# A Symmetric Approach Elucidates Multisensory Information Integration

^{1}

^{2}

^{*}

## Abstract

**:**

“A color is a physical object when we consider its dependence upon its luminous source; regarding, however, its dependence upon the retina, it becomes a psychological object, a sensation. Not the subject, but the direction of our investigation, is different in the two domains” (Mach 1885).

## 1. Classical vs. Current View

## 2. A Topological Model of Multisensory Integration

#### 2.1. The Borsuk-Ulam Theorem.

^{n}sphere [33]. There are natural ties between Borsuk’s result for antipodes and mappings called homotopies. In fact, the early work on n-spheres and antipodal points eventually led Borsuk to the study of retraction mappings and homotopic mappings [34].

Points on SEvery continuous map $f:{S}^{n}\to {R}^{n}$ must identify a pair of antipodal points.

^{n}are antipodal, provided they are diametrically opposite. Examples of antipodal points are the endpoints of a line segment S

^{1}, or the opposite points along the circumference of a circle S

^{2}, or the poles of a sphere S

^{3}[35]. An n-dimensional Euclidean vector space is denoted by ${R}^{n}$ [36,37]. Put simply, BUT states that a sphere displays two antipodal points that emit matching signals. When they are projected on a circumference, they give rise to a single point which a description matching both antipodal points (Figure 1A). Here “opposite points” means two points on the surface of a three-dimensional sphere (the surface of a beach ball is a good example) which share some characteristics in common and are at the same distance from the center of the beach ball [38]. For example, BUT dictates that on the earth’s surface there always exist two opposite points with the same pressure and temperature. Two opposite points embedded in a sphere project onto a single point on a circumference, and vice versa: this means that the projection from a higher dimension (equipped with two antipodal points) to a lower one gives rise to a single point (equipped with the characteristics of both the antipodal points). It is worth mentioning again that the two antipodal points display similar features: we will go through this central issue in the next paragraph.

#### 2.2. Borsuk-Ulam Theorem in Brain Signal Analysis.

- (Str. 1) Every union of sets in $\tau $ is a set in $\tau $
- (Str. 2) Every finite intersection of sets in $\tau $ is a set in $\tau $

^{2}have equivalent shapes, if the planer sets have the same number of holes [40]. This suggests yet another useful application of Borsuk’s view of the transformation of one shape into the other, in terms of brain signal analysis. Sets of brain signals not only will have similar descriptions, but also similar dynamic character. Moreover, the deformation of one brain signal shape into another occurs when they are descriptively near [47,48]. This expanded view of signals has interest, since every connected couple of antipodal points has a shape: therefore, signal shapes can be compared. If we evaluate physical and biological phenomena instead of “signals”, BUT leads naturally to the possibility of a region-based, not simply point-based, geometry, with many applications. In terms of activity, two antipodal regions model the description of a signal. The regions themselves live on what is known as a manifold, which is a topological space that is a snapshot (tiny part) of a locally Euclidean space. For a given signal on a sphere, we expect to find an antipodal region that describes a signal with a matching description. In sum, the mapping from the sphere to the circumference is defined by a rule which tells us how to find a single point/region [49]. The region-based view of the manifold arises naturally in terms of a comparison of shapes produced by different mappings from the sphere to the circumference [50].

#### 2.3 Borsuk-Ulam Theorem and Multisensory Integration.

^{n−1}sphere does not match perfectly, and the sensation is doubtful (Figure 2B). A superimposition of two spheres with slightly different centers occurs. The brain thus might “move” its spheres, in order to restore the coherence between the two signals. Therefore, by an operational point of view, we might be able to evaluate the distance between the central points of the two spheres, in order to achieve the discrepancy values between the two multisensory signals projected from the environment to the brain.

