Related papers: Clustering of large deviations in moving average p…
The impact of gradient noise on training deep models is widely acknowledged but not well understood. In this context, we study the distribution of gradients during training. We introduce a method, Gradient Clustering, to minimize the…
This paper addresses the aggregated monitoring problem for large-scale network systems with a few dedicated sensors. Full state estimation of such systems is often infeasible due to unobservability and/or computational infeasibility.…
Some models of clustering processes are formulated and analytically solved employing generating functions methods. Those models include events which result from combined action of the coagulation and fragmentation processes. Fragmentation…
The segmentation of data into stationary stretches also known as multiple change point problem is important for many applications in time series analysis as well as signal processing. Based on strong invariance principles, we analyse data…
In this paper, we consider asymptotic behaviors of multiscale multivalued stochastic systems with small noises. First of all, for general, fully coupled systems for multivalued stochastic differential equations of slow and fast motions with…
We develop an action formalism to calculate probabilities of rare events in cluster-cluster aggregation for arbitrary collision kernels and establish a pathwise large deviation principle with total mass being the rate. As an application,…
A new model that describes adsorption and clustering of particles on a surface is introduced. A {\it clustering} transition is found which separates between a phase of weakly correlated particle distributions and a phase of strongly…
We analyse large deviations of time-averaged quantities in stochastic processes with long-range memory, where the dynamics at time t depends itself on the value q_t of the time-averaged quantity. First we consider the elephant random walk…
We study a system of interacting particles that randomly react to form new particles. The reaction flux is the rescaled number of reactions that take place in a time interval. We prove a dynamic large-deviation principle for the reaction…
We introduce a simple model of active transport for an ensemble of particles driven by an external shear flow. Active refers to the fact that the flow of the particles is modified by the distribution of particles itself. The model consists…
We analyze systems of clusters and interacting upon colliding---a collision between two clusters may lead to merging or fragmentation---and we also investigate the influence of additional spontaneous fragmentation events. We consider both…
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…
We propose a clustering-based approach for identifying coherent flow structures in continuous dynamical systems. We first treat a particle trajectory over a finite time interval as a high-dimensional data point and then cluster these data…
We propose a computationally simple framework for clustering functional data based on Gaussian-process-generated random projections. In this approach, each curve is first projected onto a large collection of independent Gaussian process…
The zero-range process is a stochastic interacting particle system that exhibits a condensation transition under certain conditions on the dynamics. It has recently been found that a small perturbation of a generic class of jump rates leads…
Distribution-level phasor measurement units, a.k.a, micro-PMUs, report a large volume of high resolution phasor measurements which constitute a variety of event signatures of different phenomena that occur all across power distribution…
Following the work of arXiv:2101.09512, we are interested in clustering a given multi-variate series in an unsupervised manner. We would like to segment and cluster the series such that the resulting blocks present in each cluster are…
Long memory or long range dependency is an important phenomenon that may arise in the analysis of time series or spatial data. Most of the definitions of long memory of a stationary process $X=\{X_1, X_2,\cdots,\}$ are based on the…
Fluctuation-dominated phase ordering refers to a steady state in which the magnitude of long-range order varies strongly owing to fluctuations, and to the associated coarsening phenomena during the approach to steady state. Strong…
The fluctuation scaling law has universally been observed in a wide variety of phenomena. For counting processes describing the number of events occurred during time intervals, it is expressed as a power function relationship between the…