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GSI'17 Opening session

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application/pdf GSI'17 Opening session Frédéric Barbaresco, Frank Nielsen, Silvère Bonnabel

Auteurs

Optimal matching between curves in a manifold
Drone Tracking Using an Innovative UKF
Jean-Louis Koszul et les structures élémentaires de la Géométrie de l’Information
Poly-Symplectic Model of Higher Order Souriau Lie Groups Thermodynamics for Small Data Analytics
Session Geometrical Structures of Thermodynamics (chaired by Frédéric Barbaresco, François Gay-Balmaz)
Opening and closing sessions (chaired by Frédéric Barbaresco, Frank Nielsen, Silvère Bonnabel)
GSI'17-Closing session
GSI'17 Opening session
Démonstrateur franco-britannique "IRM" : gestion intelligente et homéostatique des radars multifonctions
Principes & applications de la conjugaison de phase en radar : vers les antennes autodirectives
Nouvelles formes d'ondes agiles en imagerie, localisation et communication
Compréhension et maîtrise des tourbillons de sillage
Wake vortex detection, prediction and decision support tools
Ordonnancement des tâches pour radar multifonction avec contrainte en temps dur et priorité
Symplectic Structure of Information Geometry: Fisher Metric and Euler-Poincaré Equation of Souriau Lie Group Thermodynamics
Reparameterization invariant metric on the space of curves
Probability density estimation on the hyperbolic space applied to radar processing
SEE-GSI'15 Opening session
Lie Groups and Geometric Mechanics/Thermodynamics (chaired by Frédéric Barbaresco, Géry de Saxcé)
Opening Session (chaired by Frédéric Barbaresco)
Invited speaker Charles-Michel Marle (chaired by Frédéric Barbaresco)
Koszul Information Geometry & Souriau Lie Group 4Thermodynamics
MaxEnt’14, The 34th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering
Koszul Information Geometry & Souriau Lie Group Thermodynamics
Robust Burg Estimation of stationary autoregressive mixtures covariance
Koszul Information Geometry and Souriau Lie Group Thermodynamics
Koszul Information Geometry and Souriau Lie Group Thermodynamics
Oral session 7 Quantum physics (Steeve Zozor, Jean-François Bercher, Frédéric Barbaresco)
Opening session (Ali Mohammad-Djafari, Frédéric Barbaresco)
Tutorial session 1 (Ali Mohammad-Djafari, Frédéric Barbaresco, John Skilling)
Prix Thévenin 2014
SEE/SMF GSI’13 : 1 ère conférence internationale sur les Sciences  Géométriques de l’Information à l’Ecole des Mines de Paris
Synthèse (Frédéric Barbaresco)
POSTER SESSION (Frédéric Barbaresco)
ORAL SESSION 16 Hessian Information Geometry II (Frédéric Barbaresco)
Information/Contact Geometries and Koszul Entropy
lncs_8085_cover.pdf
Geometric Science of Information - GSI 2013 Proceedings
Médaille Ampère 2007

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Geometric Science of Information SEE/SMF GSI’17 Conference Mines ParisTech GSI’17 General Chairmen: Frédéric BARBARESCO*, Frank NIELSEN** & Silvère BONNABEL*** (*) President of SEE ISIC Club (Ingéniérie des Systèmes d’Information de Communications) (**) LIX Department, Ecole Polytechnique, (***) CAOR Lab, Mines ParisTech, Société de l'électricité, de l'électronique et des technologies de l'information et de la communication GSI’13 Mines ParisTech GSI’15 Ecole Polytechnique Slides: https://www.see.asso.fr/gsi2013 Videos: https://www.youtube.com/channel/UC5HHo1jb QXusNQzU1iekaGA UNITWIN website (slides & videos): http://forum.cs-dc.org/category/90/gsi2015 Hirohiko Shima Jean-Louis Koszul Charles-Michel Marle GSI’13 Mines GSI’15 Polytechnique Roger Balian ORBITUARY Michel Marie Deza died on 23 november 2016 in an accidental fire in his apartment in Paris. He was a Soviet and French mathematician, specializing in combinatorics, discrete geometry and graph theory.He was director of research at the French National Centre for Scientific Research (CNRS), the vice president of the European Academy of Sciences, a research professor at the Japan Advanced Institute of Science and Technology, and one of the three founding editors-in-chief of the European Journal of Combinatorics. https://en.wikipedia.org/wiki/Michel_Deza 2012 video of Michel Marie Deza at IRCAM for Brillouin Seminar on « Geometric Science of Information » http://archiprod-externe.ircam.fr/video/VI02027700-282.mp4 Michel Marie Deza is author of the SPRINGER book: Encyclopedia of Distances, Authors: Deza, Michel Marie, Deza, Elena http://www.springer.com/us/book/9783662528433 Michel Marie Deza Marcel Berger greatly contributed to mathematics, through his own