^{n}and S

^{n−}

^{1}. We start from a manifold S

^{n}equipped with a pair of antipodal points. When these opposite points map to an n-Euclidean manifold (where S

^{n−}

^{1}lies), a dimensionality reduction occurs, and a single point is achieved. However, it is widely recognized that a decrease in dimensions goes together with a decrease in information. Two antipodal points contain more information than their single projection in a lower dimension, because dropping down a dimension means that each point in the lower dimensional space is simpler: each point has one less coordinate. To make an example, a two-dimensional shadow of a cat encompasses less information than a three-dimensional cat. This means that the single mapping function on S

^{n−}

^{1}displays informational parameters lower than the two corresponding antipodal functions on S

^{n}. Because information can be evaluated in terms of informational entropy, BUT and its variants yield physical quantities: we achieve a system in which entropy changes depend on affine connections and homotopies. Entropies can be evaluated in fMRI functional studies through different techniques, e.g., pairwise entropy [53,54,55], Granger causality index, phase slope index, and so on [56]. Here we propose a topological procedure in order to assess changes in informational entropies in brain fMRI multisensory integration’s studies. The method is described in Figure 3. In our example, the visual and auditory cues stand for a continuous function, from the sphere surrounding the individual to his cortical multisensory neurons. Informational entropy values can be identified in multisensory neurons after their activation: in the hypothetical case of Figure 3, we choose a putative entropy value of 1.02. According to the BUT’s dictates, the same value 1.02 must be found both in the environmental cues (a single value of 1.02 for every one of the two different cues), and in every other cortical area involved in multisensory processing. We might not know the entropy values of the sound and sight in the external environment. However, this is not important: if we identify a group of cortical multisensory neurons that fire when a visual and auditory cue are presented together, we need just to know the entropy values of such neuronal assembly. Therefore, by knowing the sole entropy values of a Blood Oxygenation Level Dependent (BOLD)-activated multisensory brain area, we are allowed to correlate different brain zones involved in multisensory integration (Figure 3). Indeed, neurons equipped with the same entropy values are functionally linked, according to BUT. Therefore, we are able to assess the cortical zones that display the same entropy values, shedding light on the pathways involved in multisensory integration. This methodology paves also the way to experimentally evaluate which model, e.g., either the traditional or the current view of multisensory integration, is valid. Note that, in the proposed fMRI context, BUT is related to a meso-level of observation that involves cortical circuits and inter-areal massive interactions, through “Communication through Coherence”. Nevertheless, once neuro-techniques will be more advanced, BUT should be applicable also to micro-levels of observation, such as single-cell spiking activity.

