Related papers: Non-binary dynamical Ising machines for combinator…

Generalized Ising models, also known as cluster expansions, are an important tool in many areas of condensed-matter physics and materials science, as they are often used in the study of lattice thermodynamics, solid-solid phase transitions,…

The one-dimensional Ising model with its connections to several physical concepts plays a vital role in comprehension of several principles, phenomena and numerical methods. The Hamiltonian of a coupled one-dimensional dissipative spin…

A non-binary Constraint Satisfaction Problem (CSP) can be solved directly using extended versions of binary techniques. Alternatively, the non-binary problem can be translated into an equivalent binary one. In this case, it is generally…

In general we are interested in dynamical systems coupled to complex hysteresis. Therefore as a first step we investigated recently the dynamics of a periodically driven damped harmonic oscillator coupled to independent Ising spins in a…

We prove that the 2D Ising model is complete in the sense that the partition function of any classical q-state spin model (on an arbitrary graph) can be expressed as a special instance of the partition function of a 2D Ising model with…

We propose a general framework for a hybrid continuous-discrete algorithm that integrates continuous-time deterministic dynamics with Metropolis-Hastings steps to combine search dynamics with and without detailed balance. Our purpose is to…

Sampling Boltzmann probability distributions plays a key role in machine learning and optimization, motivating the design of hardware accelerators such as Ising machines. While the Ising model can in principle encode arbitrary optimization…

In binary cascade dynamics, the nodes of a graph are in one of two possible states (inactive, active), and nodes in the inactive state make an irreversible transition to the active state, as soon as their precursors satisfy a predetermined…

The search for new computational machines beyond the traditional von Neumann architecture has given rise to a modern area of nonlinear science -- development of unconventional computing -- requiring the efforts of mathematicians, physicists…

We establish the set of independent variables suitable to monitor the complicated evolution of the spinning compact binary during the inspiral. Our approach is valid up to the second post-Newtonian order, including leading order spin-orbit,…

The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a…

A framework for creating and updating digital twins for dynamical systems from a library of physics-based functions is proposed. The sparse Bayesian machine learning is used to update and derive an interpretable expression for the digital…

Computationally hard problems, including combinatorial optimization, can be mapped into the problem of finding the ground-state of an Ising Hamiltonian. Building physical systems with collective computational ability and distributed…

We present a new method to close the Master Equation representing the continuous time dynamics of Ising interacting spins. The method makes use of the the theory of Random Point Processes to derive a master equation for local conditional…

This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…

Coupled spins form composite quantum systems which play an important role in many quantum technology applications, with an essential task often being the efficient generation of entanglement between two constituent qubits. The simplest such…

Learning in neural networks poses peculiar challenges when using discretized rather then continuous synaptic states. The choice of discrete synapses is motivated by biological reasoning and experiments, and possibly by hardware…

In this paper, we build on recent work using a mathematical programming approach for incremental state update in analysis of non-linear mechanics models. In particular, we consider quasi-static analysis of continuum problems in the…

Many complex systems occurring in the natural or social sciences or economics are frequently described on a microscopic level, e.g., by lattice- or agent-based models. To analyze the states of such systems and their bifurcation structure on…

Encoding classical data on quantum spin Hamiltonians yields ordered spin ground states which are used to discriminate data types for binary classification. The Ising Hamiltonian is a typical spin model to encode classical data onto qubits,…