Related papers: A Constructive Approach for Building Wavelet Bases…
A recently developed new approach, called ``Empirical Wavelet Transform'', aims to build 1D adaptive wavelet frames accordingly to the analyzed signal. In this paper, we present several extensions of this approach to 2D signals (images). We…
Cognitive modeling commonly relies on asking participants to complete a battery of varied tests in order to estimate attention, working memory, and other latent variables. In many cases, these tests result in highly variable observation…
The concept of $p$-adic quincunx Haar MRA was introduced and studied in~\cite{KS10}. In contrast to the real setting, infinitely many different wavelet bases are generated by a $p$-adic MRA. We give an explicit description for all wavelet…
Recognizing elementary underlying concepts from observations (disentanglement) and generating novel combinations of these concepts (compositional generalization) are fundamental abilities for humans to support rapid knowledge learning and…
We use a variational Monte Carlo algorithm to solve the electronic structure of two-dimensional semiconductor quantum dots in external magnetic field. We present accurate many-body wave functions for the system in various magnetic field…
The multiresolution analysis (MRA) associated with the Special affine Fourier transform (SAFT) provides a structured approach for generating orthonormal bases in \( L^2(\mathbb R) \), making it a powerful tool for advanced signal analysis.…
In this paper we formulate a general method for building completely integrable quantum systems. The method is based on the use of the so-called multi-parameter spectral equations, i.e. equations with several spectral parameters. We show…
We show that in a complex d-dimensional vector space, one can find O(d) bases whose elements form a 2-design. Such vector sets generalize the notion of a maximal collection of mutually unbiased bases (MUBs). MUBs have manifold applications…
We propose a general approach to construct weighted likelihood estimating equations with the aim of obtain robust estimates. The weight, attached to each score contribution, is evaluated by comparing the statistical data depth at the model…
The discrete wave equation in a multidimensional uniform space with local defects and sources is considered. The characterization of all possible defect configurations corresponding to given amplitudes of waves at the receivers (detectors)…
The empirical wavelet transform is an adaptive multiresolution analysis tool based on the idea of building filters on a data-driven partition of the Fourier domain. However, existing 2D extensions are constrained by the shape of the…
We report on the fabrication and characterization of composite multimode waveguide structures that consist of a stack of single-mode waveguides fabricated by ultrafast laser inscription. We explore 2 types of composite structures; those…
Variational wave functions used in the variational Monte Carlo (VMC) method are extensively improved to overcome the biases coming from the assumed variational form of the wave functions. We construct a highly generalized variational form…
A new systematic method for the explicit construction of (basis-)invariants is introduced and employed to construct the full ring of basis invariants of the Two-Higgs-Doublet-Model (2HDM) scalar sector. Co- and invariant quantities are…
Massive multiple-input multiple-output (MIMO) is a key enabler for the high data rates required by the sixth-generation networks, yet its performance hinges on effective beam management with low training overhead. This paper proposes an…
A method is suggested to build simple multiconfigurational wave functions specified uniquely by an energy cutoff $\Lambda$. These are constructed from a model space containing determinants with energy relative to that of the most stable…
Measurement error is ubiquitous in many variables - from blood pressure recordings in physiology to intelligence measures in psychology. Structural equation models (SEMs) account for the process of measurement by explicitly distinguishing…
In this article we focus on the parameterized complexity of the Multidimensional Binary Vector Assignment problem (called \BVA). An input of this problem is defined by $m$ disjoint sets $V^1, V^2, \dots, V^m$, each composed of $n$ binary…
We construct new bases of real functions from $L^{2}\left(B_{r}\right)$ and from $L^{2}\left(\mathbb{Q}_{p}\right)$. These functions are eigenfunctions of the $p$-adic pseudo-differential Vladimirov operator, which is defined on a compact…
We combine theoretical results from polytope domain meshing, generalized barycentric coordinates, and finite element exterior calculus to construct scalar- and vector-valued basis functions for conforming finite element methods on generic…