G. Tononi and G. Edelman, Consciousness and complexity, Science, vol.282, pp.1846-51, 1998.

D. Bennequin, Remarks on invariance in the primary visual systems of mammals, neuromathematics of vision part. Lecture Notes in Morphogenesis, pp.243-333, 2014.

, mathematic, physics and panpsychism: an information topology perspective, 2018.

M. Yartsev, The emperor's new wardrobe: rebalancing diversity of animal models in neuroscience research, Science, vol.358, issue.6362, pp.466-475, 2017.

S. Paulson, The spiritual, reductionist consciousness of Christoph Koch: what the neuroscientist is discovering is both humbling and frightening him, Nautilus, 2017.

T. Nagel, What is it like to be a bat?, Philos Rev, vol.4, pp.435-50, 1974.

G. Edelman and G. Tononi, A universe of consciousness. how matter becomes imagination, 2000.

S. Dehaene and J. Changeux, Reward-dependent learning in neuronal networks for planning and decision making, Prog Brain Res, 2000.

S. Dehaene and J. Changeux, Experimental and theoretical approaches to conscious processing, Neuron, vol.70, issue.2, pp.200-227, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00717254

S. Dehaene, J. Changeux, L. Naccache, J. Sackur, and C. Sergent, Conscious, preconscious, and subliminal processing: a testable taxonomy, Trends Cogn Sci, vol.10, issue.5, pp.204-215, 2006.
URL : https://hal.archives-ouvertes.fr/pasteur-00161465

R. Sperry, Cerebral organization and behavior: the split brain behaves in many respects like two separate brains, providing new research possibilities, Science, vol.133, pp.1749-57, 1961.

M. Gazzaniga, The split brain in man, Sci Am, vol.217, issue.2, pp.24-33, 1967.

D. Chalmers, Facing up to the problem of consciousness, J Conscious Stud, vol.2, issue.3, pp.200-219, 1995.

G. Leibniz, Discours de metaphysique VI, 1686.

G. Leibniz, Oxford: Opera Philos, vol.1714

L. Galvani, De viribus electricitatis in motu musculari commentarius (commentaire sur l'effet de l'électricité sur le mouvement musculaire). Bononiae -Institutus Scientiarium, vol.1791

M. Gazzaniga, The new cognitive neurosciences, 1998.

S. Sarraf and J. Sun, Functional brain imaging: a comprehensive survey, 2016.

E. John, A field theory of consciousness, Conscious Cogn, vol.10, pp.184-213, 2001.

S. Pockett, The nature of consciousness: a hypothesis, 2000.

J. Mcfadden, Synchronous firing and its influence on the brain's magnetic field, J Conscious Stud, vol.9, pp.23-50, 2002.

M. Juusola, H. Robinson, and G. De-polavieja, Coding with spike shapes and graded potentials in cortical networks, BioEssays, vol.29, issue.2, pp.178-87, 2007.

J. Schummers, H. Yu, and M. Sur, Tuned responses of astrocytes and their influence on hemodynamic signals in the visual cortex, Science, vol.320, pp.1638-1681, 2008.

T. Preat and G. Isabel, Molecular and system analysis of olfactory memory in drosophila, 2008.

M. Soden, G. Jones, C. Sanford, A. Chung, A. Guler et al., Disruption of dopamine neuron activity pattern regulation through selective expression of a human kcnn3 mutation, Neuron, vol.80, issue.4, pp.1010-1016, 2013.

J. Monod, J. Wyman, and J. Changeux, On the nature of allosteric transition: a plausible model, J Mol Biol, vol.12, pp.88-118, 1965.

D. Fuller, W. Chen, M. Adler, A. Groisman, H. Levine et al., External and internal constraints on eukaryotic chemotaxis, Proc Natl Acad Sci, vol.107, issue.21, pp.9656-9665, 2010.

E. Davies, Action potentials as multifunctional signals in plants: a unifying hypothesis to explain apparently disparate wound responses, Plant Cell Environ, vol.10, issue.8, pp.623-654, 1987.