publications, for example on holonomy groups, symmetric spaces, curvature pinching and the sphere theorem, spectral geometry or systolic geometry. His influence goes far beyond his research papers. His books and surveys have inspired not only his students, but a much broader audience. Important features of Marcel Berger's mathematical heritage are also his seminar and his influence on the round tables organized by his friend Arthur L. Besse. Marcel Berger's Riemannian geometry seminar held at the Universite Paris VII in the nineteen-seventies and eighties, hosted lectures by both reputable mathematicians and young researchers. For the participants, it was a unique place for lively and informal mathematical discussions and exchanges, as well as inspiration. IHES Riemannian Geometry Past, Present and Future: an homage to Marcel Berger :https://indico.math.cnrs.fr/event/2432/ Marcel Berger SEE at a glance • Meeting place for science, industry and society • An officialy recognised non-profit organisation • About 2000 members and 5000 individuals involved • Large participation from industry (~50%) • 19 «Clubs techniques» and 12 «Groupes régionaux» • Organizes conferences and seminars • Initiates/attracts International Conferences in France • Institutional French member of IFAC and IFIP • Awards (Glavieux/Brillouin Prize, Général Ferrié Prize, Néel Prize, Jerphagnon Prize, Blanc-Lapierre Prize,Thévenin Prize), grades and medals (Blondel, Ampère) • Publishes 3 periodical publications (REE, …) & 3 monographs each year • Web: http://www.see.asso.fr and LinkedIn SEE group • SEE Presidents: Louis de Broglie, Paul Langevin, … 1883-2017: From SIE & SFE to SEE: 134 years of Sciences Société de l'électricité, de l'électronique et des technologies de l'information et de la communication 1881 Exposition Internationale d’Electricité 1883: SIE Société Internationale des Electriciens 1886: SFE Société Française des Electriciens 2013: SEE 17 rue de l'Amiral Hamelin 75783 Paris Cedex 16 Louis de Broglie Paul Langevin Mines ParisTech Graduade School 234 years of History Joseph Bertrand Most Famous MINEURS François Massieu Henri Poincaré Paul Levy Maurice Allais Georges Matheron Roger Balian Charles-Michel Marle Pierre Rouchon Gabriel Lamé Henri Le Chatelier Jean-Michel Bismut GSI Logo: Adelard of Bath • He left England toward the end of the 11th century for Tours in France • Adelard taught for a time at Laon, leaving Laon for travel no later than 1109. • After Laon, he travelled to Southern Italy and Sicily no later than 1116. • Adelard also travelled extensively throughout the "lands of the Crusades": Greece, West Asia, Sicily, Spain, and potentially Palestine. The frontispiece of an Adelard of Bath Latin translation of Euclid's Elements, c. 1309– 1316; the oldest surviving Latin translation of the Elements is a 12th-century translation by Adelard from an Arabic version Adelard of Bath was the first to translate Euclid’s Elements in Latin Adelard of Bath has introduced the word « Algorismus » in Latin after his translation of Al Khuwarizmi GSI’17 Banner Euclide, Thales, Alexis Claude Clairaut, Adrien-Marie Legendre, Jean- Victor Poncelet, Gaston Darboux, Henri Poincaré, Elie Cartan, Maurice René Fréchet, Paulette Libermann, Jean Leray, Jean-Louis Koszul, Jacqueline Lelong-Ferrand, Jean-Marie Souriau, Roger Balian, Marcel Berger, Yvonne Choquet-Bruhat, Misha Gromov A new Grammar of Information “Mathematics is the art of giving the same name to different things” – Henri Poincaré GROUP EVERYWHERE Elie Cartan Henri Poincaré METRIC EVERYWHERE Maurice Fréchet Misha Gromov “the problems addressed by Elie Cartan are among the most important, most abstract and most general dealing with mathematics; group theory is, so to speak, the whole mathematics, stripped of its material and reduced to pure form. This extreme level of abstraction has probably made my presentation a little dry; to assess each of the results, I would have had virtually render him the material which he had been stripped; but this refund can be made in a thousand different ways; and this is the only form that can be found as well as a host of various garments, which is the common link between mathematical theories that are often surprised to find so near” H. Poincaré Elie Cartan: Group Everywhere (Henri Poincaré review of Cartan’s Works) Maurice Fréchet: Metric Everywhere • Maurice Fréchet made major contributions to the topology of point sets and introduced the entire concept of metric spaces. • His dissertation opened the entire field of functionals on metric spaces and introduced