Related papers: An Introduction to Isomorphic Mathematical Analysi…

Matrix-matrix multiplication is a fundamental operation of great importance to scientific computing and, increasingly, machine learning. It is a simple enough concept to be introduced in a typical high school algebra course yet in practice…

This paper proposes Relational Similarity Machines (RSM): a fast, accurate, and flexible relational learning framework for supervised and semi-supervised learning tasks. Despite the importance of relational learning, most existing methods…

Developing a suitable Deep Neural Network (DNN) often requires significant iteration, where different model versions are evaluated and compared. While metrics such as accuracy are a powerful means to succinctly describe a model's…

Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…

This work proposes a maximum likelihood (ML)-based parameter estimation framework for a millimeter wave (mmWave) integrated sensing and communication (ISAC) system in a multi-static configuration using energy-efficient hybrid digital-analog…

We consider the simplest gauge theories given by one- and two- matrix integrals and concentrate on their stringy and geometric properties. We remind general integrable structure behind the matrix integrals and turn to the geometric…

This paper offers what seems at first to be a minor technical correction to the current practice of computing indefinite integrals, and introduces the idea of a "Kahanian constant of integration". However, the total impact of this minor…

We introduce the notion of an approximation system as a generalization of Taylor approximation, and we give some first examples. Next we develop the general theory, including error bounds and a sufficient criterion for convergence. More…

Optical systems are becoming increasingly important by resolving many bottlenecks in today's communication, electronics, and biomedical systems. However, given the continuous nature of optics, the inability to efficiently analyze optical…

Medical images like CT and MRI provide detailed information about the internal structure of the body, and identifying key anatomical structures from these images plays a crucial role in clinical workflows. Current methods treat it as a…

We consider and discretize a mixed formulation for linear elasticity with weakly imposed symmetry in two and three dimensions. Whereas existing methods mainly deal with simplicial or polygonal meshes, we take advantage of isogeometric…

Object SLAM is considered increasingly significant for robot high-level perception and decision-making. Existing studies fall short in terms of data association, object representation, and semantic mapping and frequently rely on additional…

We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…

Symbiotic Autonomous Systems (SAS) are advanced intelligent and cognitive systems exhibiting autonomous collective intelligence enabled by coherent symbiosis of human-machine interactions in hybrid societies. Basic research in the emerging…

We propose a functional view of matrix decomposition problems on graphs such as geometric matrix completion and graph regularized dimensionality reduction. Our unifying framework is based on the key idea that using a reduced basis to…

Hybrid automata are a natural framework for modeling and analyzing systems which exhibit a mixed discrete continuous behaviour. However, the standard operational semantics defined over such models implicitly assume perfect knowledge of the…

We propose a geometrical approach to the investigation of Hamiltonian systems on (Pseudo) Riemannian manifolds. A new geometrical criterion of instability and chaos is proposed. This approach is more generic than well known reduction to the…

A method is presented to exploit adaptive integration algorithms using importance sampling, like VEGAS, for the task of scanning theoretical predictions depending on a multi-dimensional parameter space. Usually, a parameter scan is…

We introduce and investigate the concept of Stratified Algebra, a new algebraic framework equipped with a layer-based structure on a vector space. We formalize a set of axioms governing intra-layer and inter-layer interactions, study their…

The incorporation of LLMs in multi-agent systems (MASs) has the potential to significantly improve our ability to autonomously solve complex problems. However, such systems introduce unique challenges in monitoring, interpreting, and…