The Homological Nature of Entropy, Entropy, vol.17, pp.3253-3318, 2015. ,
Topological Information Data Analysis, Entropy, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-02457878
Neurotransmitter identity and electrophysiological phenotype are genetically coupled in midbrain dopaminergic neurons, Sci. Rep, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01963481
Passing Messages Between Disciplines, Science, vol.301, 1686. ,
, The unification of Mathematics via Topos Theory. arXiv 2010, 2019.
Classical and quantum probabilities as truth values, J. Math. Phys, vol.53, p.32101, 2012. ,
A Topos Foundation for Theories of Physics: I. Formal Languages for Physics, J. Math. Phys, vol.49, p.53515, 2008. ,
Science and Information Theory, 1956. ,
Information Theory and Statistical Mechanics II, Phys. Rev, vol.108, pp.171-190, 1957. ,
Information Theory and Statistical Mechanics, Phys. Rev, vol.106, pp.620-630, 1957. ,
Irreversibility and heat generation in the computing process, IBM J. Res. Dev, vol.5, pp.183-191, 1961. ,
Angular Momentum: An Approach to Combinatorial Space-Time, Quantum Theory and Beyondum, pp.151-180, 1971. ,
Quantum: The Search for Links, Complexity, Entropy, and the Physics of Information, 1990. ,
Notes on Landauer's principle, Reversible Computation and Maxwell's Demon, Stud. Hist. Philos. Mod. Phys, vol.34, pp.501-510, 2003. ,
Physics and Austerity, Law Without Law; Numéro 122 de Pamhlets on Physics, 1982. ,
The Statistical Interpretation of Quantum Mechanics. Nobel Lecture, 1954. ,
Natural Computation: Much Ado about Nothing? An Intracellular Study of Visual Coding in Natural Condition, 2006. ,
, The Structure of Information: From Probability to Homology. arXiv 2017, 2019.
Topology of Statistical Systems. A Cohomological Approach to Information Theory, 2019. ,
, , 2011.
, Homological Tools for the Quantum Mechanic. arXiv 2019, 2019.
A hodge-type decomposition for commutative algebra cohomology, J. Pure Appl. Algebr, vol.48, pp.229-247, 1987. ,
The lattice theory of information, Transactions of the IRE Professional Group on Information Theory, vol.1, pp.105-107, 1953. ,
A metric space of discrete probability distributions, Inform. Control, vol.4, pp.371-377, 1961. ,
Thermodynamic cost of computation, algorithmic complexity and the information metric, Nature, vol.341, pp.119-125, 1989. ,
Information distance, IEEE Trans. Inf. Theory, vol.44, pp.1407-1423, 1998. ,
Mutual Information Based Hierarchical Clustering, Information Theory and Statistical Learning, pp.101-123, 2009. ,
Information and its metric, In Nonlinear Structures in Physical Systems, pp.119-130, 1990. ,
The Potts model, Rev. Mod. Phys, vol.54, pp.235-268, 1982. ,
URL : https://hal.archives-ouvertes.fr/hal-02340560
One-dimensional Ising model with multispin interactions, J. Phys. A-Math. Theor, vol.49, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01352924
Electronic structure of matter-Wave functions and density functionals, Rev. Mod. Phys, vol.71, 1253. ,
, Relative Entropy in Biological Systems. Entropy, vol.18, 2016.
Synergy in a neural code, Neural Comput, vol.12, pp.1531-52, 2000. ,
Information theoretic characterization of frustrated systems, Physica A, vol.294, pp.180-190, 2001. ,
Phase transitions in small systems: Microcanonical vs. canonical ensembles, Physica A, vol.370, pp.390-406, 2006. ,
Elements of Information Theory ,
, Noether, E. Invariant Variation Problems, Transport Theor. Stat, vol.37, pp.186-207, 1971.