R. Holmes, B. Christensen, R. Wang, and P. Kwiat, Testing the limits of human vision with single photons, Frontiers in optics. OSA Technical Digest, 2015.

J. Tinsley, M. Molodtsov, R. Prevedel, D. Wartmann, J. Espigule-pons et al., Direct detection of a single photon by humans, Nat Commun, vol.7, pp.1-9, 1217.

W. Bialek and A. Schweitzer, Quantum noise and the threshold of hearing, Phys Rev Lett, vol.54, issue.7, pp.725-733, 1985.

S. Roy and R. Llinas, Relevance of quantum mechanics on some aspects of ion channel function, C R Biol, vol.332, issue.6, pp.517-539, 2009.

N. Bohr, Atomic physics and human knowledge, 1958.

S. Hameroff and R. Penrose, Conscious events as orchestrated space-time selections, J Conscious Stud, vol.3, issue.1, pp.36-53, 1996.

R. Penrose, The emperor's new mind: concerning computers, minds and the laws of physics, 1989.

S. Fusi, P. Drew, and L. Abbott, Cascade models of synaptically stored memories, Neuron, vol.45, issue.4, pp.599-611, 2005.

L. Kadanoff, Scaling laws for Ising models near tc, Physics, vol.2, issue.6, pp.263-72, 1966.

F. Dyson, The radiation theories of Tomonaga, Schwinger, and Feynman, Phys Rev, vol.75, issue.3, pp.486-502, 1949.

D. Shirkov, Evolution of the Bogoliubov renormalization group, 1999.

K. Huang, A critical history of renormalization, Int J Mod Phys A, vol.28, issue.29, pp.1-27, 2013.

F. Rieke, Spikes exploring the neural code, a Bradford book, Computational neuroscience, 1999.

E. Adrian and Y. Zotterman, The impulses produced by sensory nerve endings, part II: the response of a single end organ, J Physiol, vol.61, pp.151-71, 1926.

S. Thorpe, D. Fize, and C. Marlot, Speed of processing in the human visual system, Nature, vol.382, pp.520-522, 1996.

T. Gawne, T. Kjaer, and B. Richmond, Latency: another potential code for feature binding in striate cortex, J Neurophysiol, vol.76, issue.2, pp.1356-60, 1996.

S. Strong, R. De-ruyter-van-steveninck, W. Bialek, and R. Koberle, On the application of information theory to neural spike trains, Pac Symp Biocomput, pp.621-653, 1998.

W. Bialek, F. Rieke, R. De-ruyter-van-steveninck, and D. Warland, Reading a neural code, Science, vol.252, issue.5014, pp.1854-1861, 1991.

J. Victor and K. Purpura, Nature and precision of temporal coding in visual cortex: a metric-space analysis, J Neurophysiol, vol.76, issue.2, pp.1310-1336, 1996.

F. Mechler, J. Victor, K. Purpura, and R. Shapley, Robust temporal coding of contrast by v1 neurons for transient but not for steady-state stimuli, J Neurosci, vol.18, pp.6583-98, 1998.

P. Baudot, Natural computation: much ado about nothing? An intracellular study of visual coding in natural condition, 2006.

P. Baudot, M. Levy, O. Marre, C. Monier, M. Pananceau et al., Animation of natural scene by virtual eye-movements evokes high precision and low noise in v1 neurons, Front Neural Circuits, vol.7, issue.206, pp.1-29, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01055318

D. Debanne, A. Bialowas, and S. Rama, What are the mechanisms for analogue and digital signalling in the brain?, Nat Rev Neurosci, vol.14, pp.63-72, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01766838

M. Zbili, S. Rama, and D. Debanne, Dynamic control of neurotransmitter release by presynaptic potential, Front Cell Neurosci, vol.10, issue.278, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01766828

P. Simmons and R. De-ruyter-van-steveninck, Reliability of signal transfer at a tonically transmitting, graded potential synapse of the locust ocellar pathway, J Neurosci, vol.25, issue.33, pp.7529-7566, 2005.

R. De-ruyter-van-steveninck and S. Laughlin, The rate of information transfer at graded-potential synapses, Nature, vol.379, pp.642-647, 1996.

