Related papers: Remarks on multivariate Gaussian Gabor frames
This survey offers a systematic and streamlined exposition of the most important characterizations of Gabor frames over a lattice. The goal is to collect the most important characterizations of Gabor frames and offer a systematic exposition…
One of the most widely used properties of the multivariate Gaussian distribution, besides its tail behavior, is the fact that conditional means are linear and that conditional variances are constant. We here show that this property is also…
We show that by analyzing the spectra of lensed broad absorption line quasars (BALQSOs), it is possible to reveal key properties of the outflowing gas in the inner regions of these objects. This results from the fact that each image of the…
An analytically tractable model for Gaussian multiuser channels with fading is studied, and the capacity region of this model is found to be a good approximation of the capacity region of the original Gaussian network. This work extends the…
This work proposes a scalable probabilistic latent variable model based on Gaussian processes (Lawrence, 2004) in the context of multiple observation spaces. We focus on an application in astrophysics where data sets typically contain both…
We develop a diagrammatic method for the evaluation of general multi-band Gutzwiller wave functions in finite dimensions. Our approach provides a systematic improvement of the widely used Gutzwiller approximation. As a first application we…
We study the behavior of droplets for two dimensional Ising spin glasses with Gaussian interactions. We use an exact matching algorithm which enables study of systems with linear dimension L up to 240, which is larger than is possible with…
Dark matter caustics have specific density profiles and, therefore, precisely calculable gravitational lensing properties. We present a formalism which simplifies the relevant calculations, and apply it to four specific cases. In the first…
For classical many-body systems, our recent study reveals that expectation value of internal energy, structure, and free energy can be well characterized by a single specially-selected microscopic structure. This finding relies on the fact…
The theory of Markov processes on the square lattice has been given recently by the second author a new algebraic description in terms of operads. In particular, this new approach allows for a nice description of invariant boundary…
(Abridged) I investigate statistical properties of one-dimensional fields in the universe such as the Lyman alpha forest and inverted line-of-sight densities. Because of gravitational clustering, the cosmic density field is already quite…
Vitrification in colloidal systems typically occurs at high densities driven by sharply varying, short-ranged interactions. The possibility of glassy behavior arising from smoothly varying, long-ranged particle interactions has received…
We develop a scalable class of models for latent variable estimation using composite Gaussian processes, with a focus on derivative Gaussian processes. We jointly model multiple data sources as outputs to improve the accuracy of latent…
We study the existence of Gabor orthonormal bases with window the characteristic function of the set W=[0,a] U [b+a, b+1] of measure 1, with a, b>0. By the symmetries of the problem, we can restrict our attention to the case a<=1/2. We…
Gaussian process regression is widely used because of its ability to provide well-calibrated uncertainty estimates and handle small or sparse datasets. However, it struggles with high-dimensional data. One possible way to scale this…
We advance scale-invariance arguments for systems that are governed (or approximated) by a $q-$Gaussian distribution, i.e., a power law distribution with exponent $Q=1/(1-q); q \in \mathbb{R}$. The ensuing line of reasoning is then compared…
We summarise different results on the diffusion of a tracer particle in lattice gases of hard-core particles with stochastic dynamics, which are confined to narrow channels -- single-files, comb-like structures and quasi-one-dimensional…
A novel wavelet-like function is presented that makes it convenient to create filter banks given mainly two parameters that influence the focus area and the filter count. This is accomplished by computing the inverse Fourier transform of…
In this paper we will give the calculus, the criterion, and the existence of the arithmetic Galois covers of higher relative dimensions.
Glassy systems are characterized by an extremely sluggish dynamics without any simple sign of long range order. It is a debated question whether a correct description of such phenomenon requires the emergence of a large correlation length.…