Noether's Theorem for Smooth, Difference and Finite Element Systems, Foundations of Computational Mathematics, pp.230-257, 2005. ,
A Noether theorem for Markov processes, J. Math. Phys, vol.54, 2013. ,
Noether's theorem and discrete symmetries, Am. J. Phys, vol.63, p.489, 1995. ,
, Phase Transitions: Scaling, Universality and Renormalization. Phase Transitions Dirac V2.4. 2010, 2019.
The renormalization group and the epsilon expansion, Phys. Rep, vol.12, pp.75-200, 1974. ,
Phase Transitions and Renormalization Group, 2010. ,
The Strange Theory of Light and Matter, 1985. ,
Directions in Physics ,
Over de Continuiteit van den Gas-en Vloeistoftoestand; Luitingh-Sijthoff, p.1873 ,
Van der Waals on the Continuity of the Gaseous and Liquid States, Nature, vol.1874, p.407 ,
On the dynamical evidence of the molecular constitution of bodies, Nature, vol.1875, pp.357-359 ,
An introduction to partition logic, Log. J. IGPL, vol.22, pp.94-125, 2014. ,
The logic of partitions: introduction to the dual of the logic of subsets, The Review of Symbolic Logic, vol.3, pp.287-350, 2010. ,
Multivariate Dependence beyond Shannon Information, vol.19, 2017. ,
Communities, clustering phase transitions, and hysteresis: pitfalls in constructing network ensembles, Phys. Rev. E, vol.81, p.46115, 2010. ,
Extracting insights from the shape of complex data using topology, Sci. Rep, 1236. ,
Topological data analysis. Inverse Probl. 2011, 27, 120201. 55. Carlsson, G. Topology and data, Bull. Am. Math. Soc, vol.46, pp.255-308, 2009. ,
A Topological View of Unsupervised Learning from Noisy Data, SIAM J. Comput, vol.20, pp.646-663, 2011. ,
Efficient and Robust Persistent Homology for Measures, Comput. Geom, vol.58, pp.70-96, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01074566
An entropy-based persistence barcode, Pattern Recognit, vol.48, pp.391-401, 2015. ,
Topological Characterization of Complex Systems: Using Persistent Entropy, Entropy, vol.17, pp.6872-6892, 2015. ,
The influence of architecture of nanoparticle networks on collective charge transport revealed by the fractal time series and topology of phase space manifolds, J. Coupled Syst. Multiscale Dyn, vol.4, pp.30-42, 2016. ,
Combinatorial Laplacian and entropy of simplicial complexes associated with complex networks, Eur. Phys. J, vol.212, pp.77-97, 2012. ,
Multilevel Integration Entropies: The Case of Reconstruction of Structural Quasi-Stability in Building Complex Datasets, vol.19, p.172, 2017. ,
Information Cohomology Methods for Learning the Statistical Structures of Data. DS3 Data Science, Ecole Polytechnique, 2019. ,
Neural Networks and Physical Systems with Emergent Collective Computational Abilities, Proc. Natl. Acad. Sci, vol.79, pp.2554-2558, 1982. ,
A Learning Algorithm for Boltzmann Machines, Cogn. Sci, vol.9, pp.147-169, 1985. ,
The Helmholtz Machine, Neural Comput, vol.7, pp.889-904, 1995. ,
Elements of Consciousness and Cognition, Mathematic, Physics and Panpsychism: An Information Topology Perspective. arXiv 2018, 2019. ,
, Persistent Topology of Syntax. In Mathematics in Computer Science, vol.1, pp.33-50, 2018.
, , 1982.
Journal de l'École Polytechnique 1895, vol.1, pp.1-121 ,
A Mathematical Theory of Communication, Bell Labs Tech. J, vol.27, pp.379-423, 1948. ,
Idées Galoisiennes; Chap 4 of Leçons de Mathématiques Contemporaines à l'IRCAM, Master; cel-01359200, 2009. ,
, Ambiguity theory, old and new. arXiv 2008, 2019.
Information Inequalities, and Groups, Communications, Information and Network Security ,
, , vol.712, pp.333-359, 2003.