## 3. An Answer for Current Issues

## 4. What Does Topology Bring to the Table?

## Conflicts of Interest

## References

- Krueger, J.; Royal, D.W.; Fister, M.C.; Wallace, M.T. Spatial receptive field organization of multisensory neurons and its impact on multisensory interactions. Hear. Res.
**2009**, 258, 47–54. [Google Scholar] [CrossRef] [PubMed] - Fetsch, C.R.; DeAngelis, G.C.; Angelaki, D.E. Visual-vestibular cue integration for heading perception: Applications of optimal cue integration theory. Eur. J. Neurosci.
**2010**, 31, 1721–1729. [Google Scholar] [CrossRef] [PubMed] - Werner, S.; Noppeney, U. Superadditive responses in superior temporal sulcus predict audiovisual benefits in object categorization. Cereb. Cortex
**2009**, 20, 1829–1842. [Google Scholar] [CrossRef] [PubMed] - Stein, B.E.; Rowland, B.A. Organization and plasticity in multisensory integration: Early and late experience affects its governing principles. Prog. Brain Res.
**2011**, 191, 145–163. [Google Scholar] [PubMed] - Royal, D.W.; Krueger, J.; Fister, M.C.; Wallace, M.T. Adult plasticity of spatiotemporal receptive fields of multisensory superior colliculus neurons following early visual deprivation. Restor. Neurol Neurosci.
**2010**, 28, 259–270. [Google Scholar] [PubMed] - Burnett, L.R.; Stein, B.E.; Perrault, T.J., Jr.; Wallace, M.T. Excitotoxic lesions of the superior colliculus preferentially impact multisensory neurons and multisensory integration. Exp. Brain Res.
**2007**, 179, 325–338. [Google Scholar] [CrossRef] [PubMed] - Stein, B.E.; Perrault, T.Y., Jr.; Stanford, T.R.; Rowland, B.A. Postnatal experiences influence how the brain integrates information from different senses. Front. Integr. Neurosci.
**2009**, 3. [Google Scholar] [CrossRef] [PubMed] - Stein, B.E.; Stanford, T.R.; Rowland, B.A. Development of multisensory integration from the perspective of the individual neuron. Nat. Rev. Neurosci.
**2014**, 15, 520–535. [Google Scholar] [CrossRef] [PubMed] - Johnson, S.P.; Amso, D.; Slemmer, J.A. Development of object concepts in infancy: Evidence for early learning in an eye-tracking paradigm. Proc. Natl. Acad. Sci. USA
**2003**, 100, 10568–10573. [Google Scholar] [CrossRef] [PubMed] - Xu, J.; Yu, L.; Rowland, B.A.; Stanford, T.R.; Stein, B.E. Incorporating cross-modal statistics in the development and maintenance of multisensory integration. J. Neurosci.
**2012**, 15, 2287–2298. [Google Scholar] [CrossRef] [PubMed] - Porcu, E.; Keitel, C.; Müller, M.M. Visual, auditory and tactile stimuli compete for early sensory processing capacities within but not between senses. Neuroimage
**2014**, 97, 224–235. [Google Scholar] [CrossRef] [PubMed] - Yu, L.; Rowland, B.A.; Stein, B.E. Initiating the development of multisensory integration by manipulating sensory experience. J. Neurosci.
**2010**, 7, 4904–4913. [Google Scholar] [CrossRef] [PubMed] - Borsuk, K. Drei Sätze über die n-dimensionale euklidische Sphäre. Fundam. Math.
**1933**, 20, 177–190. (In German) [Google Scholar] - Nieuwenhuys, R.; Voogd, J.; van Huijzen, C. The Human Central Nervous System; Springer: Heidelberg, Germany, 2008. [Google Scholar]
- Pollmann, S.; Zinke, W.; Baumgartner, F.; Geringswald, F.; Hanke, M. The right temporo-parietal junction contributes to visual feature binding. Neuroimage
