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Related papers: Remarks on multivariate Gaussian Gabor frames

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We find three characterizations for a multidimensional (n+1)-web W possessing a reduct reducible subweb: its closed form equations, the integrability of an invariant distribution associated with W, and the relations between the components…

Differential Geometry · Mathematics 2007-05-23 Vladislav V. Goldberg

We review the construction of Lagrangians for higher spin fields of mixed symmetry in the framework of graded geometry. The main advantage of the graded formalism in this context is that it provides universal expressions, in the sense that…

High Energy Physics - Theory · Physics 2024-06-11 Athanasios Chatzistavrakidis , Georgios Karagiannis , Peter Schupp

Of order one in 10^3 quasars and high-redshift galaxies appears in the sky as multiple images as a result of gravitational lensing by unrelated galaxies and clusters that happen to be in the foreground. While the basic phenomenon is a…

Cosmology and Nongalactic Astrophysics · Physics 2024-01-10 Prasenjit Saha , Dominique Sluse , Jenny Wagner , Liliya L. R. Williams

The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.

Functional Analysis · Mathematics 2008-07-28 Szymon Wasowicz

We present an example of a complete and minimal Gabor system consisting of time-frequency shifts of a Gaussian, localized at the coordinate axes in the time-frequency plane (phase space). Asymptotically, the number of time-frequency shifts…

Functional Analysis · Mathematics 2008-05-28 Gerard Ascensi , Yurii I. Lyubarskii , Kristian Seip

Singularities of caustics appeared in gravitational lensing effect are discussed analytically. Multipole expansion model of lensing object is mainly studied since it is tractable and universal. Our analyses are confirmed by numerical…

Astrophysics · Physics 2009-10-28 Y. Kakigi , T. Okamura , T. Fukuyama

The four observables associated with gravitational lensing of distant quasars by intervening galaxies: image splittings, relative amplifications, time delays, and optical depths, provide separate measures of the strength of the…

Astrophysics · Physics 2009-08-18 Lawrence Krauss , Martin White

In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…

Probability · Mathematics 2018-06-22 Shane Barratt

We study Gabor frames with Hermite window functions. Gr\"ochenig and Lyubarskii provided a sufficient density condition for their frame sets, which leads to what we call the "safety region". For rectangular lattices and Hermite windows of…

Functional Analysis · Mathematics 2025-04-07 Markus Faulhuber , Irina Shafkulovska , Ilya Zlotnikov

We give a general construction of entire functions in $d$ complex variables that vanish on a lattice of the form $L = A (Z + i Z )^d$ for an invertible complex-valued matrix. As an application we exhibit a class of lattices of density >1…

Complex Variables · Mathematics 2021-09-27 Karlheinz Gröchenig , Yurii Lyubarskii

The large scale distribution of galaxies in the universe displays a complex pattern of clusters, super-clusters, filaments and voids with sizes limited only by the boundaries of the available samples. A quantitative statistical…

Cosmology and Nongalactic Astrophysics · Physics 2015-05-20 Francesco Sylos Labini , Luciano Pietronero

This work considers estimation and forecasting in a multivariate, possibly high-dimensional count time series model constructed from a transformation of a latent Gaussian dynamic factor series. The estimation of the latent model parameters…

Methodology · Statistics 2025-04-07 Younghoon Kim , Marie-Christine Düker , Zachary F. Fisher , Vladas Pipiras

We investigate the aging behavior of lattice-gas models with constrained dynamics in which particle exchange with a reservoir is allowed. Such models provide a particularly simple interpretation of aging phenomena as a slow approach to…

Statistical Mechanics · Physics 2009-10-30 Jorge Kurchan , Luca Peliti , Mauro Sellitto

One of the fundamental tasks of science is to find explainable relationships between observed phenomena. One approach to this task that has received attention in recent years is based on probabilistic graphical modelling with sparsity…

Machine Learning · Statistics 2014-04-16 Peter Orchard , Felix Agakov , Amos Storkey

This work explores the tensor and combinatorial constructs underlying the linearised higher-order variational equations of a generic autonomous system along a particular solution. The main result of this paper is a compact yet explicit and…

Exactly Solvable and Integrable Systems · Physics 2015-02-11 Sergi Simon

Continuous-variable Gaussian entanglement is an attractive notion, both as a fundamental concept in quantum information theory, based on the well-established Gaussian formalism for phase-space variables, and as a practical resource in…

Quantum Physics · Physics 2026-05-07 E. Shchukin , P. van Loock

High-dimensional chaos displayed by multi-component systems with a single time-delayed feedback is shown to be accessible to time series analysis of a scalar variable only. The mapping of the original dynamics onto scalar time-delay systems…

The envelope of an elliptical Gaussian complex vector, or equivalently, the amplitude or norm of a bivariate normal random vector has application in many weather and signal processing contexts. We explicitly characterize its distribution in…

Statistics Theory · Mathematics 2026-02-03 Sattwik Ghosal , Ranjan Maitra

Strong gravitational lenses are unique cosmological probes. These produce multiple images of a single source. Whether a single galaxy, a group or a cluster, extracting cosmologically relevant information requires an accurate modeling of the…

Cosmology and Nongalactic Astrophysics · Physics 2011-12-13 Irène Balmès

In this paper we investigate the computational aspects of some recently proposed iterative methods for approximating the canonical tight and canonical dual window of a Gabor frame (g,a,b). The iterations start with the window g while the…

Functional Analysis · Mathematics 2007-05-23 A. J. E. M. Janssen , Peter L. Soendergaard