[5] **viXra:1610.0216 [pdf]**
*submitted on 2016-10-18 10:06:20*

**Authors:** Arturo Tozzi, James F Peters

**Comments:** 153 Pages.

This manuscript encompasses our published and unpublished topological results in neuroscience. Topology, the mathematical branch that assesses objects and their properties preserved through deformations, stretching and twisting, allows the investigation of the most general brain features. In particular, the Borsuk-Ulam Theorem (BUT) states that, if a single point projects to a higher spatial dimension, it gives rise to two antipodal points with matching description. Physical and biological counterparts of BUT and its variants allow an inquiry of the brain activity. The opportunity to treat the nervous system as a topological structure makes BUT a universal principle underlying neural phenomena and brain function.

**Category:** Mind Science

[4] **viXra:1610.0113 [pdf]**
*submitted on 2016-10-10 15:21:51*

**Authors:** Arturo Tozzi, James F Peters, Pedro C. Marijuán

**Comments:** 7 Pages.

Brain activity can be assessed either at anatomical/functional micro-, meso- and macro- spatiotemporal scales of observation, or at different intertwined levels with mutual interactions. Here we show, based on topological findings, that nervous activities occurring in micro-levels project to single activities at the macro-levels. This means that brain functions assessed at the higher scale of the whole brain necessarily display a counterpart in the lower ones, and vice versa. Furthermore, we point out how it is possible for different functional and anatomical levels to be stitched (sewn) together to become condensed brain activities, giving rise, for example, to ideas and concepts. Also, a topological approach makes it possible to assess brain functions in the general terms of particle trajectories taking place on donut-like manifolds. Indeed, every macro-scale activity, independent of the subtending theoretical model, can be described in terms of a multi-dimensional torus mapping to activities at lower levels. In physics, the term duality refers to a case where two seemingly different systems turn out to be equivalent, because they are mathematically distinguishable descriptions of the same phenomenon. Our framework permits a topological duality among different neuro-techniques, because it holds for all the types of spatio-temporal brain activities, independent of their inter- and intra-level relationships, strength, magnitude and boundaries.

**Category:** Mind Science

[3] **viXra:1610.0068 [pdf]**
*submitted on 2016-10-06 04:57:02*

**Authors:** Arturo Tozzi, James F Peters

**Comments:** 10 Pages.

Recent advances in neuronal multisensory integration suggest that the five senses do not exist in isolation of each other. Perception, cognition and action are integrated at very early levels of central processing, in a densely coupled system equipped with multisensory interactions occurring at all temporal and spatial stages. In such a novel framework, a concept from the far-flung branch of topology, namely the Borsuk-Ulam theorem, comes into play. The theorem states that when two opposite points on a sphere are projected onto a circumference, they give rise to a single point containing their matching description. Here we show that the theorem applies also to multisensory integration: two environmental stimuli from different sensory modalities display similar features when mapped into cortical neurons. Topological tools not only shed new light on questions concerning the functional architecture of mind and the nature of mental states, but also provide a general methodology which as the advantage to be assessed empirically. We argue that the Borsuk-Ulam theorem is a general principle underlying nervous multisensory integration, resulting in a framework that has the potential to be operationalized.

**Category:** Mind Science

[2] **viXra:1610.0031 [pdf]**
*submitted on 2016-10-04 03:49:52*

**Authors:** Arturo Tozzi, James F. Peters, Marzieh Zare, Mehmet Niyazi Çankaya

**Comments:** 13 Pages.

Informational entropies, although proved to be useful in the evaluation of nervous function, are suitable just if we assume that nervous activity takes place under ergo dic conditions. However, widespread claims suggest that the brain operates in a non-ergodic framework. Here we show that a topological concept, namely the Borsuk-Ulam theorem, is able to wipe away this long-standing limit of both Shannon entropy and its generalizations, such as Rényi’s. We demonstrate that both ergodic and non-ergodic informational entropies can be evaluated and quantified through topological methods, in order to improve our knowledge of central nervous system function.

**Category:** Mind Science

[1] **viXra:1610.0014 [pdf]**
*submitted on 2016-10-02 15:11:22*

**Authors:** Arturo Tozzi, James F Peters

**Comments:** 10 Pages.

Plasma studies depict collisionless, collective movements of charged particles. In touch with these concepts, originally developed in the far flung branch of high energy physics, here we evaluate the role of collective behaviors and long-range functional couplings in brain dynamics. We develop a novel, empirically testable, brain model which takes into account collisionless movements of charged particles in a system, the brain, equipped with oscillations. The model is cast in a mathematical fashion with the potential of being operationalized, because it can be assessed in terms of McKean-Vlasov equations, derived from the classical Vlasov equations for plasma. We also provide insights into the possible role of the overrated extracellular neuronal space in generating and transporting the charged particles which display such a collective behavior. A plasma-like brain also elucidates cortical phase transitions in the context of a brain at the edge of chaos and describes the required order parameters. In sum, showing how the brain might exhibit plasma-like features we go through the emerging concept of holistic behavior of nervous functions.

**Category:** Mind Science