Learning Dictionaries with Bounded Self-Coherence

Sparse coding in learned dictionaries has been established as a successful approach for signal denoising, source separation and solving inverse problems in general. A dictionary learning method adapts an initial dictionary to a particular signal class by iteratively computing an approximate factorization of a training data matrix into a dictionary and a sparse coding matrix. The learned dictionary is characterized by two properties: the coherence of the dictionary to observations of the signal class, and the self-coherence of the dictionary atoms. A high coherence to the signal class enables the sparse coding of signal observations with a small approximation error, while a low self-coherence of the atoms guarantees atom recovery and a more rapid residual error decay rate for the sparse coding algorithm. The two goals of high signal coherence and low self-coherence are typically in conflict, therefore one seeks a trade-off between them, depending on the application. We present a dictionary learning method with an effective control over the self-coherence of the trained dictionary, enabling a trade-off between maximizing the sparsity of codings and approximating an equiangular tight frame.Comment: 4 pages, 2 figures; IEEE Signal Processing Letters, vol. 19, no. 12, 201

Radial functions on compact support

In this paper, radial basis functions that are compactly supported and give rise to positive definite interpolation matrices for scattered data are discussed. They are related to the well-known thin plate spline radial functions which are highly useful in applications for gridfree approximation methods. Also, encouraging approximation results for the compactly supported radial functions are show

Cubic spline prewavelets on the four-directional mesh

In this paper, we design differentiable, two dimensional, piecewise polynomial cubic prewavelets of particularly small compact support. They are given in closed form, and provide stable, orthogonal decompositions of L^2(\RR^2). In particular, the splines we use in our prewavelet constructions give rise to stable bases of spline spaces that contain all cubic polynomials, whereas the more familiar box spline constructions cannot reproduce all cubic polynomials, unless resorting to a box spline of higher polynomial degree

Surface-induced heating of cold polar molecules

We study the rotational and vibrational heating of diatomic molecules placed near a surface at finite temperature on the basis of macroscopic quantum electrodynamics. The internal molecular evolution is governed by transition rates that depend on both temperature and position. Analytical and numerical methods are used to investigate the heating of several relevant molecules near various surfaces. We determine the critical distances at which the surface itself becomes the dominant source of heating and we investigate the transition between the long-range and short-range behaviour of the heating rates. A simple formula is presented that can be used to estimate the surface-induced heating rates of other molecules of interest. We also consider how the heating depends on the thickness and composition of the surface.Comment: 17 pages, 7 figure

Ground-state van der Waals forces in planar multilayer magnetodielectrics

Within the frame of lowest-order perturbation theory, the van der Waals potential of a ground-state atom placed within an arbitrary dispersing and absorbing magnetodielectric multilayer system is given. Examples of an atom situated in front of a magnetodielectric plate or between two such plates are studied in detail. Special emphasis is placed on the competing attractive and repulsive force components associated with the electric and magnetic matter properties, respectively, and conditions for the formation of repulsive potential walls are given. Both numerical and analytical results are presented.Comment: 16 pages, 8 figures, minor correction

Casimir force on amplifying bodies

Based on a unified approach to macroscopic QED that allows for the inclusion of amplification in a limited space and frequency range, we study the Casimir force as a Lorentz force on an arbitrary partially amplifying system of linearly locally responding (isotropic) magnetoelectric bodies. We demonstrate that the force on a weakly polarisable/magnetisable amplifying object in the presence of a purely absorbing environment can be expressed as a sum over the Casimir--Polder forces on the excited atoms inside the body. As an example, the resonant force between a plate consisting of a dilute gas of excited atoms and a perfect mirror is calculated

Counting approximately-shortest paths in directed acyclic graphs

Given a directed acyclic graph with positive edge-weights, two vertices s and t, and a threshold-weight L, we present a fully-polynomial time approximation-scheme for the problem of counting the s-t paths of length at most L. We extend the algorithm for the case of two (or more) instances of the same problem. That is, given two graphs that have the same vertices and edges and differ only in edge-weights, and given two threshold-weights L_1 and L_2, we show how to approximately count the s-t paths that have length at most L_1 in the first graph and length at most L_2 in the second graph. We believe that our algorithms should find application in counting approximate solutions of related optimization problems, where finding an (optimum) solution can be reduced to the computation of a shortest path in a purpose-built auxiliary graph

Non-Perturbative Theory of Dispersion Interactions

Some open questions exist with fluctuation-induced forces between extended dipoles. Conventional intuition derives from large-separation perturbative approximations to dispersion force theory. Here we present a full non-perturbative theory. In addition we discuss how one can take into account finite dipole size corrections. It is of fundamental value to investigate the limits of validity of the perturbative dispersion force theory.Comment: 9 pages, no figure

Matter-screened Casimir force and Casimir-Polder force in planar structures

Using a recently developed theory of the Casimir force (Raabe C and Welsch D-G 2005 Phys. Rev. A 71 013814), we calculate the force that acts on a plate in front of a planar wall and the force that acts on the plate in the case where the plate is part of matter that fills the space in front of the wall. We show that in the limit of a dielectric plate whose permittivity is close to unity, the force obtained in the former case reduces to the ordinary, i.e., unscreened Casimir-Polder force acting on isolated atoms. In the latter case, the theory yields the Casimir-Polder force that is screened by the surrounding matter.Comment: 11 pages, 1 figure -- published online at J. Opt. B on Nov 16 200

Thermopower of a Kondo-correlated quantum dot

The thermopower of a Kondo-correlated gate-defined quantum dot is studied using a current heating technique. In the presence of spin correlations the thermopower shows a clear deviation from the semiclassical Mott relation between thermopower and conductivity. The strong thermopower signal indicates a significant asymmetry in the spectral density of states of the Kondo resonance with respect to the Fermi energies of the reservoirs. The observed behavior can be explained within the framework of an Anderson-impurity model. Keywords: Thermoelectric and thermomagnetic effects, Coulomb blockade, single electron tunneling, Kondo-effect PACS Numbers: 72.20.Pa, 73.23.HkComment: 4 pages, 4 figures, revised version, changed figure