Related papers: Mean Field Behavior of Cluster Dynamics
We formulate a novel technique for the detection of functional clusters in discrete event data. The advantage of this algorithm is that no prior knowledge of the number of functional groups is needed, as our procedure progressively combines…
Dynamical mean field theory and its cluster extensions provide a very useful approach for examining phase transitions in model Hamiltonians, and, in combination with electronic structure theory, constitute powerful methods to treat strongly…
A review of the Loop Algorithm, its generalizations, and its relation to some other Monte Carlo techniques is given. The loop algorithm is a Quantum Monte Carlo procedure which employs nonlocal changes of worldline configurations,…
We study, via Monte Carlo simulation, the dynamic critical behavior of the Chayes-Machta dynamics for the Fortuin-Kasteleyn random-cluster model, which generalizes the Swendsen-Wang dynamics for the q-state Potts ferromagnet to non-integer…
This paper studies a general class of stochastic population processes in which agents interact with one another over a network. Agents update their behaviors in a random and decentralized manner according to a policy that depends only on…
Monte Carlo algorithms, like the Swendsen-Wang and invaded-cluster, sample the Ising and Potts models asymptotically faster than single-spin Glauber dynamics do. Here, we generalize both algorithms to sample Potts lattice gauge theory by…
We establish the mean-field convergence for systems of points evolving along the gradient flow of their interaction energy when the interaction is the Coulomb potential or a super-coulombic Riesz potential, for the first time in arbitrary…
In this work we are interested in the mean-field formulation of kinetic models under control actions where the control is formulated through a model predictive control strategy (MPC) with varying horizon. The relation between the (usually…
Apart from the role the clustering coefficient plays in the definition of the small-world phenomena, it also has great relevance for practical problems involving networked dynamical systems. To study the impact of the clustering coefficient…
We present an efficient computational approach to sample the histories of nonlinear stochastic processes. This framework builds upon recent work on casting a $d$-dimensional stochastic dynamical system into a $d+1$-dimensional equilibrium…
Mean-field approximation is often used to explore the qualitative behaviour of phase transitions in classical spin models before employing computationally costly methods such as the Monte-Carlo techniques. We implement a 'lattice…
The asymptotic results that underlie applications of extreme random fields often assume that the variables are located on a regular discrete grid, identified with $\mathbb{Z}^2$, and that they satisfy stationarity and isotropy conditions.…
Generalized rules for building and flipping clusters in the quantum Monte Carlo loop algorithm are presented for the XXZ-model in a uniform magnetic field along the Z-axis. As is demonstrated for the Heisenberg antiferromagnet it is…
We study the speed of convergence of the Swendsen-Wang (SW) dynamics for the $q$-state ferromagnetic Potts model on the $n$-vertex complete graph, known as the mean-field model. The SW dynamics was introduced as an attractive alternative to…
We propose a model of network growth that generalizes the deactivation model previously suggested for complex networks. Several topological features of this generalized model, such as the degree distribution and clustering coefficient, have…
We perform numerical simulations to study static and dynamic critical behaviour of the 3d random-site Ising model. A distinct feature of our approach is a combination of the Metropolis, Swendsen-Wang, and Wolff Monte Carlo algorithms. For…
Nested sampling is an efficient algorithm for the calculation of the Bayesian evidence and posterior parameter probability distributions. It is based on the step-by-step exploration of the parameter space by Monte Carlo sampling with a…
Mean field limits are an important tool in the context of large-scale dynamical systems, in particular, when studying multiagent and interacting particle systems. While the continuous-time theory is well-developed, few works have considered…
We review Sweeny's algorithm for Monte Carlo simulations of the random cluster model. Straightforward implementations suffer from the problem of computational critical slowing down, where the computational effort per edge operation scales…
We discuss the analytic computation of autocorrelation functions for the generalized Hybrid Monte Carlo algorithm applied to free field theory and compare the results with numerical results for the $O(4)$ spin model in two dimensions. We…