Related papers: Algebraic approach to directed stochastic avalanch…
The Abelian Sandpile Model is a cellular automaton whose discrete dynamics reaches an out-of-equilibrium steady state resembling avalanches in piles of sand. The fundamental moves defining the dynamics are encoded by the toppling rules. The…
We study the patterns formed by adding $N$ sand-grains at a single site on an initial periodic background in the Abelian sandpile models, and relaxing the configuration. When the heights at all sites in the initial background are low…
The abelian sandpile model in two dimensions does not show the type of critical behavior familar from equilibrium systems. Rather, the properties of the stationary state follow from the condition that an avalanche started at a distance r…
Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…
This thesis is devoted to the study of extreme value statistics in stochastic processes and their applications. In the first part, we obtain exact analytical results on the extreme value statistics of both discrete-time and continuous-time…
The latent stochastic block model is a flexible and widely used statistical model for the analysis of network data. Extensions of this model to a dynamic context often fail to capture the persistence of edges in contiguous network…
To explain day-to-day (DTD) route-choice behaviors and traffic dynamics observed in a series of lab experiments, Part I of this research proposed a discrete choice-based analytical dynamic model (Qi et al., 2023). Although the deterministic…
An array of spheres descending slowly through a viscous fluid always clumps [J.M. Crowley, J. Fluid Mech. {\bf 45}, 151 (1971)]. We show that anisotropic particle shape qualitatively transforms this iconic instability of collective…
A point source on a plane constantly emits particles which rapidly diffuse and then stick to a growing cluster. The growth probability of a cluster is presented as a sum over all possible scenarios leading to the same final shape. The…
The Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) method is a cutting-edge distributed optimization algorithm known for its superior numerical performance. It relies on each agent transmitting information to a central…
We propose a new stochastic dual coordinate ascent technique that can be applied to a wide range of regularized learning problems. Our method is based on Alternating Direction Multiplier Method (ADMM) to deal with complex regularization…
The two dimensional directed sandpile with dissipation is transformed into a (1+1) dimensional problem with discrete space and continuous `time'. The master equation for the conditional probability that K grains preserve their initial order…
This paper establishes a robust link between quantum dynamics and classical ones by deriving probabilistic representation for both continuous time and discrete time quantum walks. We first adapt Molchanov formula, originally employed in the…
Elastic systems, such as magnetic domain walls, density waves, contact lines, and cracks, are all pinned by substrate disorder. When driven, they move via successive jumps called avalanches, with power law distributions of size, duration…
A theoretical analysis of the earthquake prediction problem in space-time is presented. We find an explicit structure of the optimal strategy and its relation to the generalized error diagram. This study is a generalization of the…
We study the transport of active Brownian particles (ABPs) in three-dimensional (3D) oscillatory geometries, which are spatially periodic. We establish a generalized Fick-Jacobs approach, which reduces a 3D system to an effective 1D system…
We recently demonstrated that standard fixed-time lattice random-walk models cannot be modified to properly represent biased diffusion processes in more than two dimensions. The origin of this fundamental limitation appears to be the fact…
Classical particles driven through periodically modulated potential energy landscapes are predicted to follow a Devil's staircase hierarchy of commensurate trajectories depending on the orientation of the driving force. Recent experiments…
Current decision support systems address domains that are heterogeneous in nature and becoming progressively larger. Such systems often require the input of expert judgement about a variety of different fields and an intensive computational…
Increasingly larger data sets of processes in space and time ask for statistical models and methods that can cope with such data. We show that the solution of a stochastic advection-diffusion partial differential equation provides a…