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We introduce a new version of dynamic time warping for samples of observed event times that are modeled as time-warped intensity processes. Our approach is devel- oped within a framework where for each experimental unit or subject in a…

Modern distributed systems include a class of applications in which non-functional requirements are important. In particular, these applications include multimedia facilities where real time constraints are crucial to their correct…

There are two methods for counting the number of occurrences of a string in another large string. One is to count the number of places where the string is found. The other is to determine how many pieces of string can be extracted without…

This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…

Stochastic kinetic models are often used to describe complex biological processes. Typically these models are analytically intractable and have unknown parameters which need to be estimated from observed data. Ideally we would have…

A simple model of an irreversible process is introduced. The equation of iterations in the model includes a noise generation term. We study the properties of the system when the noise generation term is a stochastic process (e.g. a random…

We study the full counting statistics of current of large open systems through the application of random matrix theory to transition-rate matrices. We develop a method for calculating the ensemble-averaged current-cumulant generating…

Cumulant mapping has been recently suggested [Frasinski, Phys. Chem. Chem. Phys. 24, 207767 (2022)] as an efficient approach to observing multi-particle fragmentation pathways, while bypassing the restrictions of the usual…

The quantum measurement process by a single-electron transistor or a quantum point contact coupled to a quantum bit is studied. We find a unified description of the statistics of the monitored quantity, the current, in the regime of strong…

Data assimilation refers to the process of obtaining an estimate of a system's state using a model for the system's time evolution and a time series of measurements that are possibly noisy and incomplete. However, for practical reasons, the…

Methods for the reduction of the complexity of computational problems are presented, as well as their connections to renormalization, scaling, and irreversible statistical mechanics. Several statistically stationary cases are analyzed; for…

Statistical significance testing is widely accepted as a means to assess how well a difference in effectiveness reflects an actual difference between systems, as opposed to random noise because of the selection of topics. According to…

We propose testing procedures for the hypothesis that a given set of discrete observations may be formulated as a particular time series of counts with a specific conditional law. The new test statistics incorporate the empirical…

We present an adaptation of Stein's method of normal approximation to the study of both discrete- and continuous-time dynamical systems. We obtain new correlation-decay conditions on dynamical systems for a multivariate central limit…

In statistical physics and information theory, although the exponent of the partition function is often of our primary interest, there are cases where one needs more detailed information. In this paper, we present a general framework to…

This paper considers the problem of cardinality estimation in data stream applications. We present a statistical analysis of probabilistic counting algorithms, focusing on two techniques that use pseudo-random variates to form…

Starting from a dataset with input/output time series generated by multiple deterministic linear dynamical systems, this paper tackles the problem of automatically clustering these time series. We propose an extension to the so-called…

This paper is concerned with classes of models of stochastic reaction dynamics with time-scales separation. We demonstrate that the existence of the time-scale separation naturally leads to the application of the averaging principle and…

Traditional statistical inference considers relatively small data sets and the corresponding theoretical analysis focuses on the asymptotic behavior of a statistical estimator when the number of samples approaches infinity. However, many…

Suppose we observe a trajectory of length $n$ from an exponentially $\alpha$-mixing stochastic process over a finite but potentially large state space. We consider the problem of estimating the probability mass placed by the stationary…