Compressed Sensing Performance Analysis via Replica Method using Bayesian framework

Compressive sensing (CS) is a new methodology to capture signals at lower rate than the Nyquist sampling rate when the signals are sparse or sparse in some domain. The performance of CS estimators is analyzed in this paper using tools from statistical mechanics, especially called replica method. This method has been used to analyze communication systems like Code Division Multiple Access (CDMA) and multiple input multi- ple output (MIMO) systems with large size. Replica analysis, now days rigorously proved, is an efficient tool to analyze large systems in general. Specifically, we analyze the performance of some of the estimators used in CS like LASSO (the Least Absolute Shrinkage and Selection Operator) estimator and Zero-Norm regularizing estimator as a special case of maximum a posteriori (MAP) estimator by using Bayesian framework to connect the CS estimators and replica method. We use both replica symmetric (RS) ansatz and one-step replica symmetry breaking (1RSB) ansatz, clamming the latter is efficient when the problem is not convex. This work is more analytical in its form. It is deferred for next step to focus on the numerical results.Comment: The analytical work and results were presented at the 2012 IEEE European School of Information Theory in Antalya, Turkey between the 16th and the 20th of Apri

Coherent pairing states for the Hubbard model

We consider the Hubbard model and its extensions on bipartite lattices. We define a dynamical group based on the $\eta$-pairing operators introduced by C.N.Yang, and define coherent pairing states, which are combinations of eigenfunctions of $\eta$-operators. These states permit exact calculations of numerous physical properties of the system, including energy, various fluctuations and correlation functions, including pairing ODLRO to all orders. This approach is complementary to BCS, in that these are superconducting coherent states associated with the exact model, although they are not eigenstates of the Hamiltonian.Comment: 5 pages, RevTe

A product formula and combinatorial field theory

We treat the problem of normally ordering expressions involving the standard boson operators a, ay where [a; ay] = 1. We show that a simple product formula for formal power series | essentially an extension of the Taylor expansion | leads to a double exponential formula which enables a powerful graphical description of the generating functions of the combinatorial sequences associated with such functions | in essence, a combinatorial eld theory. We apply these techniques to some examples related to specic physical Hamiltonians

Hopf Algebras in General and in Combinatorial Physics: a practical introduction

This tutorial is intended to give an accessible introduction to Hopf algebras. The mathematical context is that of representation theory, and we also illustrate the structures with examples taken from combinatorics and quantum physics, showing that in this latter case the axioms of Hopf algebra arise naturally. The text contains many exercises, some taken from physics, aimed at expanding and exemplifying the concepts introduced

Functional maps representation on product manifolds

We consider the tasks of representing, analysing and manipulating maps between shapes. We model maps as densities over the product manifold of the input shapes; these densities can be treated as scalar functions and therefore are manipulable using the language of signal processing on manifolds. Being a manifold itself, the product space endows the set of maps with a geometry of its own, which we exploit to define map operations in the spectral domain; we also derive relationships with other existing representations (soft maps and functional maps). To apply these ideas in practice, we discretize product manifolds and their Laplace–Beltrami operators, and we introduce localized spectral analysis of the product manifold as a novel tool for map processing. Our framework applies to maps defined between and across 2D and 3D shapes without requiring special adjustment, and it can be implemented efficiently with simple operations on sparse matrices

Sclerema neonatorum: A clinical study of 79 cases

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Electron impact promoted fragmentation of alkyl-N-(1-Phenylethyl)-carbamates of primary, secondary and tertiary alcohols

Mass spectra of alkyl carbamates derived from primary, secondary, and teriary alcohols by use of deuterium labeling and high resolution mass spectroscop

On certain non-unique solutions of the Stieltjes moment problem

We construct explicit solutions of a number of Stieltjes moment problems based on moments of the form (2rn)! and [(rn)!]2. It is shown using criteria for uniqueness and non-uniqueness (Carleman, Krein, Berg, Pakes, Stoyanov) that for r > 1 both forms give rise to non-unique solutions. Examples of such solutions are constructed using the technique of the inverse Mellin transform supplemented by a Mellin convolution. We outline a general method of generating non-unique solutions for moment problems

Dobinski-type relations: Some properties and physical applications

We introduce a generalization of the Dobinski relation through which we define a family of Bell-type numbers and polynomials. For all these sequences we find the weight function of the moment problem and give their generating functions. We provide a physical motivation of this extension in the context of the boson normal ordering problem and its relation to an extension of the Kerr Hamiltonian.Comment: 7 pages, 1 figur