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We investigate the use of conformal maps for the acceleration of convergence of the trapezoidal rule and Sinc numerical methods. The conformal map is a polynomial adjustment to the $\sinh$ map, and allows the treatment of a finite number of…

One of the fundamental results used in observational cosmology is the distance duality relation (DDR), which relates the luminosity distance, $D_L$, with angular diameter distance, $D_A$, at a given redshift $z$. We employ the observed…

We propose a metric for the space of multiple sequence alignments that can be used to compare two alignments to each other. In the case where one of the alignments is a reference alignment, the resulting accuracy measure improves upon…

Localization has been a challenging task for autonomous navigation. A loop detection algorithm must overcome environmental changes for the place recognition and re-localization of robots. Therefore, deep learning has been extensively…

For $0<p<\infty$, $\Psi:[0,\infty)\to(0,\infty)$ and a finite positive Borel measure $\mu$ on the unit disc $\mathbb{D}$, the Lebesgue--Zygmund space $L^p_{\mu,\Psi}$ consists of all measurable functions $f$ such that $\lVert f…

The paper is devoted to a categorical study of the category of probabilistic metric spaces. The study is based on an isomorphic description of the category of probabilistic metric spaces. The isomorphic description was obtained in [3] and…

Nonlinear computation is essential for various information processing tasks. Optical implementations are attractive because passive light propagation can manipulate high-dimensional signals with extreme throughput and parallelism; yet…

Driven by large-scale contrastive vision-language pre-trained models such as CLIP, recent advancements in the image-text matching task have achieved remarkable success in representation learning. Due to image-level visual-language…

This paper investigates spaces equipped with a family of metric-like functions satisfying certain axioms. These functions provide a unified framework for defining topology, uniformity, and diffeology. The framework is based on a family of…

Structured light illumination is an active 3-D scanning technique based on projecting/capturing a set of striped patterns and measuring the warping of the patterns as they reflect off a target object's surface. As designed, each pixel in…

A new notion of metric differentiability of set-valued functions at a point is introduced in terms of right and left limits of special set-valued metric divided differences of first order. A local metric linear approximant of a metrically…

Structure from Motion (SfM) often fails to estimate accurate poses in environments that lack suitable visual features. In such cases, the quality of the final 3D mesh, which is contingent on the accuracy of those estimates, is reduced. One…

Generating crisp, i.e., one-pixel-wide, edge maps remains one of the fundamental challenges in edge detection, affecting both traditional and learning-based methods. To obtain crisp edges, most existing approaches rely on two hand-crafted…

In this paper, we demonstrate that CLIP can also be adapted to downstream tasks where its vision-language alignment is suboptimally learned during pre-training on web-crawled data, all without requiring fine-tuning. We explore the case of…

Infrared and visible image fusion(IVIF) combines complementary modalities while preserving natural textures and salient thermal signatures. Existing solutions predominantly rely on extensive sets of rigidly aligned image pairs for training.…

We survey the main results of approximation theory for adaptive piecewise polynomial functions. In such methods, the partition on which the piecewise polynomial approximation is defined is not fixed in advance, but adapted to the given…

Loss functions are error metrics that quantify the difference between a prediction and its corresponding ground truth. Fundamentally, they define a functional landscape for traversal by gradient descent. Although numerous loss functions…

We use conformal maps to study a free boundary problem for a two-fluid electromechanical system, where the interface between the fluids is determined by the combined effects of electrostatic forces, gravity and surface tension. The free…

Mapping is an essential task for mobile robots and topological representation often works as a basis for the various applications. In this paper, a novel framework that can build topological maps incrementally is proposed. The algorithm is…

In this article, we have studied a 1D map, which is formed by combining the two well-known maps i.e. the tent and the logistic maps in the unit interval i.e. [0, 1]. The proposed map can behave as the piecewise smooth or non-smooth maps…