352.
  20. Peters JF, Tozzi A, Ramanna S.  2016.  Topology Underlying Gibson’s Ecological Theory of Perception.  viXra:1609.0401.
  21. 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.
  22. Tozzi A, Peters JF.  2016.  Philosophical Libellus on Matching Descriptions. viXra:1606.0023.
  23. Tozzi A, Peters JF, Ramanna S.  2016.  A topological/ecological approach to perception. BiorXiv, https://dx.doi.org/10.1101/086827. 
  24. Tozzi A. 2016.  Topology: Borsuk-Ulam theorem and its variants.  https://www.youtube.com/watch?v=oxfqraR1bIg
  25. Tozzi A, Peters JF, Deli E.  2017.  Towards plasma-like collisionless trajectories in the brain.  Neurosci Lett. 662:105-109.  https://doi.org/10.1016/j.neulet.2017.10.016
  26. Tozzi A, Peters JF.  2016.  A Topological Brain Elucidates Syntactic and Semantic Processing.  viXra:1609.0106
  27. Tozzi A, James III C, Peters J.  2016.  A logical inquiry of emotions and cognition.  BiorXiv, https://dx.doi.org/10.1101/087874.
  28. Tozzi A, Peters JF.  2016.  Symmetries, Information and Monster Groups before and after the Big Bang. Information, 7(4), 73; doi:10.3390/info7040073.
  29. Tozzi A, Peters JF. 2017.  A Symmetric Approach Elucidates Multisensory Information Integration.  Information 8,1.  doi: 10.3390/info8010004. 
  30. 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.https://dx.doi.org/10.1080/1536383X.2017.1283618.
  31. Peters JF, Tozzi A. 2016.  Region-Based Borsuk-Ulam Theorem.  arXiv.1605.02987.
  32. Peters JF, Tozzi A.  2016.  String-Based Borsuk-Ulam Theorem. arXiv:1606.04031.
  33. Tozzi A, Peters JF. 2016. Topological Framework for Brane Cosmology. viXra:1608.0397.
  34. 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.
  35. 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.
  36. Tozzi A, Peters JF, Cankaya M.  2018.  The informational entropy endowed in cortical oscillations.  Cognitive Neurodynamics.  https://doi.org/10.1007/s11571-018-9491-3. 
  37. 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
  38. Tozzi A, Peters JF.  2017.  The multidimensional world.  Lambert Academic Publishing, Saarbrücken, Germany.  ISBN-13: 978-3-330-03530-0.
  39. Tozzi A, Peters JF. 2017.  Does a Toy Shadow Encompass More Information Than the Toy Itself?.  viXra:1703.0060.
  40. Tozzi A, Peters JF.  2017.  Just One Brain Activity.  bioRxiv, doi: https://doi.org/10.1101/147447
  41. Tozzi A. 2017.  Unexpected numeric correlation between Feigenbaum constant and Zeeman effect.  Researchgate, DOI:10.13140/RG.2.2.28438.55362.
  42. Tozzi A, Peters JF.  2017. Life and evolution: what for? An unpleasant answer. Researchgate, DOI:10.13140/RG.2.2.25425.74089
  43. Tozzi A, Peters JF.  2017.  From abstract topology to real thermodynamic brain activity.  Cognitive Neurodynamics.  11: 283. Doi:10.1007/s11571-017-9431-7. 
  44. Tozzi A, Peters JF, Fingelkurts AA, Fingelkurts AA, Marijuán PC.  2017.  Topodynamics of metastable brains.  Physics of Life Reviews. https://dx.doi.org/10.1016/j.plrev.2017.03.001.
  45. 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.  DOI: 10.1007/s11571-0­17-9428-2.
  46. 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.   https://doi.org/10.1016/j.ijar.2017.04.005.
  47. Tozzi A, Peters JF, Jausovec N.  2016.  A repetitive modular oscillation underlies human brain electric activity.  Neurosci Lett.  10.1016/j.neulet.2017.05.051.
