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Memory dephasing and its impact on the rate of entanglement generation in quantum repeaters is addressed. For systems that rely on probabilistic schemes for entanglement distribution and connection, we estimate the maximum achievable rate…
We consider a stochastic search model with resetting for an unknown stationary target $a\in\mathbb{R}^d,\ d\ge1$, with known distribution $\mu$. The searcher begins at the origin and performs Brownian motion with diffusion coefficient $D$.…
In Partially Observable Markov Decision Processes, integrating an agent's history into memory poses a significant challenge for decision-making. Traditional imitation learning, relying on observation-action pairs for expert demonstrations,…
We provide and analyze the high order algorithms for the model describing the functional distributions of particles performing anomalous motion with power-law jump length and tempered power-law waiting time. The model is derived in [Wu,…
This paper considers the problem of reconstructing missing parts of functions based on their observed segments. It provides, for Gaussian processes and arbitrary bijective transformations thereof, theoretical expressions for the…
We study path-complete Lyapunov functions, which are stability criteria for switched systems, described by a combinatorial component (namely, an automaton), and a functional component (a set of candidate Lyapunov functions, called 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…
Random walks on lattices with preferential relocation to previously visited sites provide a simple framework for modeling the displacements of animals and humans. When the lattice contains a few impurities or resource sites where the walker…
We develop an estimation methodology for a factor model for high-dimensional matrix-valued time series, where common stochastic trends and common stationary factors can be present. We study, in particular, the estimation of (row and column)…
We describe an exact approach for calculating transition probabilities and waiting times in finite-state discrete-time Markov processes. All the states and the rules for transitions between them must be known in advance. We can then…
We consider the problem of computing first-passage time distributions for reaction processes modelled by master equations. We show that this generally intractable class of problems is equivalent to a sequential Bayesian inference problem…
Let $V(k)$ denote the waiting time, the number of trials needed to get a consecutive $k$ ones. We propose recurrence algorithms for the probability distribution function (pdf) and the probability generating function (pgf) of $V(k)$ in…
This paper introduces a discrete-time fractional Poisson process defined as a renewal process, where the waiting times follow a discrete Mittag-Leffler distribution. We investigate its fundamental properties by explicitly deriving the…
This work presents an approach to express the second moment of the completion time with a preempt-repeat model job processed on a machine subject to stochastic breakdowns by some distribution characters of the uptime, downtime and…
We study stochastic approximation algorithms with Markovian noise and constant step-size $\alpha$. We develop a method based on infinitesimal generator comparisons to study the bias of the algorithm, which is the expected difference between…
Exemplar-based class-incremental learning is to recognize new classes while not forgetting old ones, whose samples can only be saved in limited memory. The ratio fluctuation of new samples to old exemplars, which is caused by the variation…
Temporal difference methods enable efficient estimation of value functions in reinforcement learning in an incremental fashion, and are of broader interest because they correspond learning as observed in biological systems. Standard value…
Stable subordinators, and more general subordinators possessing power law probability tails, have been widely used in the context of subdiffusions, where particles get trapped or immobile in a number of time periods, called constant…
The execution time of programs is a key element in many areas of computer science, mainly those where achieving good performance (e.g., scheduling in cloud computing) or a predictable one (e.g., meeting deadlines in embedded systems) is the…
Iterative phase retrieval algorithms typically employ projections onto constraint subspaces to recover the unknown phases in the Fourier transform of an image, or, in the case of x-ray crystallography, the electron density of a molecule.…