the notion of compactness. • He has extended Probability in Metric space 1948 (Annales de l’IHP) Les éléments aléatoires de nature quelconque dans un espace distancié Extension of Probability/Statistic in abstract/Metric space GSI’13 Springer Proceedings: http://www.springer.com/us/book/9 783642400193 GSI’15 Springer Proceedings: http://www.springer.com/la/book/97 83319250397 Available online: https://link.springer.com/book/10.1 007/978-3-319-68445-1 GSI’17 Springer Proceedings: http://www.springer.com/cn/book/9 783319684444 GSI SPRINGER PROCEEDINGS GSI’17 Sponsors GSI’17 Program • 145 attendees from 37 different countries (France 38%, Germany 9%, Japan 9%, Italy 8%, USA 6%, Belgium 4%, Brazil 3%, Russia 3%, UK 3%, NL 2%, DK 2%, SW 2%, …) • 101 papers/talks on 3 days (rate: 89% based on 314 reviews) • 1 Guest Honorary speaker • Jean-Michel BISMUT (Paris-Sud University): “The hypoelliptic Laplacian” • 1 Invited Honorary speaker • Daniel BENNEQUIN (Paris-Diderot University): “Geometry and Vestibular Information” • 3 keynote speakers • Alain TROUVE (ENS Paris-Saclay): “Hamiltonian modeling for shape evolution and Statistical modeling of shapes variability” • Mark GIROLAMI (Imperial College London): “Riemann Manifold Langevin and Hamiltonian Monte Carlo Methods” • Barbara TUMPACH (Lille University): “Riemannian metrics on shape spaces of curves and surfaces” GSI’17: 19 sessions • Computational Information Geometry • Geometrical Structures of Thermodynamics • Geometry of Tensor-Valued Data • Probability on Riemannian Manifolds • Information Structure in Neuroscience • Geometric Mechanics & Robotics • Optimization on Manifold • Geometric Robotics & Tracking • Probability Density Estimation • Applications of Distance Geometry • Statistics on non-linear data • Shape Space • Divergence Geometry • Geodesic Methods with Constraints • Optimal Transport & Applications • Monotone Embedding in Information Geometry • Non-parametric Information Geometry • Optimal Transport & Applications • Statistical Manifold & Hessian Information Geometry GSI’17 Map GSI’17 Program Tuesday November 7th GSI’17 Group Photo, during Coffee Break 10.00 GSI’17 Program Wednesday November 8th GSI’17 Program Thursday November 9th V334 Guest Honorary speaker Jean-Michel Bismut Jean-Michel Bismut (professor at Paris-Sud Orsay university, member of Académie des Sciences) Jean-Michel Bismut was born in 1948 in Lisbon (Portugal). He studied at Ecole Polytechnique in 1967-1969, and he received his Doctorat d’Etat from Université Paris VI in 1973. He became a professor of Mathematics in Orsay in 1981. He was a plenary speaker at ICM-Berlin 1998, and a vice- president of International Mathematical Union from 2002 to 2006. His research has been devoted to stochastic control, to the Malliavin calculus, to index theory, and its connections with spectral theory and number theory. The hypoelliptic Laplacian If X is a Riemannian manifold, the hypoelliptic Laplacian is a family of hypoelliptic operators acting on X , the total space of the tangent bundle of X , that interpolates between the ordinary Laplacian and the geodesic flow. The probabilistic counterpart is an interpolation between Brownian motion and geodesics. In the talk, I will explain the construction of the hypoelliptic Laplacian, and describe some of its properties. Invited Honorary speaker Daniel Bennequin Daniel Bennequin (Université Paris 7 - Institut Mathématique de Jussieu). Born 3 January 1952. Graduate from Ecole Normale Supérieure. PHD in 1982 with Alain Chenciner at Paris VII. Then Professor at Strasbourg University. Today Professor at Paris-Diderot University, and member of the IMJ. During the 1980’s he was initiator of contact topology with Y.Eliashberg. During the 1990’s, he worked on integrable systems and geometry of Mathematical Physics. Since 2000 he has been working in Neurosciences (mainly with A.Berthoz, C-d-F, and T.Flash, Weizmann Institute); he made contributions to the study of human movements duration, vestibular informatin flow and gaze functions during locomotion. His most recent publications are on information topology (with P.Baudot), psychic pain (with M.Bompard-Porte) and labyrinths (with R.David et al.). Geometry and Vestibular Information Every complex living entities, as plants, insects or vertebrates, possess visuo-vestibular systems which sense their own motion in space and are crucial for controling volontary movements and for understanding space. We will show how the Galilée group guides the visuo-vestibular information flows. Differential Geometry permits to understand