Related papers: Sampling from the low temperature Potts model thro…
The problem of minimizing the Potts energy function frequently occurs in computer vision applications. One way to tackle this NP-hard problem was proposed by Kovtun [19,20]. It identifies a part of an optimal solution by running $k$ maxflow…
We discuss the efficiency of the so-called parallel tempering method to equilibrate glassy systems also at low temperatures. The main focus is on two structural glass models, SiO_2 and a Lennard-Jones system, but we also investigate a fully…
Many classical randomized algorithms (e.g., approximation algorithms for #P-complete problems) utilize the following random walk algorithm for {\em almost uniform sampling} from a state space $S$ of cardinality $N$: run a symmetric ergodic…
A method based on Monte Carlo sampling of the probability flows projected onto the subspace of one or more slow variables is proposed for investigation of dynamic and static properties of lattice spin systems. We illustrate the method by…
Particle splitting methods are considered for the estimation of rare events. The probability of interest is that a Markov process first enters a set $B$ before another set $A$, and it is assumed that this probability satisfies a large…
We analyze the mixing time of a natural local Markov chain (the Glauber dynamics) on configurations of the solid-on-solid model of statistical physics. This model has been proposed, among other things, as an idealization of the behavior of…
Thompson sampling (TS) is a class of algorithms for sequential decision-making, which requires maintaining a posterior distribution over a model. However, calculating exact posterior distributions is intractable for all but the simplest…
We describe a new sampling-based method to determine cuts in an undirected graph. For a graph (V, E), its cycle space is the family of all subsets of E that have even degree at each vertex. We prove that with high probability, sampling the…
A method is presented, which allows to sample directly low-temperature configurations of glassy systems, like spin glasses. The basic idea is to generate ground states and low lying excited configurations using a heuristic algorithm. Then,…
We give an efficient perfect sampling algorithm for weighted, connected induced subgraphs (or graphlets) of rooted, bounded degree graphs. Our algorithm utilizes a vertex-percolation process with a carefully chosen rejection filter and…
Spike-sorting techniques attempt to classify a series of noisy electrical waveforms according to the identity of the neurons that generated them. Existing techniques perform this classification ignoring several properties of actual neurons…
We give algorithms for approximating the partition function of the ferromagnetic $q$-color Potts model on graphs of maximum degree $d$. Our primary contribution is a fully polynomial-time approximation scheme for $d$-regular graphs with an…
We develop a new simulation technique based on path-integral molecular dynamics for calculating ground-state tunneling splitting patterns from ratios of symmetrized partition functions. In particular, molecular systems are rigorously…
This paper presents an algorithm for sampling random variables that allows to separation of the sampling process into subproblems by dividing the sample space into overlapping parts. The subproblems can be solved independently of each other…
The Potts model is one of the most popular spin models of statistical physics. The prevailing majority of work done so far corresponds to the lattice version of the model. However, many natural or man-made systems are much better described…
Filtering is concerned with the sequential estimation of the state, and uncertainties, of a Markovian system, given noisy observations. It is particularly difficult to achieve accurate filtering in complex dynamical systems, such as those…
I show how to run an N-time-step Markov chain simulation in a circular fashion, so that the state at time 0 follows the state at time N-1 in the same way as states at times t follow those at times t-1 for 0<t<N. This wrap-around of the…
We consider the problem of sampling from the distribution of measurement outcomes when applying a POVM to a superposition $|\Psi\rangle = \sum_{j=0}^{\chi-1} c_j |\psi_j\rangle$ of $\chi$ pure states. We relate this problem to that of…
We implemented a parallel version of the multicanonical algorithm and applied it to a variety of systems with phase transitions of first and second order. The parallelization relies on independent equilibrium simulations that only…
Given a semi-Markov law, using an additional parameter, we consider a family of stochastic flows corresponding to that law. Then we suitably select a particular flow, for which we obtain expressions of the meeting and merging probabilities…