相关论文: Density, Overcompleteness, and Localization of Fra…
Given the ever increasing bandwidth of the visual information available to many intelligent systems, it is becoming essential to endow them with a sense of what is worthwhile their attention and what can be safely disregarded. This article…
We investigate the approximation of high-dimensional target measures as low-dimensional updates of a dominating reference measure. This approximation class replaces the associated density with the composition of: (i) a feature map that…
We display four approximation theorems for manifold-valued mappings. The first one approximates holomorphic embeddings on pseudoconvex domains in $\Bbb C^n$ with holomorphic embeddings with dense images. The second theorem approximates…
Defect of compactness, relative to an embedding of two Banach spaces E and F, is a difference between a weakly convergent sequence in E and its weak limit taken up to a remainder that vanishes in the norm of F. For Sobolev embeddings in…
In this paper, we use a unified framework introduced in [3] to study two classes of nonconforming immersed finite element (IFE) spaces with integral value degrees of freedom. The shape functions on interface elements are piecewise…
We consider Gabor frames generated by a Gaussian function and describe the behavior of the frame constants as the density of the lattice approaches the critical value.
This paper presents a comprehensive analysis of hyperparameter estimation within the empirical Bayes framework (EBF) for sparse learning. By studying the influence of hyperpriors on the solution of EBF, we establish a theoretical connection…
We present a method to infer a dense depth map from a color image and associated sparse depth measurements. Our main contribution lies in the design of an annealing process for determining co-visibility (occlusions, disocclusions) and the…
O(N) methods are based on the decay properties of the density matrix in real space, an effect sometimes refered to as near-sightedness. We show, that in addition to this near-sightedness in real space there is also a near-sightedness in…
This work considers the problem of estimating the unscaled relative positions of a multi-robot team in a common reference frame from bearing-only measurements. Each robot has access to a relative bearing measurement taken from the local…
Effective field theories consistent with quantum gravity obey surprising finiteness constraints, appearing in several distinct but interconnected forms. In this work we develop a framework that unifies these observations by proposing that…
We investigate approximation algorithms for several fundamental optimization problems on geometric packing. The geometric objects considered are very generic, namely $d$-dimensional convex fat objects. Our main contribution is a versatile…
Neural networks represent more features than they have dimensions via superposition, forcing features to share representational space. Current methods decompose activations into sparse linear features but discard geometric structure. We…
Let $S$ be a semigroup, let $n\in\mathbb{N}$ be a positive natural number, let $A,B\subseteq S$, let $\mathcal{U},\mathcal{V}\in\beta S$ and let let $\mathcal{F}\subseteq\{f:S^{n}\rightarrow S\}$. We say that $A$ is $\mathcal{F}$-finitely…
We demonstrate that for an arbitrary number of identical particles, each defined on a Hilbert-space of arbitrary dimension, there exists a whole ladder of relations of complementarity between local, and every conceivable kind of joint (or…
As a fundamental piece of multi-object Bayesian inference, multi-object density has the ability to describe the uncertainty of the number and values of objects, as well as the statistical correlation between objects, thus perfectly matches…
To what extent are two images picturing the same 3D surfaces? Even when this is a known scene, the answer typically requires an expensive search across scale space, with matching and geometric verification of large sets of local features.…
Approximate algebraic structures play a defining role in arithmetic combinatorics and have found remarkable applications to basic questions in number theory and pseudorandomness. Here we study approximate representations of finite groups:…
In this paper a new concept related to the frame theory is introduced; the notion of pair frame. By investigating some properties of such frames, it is shown that pair frames are a generalization of ordinary frames. Some classes of of them…
We discuss the concepts of pseudo-dual frames and approximately dual frames, and illuminate their relationship to classical frames. Approximately dual frames are easier to construct than the classical dual frames, and might be tailored to…