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Parallel tempering, also known as replica exchange sampling, is an important method for simulating complex systems. In this algorithm simulations are conducted in parallel at a series of temperatures, and the key feature of the algorithm is…
The Extended Fermi-Hubbard model is a rather studied Hamiltonian due to both its many applications and a rich phase diagram. Here we prove that all the phase transitions encoded in its one dimensional version are detectable via non-local…
Restricted Boltzmann Machines are a class of undirected graphical models that play a key role in deep learning and unsupervised learning. In this study, we prove a phase transition phenomenon in the mixing time of the Gibbs sampler for a…
The widespread popularity of replica exchange and expanded ensemble algorithms for simulating complex molecular systems in chemistry and biophysics has generated much interest in enhancing phase space mixing of these protocols, thus…
The possible paralelism existing between phase transitions and fracture in disordered materials, is discussed using the well-known Fiber Bundle Models and a probabilistic approach suited to smooth fluctuations near the critical point. Two…
We study the phases and phase transition lines of the finite temperature G(2) Higgs model. Our work is based on an efficient local hybrid Monte-Carlo algorithm which allows for accurate measurements of expectation values, histograms and…
In an experimental study of single enzyme reactions, it has been proposed that the rate constants of the enzymatic reactions fluctuate randomly, according to a given distribution. To quantify the uncertainty arising from random rate…
We present a study of the phase diagram of a random optimization problem in presence of quantum fluctuations. Our main result is the characterization of the nature of the phase transition, which we find to be a first-order quantum phase…
Yang et al. (2016) proved that the symmetric random walk Metropolis--Hastings algorithm for Bayesian variable selection is rapidly mixing under mild high-dimensional assumptions. We propose a novel MCMC sampler using an informed proposal…
Multi-task learning leverages shared information among data sets to improve the learning performance of individual tasks. The paper applies this framework for data where each task is a phase-shifted periodic time series. In particular, we…
A popular method for sampling from high-dimensional distributions is the \emph{Gibbs sampler}, which iteratively resamples sites from the conditional distribution of the desired measure given the values of the other coordinates. It is…
In this paper we provide a new analysis of the SEM algorithm. Unlike previous work, we focus on the analysis of a single run of the algorithm. First, we discuss the algorithm for general mixture distributions. Second, we consider Gaussian…
Exponential random graph models have become increasingly important in the study of modern networks ranging from social networks, economic networks, to biological networks. They seek to capture a wide variety of common network tendencies…
We construct an adaptive independent Metropolis-Hastings sampler that uses a mixture of normals as a proposal distribution. To take full advantage of the potential of adaptive sampling our algorithm updates the mixture of normals…
It has been recently shown that the double exchange Hamiltonian, with weak antiferromagnetic interactions, has a richer variety of first and second order transitions than previously anticipated, and that such transitions are consistent with…
The effects of locally random magnetic fields are considered in a nonequilibrium Ising model defined on a square lattice with nearest-neighbors interactions. In order to generate the random magnetic fields, we have considered random…
The degenerate Blume-Emery-Griffiths (DBEG) model has recently been introduced in the study of martensitic transformation problems. This model has the same Hamiltonian as the standard Blume-Emery-Griffiths (BEG) model but, to take into…
We study the non-equilibrium phase diagram of a fully-connected Ising $p$-spin model, for generic $p>2$, and investigate its robustness with respect to the inclusion of spin-wave fluctuations, resulting from a ferromagnetic, short-range…
Shuffling is the process of rearranging a sequence of elements into a random order such that any permutation occurs with equal probability. It is an important building block in a plethora of techniques used in virtually all scientific…
The possibility to apply phase-space methods to many-body interacting systems might provide accurate descriptions of correlations with a reduced numerical cost. For instance, the so--called stochastic mean-field phase-space approach, where…