Related papers: Can nonlinear parametric oscillators solve random …
We develop a recently-proposed mapping of the two-dimensional Ising model with random exchange (RBIM), via the transfer matrix, to a network model for a disordered system of non-interacting fermions. The RBIM transforms in this way to a…
Li\'{e}nard-type nonlinear oscillators with linear and nonlinear damping terms exhibit diverse dynamical behavior in both the classical and quantum regimes. In this paper, we consider examples of various one-dimensional Li\'{e}nard type-I…
We are interested in the problem of robust parametric estimation of a density from $n$ i.i.d. observations. By using a practice-oriented procedure based on robust tests, we build an estimator for which we establish non-asymptotic risk…
Neurons in the brain are wired into adaptive networks that exhibit a range of collective dynamics. Oscillations, for example, are paradigmatic synchronous patterns of neural activity with a defined temporal scale. Neuronal avalanches, in…
A main puzzle of deep networks revolves around the absence of overfitting despite large overparametrization and despite the large capacity demonstrated by zero training error on randomly labeled data. In this note, we show that the dynamics…
Ising machines, which are dynamical systems designed to operate in a parallel and iterative manner, have emerged as a new paradigm for solving combinatorial optimization problems. Despite computational advantages, the quality of solutions…
The replicated field theory of the random field Ising model involves the couplings of replicas of different indices. The resulting correlation functions involve a superposition of different types of long distance behaviours. However the…
Optimization problems pose challenges across various fields. In recent years, quantum annealers have emerged as a promising platform for tackling such challenges. To provide a new perspective, we develop a heuristic tensor network (TN)…
Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and is currently used in numerous physical and engineering…
Stochastic Ising machines, sIMs, are highly promising accelerators for optimization and sampling of computational problems that can be formulated as an Ising model. Here we investigate the computational advantage of sIM for simulations of…
The Ising model on networks plays a fundamental role as a testing ground for understanding cooperative phenomena in complex systems. Here we solve the synchronous dynamics of the Ising model on random graphs with an arbitrary degree…
The emergence of synchronization in a network of coupled oscillators is a fascinating topic in various scientific disciplines. A coupled oscillator network is characterized by a population of heterogeneous oscillators and a graph describing…
Synchronization is ubiquitous in nature, which is mathematically described by coupled oscillators. Synchronization strongly depends on the interaction network, and the network plays a crucial role in controlling the dynamics. To understand…
In this paper, we propose quasilinearization methods that convert nonlocal fully-nonlinear parabolic systems into the nonlocal quasilinear parabolic systems. The nonlocal parabolic systems serve as important mathematical tools for modelling…
This chapter provides a general introduction of network modeling in psychometrics. The chapter starts with an introduction to the statistical model formulation of pairwise Markov random fields (PMRF), followed by an introduction of the PMRF…
The Ising model is a simple statistical model for ferromagnetism. There are analytic solutions for low dimensions and very efficient Monte Carlo methods, such as cluster algorithms, for simulating this model in special cases. However most…
Various combinatorial optimization NP-hard problems can be reduced to finding the minimizer of an Ising model, which is a discrete mathematical model. It is an intellectual challenge to develop some mathematical tools or algorithms for…
We consider the Ising model between 2 and 4 dimensions perturbed by quenched disorder in the strength of the interaction between nearby spins. In the interval 2<d<4 this disorder is a relevant perturbation that drives the system to a new…
Turing patterns formed by activator-inhibitor systems on networks are considered. The linear stability analysis shows that the Turing instability generally occurs when the inhibitor diffuses sufficiently faster than the activator. Numerical…
Coupled Kerr parametric oscillators (KPOs) are a promising resource for classical and quantum analog computation, for example to find the ground state of Ising Hamiltonians. Yet, the state space of strongly coupled KPO networks is very…