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► Journal MenuSpecial Issue "Differential Geometrical Theory of Statistics"
A special issue of Entropy (ISSN 10994300). This special issue belongs to the section "Statistical Mechanics".
Deadline for manuscript submissions: closed (15 September 2016)
Special Issue Editors
Guest Editor
Dr. Frédéric Barbaresco
Department of Advanced Radar Concepts, Thales Air Systems, Voie PierreGilles de Gennes F91470 Limours, France
Interests: entropy; maximum entropy; information geometry; information topology; statistical physics 

Special Issue Information
Dear Colleagues,
This Special Issue will collect a limited number of selected invited and contributed talks presented during the conference GSI'15 on "Geometric Science of Information" which will be held at Ecole Polytechnique, ParisSaclay Campus, France, in October 2015. Conference web site: http://www.see.asso.fr/gsi2015 .
Dr. Frédéric Barbaresco
Prof. Dr. Frank Nielsen
Guest Editors
Manuscript Submission Information
Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peerreviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.
Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a singleblind peerreview process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peerreviewed open access monthly journal published by MDPI.
Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1500 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.
Planned Papers
The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peerreview.
Title: Secondorder Optimization over the Multivariate Gaussian Distribution
Author: Luigi Malagò and Giovanni Pistone
Abstract: We discuss the optimization of the stochastic relaxation of a realvalued function, i.e., we introduce a new search space given by a statistical model and we optimize the expected value of the original function with respect to a distribution in the model. From the point of view of Information Geometry, statistical models are Riemannian manifolds of distributions endowed with the Fisher information metric, thus the stochastic relaxation can be seen as a continuous optimization problem defined over a differentiable manifold. In this paper we explore the secondorder geometry of the exponential family, with applications to the multivariate Gaussian distributions, to generalize secondorder optimization methods. Besides the Riemannian Hessian, we introduce the exponential and the mixture Hessians, which come from the dually flat structure of an exponential family. This allows us to obtain different Taylor formulae according to the choice of the Hessian and of the geodesic used, and thus different approaches to the design of secondorder methods, such as the Newton method.
Title: Geometry of Generalized Statistical Manifold Induced from ψFunctions
Author: David Carneiro de Souza, Charles Casimiro Cavalcante and Rui Facundo Vigelis
Title: Kernel density estimation on the Siegel disc applied to radar signal processing
Author: Emmanuel Chevallier
Abstract: This article provides expressions of kernels for density estimation on the Siegel disc. The Siegel disc plays a role in radar signal processing as a model of the geometry of covariance matrices of stationary processes. The density estimation on the Siegel disc is applied to classification of radar signals.
Title: From tools in Symplectic and Poisson geometry to J.M. Souriau's theory of Statistical Mechanics and Thermodynamics of Lie groups
Author: CharlesMichel Marle
Abstract: I present in this paper some tools in Symplectic and Poisson Geometry in view of their applications in Geometric Mechanics and Mathematical Physics. After a short discussion of the Lagrangian an Hamiltonian formalisms, including the use of symmetry groups, and a presentation of the Tulczyjew's isomorphisms (which explain some aspects of the relations between these formalisms), I explain the concept of manifold of motions of a mechanical system and its use, due to J.M. Souriau, in Statistical Mechanics and Thermodynamics. The generalization of the notion of thermodynamic equilibrium in which the onedimensional group of time translations is replaced by a multidimensional, may be noncommutative Lie group, is fully discussed and examples of applications in Physics are given.
Title: Nonasymptotic universal confidence sets for circular means
Author: Thomas Hotz, Florian Kelma and Johannes Wieditz
Abstract: Given i.i.d. observations on the circle, confidence sets for circular means are constructed, using Hoeffding's mass concentration inequalities for estimating mean and variance. These are nonasymptotic, i.e. they guarantee coverage for finite sample sizes, and universal in the sense that no distributional assumptions are required. For their efficient computation an algorithm is developed and applied to simulated and real data; the results are then compared with the asymptotic confidence sets classically used.
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