Related papers: Cellular Dynamical Mean Field Approach to Strongly…

Strong electronic correlations pose one of the biggest challenges to solid state theory. We review recently developed methods that address this problem by starting with the local, eminently important correlations of dynamical mean field…

Electronic correlations beyond static mean-field theories are of fundamental importance in describing the properties of complex materials - such as transition-metal oxides - where the low-energy physics is driven by localized d or f…

From ancient philosophers to modern economists, biologists, and other researchers, there has been a continuous effort to unveil causal relations. The most formidable challenge lies in deducing the nature of the causal relationship: whether…

We develop a unified theory that encompasses the macroscopic dynamics of recurrent interactions of binary units within arbitrary network architectures. Using the martingale theory, our mathematical analysis provides a complete description…

A simple relation of the order of $n$ abstract objects generates an $n-2$ dimensional basis of three dimensional vectors. A cellular automaton-like model of evolution of this system is postulated. During this evolution, some quantities…

Ordered polarity alignment of a cell population plays a vital role in biology, such as in hair follicle alignment and asymmetric cell division. Here, we propose a theoretical framework for the understanding of generic dynamical properties…

Dynamical Mean-Field Theory (DMFT) is a powerful theoretical framework for analyzing systems with many interacting degrees of freedom. This tutorial provides an accessible introduction to DMFT. We begin with a linear model where the DMFT…

To simulate a macroscopic system from a simulation cell, a direct summation of the elastic fields produced by periodic images can be used. If the cell contains a non-zero elastic dipole component, the sum is known to be conditionally…

Mean-field theory is a powerful tool for studying large neural networks. However, when the system is composed of a few neurons, macroscopic differences between the mean-field approximation and the real behavior of the network can arise.…

We introduce an extension of the dynamical mean field approximation (DMFA) which retains the causal properties and generality of the DMFA, but allows for systematic inclusion of non-local corrections. Our technique maps the problem to a…

In this paper, we adopt results in nonlinear time series analysis for causal inference in dynamical settings.~Our motivation is policy analysis with panel data, particularly through the use of "synthetic control" methods. These methods…

This work focuses on the mean field stochastic partial differential equations with nonlinear kernels. We first prove the existence and uniqueness of strong and weak solutions for mean field stochastic partial differential equations in the…

A uniform derivation is presented of the self-consistent field equations in a finite basis set. Both restricted and unrestricted Hartree-Fock (HF) theory as well as various density functional (DF) approximations are considered. The unitary…

We introduce a model for describing the dynamics of large numbers of interacting cells. The fundamental dynamical variables in the model are sub-cellular elements, which interact with each other through phenomenological intra- and…

Dynamic trees are mixtures of tree structured belief networks. They solve some of the problems of fixed tree networks at the cost of making exact inference intractable. For this reason approximate methods such as sampling or mean field…

We predict spontaneous nematic order in an ensemble of active force generators with elastic interactions as a minimal model for early nematic alignment of short stress fibers in non-motile, adhered cells. Mean-field theory is formally…

A self-consistent many-body approach is proposed to build a first-principles crystal field theory, where crystal field parameters are calculated ab initio. Many-body theory is used to write the energy of the interacting system as a function…

We study locally interacting processes in discrete time, often called probabilistic cellular automata, indexed by locally finite graphs. For infinite regular trees and certain generalized Galton-Watson trees, we show that the marginal…

We review some aspects of the realistic implementation of the dynamical mean-field method. We extend the techniques introduced in Ref.[A. Georges, G. Kotliar, W. Krauth, and M.J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996)] to include the…

A dynamical model based on the two-fluid dynamical equations with energy generation and loss is obtained and used to investigate the self-generated magnetic fields in high-temperature dense plasmas such as the solar core. The…