**2014**, 101, 289–297. [Google Scholar] [CrossRef] [PubMed] - Van den Heuvel, M.P.; Sporns, O. Rich-club organization of the human connectome. J. Neurosci.
**2011**, 31, 15775–15786. [Google Scholar] [CrossRef] [PubMed] - Allman, B.L.; Keniston, L.P.; Meredith, M.A. Not just for bimodal neurons anymore: The contribution of unimodal neurons to cortical multisensory processing. Brain Topogr.
**2009**, 21, 157–167. [Google Scholar] [CrossRef] [PubMed] - Hackett, T.A.; Schroeder, C.E. Multisensory integration in auditory and auditory-related areas of Cortex. Hear. Res.
**2009**, 258, 72–79. [Google Scholar] [CrossRef] [PubMed] - Shinder, M.E.; Newlands, S.D. Sensory convergence in the parieto-insular vestibular cortex. J. Neurophysiol.
**2014**, 111, 2445–2464. [Google Scholar] [CrossRef] [PubMed] - Reig, R.; Silberberg, G. Multisensory integration in the mouse striatum. Neuron
**2014**, 83, 1200–1212. [Google Scholar] [CrossRef] [PubMed] - Kuang, S.; Zhang, T. Smelling directions: Olfaction modulates ambiguous visual motion perception. Sci. Rep.
**2014**, 23. [Google Scholar] [CrossRef] [PubMed] - Kim, S.S.; Gomez-Ramirez, M.; Thakur, P.H.; Hsiao, S.S. Multimodal Interactions between Proprioceptive and Cutaneous Signals in Primary Somatosensory Cortex. Neuron
**2015**, 86, 555–566. [Google Scholar] [CrossRef] [PubMed] - Murray, M.M.; Thelen, A.; Thut, G.; Romei, V.; Martuzzi, R.; Matusz, P.J. The multisensory function of the human primary visual cortex. Neuropsychologia
**2015**. [Google Scholar] [CrossRef] [PubMed] - Nys, J.; Smolders, K.; Laramée, M.E.; Hofman, I.; Hu, T.T.; Arckens, L. Regional Specificity of GABAergic Regulation of Cross-Modal Plasticity in Mouse Visual Cortex after Unilateral Enucleation. J. Neurosci.
**2015**, 35, 11174–11189. [Google Scholar] [CrossRef] [PubMed] - Bedny, M.; Richardson, H.; Saxe, R. “Visual” Cortex Responds to Spoken Language in Blind Children. J. Neurosci.
**2015**, 35, 11674–11681. [Google Scholar] [CrossRef] [PubMed] - Yan, K.S.; Dando, R. A crossmodal role for audition in taste perception. J. Exp. Psychol. Hum. Percept. Perform.
**2015**, 41, 590–596. [Google Scholar] [CrossRef] [PubMed] - Escanilla, O.D.; Victor, J.D.; di Lorenzo, P.M. Odor-taste convergence in the nucleus of the solitary tract of the awake freely licking rat. J. Neurosci.
**2015**, 35, 6284–6297. [Google Scholar] [CrossRef] [PubMed] - Maier, J.X.; Blankenship, M.L.; Li, J.X.; Katz, D.B. A Multisensory Network for Olfactory Processing. Curr. Biol.
**2015**, 25, 2642–2650. [Google Scholar] [CrossRef] [PubMed] - Klemen, J.; Chambers, C.D. Current perspectives and methods in studying neural mechanisms of multisensory interactions. Neurosci. Biobehav. Rev.
**2012**, 36, 111–133. [Google Scholar] [CrossRef] [PubMed] - Bastos, A.M.; Litvak, V.; Moran, R.; Bosman, C.A.; Fries, P.; Friston, K.J. A DCM study of spectral asymmetries in feedforward and feedback connections between visual areas V1 and V4 in the monkey. Neuroimage
**2015**, 108, 460–475. [Google Scholar] [CrossRef] [PubMed] - Dodson, C.T.J.; Parker, P.E. A User’s Guide to Algebraic Topology; Kluwer: Dordrecht, The Netherlands, 1997. [Google Scholar]
- Matoušek, J. Using the Borsuk-Ulam Theorem; Lectures on Topological Methods in Combinatorics and Geometry; Springer: Berlin/Heidelberg, Germany, 2003. [Google Scholar]
- Weisstein, E.W. Antipodal Points. Available online: http://mathworld.wolfram.com/AntipodalPoints.html (accessed on 15 November 2016).
- Borsuk, M.; Gmurczyk, A. On Homotopy Types of 2-Dimensional Polyhedral. Fundam. Math.
**1980**, 109, 123–142. [Google Scholar] - Moura, E.; Henderson, D.G. Experiencing Geometry: On Plane and Sphere; Prentice Hall: Englewood Cliffs, NJ, USA, 1996. [Google Scholar]
- Tozzi, A.; Peters, J.F. Towards a Fourth Spatial Dimension of Brain Activity. Cogn. Neurodyn.
**2016**, 10, 189–199. [Google Scholar] [CrossRef] [PubMed] - Tozzi, A.; Peters, J.F. A Topological Approach Unveils System Invariances and Broken Symmetries in the Brain. J. Neurosci. Res.
**2016**, 94, 351–365. [Google Scholar] [CrossRef] [PubMed] - Marsaglia, G. Choosing a Point from the Surface of a Sphere. Ann. Math. Stat.
**1972**, 43, 645–646. [Google Scholar] [CrossRef] - Van Essen, D.C. A Population-Average, Landmark—And Surface-based (PALS) atlas of human cerebral cortex. Neuroimage
**2005**, 28, 635–666. [Google Scholar] [CrossRef] [PubMed] - Krantz, S.G. A Guide to Topology; The Mathematical Association of America: Washington, DC, USA, 2009; p. 107. [Google Scholar]
- Manetti, M. Topology; Springer: Heidelberg, Germany, 2015. [Google Scholar]