Sur l'homologie de sl2 a coefficients dans l'action adjointe, Math. Scand, vol.63, pp.51-86, 1988. ,
On poly(ana)logs I, Compos. Math, vol.130, pp.161-214, 2002. ,
Finite polylogarithms, their multiple analogues and the Shannon entropy, International Conference on Geometric Science of Information, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01176710
Characteristic 1, entropy and the absolute point, Noncommutative Geometry, Arithmetic, and Related Topics, 2009. ,
Entropy algebras and Birkhoff factorization, J. Geom. Phys, vol.97, pp.243-265, 2018. ,
A Characterization of Entropy in Terms of Information Loss, Entropy, vol.13, 1945. ,
A Bayesian characterization of relative entropy, Theory Appl. Categ, vol.29, pp.422-456, 2014. ,
Foliations-Webs-Hessian Geometry-Information Geometry-Entropy and Cohomology, Entropy, vol.18, p.433, 2016. ,
Homotopy probability theory I, J. Homotopy Relat. Struct, vol.10, pp.425-435, 2015. ,
Homotopy probabilty Theory II, J. Homotopy Relat. Struct, vol.10, pp.623-635, 2015. ,
Homotopy Theory of Probability Spaces I: Classical independence and homotopy Lie algebras, 2015. ,
Aomoto dilogarithms, mixed Hodge structures and motivic cohomology of pairs of triangles on the plane, The Grothendieck Festschrift, vol.1, pp.135-172, 1990. ,
Addition theorem of Abel type for Hyper-logarithms, Nagoya Math. J, vol.88, pp.297-324, 1982. ,
On information and sufficiency, Ann. Math. Stat, vol.22, pp.79-86, 1951. ,
On the Amount of Information, Theory Probab. Appl, vol.7, pp.439-447, 1962. ,
Information Theory and Network Coding, 2007. ,
Multivariate information transmission, Psychometrika, vol.19, pp.97-116, 1954. ,
Information theoretical analysis of multivariate correlation, IBM J. Res. Dev, vol.4, pp.66-81, 1960. ,
Consciousness and Complexity, Science, vol.282, pp.1846-1851, 1998. ,
The multiinformation function as a tool for measuring stochastic dependence, Learning in Graphical Models, pp.261-296, 1999. ,
Nemenman, I. Multivariate dependence and genetic networks inference, IET Syst. Biol, vol.4, pp.428-440, 2010. ,
The Theory of Partitions, 1998. ,
Koszul duality of operads and homology of partitionn posets, Contemp. Math. Am. Math. Soc, vol.346, pp.115-215, 2004. ,
On the cohomology groups of an associative algebra, Ann. Math, vol.46, pp.58-67, 1945. ,
An Introduction to Homological Algebra, 1995. ,
Homology and Cohomology of Associative Algebras-A Concise Introduction to Cyclic Homology, 2004. ,
URL : https://hal.archives-ouvertes.fr/cel-00119891
,
, Springer Science & Business Media: Berlin/Heidelberger, 1991.
, , 1956.
,
, Springer Science & Business Media: Berlin/Heidelberger, 1975.
Functional Equations in Information Theory, vol.2, pp.225-229, 1964. ,
On the Axioms of Information Theory, Ann. Math. Stat, vol.35, pp.415-418, 1964. ,
Topological Information Data Analysis: Poincare-Shannon Machine and Statistical Physic of Finite Heterogeneous Systems, 2018. ,
The Best-partitions Problem: How to Build Meaningful Aggregations?, Proceedings of the 2013 IEEE/WIC/ACM International Joint Conferences on Web Intelligence (WI) and Intelligent Agent Technologies (IAT), p.18, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00918433
Every finite lattice can be embedded in a finite partition lattice. Algebra Univ, vol.10, pp.74-95, 1980. ,
, Simplicial cohomology is Hochschild Cohomology. J. Pure Appl. Algebr, vol.30, pp.143-156, 1983.
