Publication

Dirac Lie Groups, Dirac Homogeneous Spaces and the Theorem of Drinfeld

Publications associées (22)

Structure-Preserving Reduced Basis Methods For Poisson Systems

Cecilia Pagliantini, Jan Sickmann Hesthaven

We develop structure-preserving reduced basis methods for a large class of nondissipative problems by resorting to their formulation as Hamiltonian dynamical systems. With this perspective, the phase space is naturally endowed with a Poisson manifold struc ...

AMER MATHEMATICAL SOC2021

Fréchet means in Wasserstein space : theory and algorithms

Yoav Zemel

This work studies the problem of statistical inference for Fréchet means in the Wasserstein space of measures on Euclidean spaces,

\mathcal W_2 ( \mathbb R^d )

. This question arises naturally from the problem of separating amplitude and phase variation i ...

EPFL2017

Gaussian versus Sparse Stochastic Processes : Construction, Regularity, Compressibility

Julien René Pierre Fageot

Although our work lies in the field of random processes, this thesis was originally motivated by signal processing applications, mainly the stochastic modeling of sparse signals. We develop a mathematical study of the innovation model, under which a signal ...

EPFL2017

Stochastic partial differential equations driven by Lévy white noises : generalized random processes, random field solutions and regularity

Thomas Marie Jean-Baptiste Humeau

We study various aspects of stochastic partial differential equations driven by Lévy white noise. This driving noise, which is a generalization of Gaussian white noise, can be viewed either as a generalized random process or as an independently scattered r ...

EPFL2017

Interference Functionals in Poisson Networks

Martin Haenggi

We propose and prove a theorem that allows the calculation of a class of functionals on Poisson point processes that have the form of expected values of sum-products of functions. In proving the theorem, we present a variant of the Campbell-Mecke theorem f ...

Ieee-Inst Electrical Electronics Engineers Inc2016

A Levy-derived process seen from its supremum and max-stable processes

Sebastian Engelke

We consider a process Z on the real line composed from a Levy process and its exponentially tilted version killed with arbitrary rates and give an expression for the joint law of the supremum (Z) over bar, its time T, and the process Z(T + center dot) - (Z ...

Univ Washington, Dept Mathematics2016

Max-stable processes and stationary systems of Levy particles

Sebastian Engelke

We study stationary max-stable processes {n(t): t is an element of R} admitting a representation of the form n(t) = max(i is an element of N) (U-i +Y-i(t)), where Sigma(infinity)(i=1) delta U-i is a Poisson point process on R with intensity e(-u)du, and Y1 ...

Elsevier2015

Secure Wireless Communications via Cooperative Transmitting

Ninoslav Marina

Information-theoretic secrecy is combined with cryptographic secrecy to create a secret-key exchange protocol for wireless networks. A network of transmitters, which already have cryptographically secured channels between them, cooperate to exchange a secr ...

Hindawi Publishing Corporation2014

Extensions of Lie-Rinehart algebras and cotangent bundle reduction

Tudor Ratiu

Let Q denote a smooth manifold acted upon smoothly by a Lie group G. The G-action lifts to an action on the total space TQ of the cotangent bundle of Q and hence on the standard symplectic Poisson algebra of smooth functions on TQ. The Poisson algebra of ...

Oxford University Press2013

Dirac Group(oid)s and Their Homogeneous Spaces

Madeleine Jotz

A theorem of Drinfel'd (Drinfel'd (1993)) classifies the Poisson homogeneous spaces of a Poisson Lie group (G,πG) via a special class of Lagrangian subalgebras of the Drinfel'd double of its Lie bialgebra. This result is extended in Liu et al. (1998) to a ...

EPFL2011

Stochastic Models for Sparse and Piecewise-Smooth Signals

Michaël Unser, Pouya Dehghani Tafti

We introduce an extended family of continuous-domain stochastic models for sparse, piecewise-smooth signals. These are specified as solutions of stochastic differential equations, or, equivalently, in terms of a suitable innovation model; the latter is ana ...

IEEE2011

Higher order Lagrange-Poincar, and Hamilton-Poincar, reductions

Tudor Ratiu, François Gay-Balmaz

Motivated by the problem of longitudinal data assimilation, e.g., in the registration of a sequence of images, we develop the higher-order framework for Lagrangian and Hamiltonian reduction by symmetry in geometric mechanics. In particular, we obtain the r ...

2011

Singular Reduction Of Dirac Structures

Tudor Ratiu, Madeleine Jotz

The regular reduction of a Dirac manifold acted upon freely and properly by a Lie group is generalized to a nonfree action. For this, several facts about G-invariant vector fields and one-forms are shown. ...

2011

A Class of Integrable Flows on the Space of Symmetric Matrices

Tudor Ratiu

For a given skew symmetric real n x n matrix N, the bracket X, Y = XNY - YNX defines a Lie algebra structure on the space Sym(n, N) of symmetric n x n real matrices and hence a corresponding Lie-Poisson structure. The purpose of this paper is to inves ...

Springer Verlag2009

Geodesic Vlasov Equations And Their Integrable Moment Closures

Cesare Tronci

Various integrable geodesic flows on Lie groups are shown to arise by taking moments of a geodesic Vlasov equation on the group of canonical transformations. This was already known for both the one- and two-component Camassa-Holm systems [18, 19]. The pres ...

2009

Infinite dimensional geodesic flows and the universal Teichmüller space

François Gay-Balmaz

The subject of this thesis lies in the intersection of differential geometry and functional analysis, a domain usually called global analysis. A central object in this work is the group Ds(M) of all orientation preserving diffeomorphisms of a compact manif ...

EPFL2009

The Momentum Map In Poisson Geometry

Juan-Pablo Ortega, Tudor Ratiu

Every action on a Poisson manifold by Poisson diffeomorphisms lifts to a Hamiltonian action on its symplectic groupoid which has a canonically defined momentum map. We study various properties of this momentum map as well as its use in reduction. ...

2009

Percolation in the signal to interference ratio graph

Olivier Dousse, Patrick Thiran, Nicolas Macris

Continuum percolation models in which pairs of points of a two-dimensional Poisson point process are connected if they are within some range to each other have been extensively studied. This paper considers a variation in which a connection between two poi ...

2006

Percolation in the signal to interference ratio graph

Olivier Dousse, Patrick Thiran, Nicolas Macris

2005

Power spectra of random spike fields and related processes

Pierre Bremaud, Andrea Ridolfi

This article reviews known results and contains new ones concerning the power spectra of large classes of signals and random fields driven by an underlying point process, such as spatial shot noises (with random impulse response and arbitrary basic station ...

2005