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We study the dynamics of multimode polariton lasing in organic microcavities by using a second-order cumulant equation approach. By inspecting the time evolution of the photon mode occupations, we show that if multiple lasing peaks are…
We propose a Cholesky factor parameterization of correlation matrices that facilitates a priori restrictions on the correlation matrix. It is a smooth and differentiable transform that allows additional boundary constraints on the…
Chain-of-Thought (CoT) is often viewed as a window into LLM decision-making, yet recent work suggests it may function merely as post-hoc rationalization. This raises a critical alignment question: Does the reasoning trace causally shape…
We consider additive functionals of Markov processes in continuous time with general (metric) state spaces. We derive concentration bounds for their exponential moments and moments of finite order. Applications include diffusions,…
While it is an important problem to identify the existence of causal associations between two components of a multivariate time series, a topic addressed in Runge et al. (2012), it is even more important to assess the strength of their…
Transitions between solid-like and fluid-like states in living tissues have been found in steps of embryonic development and in stages of disease progression. Our current understanding of these transitions has been guided by experimental…
The ambiguities inherent in renormalization are considered when using mass-independent renormalization in massless theories that involve two coupling coupling constants. We review how there is no renormalization scheme in which the…
Consensus algorithms on networks have received increasing attention in recent years for various applications ranging from animal flocking to multi-vehicle co-ordination. Building on the established model for second-order consensus of…
We provide a review of recently-develop dynamical mean-field theory (DMFT) approaches to the general problem of strongly correlated electronic systems with disorder. We first describe the standard DMFT approach, which is exact in the limit…
Couplings play a central role in the analysis of Markov chain Monte Carlo algorithms and appear increasingly often in the algorithms themselves, e.g. in convergence diagnostics, parallelization, and variance reduction techniques. Existing…
In real magnets the tendency towards ferromagnetism, promoted by exchange coupling, is usually frustrated by dipolar interaction. As a result, the uniformly ordered phase is replaced by modulated (multi-domain) phases, characterized by…
A fundamental assumption of the dynamical density functional theory (DDFT) of colloidal systems is that a grand-canonical free energy functional may be employed to generate the thermodynamic driving forces. Using one-dimensional hard-rods…
In a quenched mesoscopic fluid, modelling transport processes at high densities, we perform computer simulations of the single particle energy autocorrelation function C_e(t), which is essentially a return probability. This is done to test…
Individuals are always limited by some inelastic resources, such as time and energy, which restrict them to dedicate to social interaction and limit their contact capacity. Contact capacity plays an important role in dynamics of social…
We apply the macroscopic fluctuation theory (MFT) to study the large-scale dynamical properties of Brownian particles with arbitrary pairwise interaction. By combining it with standard results of equilibrium statistical mechanics for the…
We study the dynamics of long-wavelength fluctuations in one-dimensional (1D) many-particle systems as described by self-consistent mode-coupling theory. The corresponding nonlinear integro-differential equations for the relevant…
Selective rationalization has become a common mechanism to ensure that predictive models reveal how they use any available features. The selection may be soft or hard, and identifies a subset of input features relevant for prediction. The…
The dependence of the dynamics of open quantum systems upon initial correlations between the system and environment is an utterly important yet poorly understood subject. For technical convenience most prior studies assume factorizable…
Mixed order phase transitions (MOT), which display discontinuous order parameter and diverging correlation length, appear in several seemingly unrelated settings ranging from equilibrium models with long-range interactions to models far…
In this paper, we consider a leader-following consensus problem of a group of autonomous agents with time-varying coupling delays. Two different cases of coupling topologies are investigated. At first, a necessary and sufficient condition…