S. Rama, M. Zbili, A. Bialowas, L. Fronzaroli-molinieres, N. Ankri et al., Presynaptic hyperpolarization induces a fast analogue modulation of spike-evoked transmission mediated by axonal sodium channels, Nat Commun, vol.6, p.10163, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01766831

H. Barlow, Banishing the homonculus, Perception as Bayesian inference, 1995.

P. Foldiack, The 'ideal homunculus': statistical inference from neural population responses, Comput Neural Syst, pp.55-60, 1993.

A. Borst and F. Theunissen, Information theory and neural coding, Nat Neurosci, vol.2, pp.947-57, 1999.

D. Hebb, The organization of behaviour, 1949.

V. Der-malsburg and C. , The correlation theory of brain function, p.3400, 1981.

M. Abeles, Local cortical circuits: an electrophysiological study, 1982.

M. Diesmann, M. Gewaltig, and A. Aertsen, Stable propagation of synchronous spiking in cortical neural networks, Nature, vol.402, pp.529-562, 1999.

W. Singer and C. Gray, Visual feature integration and the temporal correlation hypothesis, Annu Rev Neurosci, vol.18, pp.555-86, 1995.

A. Engel, P. Fries, P. Koenig, M. Brecht, and W. Singer, Temporal binding, binocular rivalry, and consciousness, Conscious Cogn, vol.8, issue.2, pp.128-51, 1999.

I. Gold, Does 40-Hz oscillation play a role in visual consciousness?, Conscious Cogn, vol.8, issue.2, pp.186-95, 1999.

C. Curto and V. Itskov, Cell groups reveal structure of stimulus space, PLoS Comput Biol, vol.4, issue.10, 2008.

G. Singh, F. Memoli, T. Ishkhanov, G. Sapiro, G. Carlsson et al., Topological analysis of population activity in visual cortex, J Vis, vol.8, issue.11, pp.1-18, 2008.

G. Petri, P. Expert, F. Turkheimer, R. Carhart-harris, D. Nutt et al., Homological scaffolds of brain functional networks, J R Soc Interface, vol.6, issue.11, p.101, 2014.

W. Kohler, Gestalt psychology: an introduction to new concepts in modern psychology, 1947.

M. Wertheimer, A source book of Gestalt psychology, 1924.

M. Wertheimer, Laws of organization in perceptual forms, 1923.

M. Wertheimer and . Isomorphism, Corsini Encyclopedia of Psychology, pp.1-2, 2010.

W. Kohler, Die physischen gestalten in ruhe und im stationaren zustand, abridged trans, pp.71-88, 1920.

F. Attneave, Some informational aspects of visual perception, Psychol Rev, vol.61, issue.3, pp.183-94, 1954.

H. Barlow, Possible principles underlying the transformation of sensory messages, pp.217-251, 1961.

R. Kubo, The fluctuation-dissipation theorem, Rep Prog Phys, vol.29, issue.1, pp.255-84, 1966.

C. Stevens, Inferences about membrane properties from electrical noise measurements, Biophys J, vol.12, issue.8, pp.1028-1075, 1972.

N. Wiener, Nonlinear problems in random theory, 1958.

G. Palm and T. Poggio, The Volterra representation and the wiener expansion: validity and pitfalls, SIAM J Appl Math, vol.33, issue.2, pp.195-216, 1977.

G. Palm and T. Poggio, Stochastic identification methods for nonlinear systems: an extension of wiener theory, SIAM J Appl Math, vol.34, issue.3, pp.524-558, 1978.

D. Hubel and T. Wiesel, Receptive fields of single neurones in the cat's striate cortex, J Physiol, vol.148, pp.574-91, 1959.

D. Hubel and T. Wiesel, Receptive fields, binocular interaction and functional architecture in the cat's visual cortex, J Physiol, vol.160, issue.1, pp.106-54, 1962.

G. Deangelis, I. Ohzawa, and R. Freeman, Receptive-field dynamics in the central visual pathways, Trends Neurosci, vol.8, issue.10, pp.451-459, 1995.