  48. Tozzi A, Peters JF. 2017.  What does it mean “the same”?. Progress in Biophysics and Molecular Biology.  https://doi.org/10.1016/j.pbiomolbio.2017.10.005.
  49. 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. 
  50. Tozzi A, Peters JF.  2018.  Multidimensional brain activity dictated by winner-take-all mechanisms.  Neuroscience Letters, 678 (21):83-89.  https://doi.org/10.1016/j.neulet.2018.05.014. 
  51. Tozzi A, Peters JF, Fingelkurts A, Fingelkurts A, Perlovsky L.  2018. Syntax meets semantics during brain logical computations.  Progr Biophys Mol Biol.  https://doi.org/10.1016/j.pbiomolbio.2018.05.010. 
  52. 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.  https://doi.org/10.1016/j.pbiomolbio.2017.06.004
  53. 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.  https://doi.org/10.1016/j.pbiomolbio.2017.06.007. 
  54. 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.  https://doi.org/10.1016/j.plrev.2017.06.020
  55. Tozzi A, Peters JF, Navarro J, Marijuán PC.  2017.   Heidegger’s being and quantum vacuum.  Progress in Biophysics and Molecular Biology.
  56. 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.
  57. Tozzi A, Sengupta B, Peters JF, Friston KJ. 2017. Gauge Fields in the Central Nervous System. 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.  ISBN: 978-3-319-29674-6.
  58. Tozzi A, Peters JF. 2017.  What does it mean “the same”? Progress in Biophysics and Molecular Biology.  https://doi.org/10.1016/j.pbiomolbio.2017.10.005
  59. Tozzi A, Peters JF, Jaušovec N.  2018.  EEG dynamics on hyperbolic manifolds.  Neurosci Lett.  https://doi.org/10.1016/j.neulet.2018.07.035. 
  60. Deli E, Peters JF, Tozzi A.  2018.  The Thermodynamic Analysis of Neural Computation. J Neurosci Clin Res 3:1. 
  61. Tozzi A, Peters JF.  2018.  Euclid’s Geometry is Just in Our Mind, Rather Than Describing the Real World.  viXra:1804.0132. 
  62. Tozzi A.  2018.  Nervous Oscillations on a Twisted Cylinder.  viXra:1803.0284. 
  63. Staiano A, Basile P, Simeone D, Stanco A, Tozzi A, Caria MC.  1996. Proximal esophageal pH metry in children with respiratory symptoms. The Italian journal of gastroenterology 05/1996; 28(3):136-9.
  64. Staiano A, Santoro L, De Marco R, Stanco A, Fiorillo F, Tozzi A.  1996. Autonomic dysfunction in children with Hirschsprung’s disease. Journal of Pediatric Gastroenterology and Nutrition 05/1996; 22(4)., DOI:10.1097/00005176-199605000-00065. 
  65. Tozzi A, Mossetti G, Miele E, D’Armiento FP, Toraldo C, Staiano A.  1997. Development of submucosal and myenteric plexuses in relation to gestational age. Journal of Pediatric Gastroenterology and Nutrition 04/1997; 24(4)., DOI:10.1097/00005176-199704000-00122. 
  66. Tozzi A, Ascione G, Carpentieri ML, Staiano A.  1997.  Intestinal neuronal dysplasia associated with cystic fibrosis. Archives of Disease in Childhood 10/1997; 77(3):277. DOI:10.1136/adc.77.3.276a.
  67. Oderda G, Palli D, Saieva C, Chiorboli E, Bona G, Tozzi A.  1998.  Short stature and Helicobacter pylori infection in italian children: prospective multicenter hospital based case-control study. The Italian Study Group on Short Stature and H pylori. BMJ Clinical Research 09/1998; 317(7157):514-5.
  68. Staiano A, Tozzi A.  1998.  Diagnosis and treatment of constipation in children. Current Opinion in Pediatrics 11/1998; 10(5):512-5., DOI:10.1097/00008480-199810000-00011. 
