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A prototype for an extensible interactive graphical term manipulation system is presented that combines pattern matching and nondeterministic evaluation to provide a convenient framework for doing tedious algebraic manipulations that so far…
Multidimensional Scaling (MDS) is one of the first fundamental manifold learning methods. It can be categorized into several methods, i.e., classical MDS, kernel classical MDS, metric MDS, and non-metric MDS. Sammon mapping and Isomap can…
A novel multistatic multiple-input multiple-output (MIMO) integrated sensing and communication (ISAC) system in cellular networks is proposed. It can make use of widespread base stations (BSs) to perform cooperative sensing in wide area.…
The ability to estimate rich geometry and camera motion from monocular imagery is fundamental to future interactive robotics and augmented reality applications. Different approaches have been proposed that vary in scene geometry…
Infrared-visible image fusion methods aim at generating fused images with good visual quality and also facilitate the performance of high-level tasks. Indeed, existing semantic-driven methods have considered semantic information injection…
Assessing the similarity of matrices is valuable for analyzing the extent to which data sets exhibit common features in tasks such as data clustering, dimensionality reduction, pattern recognition, group comparison, and graph analysis.…
The paper opens with an overview of the discussion of international comparisons (including goals) in mathematics education. Afterwards, the two most important recent international studies, the PISA Study and TIMSS-Repeat, are described.…
We present a real-time semantic mapping approach for mobile vision systems with a 2D to 3D object detection pipeline and rapid data association for generated landmarks. Besides the semantic map enrichment the associated detections are…
We present the first steps of interaction spaces theory, a universal mathematical theory of complex systems which is able to embed cellular automata, agent based models, master equation based models, stochastic or deterministic, continuous…
This paper presents the first active object mapping framework for complex robotic manipulation and autonomous perception tasks. The framework is built on an object SLAM system integrated with a simultaneous multi-object pose estimation…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
In this paper, we consider systems of algebraic and non-linear partial differential equations and inequations. We decompose these systems into so-called simple subsystems and thereby partition the set of solutions. For algebraic systems,…
Uniform Manifold Approximation and Projection (UMAP) is one of the state-of-the-art methods for dimensionality reduction and data visualization. This is a tutorial and survey paper on UMAP and its variants. We start with UMAP algorithm…
Statistical Shape Modeling (SSM) effectively analyzes anatomical variations within populations but is limited by the need for manual localization and segmentation, which relies on scarce medical expertise. Recent advances in deep learning…
Isospectral reduction is an important tool for network/matrix analysis as it reduces the dimension of a matrix/network while preserving its eigenvalues and eigenvectors. The main contribution of this manuscript is a proposed algorithmic…
Spatial numerical integration is essential for finite element analysis. Currently, numerical integration schemes, mostly based on Gauss quadrature, are widely used. Herein, we present an alternative semi-analytical approach for mass matrix…
The movable antenna (MA)-enabled integrated sensing and communication (ISAC) system attracts widespread attention as an innovative framework. The ISAC system integrates sensing and communication functions, achieving resource sharing across…
We adapt concepts, methodology, and theory originally developed in the areas of multidimensional scaling and dimensionality reduction for multivariate data to the functional setting. We focus on classical scaling and Isomap -- prototypical…
This work introduces a scaffolding framework to compactly parametrise solid structures with conforming NURBS elements for isogeometric analysis. A novel formulation introduces a topological, geometrical and parametric subdivision of the…
Neuromorphic systems or dedicated hardware for neuromorphic computing is getting popular with the advancement in research on different device materials for synapses, especially in crossbar architecture and also algorithms specific or…