- Cohen, M.M. A Course in Simple Homotopy Theory; Springer: New York, NY, USA, 1973; p. MR0362320. [Google Scholar]
- Borsuk, K. Concerning the classification of topological spaces from the standpoint of the theory of retracts. Fundam. Math.
**1959**, 46, 321–330. [Google Scholar] - Borsuk, K. Fundamental Retracts and Extensions of Fundamental Sequences. Fundam. Math.
**1969**, 64, 55–85. [Google Scholar] - Collins, G.P. The Shapes of Space. Sci. Am.
**2004**, 291, 94–103. [Google Scholar] [CrossRef] [PubMed] - Weeks, J.R. The Shape of Space, 2nd ed.; Marcel Dekker, Inc.: New York, NY, USA, 2002. [Google Scholar]
- Peters, J.F. Topology of Digital Images. Visual Pattern Discovery in Proximity Spaces, Intelligent Systems Reference Library; Springer: Berlin, Germany, 2014; Volume 63, pp. 1–342. [Google Scholar]
- Peters, J.F. Computational Proximity. Excursions in the Topology of Digital Images, Intelligent Systems Reference Library; Springer: Berlin, Germany, 2016; pp. 1–468. [Google Scholar]
- Willard, S. General Topology; Dover Pub., Inc.: Mineola, NY, USA, 1970. [Google Scholar]
- Peters, J.F.; Tozzi, A. Region-Based Borsuk-Ulam Theorem. arXiv, 2016; arXiv:1605.02987. [Google Scholar]
- Perrault, T.J., Jr.; Stein, B.E.; Rowland, B.A. Non-stationarity in multisensory neurons in the superior colliculus. Front. Psychol.
**2011**, 2, 144. [Google Scholar] [CrossRef] [PubMed] - Benson, K.; Raynor, H.A. Occurrence of habituation during repeated food exposure via the olfactory and gustatory systems. Eat Behav.
**2014**, 15, 331–333. [Google Scholar] [CrossRef] [PubMed] - Schneidman, E.; Berry, M.J.; Segev, R.; Bialek, W. Weak pairwise correlations imply strongly correlated network states in a neural population. Nature
**2006**, 440, 1007–1012. [Google Scholar] [CrossRef] [PubMed] - Watanabe, T.; Kan, S.; Koike, T.; Misaki, M.; Konishi, S.; Miyauchi, S.; Masuda, N. Network-dependent modulation of brain activity during sleep. NeuroImage
**2014**, 98, 1–10. [Google Scholar] [CrossRef] [PubMed] - Wang, Z.; Li, Y.; Childress, A.R.; Detre, J.A. Brain entropy mapping using fMRI. PLoS ONE
**2014**, 9, 1–8. [Google Scholar] [CrossRef] [PubMed] - Kida, T.; Tanaka, E.; Kakigi, R. Multi-Dimensional Dynamics of Human Electromagnetic Brain Activity. Front. Hum. Neurosci.
**2016**, 9, 713. [Google Scholar] [CrossRef] [PubMed] - Sutter, C.; Drewing, K.; Müsseler, J. Multisensory integration in action control. Front. Psychol.
**2014**. [Google Scholar] [CrossRef] [PubMed] - Drugowitsch, J.; de Angelis, G.C.; Klier, E.M.; Angelaki, D.E.; Pouget, A. Optimal multisensory decision-making in a reaction-time task. Elife
**2014**. [Google Scholar] [CrossRef] [PubMed] - Jones, D.M.B. Models, Metaphors and Analogies. In The Blackwell Guide to the Philosophy of Science; Machamer, P., Silberstein, M., Eds.; Blackwell: Oxford, UK, 2002. [Google Scholar]
- Mach, E. Analysis of the Sensations; The Open Court Publishing Company: Chicago, IL, USA, 1896. [Google Scholar]
- Van Ackeren, M.J.; Schneider, T.R.; Müsch, K.; Rueschemeyer, S.A. Oscillatory neuronal activity reflects lexical-semantic feature integration within and across sensory modalities in distributed cortical networks. J. Neurosci.
