Related papers: Transients from Initial Conditions: A Perturbative…
Transformers trained in low precision can suffer forward-error amplification. We give a first-order, module-wise theory that predicts when and where errors grow. For self-attention we derive a per-layer bound that factorizes into three…
The conventional method of generating initial conditions for cosmological N-body simulations introduces a significant error in the real-space statistical properties of the particles. More specifically, the finite box size leads to a…
We consider the non-equilibrium dynamics of disordered systems as defined by a master equation involving transition rates between configurations (detailed balance is not assumed). To compute the important dynamical time scales in…
Non-Markovian models have great expressive power, at the cost of complex analysis of the stochastic process. The method of Stochastic State Classes (SSCs) derives closed-form analytical expressions for the joint Probability Density…
We implement a new and accurate numerical entropic scheme to investigate the first-order transition features of the triangular Ising model with nearest-neighbor ($J_{nn}$) and next-nearest-neighbor ($J_{nnn}$) antiferromagnetic interactions…
Time series forecasting is an important problem, with many real world applications. Ensembles of deep neural networks have recently achieved impressive forecasting accuracy, but such large ensembles are impractical in many real world…
Measurement-induced phase transition (MIPT) describes the nonanalytical change of the entanglement entropy resulting from the interplay between measurement and unitary evolution. In this paper, we investigate the relaxation critical…
Classically, the time complexity of a first-order method is estimated by its number of gradient computations. In this paper, we study a more refined complexity by taking into account the `lingering' of gradients: once a gradient is computed…
Fastest arrival events, where the first among many diffusing particles reaches a target, are central in triggering signal initiation in molecular stochastic systems. Classical approaches to simulate such events rely on full trajectory…
Temporal correlation for randomly growing interfaces in the KPZ universality class is a topic of recent interest. Most of the works so far have been concentrated on the zero temperature model of exponential last passage percolation, and…
We give evidence of a clear structural signature of the glass transition, in terms of a static correlation length with the same dependence on the system size which is typical of critical phenomena. Our approach is to introduce an external,…
We present general results for the contact process by a method which applies to all transitive graphs of bounded degree, including graphs of exponential growth. The model's infection rates are varied through a control parameter, for which…
A transfer matrix scaling technique is developed for randomly diluted systems, and applied to the site-diluted Ising model on a square lattice in two dimensions. For each allowed disorder configuration between two adjacent columns, the…
We investigate the forcing-induced transient between statistically stationary and cyclostationary states. The transient dynamics of a turbulent supersonic twin-rectangular jet flow, forced symmetrically at a Strouhal number of 0.9, are…
We present the statistical method as a direct extension of the mean first-passage time concept to the analysis of molecular dynamics simulation data of a phase transformation. According to the method, the mean first-passage time…
It has long been known that a uniform distribution of matter cannot produce a Poisson distribution of density fluctuations on very large scales $1/k > ct$ by the motion of discrete particles over timescale $t$. The constraint is part of…
Persistence, defined as the probability that a fluctuating signal has not reached a threshold up to a given observation time, plays a crucial role in the theory of random processes. It quantifies the kinetics of processes as varied as phase…
Imitation learning (IL) is notably effective for robotic tasks where directly programming behaviors or defining optimal control costs is challenging. In this work, we address a scenario where the imitator relies solely on observed behavior…
Piecewise Diffusion Markov Processes (PDifMPs) are valuable for modelling systems where continuous dynamics are interrupted by sudden shifts and/or changes in drift and diffusion. The first-passage time (FPT) in such models plays a central…
The set-up of the initial conditions in cosmological N-body simulations is usually implemented by rescaling the desired low-redshift linear power spectrum to the required starting redshift consistently with the Newtonian evolution of the…