Related papers: Using wave packet decompositions to construct func…
Comparison of stellar catalogues with position and proper motion components using a decomposition on a set of orthogonal vector spherical harmonics. We show the theoretical and practical advantages of this technique as a result of…
Wavelet analysis is proposed as a new tool for studying the large-scale structure formation of the universe. To reveal its usefulness, the wavelet decomposition of one-dimensional cosmological density fluctuations is performed. In contrast…
The rapidly evolving field of engineering design of functional surfaces necessitates sophisticated tools to manage the inherent complexity of high-dimensional design spaces. This survey paper offers a scoping review, i.e., a literature…
Hagedorn functions are carefully constructed generalizations of Hermite functions to the setting of many-dimensional squeezed and coupled harmonic systems. Wavepackets formed by superpositions of Hagedorn functions have been successfully…
We present a rigorous theoretical framework for designing full-space spatial power dividers using metagratings. In our study, the current restrictions of spatial power dividing platforms such as reflection-only performance, operating at…
Geometric decomposition is a widely used tool for constructing local bases for finite element spaces. For finite element spaces of differential forms on simplicial meshes, Arnold, Falk, and Winther showed that geometric decompositions can…
This paper develops new theory and algorithms for 1D general mode decompositions. First, we introduce the 1D synchrosqueezed wave packet transform and prove that it is able to estimate the instantaneous information of well-separated modes…
Finite Element discretizations of coupled multi-physics partial differential equation models require the handling of composed function spaces. In this paper we discuss software concepts and abstractions to handle the composition of function…
Decoupling is a recent development in Fourier analysis, which has applications in harmonic analysis, PDE, and number theory. We survey some applications of decoupling and some of the ideas in the proof. This survey is aimed at a general…
We propose a formal framework based on collective coordinates to reduce infinite-dimensional stochastic partial differential equations (SPDEs) with symmetry to a set of finite-dimensional stochastic differential equations which describe the…
We propose a functional view of matrix decomposition problems on graphs such as geometric matrix completion and graph regularized dimensionality reduction. Our unifying framework is based on the key idea that using a reduced basis to…
This work is concerned with the convex analysis of functions defined on (not necessarily finite-dimensional) Hilbert spaces whose values depend solely on a certain ``spectrum'' of the arguments, a class we term ``spectral functions.'' We…
In this exploration paper, we design algorithms for deforming and contracting a simply connected discrete closed manifold to a discrete sphere. Such a contraction is a kind of shrinking or reducing process. In our algorithms, we need to…
Designing and implementing systems as an interconnection of smaller subsystems is a common practice for modularity and standardization of components and design algorithms. Although not typically cast in this framework, many of these…
We propose an approach for approximating the partition function which is based on two steps: (1) computing the partition function of a simplified model which is obtained by deleting model edges, and (2) rectifying the result by applying an…
Families of energy operators and generalized energy operators have recently been introduced in the definition of the solutions of linear Partial Differential Equations (PDEs) with a particular application to the wave equation [Montillet,…
Shape-constrained functional data encompass a wide array of application fields, such as activity profiling, growth curves, healthcare and mortality. Most existing methods for general functional data analysis often ignore that such data are…
This paper presents a method to decompose an op-amp into its functional blocks. The method is able to recognize functional blocks on a high level of abstraction as loads or amplification stages which have a large set of possible structural…
Wavelet decompositions of integral operators have proven their efficiency in reducing computing times for many problems, ranging from the simulation of waves or fluids to the resolution of inverse problems in imaging. Unfortunately,…
This work presents generalized low-rank signal decompositions with the aid of switching techniques and adaptive algorithms, which do not require eigen-decompositions, for space-time adaptive processing. A generalized scheme is proposed to…