the particular forms of the end vestibular organs, that are situated in the inner ear of mammals and birds, from a principle of energy minimization and information maximization. These forms correspond to the surfaces of divisors of real (resp. imaginary) twisted curves, for the epithelia which sense linear accelerations (resp. rotations) of the head. The Hodge-DeRham theory, applied to the labyrinths volume of vertebrates, permits to explain how a complex fluid movement is transformed in six solutions of ordinary second order differential equations, for registering the head rotations in space. Combined with an original and delicate method of analysis of the membranous tissues, invented by Romain David, this allows for the first time, to describe the precise relation between the structure and the function of the labyrinth. Keynote speaker Alain Trouvé Alain Trouvé (ENS Paris-Saclay, CMLA Department). Alain Trouvé, bachelor’s degree from Ecole Normale Supérieure Ulm, a doctor of the University of Orsay, began his career as “agrégé préparateur” at the ENS Ulm before becoming a professor at the University of Paris13 (1996) and then at ENS Cachan (2003). Alain Trouvé is currently Professor at the Center of Mathematics and Their Application (CMLA) at ENS Paris-Saclay. He did his Ph.D. in Stochastic Optimization and Bayesian Image Analysis under the supervision of Robert Azencott. His main research interests are computational vision and shape analysis with a particular emphasis on the use of Riemannian geometry and infinite dimensional group actions driven by applications in computational anatomy and medical imaging. Hamiltonian modeling for shape evolution and Statistical modeling of shapes variability In his book "Growth and Forms", first published in 1917, d’Arcy Thompson, a Scottish naturalist and mathematician, develops his theory of transformations, whose central idea is the morphological comparison of anatomies through groups of transformations of Space that act on it. This idea, a century later, remains at the heart of contemporary geometric approaches of quantitative comparison of forms but in a very different mathematical and technological context. In this talk, we present the ideas and techniques that underlie the "diffeomorphometric" approach developed in the context of computational anatomy, its links with infinite dimensional Riemannian geometry, the theory of control And Hamiltonian systems, but also the dimension reduction tools that underlie the algorithms used in the analysis of sub-varieties and make them effective. We will also present new prospects for extension on the geometric-functional objects that combine geometric and functional information and pose new and numerous challenges. Keynote speaker Mark Girolami Mark Girolami (Imperial College London - Department of Mathematics). Mark Girolami holds a Chair in Statistics in the Department of Mathematics of Imperial College London. He is an EPSRC Established Career Research Fellow (2012 - 2017) and previously an EPSRC Advanced Research Fellow (2007 - 2012). He is the Director of the Alan Turing Institute-Lloyds Register Foundation Programme on Data Centric Engineering and in 2011 was elected to the Fellowship of the Royal Society of Edinburgh when he was also awarded a Royal Society Wolfson Research Merit Award. He was one of the founding Executive Directors of the Alan Turing Institute for Data Science from 2015 to 2016. He has been nominated by the IMS to deliver a Medallion Lecture at JSM 2017 and has been invited to give a Forum Lecture at the European Meeting of Statisticians 2017. His paper on Riemann manifold Langevin and Hamiltonian Monte Carlo Methods was publicly read before the Royal Statistical Society and received the largest number of contributed discussions for any paper in the entire history of the society, discussants included Sir D.R. Cox and C.R. Rao. Riemann Manifold Langevin and Hamiltonian Monte Carlo Methods The talk considers Metropolis adjusted Langevin and Hamiltonian Monte Carlo sampling methods defined on the Riemann manifold to resolve the shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations. The methods provide fully automated adaptation mechanisms that circumvent the costly pilot runs that are required to tune proposal densities for Metropolis–Hastings or indeed Hamiltonian Monte Carlo and Metropolis adjusted Langevin algorithms. This allows for highly efficient sampling even in very high dimensions where different scalings may be required for the transient and stationary phases of the Markov chain. The methodology