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Digital MemComputing machines (DMMs), which employ nonlinear dynamical systems with memory (time non-locality), have proven to be a robust and scalable unconventional computing approach for solving a wide variety of combinatorial…

Digital memcomputing machines (DMMs) are a class of computational machines designed to solve combinatorial optimization problems. A practical realization of DMMs can be accomplished via electrical circuits of highly non-linear,…

It is well known that physical phenomena may be of great help in computing some difficult problems efficiently. A typical example is prime factorization that may be solved in polynomial time by exploiting quantum entanglement on a quantum…

Digital memcomputing machines (DMMs) are a new class of computing machines that employ non-quantum dynamical systems with memory to solve combinatorial optimization problems. Here, we show that the time to solution (TTS) of DMMs follows an…

Digital Memcomputing machines (DMMs) are dynamical systems with memory (time non-locality) that have been designed to solve combinatorial optimization problems. Their corresponding ordinary differential equations depend on a few…

Digital memcomputing machines (DMMs) are non-linear dynamical systems designed so that their equilibrium points are solutions of the Boolean problem they solve. In a previous work [Chaos 27, 023107 (2017)] it was argued that when DMMs…

We introduce a class of digital machines we name Digital Memcomputing Machines (DMMs) able to solve a wide range of problems including Non-deterministic Polynomial (NP) ones with polynomial resources (in time, space and energy). An abstract…

In this article, we present the potential benefits of incorporating jumps into the dynamics of digital memcomputing machines (DMMs), which have been developed to address complex optimization problems. We illustrate the potential speed…

This paper serves as a review and discussion of the recent works on memcomputing. In particular, the $\textit{universal memcomputing machine}$ (UMM) and the $\textit{digital memcomputing machine}$ (DMM) are discussed. We review the…

Viewing optimization methods as numerical integrators for ordinary differential equations (ODEs) provides a thought-provoking modern framework for studying accelerated first-order optimizers. In this literature, acceleration is often…

For the last thirty years, several Dynamic Memory Managers (DMMs) have been proposed. Such DMMs include first fit, best fit, segregated fit and buddy systems. Since the performance, memory usage and energy consumption of each DMM differs,…

In the fields of statistics, machine learning, image science, and related areas, there is an increasing demand for decentralized collection or storage of large-scale datasets, as well as distributed solution methods. To tackle this…

Memcomputing is a novel computing paradigm beyond the von-Neumann one. Its digital version is designed for the efficient solution of combinatorial optimization problems, which emerge in various fields of science and technology. Previously,…

An exact arithmetic, memory efficient direct solution method for finite element method (FEM) computations is outlined. Unlike conventional black-box or low-rank direct solvers that are opaque to the underlying physical problem, the proposed…

We propose to use Digital Memcomputing Machines (DMMs), implemented with self-organizing logic gates (SOLGs), to solve the problem of numerical inversion. Starting from fixed-point scalar inversion we describe the generalization to solving…

Probabilistic solvers for ordinary differential equations (ODEs) provide efficient quantification of numerical uncertainty associated with simulation of dynamical systems. Their convergence rates have been established by a growing body of…

A parallel direct solution approach based on domain decomposition method (DDM) and directed acyclic graph (DAG) scheduling is outlined. Computations are represented as a sequence of small tasks that operate on domains of DDM or dense matrix…

Discrete flow models (DFMs) have been proposed to learn the data distribution on finite state space, offering a flexible framework as an alternative to discrete diffusion models. A line of recent work has studied samplers for discrete…

By coordinating terminal smart devices or microprocessors to engage in cooperative computation to achieve systemlevel targets, distributed optimization is incrementally favored by both engineering and computer science. The well-known…

Domain decomposition methods (DDMs) provide a unifying framework for the scalable numerical solution of partial differential equations. Originating from Schwarz's alternating method, they have evolved into a rich family of algorithms that…