J. Fournier, C. Monier, M. Levy, O. Marre, and Y. Fregnac, Hidden complexity of synaptic receptive fields in cat v1, J Neurosci, vol.34, issue.16, pp.5515-5543, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01055317

T. L. Griffiths, C. Kemp, and J. B. Tenenbaum, Cambridge handbook of computational cognitive modeling, 2008.

K. Friston, The history of the future of the Bayesian brain, NeuroImage, vol.62, issue.2, pp.1230-1233, 2012.

A. Kolmogorov, Combinatorial foundations of information theory and the calculus of probabilities, Russ Math Surv, vol.38, p.29, 1983.

E. Jaynes, Probability theory: the logic of science, 2003.

P. Baudot and D. Bennequin, The homological nature of entropy, Entropy, vol.17, issue.5, pp.3253-318, 2015.

J. Vigneaux, Topology of statistical systems. A cohomological approach to information theory, 2019.

L. Martignon, G. Deco, K. Laskey, M. Diamond, W. Freiwald et al., Neural coding: higher-order temporal patterns in the neurostatistics of cell assemblies, Neural Comput, vol.12, issue.11, pp.2621-53, 2000.

S. Amari, Information geometry on hierarchy of probability distributions, IEEE Trans Inf Theory, vol.47, issue.5, pp.1701-1712, 2001.

W. Ma, J. Beck, P. Latham, and A. Pouget, Bayesian inference with probabilistic population codes, Nat Neurosci, vol.9, issue.11, pp.1432-1440, 2006.

S. Dehaene and J. Changeux, Ongoing spontaneous activity controls access to consciousness: a neuronal model for inattentional blindness, PLoS Biol, vol.3, issue.5, 2005.
URL : https://hal.archives-ouvertes.fr/inserm-00079979

V. Wyart and C. Sergent, The phase of ongoing eeg oscillations uncovers the fine temporal structure of conscious perception, J Neurosci, vol.29, issue.41, pp.12839-12880, 2009.

R. Brown, on the particles contained in the pollen of plants and on the general existence of active molecules, vol.1828, 1827.

A. Vilardi, The role of noise in brain dynamics processes, CIMeC, 2009.

A. Eldar and M. Elowitz, Functional roles for noise in genetic circuits, Nature, vol.467, issue.7312, pp.167-73, 2014.

P. Bak, C. Tang, and K. Wiesenfeld, Self-organized criticality: an explanation of 1/f noise, Phys Rev Lett, vol.59, issue.4, pp.381-385, 1987.

C. E. Shannon, A mathematical theory of communication, Bell Syst Tech J, vol.27, pp.379-423, 1948.

V. Baji and T. Tan, Information processing and living systems, 2005.

P. Dayan, G. Hinton, R. Neal, and R. Zemel, The Helmholtz machine, Neural Comput, vol.7, pp.889-904, 1995.

M. Merleau-ponty, Phenomenologie de la perception, Gallimard, coll. Tel, 1945.

R. Llinas and . Vortex, From neurons to self. A Bradford book, 2002.

A. Berthoz, Physiologie de la perception et de l'action. Cours du collége de France, 2000.

M. Jeannerod, Motor cognition: what actions tell to the self, 2006.

I. Saraf-sinik, E. Assa, and E. Ahissar, Motion makes sense: an adaptive motor-sensory strategy underlies the perception of object location in rats, J Neurosci, vol.35, issue.23, pp.8777-89, 2015.

J. O'regan and A. Noe, A sensorimotor account of vision and visual consciousness, Behav Brain Sci, vol.24, pp.939-73, 2001.

K. Friston, J. Kilner, and L. Harrison, A free energy principle for the brain, J Physiol (Paris), vol.100, issue.1-3, pp.70-87, 2006.

M. Srinivasan, S. Laughlin, and A. Dubs, Predictive coding, a fresh view of inhibition in the retina, Proc R Soc Lond, vol.216, pp.427-59, 1205.