Products of Cocycles and Extensions of Mapping, Ann. Math, vol.48, pp.290-320, 1947. ,
Topological quantum field theory, Publ. Math. IHÉS, vol.68, pp.175-186, 1988. ,
Topological Quantum Field Theory, Commun. Math. Phys, vol.117, pp.353-386, 1988. ,
, Topological Quantum Field Theory. arXiv, 2000.
Detecting Novel Associations in Large Data Sets, Science, vol.334, 1518. ,
Inhomogeneous electron gas, Phys. Rev, vol.136, pp.864-871, 1964. ,
Self-Consistent Equations Including Exchange and Correlation Effects, Phys. Rev, vol.140, pp.1133-1138, 1965. ,
Information, Physics, quantum: The search for the links, Proceedings of the 3rd International Symposium on Foundations of Quantum Mechanics, pp.354-368, 1989. ,
On the central limit theorem in Rk, Ark. Mat, vol.7, pp.61-69, 1967. ,
Multivariate maximum entropy identification, transformation, and dependence, J. Multivar. Anal, vol.99, pp.1217-1231, 2008. ,
Probability distributions and maximum entropy, Entropy, vol.6, p.10, 2005. ,
Prolegomena to a non-equilibrium quantum statistical mechanics, Chaos Solition Fract, vol.10, pp.1637-1650, 1999. ,
, Thermodynamics and the moment map. arXiv 2011, 2019.
On the distribution function of additive functions, Ann. Math, vol.47, pp.1-20, 1946. ,
On Measures of Information and Their Characterizations, 1975. ,
, Physics (Course of Theoretical Physics, vol.5
, , 1969.
Linear dependence structure of the entropy space, Inf. Control, vol.29, pp.337-368, 1975. ,
Continuous partition lattice, Proc. Natl. Acad. Sci, vol.84, pp.6327-6329, 1987. ,
, Int. Math. Res. Not, pp.1026-1106, 2009.
Conditional probabilities and permutahedron, Annales de l'Institut Henri Poincare (B) Probability and Statistics, 2003. ,
Facets of entropy. In Communications in Information and Systems, vol.15, pp.87-117, 2015. ,
A framework for linear information inequalities, IEEE Trans. Inf. Theory, vol.43, 1924. ,
On Characterization of Entropy Function via Information Inequalities, IEEE Trans. Inf. Theory, vol.44, pp.1440-1452, 1997. ,
Infinitely Many Information Inequalities, pp.41-47, 2007. ,
Stochastic Processes Problems and Solutions ,
Theory of Sets-Elements of Mathematic, 1968. ,
Scientific Uncertainty, and Information, 2014. ,
Consistent Histories and the Interpretation of Quantum Mechanics, J. Stat. Phys, vol.35, 1984. ,
Logical reformulation of quantum mechanics I. Foundations, J. Stat. Phys, vol.53, pp.893-932, 1988. ,
Quantum mechanics in the light of quantum cosmology, Complexity, Entropy, and the Physics of Information, pp.425-458, 1990. ,
A Guide to Entropy and the Second Law of Thermodynamics, Statistical Mechanics, vol.45, pp.571-581, 1998. ,
Space-Time Approach to Non-Relativistic Quantum Mechanics, Rev. Mod. Phys, vol.20, pp.367-387, 1948. ,
Factorized Mutual Information Maximization, 2019. ,
, J. Phys. Theor. Appl, vol.6, pp.661-690, 1907.
Van der Waals Forces: A Handbook for Biologists, Chemists, Engineers, and Physicists, 2006. ,
Tensor Renormalization of Quantum Many-Body Systems Using Projected Entangled Simplex States, Phys. Rev. X, 2014. ,
Resolutions of square-free monomial ideals via facet ideals: A survey, 2006. ,
, Complex Systems: A Survey. arXiv 2011, 2019.