proposed exploits the Riemann geometry of the parameter space of statistical models and thus automatically adapts to the local structure when simulating paths across this manifold, providing highly efficient convergence and exploration of the target density. The performance of these Riemann manifold Monte Carlo methods is rigorously assessed by performing inference on logistic regression models, log-Gaussian Cox point processes, stochastic volatility models and Bayesian estimation of dynamic systems described by non-linear differential equations. Substantial improvements in the time-normalized effective sample size are reported when compared with sampling approaches. Keynote speaker Barbara Tumpach Barbara Tumpach (Lille University/ Painlevé Laboratory) Alice Barbara Tumpach is an Associate Professor in Mathematics (University Lille 1, France) and member of the Laboratoire Painlevé (Lille 1/CNRS UMR 8524), since 2007. She received a Ph.D degree in Mathematics in 2005 at the Ecole Polytechnique, Palaiseau, France. She spent two years at the Ecole Polytechnique Fédérale de Lausanne as a Post-Doc, and two years at the Pauli Institut in Vienna, Austria, as an invited researcher. Her research interests lie in the area of infinite-dimensional Geometry, Lie Groups and Functional Analysis. She gives Master courses on Lie groups and organizes conferences on infinite-dimensional geometry for the Federation of Mathematical Research of Nord-Pas-Calais, France. She also acts in videos for Exo7, available on youtube, where she explains basic notions of Linear Algebra. Riemannian metrics on shape spaces of curves and surfaces The aim of the talk is to give an overview of geometric tools used in Shape Analysis. We will see that we can interpret the Shape space of (unparameterized) curves (or surfaces) either as a quotient space or as a section of the Preshape space of parameterized curves (or surfaces). Starting from a diffeomorphism-invariant Riemannian metric on Preshape space, these two different interpretations lead to different Riemannian metrics on Shape space. Another possibility is to start with a degenerate Riemannian metric on Preshape space, with degeneracy along the orbits of the diffeomorphism group. This leads to a framework where the length of a path of curves (or surfaces) does not depend on the parameterizations of the curves (or surfaces) along the path. Of course the choice of the metrics has to be motivated either from the applications or from their mathematical behaviour. We will compare some natural metrics used in the litterature. On the occasion of the 150th Marie Curie Birthday (November 7th 1867), Barbara Tumpach will animate a session “Women in Science”, November 8th from 18h20 to 19h05 in Poincaré Amphi, with Nina Miolane and Alice Le Brigant. We have coupled this session with two other events, November 8th: - during 10.00-1030 Coffee Break : Natacha Henri’s book dedication on "Sisters in Science, Marie Curie and Bronia Dluska" https://www.youtube.com/watch?v=2JKHpgHHoAM - during 12.30-13.30 Lunch break: exhibition on “ Women and Science in the Heritage Funds” at the Ecole des Mines Library http://www.mines-paristech.fr/Actualites/Exposition-Les-femmes- et-la-science/3086 10 minutes walk from Ecole des Mines, we invite you to visit "Marie Curie 150th Birthday Exhibition" at PANTHEON (that will start November 8th) and Curie Museum: http://musee.curie.fr/visiter/evenements/marie-curie-150e- anniversaire GSI’17 « Women in Science » Barbara Tumpach Nina Miolane Alice Le Brigant 150th Marie Curie Birthday (November 7th 1867) Mines Exhibition on “ Women and Science in the Heritage Funds” at the Ecole des Mines Library Original edition of Marie Curie's thesis on radioactive substances of 1903 For GSI’17, Exhibition visit November 8th during 12.30-13.30 Lunch break For GSI’17, Natacha Henri (Marie Curie Biographer) will dedicate her book on "Sisters in Science, Marie Curie and Bronia Dluska“, November 8th during 10.00-1030 Coffee Break https://www.youtube.com/watch?v=2JKHpgHHoAM http://www.mines- paristech.fr/Actualites/Exposition-Les-femmes-et- la-science/3086 Exhibition « Marie Curie a women in PANTHEON” (Panthéon, opening November 8th) http://musee.curie.fr/visiter/evenements/marie-curie- 150e-anniversaire http://musee.curie.fr/ GSI’17 Gala Dinner Café LE PROCOPE since 1686 GSI’17 Gala Dinner Café LE PROCOPE since 1686 When the French comedy theatre was set up not far from the café in 1689, the Procope quickly became a place for the rendez-vous of literary and theatre critics, writers and philosophers. It