S. Laughlin, The role of sensory adaptation in the retina, J Exp Biol, vol.146, pp.39-62, 1989.

R. Linsker, From basic network principles to neural architecture, Proc Natl Acad Sci, vol.83, pp.7508-7520, 1986.

R. Linsker, Self-organization in a perceptual network, Computer, vol.21, issue.3, pp.105-122, 1988.

D. Ackley, G. Hinton, and T. J. Sejnowski, A learning algorithm for Boltzmann machines, Cogn Sci, vol.9, issue.1, pp.147-69, 1985.

N. Nadal and J. Parga, Sensory coding: information maximization and redundancy reduction, Neural information processing, vol.7, pp.164-71, 1999.

N. Nadal and J. Parga, Nonlinear neurons in the low noise limit: a factorial code maximizes information transfer, Netw Comput Neural Syst, vol.5, pp.565-81, 1994.
URL : https://hal.archives-ouvertes.fr/hal-00143844

T. Bell and A. J. Sejnowski, An information maximisation approach to blind separation and blind deconvolution, Neural Comput, vol.7, issue.6, pp.1129-59, 1995.

F. Klein, Vergleichende bertrachtungen uber neuere geometrische forschungen erlangen, Math Ann, vol.1893, issue.1, pp.460-97, 1872.

G. Birkhoff and M. Bennett, Felix Klein and his "erlanger programm, History and philosophy of modern mathematics, pp.145-76, 1988.

G. Andrews, The theory of partitions, 1998.

B. Fresse, Koszul duality of operads and homology of partition posets, Contemp Math Amer Math Soc, vol.346, pp.115-215, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00015642

F. Schoeller, L. Perlovsky, and D. Arseniev, Physics of mind: experimental confirmations of theoretical predictions, Phys Life Rev, 2018.

M. Costa, A. Goldberger, and C. Peng, Multiscale entropy to distinguish physiologic and synthetic rr time series, Comput Cardiol, vol.29, pp.137-177, 2002.

M. Costa, A. Goldberger, and C. Peng, Multiscale entropy analysis of biological signals, Phys Rev E, vol.71, p.21906, 2005.

G. Hochschild, On the cohomology groups of an associative algebra, Ann Math (2), vol.46, pp.58-67, 1945.

J. Tate and . Galois, , 1991.

H. Cartan and S. Eilenberg, Homological algebra, 1956.

M. Lane and S. Homology, Classic in Mathematics, 1975.

D. Kendall, Functional equations in information theory, Z Wahrscheinlichkeitstheor Verw Geb, vol.2, pp.225-234, 1964.

P. Lee, On the axioms of information theory, Ann Math Stat, vol.35, issue.1, pp.415-423, 1964.

M. Gerstenhaber and S. Schack, A hodge-type decomposition for commutative algebra cohomology, J Pure Appl Algebra, vol.48, issue.1-2, pp.229-276, 1987.

P. Baudot, The Poincare-Shannon machine: statistical physics and machine learning aspects of information cohomology, Entropy, vol.21, issue.9, p.881, 2019.

P. Baudot, M. Tapia, D. Bennequin, and J. Goaillard, Topological information data analysis, Entropy, vol.21, issue.9, p.869, 2019.

D. Hilbert, Hilbert's lectures on the infinite. Traduit par Andre Weil Paris; 1926. Edited in David Hilbert's Lectures on the Foundations of Arithmetic and Logic 1917-1933, 1924.

H. Poincare, Science and hypothesis, 1902.

P. Baudot, M. Tapia, and J. Goaillard, Topological information data analysis: Poincare-Shannon machine and statistical physic of finite heterogeneous systems, 2018.

M. Tapia, P. Baudot, M. Dufour, C. Formizano-treziny, S. Temporal et al., Information topology of gene expression profile in dopaminergic neurons, 2017.

D. Silver, Mastering the game of go without human knowledge, Nature, vol.550, issue.7676, pp.354-363, 2017.

V. Mnih, K. Kavukcuoglu, and D. Silver, Human-level control through deep reinforcement learning, Nature, vol.518, issue.7540, pp.529-562, 2015.