**2014**, 34, 14318–14323. [Google Scholar] [CrossRef] [PubMed] - Doehrmann, O.; Naumer, M.J. Semantics and the multisensory brain: How meaning modulates processes of audio-visual integration. Brain Res.
**2008**, 25, 136–150. [Google Scholar] [CrossRef] [PubMed] - Diaconescu, A.O.; Alain, C.; McIntosh, A.R. The co-occurrence of multisensory facilitation and cross-modal conflict in the human brain. J. Neurophysiol.
**2011**, 106, 2896–2909. [Google Scholar] [CrossRef] [PubMed] - Gärdenfors, P. Six Tenets of Cognitive Semantics. 2011. Available online: http://www.ling.gu.se/~biljana/ st1-97/ tenetsem.html (accessed on 11 December 2016).
- Gärdenfors, P. Conceptual Spaces: The Geometry of Thought; The MIT Press: Cambridge, UK, 2000. [Google Scholar]
- Kuhn, W. Why Information Science Needs Cognitive Semantics—And What It Has to Offer in Return; DRAFT Version 1.0; Meaning and Computation Laboratory, Department of Computer Science and Engineering, University of California at San Diego: La Jolla, CA, USA, 31 March 2003. [Google Scholar]
- Stevenson, R.A.; Fister, J.K.; Barnett, Z.P.; Nidiffer, A.R.; Wallace, M.T. Interactions between the spatial and temporal stimulus factors that influence multisensory integration in human performance. Exp. Brain Res.
**2012**, 219, 121–137. [Google Scholar] [CrossRef] [PubMed] - Langacker, R.W. Cognitive Grammar—A Basic Introduction; Oxford University Press: New York, NY, USA, 2008. [Google Scholar]
- Fauconnier, G. Mappings in Thought and Language; Cambridge University Press: Cambridge, UK, 1997. [Google Scholar]
- Kim, J. Making Sense of Emergence. Philos. Stud.
**1999**, 95, 3–36. [Google Scholar] [CrossRef] - Parise, C.V.; Spence, C.; Ernst, M.O. When correlation implies causation in multisensory integration. Curr. Biol.
**2012**, 22, 46–49. [Google Scholar] [CrossRef] [PubMed] - Körding, K.P.; Beierholm, U.; Ma, W.J.; Quartz, S.; Tenenbaum, J.B.; Shams, L. Causal inference in multisensory perception. PLoS ONE
**2007**, 26, e943. [Google Scholar] [CrossRef] [PubMed] - Friston, K. The free-energy principle: A unified brain theory? Nat. Rev. Neurosci.
**2010**, 11, 127–138. [Google Scholar] [CrossRef] [PubMed] - Grush, R. Cognitive Science. In The Blackwell Guide to the Philosophy of Science; Machamer, P., Silberstein, M., Eds.; Blackwell: Oxford, UK, 2002. [Google Scholar]
- McLean, J.; Freed, M.A.; Segev, R.; Freed, M.A.; Berry, M.J.; Balasubramanian, V.; Sterling, P. How much the eye tells the brain. Curr. Biol.
**2006**, 25, 1428–1434. [Google Scholar] - Royal, D.W.; Carriere, B.N.; Wallace, M.T. Spatiotemporal architecture of cortical receptive fields and its impact on multisensory interactions. Exp. Brain Res.
**2009**, 198, 127–136. [Google Scholar] [CrossRef] [PubMed] - Méndez, J.C.; Pérez, O.; Prado, L.; Merchant, H. Linking perception, cognition, and action: Psychophysical observations and neural network modelling. PLoS ONE
**2014**, 9, e102553. [Google Scholar] [CrossRef] [PubMed] - Sengupta, B.; Tozzi, A.; Cooray, G.K.; Douglas, P.K.; Friston, K.J. Towards a Neuronal Gauge Theory. PLoS Biol.
**2016**, 14, e1002400. [Google Scholar] [CrossRef] [PubMed] - Peters, J.F.; Tozzi, A.; Ramanna, S. Brain tissue tessellation shows absence of canonical microcircuits. Neurosci. Lett.
**2016**, in press. [Google Scholar] [CrossRef] [PubMed] - Holldobler, B.; Wilson, E.O. Formiche—Storia di Un’Esplorazione Scientifica; Adelphi: Milano, Italy, 2002. [Google Scholar]
- Peirce, C.S. Philosophical Writings of Peirce; Buchler, J., Ed.; Courier Dover Publications: New York, NY, USA, 2011; p. 344. [Google Scholar]
- Goodman, R.B. Pragmatism: Critical Concepts in Philosophy; Taylor & Francis: New York, NY, USA, 2005; Volume 2, p. 345. [Google Scholar]
- Magosso, E.; Cuppini, C.; Serino, A.; di Pellegrino, G.; Ursino, M. A theoretical study of multisensory integration in the superior colliculus by a neural network model. Neural Netw.
**2008**, 21, 817–829. [Google Scholar] [CrossRef] [PubMed] - Ohshiro, T.; Angelaki, D.E.; DeAngelis, G.C. A normalization model of multisensory integration. Nat. Neurosci.
**2011**, 14, 775–782. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**(