Information, Physics, and Computation, 2009. ,
Theory of the frustration effect. II. Ising spins on a square lattice, J. Phys. Condens. Matter, vol.10, 1977. ,
Notes for a brief history of quantum gravity, 2008. ,
Finitary Substitute for Continuous Topology, Int. J. Theor. Phys, vol.30, pp.923-947, 1991. ,
On the application of information theory to neural spike trains, Proceedings of the Pacific Symposium on Biocomputing, pp.621-632, 1998. ,
Non-asymptotic thermodynamic ensembles, EPL, vol.86, pp.1-6, 2009. ,
Combinatorial entropies and statistics, Eur. Phys. J, vol.70, pp.49-63, 2009. ,
Exact Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics, Phys. Lett. A, vol.342, pp.286-293, 2005. ,
Toward a quantitative theory of self-generated complexity, Int. J. Theor. Phys, vol.25, pp.907-938, 1986. ,
, Complexity through nonextensivity. Physica A, vol.302, pp.89-99, 2001.
Entropic Nonextensivity: A possible measure of Complexity, Chaos Solition Fract, vol.13, pp.371-391, 2002. ,
Nonequilibrium fluctuations in small systems: From physics to biology, Adv. Chem. Phys, vol.137, pp.31-123, 2008. ,
, Theorie des Topos et Cohomologie Etale des Schemas-(SGA 4, 1972.
Grundbegriffe der Wahrscheinlichkeitsrechnung, 1933. ,
Searching for collective behavior in a large network of sensory neurons, PLoS Comput. Biol, vol.10, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01342627
Information theory with finite vector spaces, IEEE Trans. Inf. Theory, vol.99, 2019. ,
The k-Generalizations of Stirling Approximation and Multinominal Coefficients, Entropy, vol.15, pp.5144-5153, 2013. ,
Negative entropy and information in quantum mechanic, Phys. Rev. Lett, vol.79, 1997. ,
Entropic Bell Inequalities, Phys. Rev. A, vol.55, 1997. ,
Persistence Theory: From Quiver Representations to Data Analysis ,
URL : https://hal.archives-ouvertes.fr/hal-01247501
Two visual systems, Science, vol.163, pp.895-902, 1969. ,
Separate visual pathways for perception and action, Trends Neurosci, vol.15, pp.20-25, 1992. ,
Gradient theory of optimal flight paths, vol.30, pp.947-954, 1960. ,
The numerical solution of variational problems, J. Math. Anal. Appl, vol.5, pp.30-45, 1962. ,
Learning representations by back-propagating errors, Nature, vol.323, pp.533-536, 1986. ,
Discrete Restricted Boltzmann Machines, J. Mach. Learn. Res, vol.21, pp.653-672, 2015. ,
Neural learning in structured parameter spaces-Natural Riemannian gradient, Advances in Neural Information Processing Systems, pp.127-133, 1997. ,
, New Insights and Perspectives on the Natural Gradient Method, 2017.
Geometry of Quantum States: An Introduction to Quantum Entanglement ,
Revisiting Natural Gradient for Deep Networks, 2014. ,
The Strategy of the Genes, vol.Routledge, 1957. ,
Single-cell entropy for accurate estimation of differentiation potency from a cell's transcriptome, Nat. Commun, 2017. ,
Energy landscape-based inference of transition probabilities and cellular trajectories from single-cell transcriptomic data, Bioinformatics, vol.34, pp.2077-2086, 2018. ,
, Poetics, vol.3, pp.7-19, 1974.
Self-organization in a perceptual network, Computer, vol.21, pp.105-117, 1988. ,
Sensory coding: information maximization and redundancy reduction, Proceedings of the Neuronal Information Processing, vol.7, pp.164-171, 1997. ,
An information maximisation approach to blind separation and blind deconvolution, Neural Comput, vol.7, pp.1129-1159, 1995. ,
A parallel implementation of the Cellular Potts Model for simulation of cell-based morphogenesis, Comput. Phys. Commun, vol.176, pp.670-681, 2007. ,
, Neural plasticity of development and learning. Hum. Brain Mapp, vol.31, pp.879-890, 2010.