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Isometric feature mapping (Isomap) is a promising manifold learning method. However, Isomap fails to work on data which distribute on clusters in a single manifold or manifolds. Many works have been done on extending Isomap to…
Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…
This study proposes a low-complexity interpretable classification system. The proposed system contains three main modules including feature extraction, feature reduction, and classification. All of them are linear. Thanks to the linear…
Document preparation systems like LaTeX offer the ability to render mathematical expressions as one would write these on paper. Using LaTeX, LaTeXML, and tools generated for use in the National Institute of Standards (NIST) Digital Library…
Mathematical information is essential for technical work, but its creation, interpretation, and search are challenging. To help address these challenges, researchers have developed multimodal search engines and mathematical question…
This paper examines various methods and ideas for humanizing mathematics. The term 'humanizing mathematics' which includes elements of 'aesthetic mathematics' refers to approaches that emphasize the aesthetic, philosophical, and subjective…
A joint design of both sensing and communication can lead to substantial enhancement for both subsystems in terms of size, cost as well as spectrum and hardware efficiency. In the last decade, integrated sensing and communications (ISAC)…
While there are numerous linear algebra teaching tools, they tend to be focused on the basics, and not handle the more advanced aspects. This project aims to fill that gap, focusing specifically on methods like Strassen's fast matrix…
Intelligent Process Automation (IPA) is emerging as a sub-field of AI to support the automation of long-tail processes which requires the coordination of tasks across different systems. So far, the field of IPA has been largely driven by…
Large Language Model Powered Multi-Agent Systems (MASs) are increasingly employed to automate complex real-world problems, such as programming and scientific discovery. Despite their promising, MASs are not without their flaws. However,…
The aim of this paper is to analyze from a mathematical perspective some existing schemes to partition a molecular density into several atomic contributions, with a specific focus on Iterative Stockholder Atom (ISA) methods. We provide a…
Finding correspondences between shapes is a fundamental problem in computer vision and graphics, which is relevant for many applications, including 3D reconstruction, object tracking, and style transfer. The vast majority of correspondence…
This paper describes a novel approach to grammar induction that has been developed within a framework designed to integrate learning with other aspects of computing, AI, mathematics and logic. This framework, called "information compression…
High-dimensional classification has become an increasingly important problem. In this paper we propose a "Multivariate Adaptive Stochastic Search" (MASS) approach which first reduces the dimension of the data space and then applies a…
We introduce MOS, a software application designed to facilitate the deployment, integration, management, and analysis of mathematical optimization models. MOS approaches mathematical optimization at a higher level of abstraction than…
Finite frame theory has become a powerful tool for many applications of mathematics. In this paper we introduce a new area of research in frame theory: Integer frames. These are frames having all integer coordinates with respect to a fixed…
Geometry foundation models have significantly advanced dense geometric SLAM, yet existing systems often lack deep semantic understanding and robust loop closure capabilities. Meanwhile, contemporary semantic mapping approaches are…
In this paper, we investigate a novel integrated sensing and communication (ISAC) system aided by movable antennas (MAs). A bistatic radar system, in which the base station (BS) is configured with MAs, is integrated into a multi-user…
In this contribution, we provide a new mass lumping scheme for explicit dynamics in isogeometric analysis (IGA). To this end, an element formulation based on the idea of dual functionals is developed. Non-Uniform Rational B-splines (NURBS)…
The Ising model was generalized to a system of cells interacting exclusively by presence of shared spins. Within the cells there are interactions of any complexity, the simplest intracell interactions come down to the Ising model. The…