Related papers: Beyond-mean-field fluctuations for the solution of…
A wide range of problems can be modelled as constraint satisfaction problems (CSPs), that is, a set of constraints that must be satisfied simultaneously. Constraints can either be represented extensionally, by explicitly listing allowed…
Constraint Satisfaction Problem (CSP) is a fundamental algorithmic problem that appears in many areas of Computer Science. It can be equivalently stated as computing a homomorphism $\mbox{$\bR \rightarrow \bGamma$}$ between two relational…
The local behavior of typical solutions of random constraint satisfaction problems (CSP) describes many important phenomena including clustering thresholds, decay of correlations, and the behavior of message passing algorithms. When the…
Random constraint satisfaction problems (CSP) have been studied extensively using statistical physics techniques. They provide a benchmark to study average case scenarios instead of the worst case one. The interplay between statistical…
The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is strongly utilized in engineering, biology and finance. In this paper, a stochastic…
We study spin-2 fluctuations around an infinite family of warped backgrounds of the form $\text{AdS}_2 \times \text{S}^2 \times \text{T}^4 \times \text{S}^1 \times \mathcal{I}_{\rho}$ in the type IIB theory, which possesses $\mathcal{N}=4$…
There are many ways of establishing upper bounds on fluctuations of random variables, but there is no systematic approach for lower bounds. As a result, lower bounds are unknown in many important problems. This paper introduces a general…
This paper focuses on the branching process for solving any constraint satisfaction problem (CSP). A parametrised schema is proposed that (with suitable instantiations of the parameters) can solve CSP's on both finite and infinite domains.…
An approach is proposed to the Hopfield model where the mean-field treatment is made for a given set of stored patterns (sample) and then the statistical average over samples is taken. This corresponds to the approach made by Thouless,…
This paper reviews the connections between Graphplan's planning-graph and the dynamic constraint satisfaction problem and motivates the need for adapting CSP search techniques to the Graphplan algorithm. It then describes how explanation…
We study the dynamics of a spin-flip model with a mean field interaction. The system is non reversible, spacially inhomogeneous, and it is designed to model social interactions. We obtain the limiting behavior of the empirical averages in…
We report new results on the complexity of the valued constraint satisfaction problem (VCSP). Under the unique games conjecture, the approximability of finite-valued VCSP is fairly well-understood. However, there is yet no characterisation…
For randomly selected couplers and fields, the D-Wave device typically yields a highly Boltzmann like distribution [ indicating equilibration. These equilibrated data however do not contain much useful information about the dynamics which…
We introduce a new solution to Glauber multi-spin dynamics on random graphs. The solution is based on the recently introduced Cavity Master Equation (CME), a time-closure turning the in principle exact Dynamic Cavity Method into a practical…
Stochastic maximum principle of nonlinear controlled forward-backward systems, where the set of strict (classical) controls need not be convex and the diffusion coefficient depends explicitly on the variable control, is an open problem…
The CLP scheme uses Horn clauses and SLD resolution to generate multiple constraint satisfaction problems (CSPs). The possible CSPs include rational trees (giving Prolog) and numerical algorithms for solving linear equations and linear…
This paper presents an algorithmic framework for solving unconstrained stochastic optimization problems using only stochastic function evaluations. We employ central finite-difference based gradient estimation methods to approximate the…
The pseudogap phenomena in High-$T_{{\rm c}}$ cuprates are investigated on the basis of the Hubbard model which includes only the on-site repulsive interaction $U$. We consider the pairing scenario for the pseudogap. The pseudogap arises…
We present a method to approximately solve general instances of combinatorial optimization problems using the physical dynamics of 3d rotors obeying Landau-Lifshitz-Gilbert dynamics. Conventional techniques to solve discrete optimization…
Many practical applications of control require that constraints on the inputs and states of the system be respected, while optimizing some performance criterion. In the presence of model uncertainties or disturbances, for many control…