**A**) A simplified sketch of the Borsuk-Ulam theorem: two antipodal points (black spheres) on a three-dimensional sphere project to a single point on a two-dimensional circumference. (

**B**) The Figure shows what happens when an observer is in front of a guitar player. The environmental inputs from different sensory modalities (in this case sound and sight are depicted in guise of shapes instead of points) converge on a single group of multisensory neurons in the cortical layers of brain’s observer. Note that the brain is flattened and displayed in 2D [39]. According to the dictates of the Borsuk-Ulam theorem, the single shape contains a melted message from the two modalities. Modified from Tozzi and Peters [37].

**Figure 2.**(

**A**) A simplified sketch of the reBUT (a variant of the Borsuk-Ulam theorem). The functions with matching description do not need necessarily to be antipodal. Thus, the two inputs from different sensory modalities may arise from every point of the environment, if they are just equipped with a signal matching. (

**B**) When the two inputs from different modalities do not match on the 2-D brain surface, a discrepancy occurs between two brain spheres, which can be quantified by evaluating the distance between their two centres. Modified from Tozzi and Peters [37].

**Figure 3.**The use of BUT in the evaluation of brain computations during multisensory integration. The figure displays a hypothetical case for illustrative purposes. The red circles are equipped with a number standing for the corresponding entropy value (in this hypothetical case: 1.02). The right Figure displays the environment containing two cues with matching description, e.g., equipped with entropy values: 1.02. The same entropy value can be found in the corresponding multisensory neuronal assembly located in the brain sensory cortex (left figure). This means that there must be at least a cortical area (or micro-area) with the same entropy value of the two matching points encompassed in the environment. Because multisensory interactions occur at all temporal and spatial stages, their extensive cortical connections must have something in common: they must display the same values of entropy (in this case, 1.02). This allows us to recognize which zones of the brain are functionally correlated during multisensory integration.

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Tozzi, A.; Peters, J.F.
A Symmetric Approach Elucidates Multisensory Information Integration. *Information* **2017**, *8*, 4.
https://doi.org/10.3390/info8010004

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Tozzi A, Peters JF.
A Symmetric Approach Elucidates Multisensory Information Integration. *Information*. 2017; 8(1):4.
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**Chicago/Turabian Style**

Tozzi, Arturo, and James F. Peters.
2017. "A Symmetric Approach Elucidates Multisensory Information Integration" *Information* 8, no. 1: 4.
https://doi.org/10.3390/info8010004