A. Seth, E. Izhikevich, G. Reeke, and G. Edelman, Theories and measures of consciousness: an extended framework, Proc Natl Acad Sci, vol.103, issue.28, pp.10799-804, 2006.

K. T. Hu, On the amount of information, Theory Probab Appl, vol.7, issue.4, pp.439-486, 1962.

P. Williams and R. Beer, Nonnegative decomposition of multivariate information, 2010.

E. Olbrich, N. Bertschinger, and J. Rauh, Information decomposition and synergy, Entropy, vol.17, issue.5, pp.3501-3518, 2015.

N. Bertschinger, J. Rauh, E. Olbrich, J. Jost, and N. Ay, Quantifying unique information, Entropy, vol.16, pp.2161-83, 2014.

V. Griffith and C. Koch, Guided self-organization: inception. Berlin/Heidelberg, pp.159-90, 2014.

M. Tapia, P. Baudot, C. Formizano-treziny, M. Dufour, S. Temporal et al., Neurotransmitter identity and electrophysiological phenotype are genetically coupled in midbrain dopaminergic neurons, Nat Commun, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01963481

S. Watanabe, Information theoretical analysis of multivariate correlation, IBM J Res Dev, vol.4, pp.66-81, 1960.

M. Studeny and J. Vejnarova, The multiinformation function as a tool for measuring stochastic dependence, pp.261-96, 1999.

G. Tononi, M. Boly, M. Massimini, and C. Koch, Integrated information theory: from consciousness to its physical substrate, Nat Rev Neurosci, vol.17, issue.7, 2016.

C. Adami and N. Cerf, Prolegomena to a non-equilibrium quantum statistical mechanics, Chaos Solitons Fractals, vol.10, issue.10, pp.1637-50, 1999.

M. Kapranov, Thermodynamics and the moment map, 2011.

T. Cover, Which processes satisfy the second law, pp.98-107, 1994.

J. Baez and B. Fong, A Noether theorem for Markov processes, J Math Phys, vol.54, p.13301, 2013.

L. Barnett and A. Barrett, Granger causality and transfer entropy are equivalent for Gaussian variables, Phys Rev Lett, vol.103, p.238701, 2009.

T. Schreiber, Measuring information transfer, Phys Rev Lett, vol.85, issue.2, pp.461-465, 2000.

H. Bergson, Time and free will: an essay on the immediate data of consciousness, 1910.

R. Yeung, Information theory and network coding, 2007.

M. Oizumi, L. Albantakis, and G. Tononi, From the phenomenology to the mechanisms of consciousness: Integrated information theory 3.0, PLoS Comput Biol, vol.10, issue.5, 2014.

R. Griffiths, Consistent histories and the interpretation of quantum mechanics, J Stat Phys, vol.35, p.219, 1984.

R. Omnes, Logical reformulation of quantum mechanics, I: foundations, J Stat Phys, vol.53, pp.893-932, 1988.

M. Gell-mann and J. Hartle, Quantum mechanics in the light of quantum cosmology, pp.425-58, 1990.

D. Rudrauf, D. Bennequin, I. Granic, G. Landini, K. Friston et al., A mathematical model of embodied consciousness, J Theor Biol, vol.428, pp.106-137, 2017.

G. D'agostino and A. Scala, Networks of networks: the last frontier of complexity. Understanding complex systems, 2014.

D. Reshef, Y. Reshef, H. Finucane, S. Grossman, G. Mcvean et al., Detecting novel associations in large data sets, Science, vol.334, p.1518, 2011.

N. Brenner, S. Strong, R. Koberle, and W. Bialek, Synergy in a neural code, Neural Comput, vol.12, pp.1531-52, 2000.

E. Schrodinger, What is life?; 1944. Based on lectures delivered under the auspices of the Dublin Institute for Advanced Studies at Trinity College, 1943.

H. Atlan, Entre le cristal et la fumee. Essai sur l'organisation du vivant. Seuil, 1979.

J. Gibson, The ecological approach to visual perception, 1979.

J. Atick, Could information theory provide an ecological theory of sensory processing, Netw Comput Neural Syst, vol.3, pp.213-51, 1992.