Concept

Geometric quantization

Related publications (25)

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Quantization Design for Unconstrained Distributed Optimization

Colin Neil Jones, Ye Pu, Melanie Nicole Zeilinger

We consider an unconstrained distributed optimization problem and assume that the bit rate of the communication in the network is limited. We propose a distributed optimization algorithm with an iteratively refining quantization design, which bounds the qu ...

2015

Quantization Design for Distributed Optimization

Colin Neil Jones, Ye Pu, Melanie Nicole Zeilinger

We consider the problem of solving a distributed optimization problem using a distributed computing platform, where the communication in the network is limited: each node can only communicate with its neighbours and the channel has a limited data-rate. A c ...

2015

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

Distributed average consensus with quantization refinement

Pascal Frossard, Ye Pu, Effrosyni Kokiopoulou

We consider the problem of distributed average consensus in a sensor network where sensors exchange quantized information with their neighbors. We propose a novel quantization scheme that exploits the increasing correlation between the values exchanged by ...

Institute of Electrical and Electronics Engineers2013

The research program of Stochastic Deformation (with a view toward Geometric Mechanics)

This is an overview of a program of stochastic deformation of the mathematical tools of classical mechanics, in the Lagrangian and Hamiltonian approaches. It can also be regarded as a stochastic version of Geometric Mechanics.The main idea is to construct ...

2012

The quantum mechanics of perfect fluids

Riccardo Rattazzi, Solomon G Shamsuddin Osman Endlich

We consider the canonical quantization of an ordinary fluid. The resulting long-distance effective field theory is derivatively coupled, and therefore strongly coupled in the UV. The system however exhibits a number of peculiarities, associated with the vo ...

2011

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

Sparse image approximation with application to flexible image coding

Natural images are often modeled through piecewise-smooth regions. Region edges, which correspond to the contours of the objects, become, in this model, the main information of the signal. Contours have the property of being smooth functions along the dire ...

EPFL2005

A Posteriori Quantization of Progressive Matching Pursuit Streams

Pascal Frossard, Pierre Vandergheynst, Murat Kunt

This paper proposes a rate-distortion optimal a posteriori quantization scheme for Matching Pursuit coefficients. The a posteriori quantization applies to a Matching Pursuit expansion that has been generated off-line, and cannot benefit of any feedback loo ...

2004

Oversampled A/D Conversion of Non-Bandlimited Signals with Finite Rate of Innovation

Ivana Jovanovic

We consider the problem of A/D conversion for non-bandlimitedsignals that have a finite rate of innovation, in particular, theclass of continuous periodic stream of Diracs, characterized by aset of time positions and weights. Previous research has onlycons ...

2004