  69. Fitzgerald JF, Troncone R, Tozzi A, Tramontano A, Toraldo C.  1998.   Clinical Quiz. Journal of Pediatric Gastroenterology and Nutrition 11/1998; 27(5):546-+., DOI:10.1097/00005176-199811000-00005. 
  70. Tozzi A, Tramontano A, Toraldo C.  1998.  Clinical quiz. Long-segment Hirschsprung's disease (total colonic aganglionosis). Journal of Pediatric Gastroenterology and Nutrition 12/1998; 27(5):546,559.
  71. Auricchio A, Griseri P, Carpentieri ML, Betsos N, Staiano A, Tozzi A, Priolo M, Thompson H, Bocciardi R, Romeo G, Ballabio A, Ceccherini I.  1999.  Double Heterozygosity for a RET Substitution Interfering with Splicing and an EDNRB Missense Mutation in Hirschsprung Disease. The American Journal of Human Genetics 05/1999; 64(4):1216-21., DOI:10.1086/302329. 
  72. Miele M, Staiano A, Troncone R, Tozzi A, Ciarla C, Paparo F.  1999. Clinical Response to Amino Acid-Based Enteral Formula in Neurologically Impaired Children With Refractory Esophagitis. Journal of Pediatric Gastroenterology and Nutrition 05/1999; 28(5):561., DOI:10.1097/00005176-199905000-00090. 
  73. Tozzi A, Staiano A, Tramontano A, Miele E, Toraldo C.  1999.  Hyperganglionosis and Hirschsprung's disease. Journal of Pediatric Gastroenterology and Nutrition 05/1999; 28(5)., DOI:10.1097/00005176-199905000-00132. 
  74. Staiano A, Tozzi A. 2000.  Approccio alla stipsi cronica.
  75. Staiano A, Simeone D, Del Giudice E, Miele E, Tozzi A, Toraldo C.  2000. Effect of the dietary fiber glucomannan on chronic constipation in neurologically impaired children. Journal of Pediatrics 02/2000; 136(1):41-5., DOI:10.1016/S0022-3476(00)90047-7. 
  76. Miele E, Tozzi A, Staiano A, Toraldo C, Esposito C, Clouse RE.  2000.  Persistence of abnormal gastrointestinal motility after operation for Hirschsprung's disease. The American Journal of Gastroenterology 06/2000; 95(5):1226-30., DOI:10.1111/j.1572-0241.2000.02014.x.
  77. Tozzi A, De Angelis A, Tramontano A, Scoppa A, Pinto L, Staiano A.  2001.  colonic transit times in children with anorectal malformations. Journal of Pediatric Gastroenterology and Nutrition 04/2001; 32:S55., DOI:10.1097/00005176-200104001-00048. 
  78. Tozzi A, Staiano A, Paparo F, Miele E, Maglio M, Di Meo M, Simeone D, Troncone R.  2001.  Characterization of the inflammatory infiltrate in peptic oesophagitis. Digestive and Liver Disease 08/2001; 33(6):452-8., DOI:10.1016/S1590-8658(01)80021-9.
  79. Miele E, Staiano A, Tozzi A, Auricchio R, Paparo F, Troncone R.  2002.  Clinical Response to Amino Acid-Based Formula in Neurologically Impaired Children With Refractory Esophagitis. Journal of Pediatric Gastroenterology and Nutrition 10/2002; 35(3):314-9., DOI:10.1097/00005176-200209000-00014. 
  80. Buccigrossi V, Armellino C, Tozzi A, Nicastro E, Esposito C, Alicchio F, Cozzolino S, Guarino A.  2012.  Time-and Segment-Related Changes of Post-Resected Intestine: A 4 Dimensional Model of Intestinal Adaptation.  .Journal of pediatric gastroenterology and nutrition 07/2012; 56(1)., DOI:10.1097/MPG.0b013e318268a9a4. 
  81. Tozzi A. 2015. Oral Propranolol for Infantile Hemangioma. The New England Journal of Medicine 373 (3): 284–85. doi:10.1056/NEJMc1505699.