was also at the Procope where the idea to create an encyclopedia took place during a conversation between Diderot and d’Alembert. Meetings and exchanges between regulars such as Voltaire, Rousseau, etc. gave birth to the liberal and progressive ideas of the 18th century. Cradle of the Diderot & d’Alembert Encyclopedia http://www.academie-sciences.fr/fr/Transmettre-les-connaissances/le-comite-d-alembert.html Digital, Collaborative & Critical Edition of Diderot-d’Alembert Encyclopedia http://enccre.academie-sciences.fr/encyclopedie/ Nov. 14th, D’Alembert : tricentenaire du mathématicien et philosophe des Lumières http://www.academie-sciences.fr/fr/Colloques-conferences-et-debats/d-alembert-tricentenaire-du-mathematicien-et-philosophe-des-lumieres.html Geometry in Diderot-d’Alembert Encyclopedia Last Publications on Geometric Science of Information Introduction to Symplectic Geometry Jean-Louis Koszul Science Press, Beijing (1986) (in Chinese) (with reference to Souriau work) Translation by SPRINGER in 2018 TGSI’17 Videos/slides available http://forum.cs-dc.org/category/94/tgsi2017 Special Issue "Topological and Geometrical Structure of Information”, Selected Papers from CIRM conferences 2017" http://www.mdpi.com/journal/entropy/speci al_issues/topological_geometrical_info 14–16 May 2018 From Physics to Information Sciences and Geometry Barcelona, Spain The main topics and sessions of the conference cover: • Physics: classical Thermodynamics and Quantum • Statistical physics and Bayesian computation • Geometrical science of information, topology and metrics • Maximum entropy principle and inference • Kullback and Bayes or information theory and Bayesian inference • Entropy in action (applications) The inter-disciplinary nature of contributions from both theoretical and applied perspectives are very welcome, including papers addressing conceptual and methodological developments, as well as new applications of entropy and information theory. https://sciforum.net/conference/Entropy2018-1 ALEAE GEOMETRIA, the Geometry of Chance by Blaise Pascal The "calculation of probabilities" began four years after the death of René Descartes, in 1654, in a correspondence between Blaise Pascal and Pierre Fermat. We do not find in Pascal's writings, the words of “Doctrine des chances”, or “Calcul des chances”, but only “Géométrie du hasard” (geometry of chance). In 1654, Blaise Pascal submitted a short paper to "Celeberrimae matheseos Academiae Parisiensi" with the title "Aleae Geometria” (Geometry of Chance), that was the seminal paper founding Probability as a new discipline in Science. Blaise Pascal was also the inventor of computer with his “Pascaline” machine. The introduction of Pascaline marks the beginning of the development of mechanical calculus in Europe. It was Charles Babbage who conceived an analytical machine from 1834 to 1837, a programmable calculating machine which was the ancestor of the computers of the 1940s, combining the inventions of Blaise Pascal and Jacquard’s machine, with instructions written on perforated cards. Blaise Pascal Pascaline Machine From PASCALINE Machine to HPC or Geometric Integrating Machines Pascaline Jacquard Loom Babbage Analytic Machine High Power Computing Geometric Machines Geometric, Variational, Symplectic & Polysymplectic Integrators (Intrinsic Computation without coordinates, conservation of symplectic 2-form) Descartes computation with coordinates 2018: 250th Birthday of Jean-Baptiste-Joseph Fourier • A special Issue will be organized for this 250th birthday in “From Physics to Information Sciences and Geometry” conference • A MDPI special issue will explore modern topics related to Fourier Analysis and Heat Equation. • Classical Fourier commutative harmonic analysis is restricted to functions defined on a topological locally compact and Abelian group G. Modern developments of Fourier analysis during XXth century have explored generalization of Fourier and Fourier-Plancherel formula for non-commutative harmonic analysis, applied to locally compact non Abelian groups, by geometric approaches based on “orbits methods”. • The name of Joseph Fourier is also inseparable from the study of mathematics of heat. Modern research on Heat equation explores extension of classical diffusion equation on Riemannian and sub-Riemannian manifolds. In parallel in Geometric Mechanics, Geometric Theory of Heat has been explored to study relativistic models of a dissipative continuum that complies with the laws of both mechanics and thermodynamics. Fourier’s tomb in the Parisian Père-Lachaise Cemetery