Related papers: Mean Field Behavior of Cluster Dynamics
In this work we build a unifying framework to interpolate between density-driven and geometry-based algorithms for data clustering, and specifically, to connect the mean shift algorithm with spectral clustering at discrete and continuum…
We introduce $S_z$ spin-projection based on cluster mean-field theory and apply it to the ground state of strongly-correlated spin systems. In cluster mean-field, the ground state wavefunction is written as a factorized tensor product of…
We study the performance of a Wolff-type embedding algorithm for $RP^N$ $\sigma$-models. We find that the algorithm in which we update the embedded Ising model \`a la Swendsen-Wang has critical slowing-down as $z_\chi \approx 1$. If instead…
Decentralized algorithms have gained substantial interest owing to advancements in cloud computing, Internet of Things (IoT), intelligent transportation networks, and parallel processing over sensor networks. The convergence of such…
We present an optimized version of a cluster labeling algorithm previously introduced by the authors. This algorithm is well suited for large-scale Monte Carlo simulations of spin models using cluster dynamics on parallel computers with…
We analyze in a closed form the learning dynamics of stochastic gradient descent (SGD) for a single-layer neural network classifying a high-dimensional Gaussian mixture where each cluster is assigned one of two labels. This problem provides…
We discuss the short-time behavior of the majority vote dynamics on scale-free networks at the critical threshold. We introduce a heterogeneous mean-field theory on the critical short-time behavior of the majority-vote model on scale-free…
In this note, we consider generalizations of the Cucker-Smale dynamical system and we derive rigorously in Wasserstein's type topologies the mean-field limit (and propagation of chaos) to the Vlasov-type equation introduced in [12].Unlike…
Random networks with complex topology are common in Nature, describing systems as diverse as the world wide web or social and business networks. Recently, it has been demonstrated that most large networks for which topological information…
Recently we reported some interesting features of the Wolff's algorithm behavior when applied to the site-bond-correlated Ising model.Our main results were that a stronger correlation diminishes the autocorrelation time but it does not…
We describe a novel switching algorithm based on a ``reverse'' Monte Carlo method, in which the potential is stochastically modified before the system configuration is moved. This new algorithm facilitates a generalized formulation of…
We introduce perturbation and coupled-cluster theories based on a cluster mean-field reference for describing the ground state of strongly-correlated spin systems. In cluster mean-field, the ground state wavefunction is written as a simple…
We present a stochastic version of the mean-shift clustering algorithm. In this stochastic version a randomly chosen sequence of data points move according to partial gradient ascent steps of the objective function. Theoretical results…
We develop, clarify and test various aspects of cluster methods dynamical mean field methods using a soluble toy model as a benchmark. We find that the Cellular Dynamical Mean Field Theory (C-DMFT) converges very rapidly and compare its…
We applied a mean field approach to study clustering coefficients in Barabasi-Albert networks. We found that the local clustering in BA networks depends on the node degree. Analytic results have been compared to extensive numerical…
Simulations of the two-dimensional Ising and 3-state Potts models at their critical points are performed using the invaded cluster (IC) algorithm. It is argued that observables measured on a sub-lattice of size l should exhibit a crossover…
We apply the event-chain Monte Carlo algorithm to the three-dimensional ferromagnetic Heisenberg model. The algorithm is rejection-free and also realizes an irreversible Markov chain that satisfies global balance. The autocorrelation…
We study the zero-temperature Ising chain evolving according to the Swendsen-Wang dynamics. We determine analytically the domain length distribution and various ``historical'' characteristics, e.g., the density of unreacted domains is shown…
Rich out of equilibrium collective dynamics of strongly interacting large assemblies emerge in many areas of science. Some intriguing and not fully understood examples are the glassy arrest in atomic, molecular or colloidal systems,…
In the context of growing networks, we introduce a simple dynamical model that unifies the generic features of real networks: scale-free distribution of degree and the small world effect. While the average shortest path length increases…