Related papers: A Constructive Approach for Building Wavelet Bases…
In this paper we consider the continuous wavelet transform using Gaussian wavelets multiplied by an appropriate rational term. The zeros and poles of this rational modifier act as free parameters and their choice highly influences the shape…
We present a novel framework for discrete multiresolution analysis of graph signals. The main analytical tool is the samplet transform, originally defined in the Euclidean framework as a discrete wavelet-like construction, tailored to the…
In this paper we construct general vector-valued infinite-divisible independently scattered random measures with values in $\mathbb{R}^m$ and their corresponding stochastic integrals. Moreover, given such a random measure, the class of all…
Vector Fitting is a popular method of constructing rational approximants designed to fit given frequency response measurements. The original method, which we refer to as VF, is based on a least-squares fit to the measurements by a rational…
This paper presents a discussion on $p$-adic multiframe by means of its wavelet structure, called as multiframelet, which is build upon $p$-adic wavelet construction. Multiframelets create much excitement in mathematicians as well as…
Most deep learning pipelines are built on real-valued operations to deal with real-valued inputs such as images, speech or music signals. However, a lot of applications naturally make use of complex-valued signals or images, such as MRI or…
Geometric structures on $\mathbb N Q$-manifolds, i.e.~non-negatively graded manifolds with an homological vector field, encode non-graded geometric data on Lie algebroids and their higher analogues. A particularly relevant class of…
Generating highly detailed, complex data is a long-standing and frequently considered problem in the machine learning field. However, developing detail-aware generators remains an challenging and open problem. Generative adversarial…
Variational quantum algorithms have emerged as a powerful tool for harnessing the potential of near-term quantum devices to address complex challenges across quantum science and technology. Yet, the robust and scalable quantification of…
A theory of higher rank multiresolution analysis is given in the setting of abelian multiscalings. This theory enables the construction, from a higher rank MRA, of finite wavelet sets whose multidilations have translates forming an…
While researchers often study message features like moral content in text, such as party manifestos and social media, their quantification remains a challenge. Conventional human coding struggles with scalability and intercoder reliability.…
We construct solitary waves for the fractional Korteweg-De Vries type equation $u_t + (\Lambda^{-s}u + u^2)_x = 0$, where $\Lambda^{-s}$ denotes the Bessel potential operator $(1 + |D|^2)^{-\frac{s}{2}}$ for $s \in (0,\infty)$. The approach…
A recursive method for construction of symmetric irreducible representations of O(2l+1) in the O(2l + 1) supset O(3) basis for identical boson systems is proposed. The formalism is realized based on the group chain U(2l + 1) supset U(2l- 1)…
Wavelet Transforms are a widely used technique for decomposing a signal into coefficient vectors that correspond to distinct frequency/scale bands while retaining time localization. This property enables an adaptive analysis of signals at…
Recent progress in medical vision-language models (VLMs) has achieved strong performance on image-level text-centric tasks such as report generation and visual question answering (VQA). However, achieving fine-grained visual grounding and…
Despite a plethora of applications ranging from quantum memories to high-resolution lithography, the current technologies to generate vector vortex beams (VVBs) suffer from less efficient energy use, poor resolution, low damage threshold,…
This note aims at obtaining a variational characterization of complex structures by means of a calculus of variations for real vector bundle valued differential forms, and outlines a perspective to study existence questions via functionals…
We propose and analyse numerical algorithms based on weighted least squares for the approximation of a real-valued function on a general bounded domain $\Omega \subset \mathbb{R}^d$. Given any $n$-dimensional approximation space $V_n…
Criteria and constructive methods for the completion of an incomplete basis of, or context in, a four-dimensional Hilbert space by (in)decomposable vectors are given.
Volumetric design is the first and critical step for professional building design, where architects not only depict the rough 3D geometry of the building but also specify the programs to form a 2D layout on each floor. Though 2D layout…