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Retraction maps are known to be the seed for all numerical integrators. These retraction maps-based integrators can be further lifted to tangent and cotangent bundles, giving rise to structure-preserving integrators for mechanical systems.…

Optical computing has emerged as a promising candidate for real-time and parallel continuous data processing. Motivated by recent progresses in metamaterial-based analog computing [Science 343, 160 (2014)], we theoretically investigate…

Many iterative algorithms in optimization, computational geometry, computer algebra, and other areas of computer science require repeated computation of some algebraic expression whose input changes slightly from one iteration to the next.…

In this work, we introduce the concept of an entirely new circuit architecture based on the novel, physics-inspired computing paradigm: Memcomputing. In particular, we focus on digital memcomputing machines (DMMs) that can be designed…

Conceptual memristors have recently gathered wider interest due to their diverse application in non-von Neumann computing, machine learning, neuromorphic computing, and chaotic circuits. We introduce a compact CMOS circuit that emulates…

We present a novel algorithm which can overcome the drawbacks of the conventional linear scaling method with minimal computational overhead. This is achieved by introducing additional constraints, thus eliminating the redundancy of the…

This paper presents a system for solving binary-valued linear equations using quantum computers. The system is called Mod2VQLS, which stands for Modulo2 Variational Quantum Linear Solver. As far as we know, this is the first such proposal.…

Coupled relaxation oscillators, realized via chemical or other means, can exhibit a multiplicity of steady states, characterized by spatial patterns resulting from lateral inhibition. We show that perturbation-initiated transformations…

A non-equilibrium open-dissipative neural network, such as a coherent Ising machine based on mutually coupled optical parametric oscillators, has been proposed and demonstrated as a novel computing machine for hard combinatorial…

We construct several variational integrators--integrators based on a discrete variational principle--for systems with Lagrangians of the form L = L_A + epsilon L_B, with epsilon << 1, where L_A describes an integrable system. These…

Magnetic quadrupoles are essential components of particle accelerators like the Large Hadron Collider. In order to study numerically the stability of the particle beam crossing a quadrupole, a large number of particle revolutions in the…

Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…

We use algebraic geometry to study matrix rigidity, and more generally, the complexity of computing a matrix-vector product, continuing a study initiated by Kumar, et. al. We (i) exhibit many non-obvious equations testing for (border)…

We propose a novel approach, OrQstrator, which is a modular framework for conducting quantum circuit optimization in the Noisy Intermediate-Scale Quantum (NISQ) era. Our framework is powered by Deep Reinforcement Learning (DRL). Our…

Coordinate transformations provide dimensional reduction benefits across power system analysis, electric machine modeling, and power electronic converter control. This paper introduces a novel transformation based on Geometric Algebra that…

Modern integrated circuits are essentially two-dimensional (2D). Partial three-dimensional (3D) integration and 3D-transistor-level integrated circuits have long been anticipated as routes to improve the performance, cost and size of…

Signal processing in wireless communications, such as precoding, detection, and channel estimation, are basically about solving inverse matrix problems, which, however, are slow and inefficient in conventional digital computers, thus…

Analog computing using bosonic computational states is a leading approach to surpassing the computational speed and energy limitations of von Neumann architectures. But the challenges of manufacturing large-scale photonic integrated…

Binary embedding of high-dimensional data requires long codes to preserve the discriminative power of the input space. Traditional binary coding methods often suffer from very high computation and storage costs in such a scenario. To…

As dynamic and control systems become more complex, relying purely on numerical computations for systems analysis and design might become extremely expensive or totally infeasible. Computer algebra can act as an enabler for analysis and…