Related papers: Phase transition in the knapsack problem
Phase transitions generically occur in random matrix models as the parameters in the joint probability distribution of the random variables are varied. They affect all main features of the theory and the interpretation of statistical models…
In the Knapsack problem, one is given the task of packing a knapsack of a given size with items in order to gain a packing with a high profit value. An important connection to the $(\max,+)$-convolution problem has been established, where…
Many complex systems satisfy a set of constraints on their degrees of freedom, and at the same time, they are able to work and adapt to different conditions. Here, we describe the emergence of this ability in a simplified model in which the…
We give an introduction to phase transitions in the steady states of systems that evolve stochastically with equilibrium and nonequilibrium dynamics, the latter defined as those that do not possess a time-reversal symmetry. We try as much…
A known limitation of time-dependent mean-field approaches is a lack of quantum tunneling for collective motions such as in sub-barrier fusion reactions. As a first step toward a solution, a time-dependent model is considered using a…
A new mean field statistical mechanics model of two interacting groups of spins is introduced and the phase transition studied in terms of their relative size. A jump of the average magnetization is found for large values of the mutual…
The elsewhere surmised topological origin of phase transitions is given here new important evidence through the analytic study of an exactly solvable model for which both topology and thermodynamics are worked out. The model is a mean-field…
Scaling properties in financial fluctuations are reviewed from the standpoint of statistical physics. We firstly show theoretically that the balance of demand and supply enhances fluctuations due to the underlying phase transition…
An instance of a random constraint satisfaction problem defines a random subset S (the set of solutions) of a large product space (the set of assignments). We consider two prototypical problem ensembles (random k-satisfiability and…
We consider fluctuations of the time-averaged current in the one-dimensional weakly-asymmetric exclusion process on a ring. The optimal density profile which sustains a given fluctuation exhibits an instability for low enough currents,…
It is shown how simple assumptions lead to piecewise linear behavior, which is observed in certain phase transitions.
We study the large-time behavior of a class of periodically driven macroscopic systems. We find, for a certain range of the parameters of either the system or the driving fields, the time-averaged asymptotic behavior effectively is that of…
Rollout algorithms have demonstrated excellent performance on a variety of dynamic and discrete optimization problems. Interpreted as an approximate dynamic programming algorithm, a rollout algorithm estimates the value-to-go at each…
Repulsive point processes arise in models where competition forces entities to be more spread apart than if placed independently. Simulation of these types of processes can be accomplished using dominated coupling from the past with a…
In the online general knapsack problem, an algorithm is presented with an item $x=(s,v)$ of size $s$ and value $v$ and must irrevocably choose to pack such an item into the knapsack or reject it before the next item appears. The goal is to…
We review the connection between statistical mechanics and the analysis of random optimization problems, with particular emphasis on the random k-SAT problem. We discuss and characterize the different phase transitions that are met in these…
Phase transitions between two competing vacua of a given theory are quite common in physics. We discuss how to construct the space-time solutions that allow the description of phase transitions between different branches (or asymptotics) of…
A heuristic model procedure for determining satisfiability of CNF-formulae is set up and described by nonlinear recursion relations for m (number of clauses), n (number of variables) and clause filling k. The system mimicked by the…
Drift analysis is a powerful tool for analyzing the time complexity of evolutionary algorithms. However, it requires manual construction of drift functions to bound hitting time for each specific algorithm and problem. To address this…
Recent research indicates that many convex optimization problems with random constraints exhibit a phase transition as the number of constraints increases. For example, this phenomenon emerges in the $\ell_1$ minimization method for…