相关论文: Exact Phase Transitions in Random Constraint Satis…

In this paper, we prove the maximal $L_p$-$L_q$ regularity of the compressible and incompressible two phase flow with phase transition in the model problem case with the help of ${\mathcal R}$-bounded solution operators corresponding to…

We discuss a notion of phase transitions in multicomponent systems and clarify relations between deterministic chaotic and stochastic models of this type of systems. Connections between various definitions of SRB measures are considered as…

This paper is concerned with a new optimization problem named "phase change rate maximization" for single-input-single-output linear time-invariant systems. The problem relates to two control problems, namely robust instability analysis…

For several models of random constraint satisfaction problems, it was conjectured by physicists and later proved that a sharp satisfiability transition occurs. For random $k$-SAT and related models it happens at clause density $\alpha$…

The quantified constraint satisfaction problem (QCSP) is a powerful framework for modelling computational problems. The general intractability of the QCSP has motivated the pursuit of restricted cases that avoid its maximal complexity. In…

The satisfiability threshold for constraint satisfaction problems is that value of the ratio of constraints (or clauses) to variables, above which the probability that a random instance of the problem has a solution is zero in the large…

In a broad class of sparse random constraint satisfaction problems(CSP), deep heuristics from statistical physics predict that there is a condensation phase transition before the satisfiability threshold, governed by one-step replica…

In this paper we study random linear systems with $k$ variables per equation over the finite field GF(2), or equivalently $k$-XOR-CNF formulas. In a previous paper Creignou and Daud\'e proved that the phase transition for the consistency…

An important challenge in statistical analysis concerns the control of the finite sample bias of estimators. For example, the maximum likelihood estimator has a bias that can result in a significant inferential loss. This problem is…

To study the structure of solutions for random k-SAT and random CSPs, this paper introduces the concept of average similarity degree to characterize how solutions are similar to each other. It is proved that under certain conditions, as r…

Recent studies have shown that one-dimensional driven systems can exhibit phase separation even if the dynamics is governed by local rules. The ABC model, which comprises three particle species that diffuse asymmetrically around a ring,…

In the maximum constraint satisfaction problem (MAX CSP), one is given a finite collection of (possibly weighted) constraints on overlapping sets of variables, and the goal is to assign values from a given finite domain to the variables so…

This paper analyzes the scaling window of a random CSP model (i.e. model RB) for which we can identify the threshold points exactly, denoted by $r_{cr}$ or $p_{cr}$. For this model, we establish the scaling window…

We report an analytic and numerical study of a phase transition in a P problem (the assignment problem) that separates two phases whose representatives are the simple matching problem (an easy P problem) and the traveling salesman problem…

We study a simple and exactly solvable model for the generation of random satisfiability problems. These consist of $\gamma N$ random boolean constraints which are to be satisfied simultaneously by $N$ logical variables. In…

For random CNF formulae with m clauses, n variables and an unrestricted number of literals per clause the transition from high to low satisfiability can be determined exactly for large n. The critical density m/n turns out to be strongly…

A fundamental question in Computer Science is understanding when a specific class of problems go from being computationally easy to hard. Because of its generality and applications, the problem of Boolean Satisfiability (aka SAT) is often…

Specifying a proper input distribution is often a challenging task in simulation modeling. In practice, there may be multiple plausible distributions that can fit the input data reasonably well, especially when the data volume is not large.…

A constant-rate multi-mode system is a hybrid system that can switch freely among a finite set of modes, and whose dynamics is specified by a finite number of real-valued variables with mode-dependent constant rates. Alur, Wojtczak, and…

We consider a many-fermion model which exhibits a transition from a superconducting to a rotational phase with variation of a parameter in its Hamiltonian. The model has analytical solutions in its two limits due to the presence of…