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The ability to store data in the DNA of a living organism has applications in a variety of areas including synthetic biology and watermarking of patented genetically-modified organisms. Data stored in this medium is subject to errors…
Large deviation theory is a branch of probability theory that is devoted to a study of the "rate" at which empirical estimates of various quantities converge to their true values. The object of study in this paper is the rate at which…
A tacit assumption in linear regression is that (response, predictor)-pairs correspond to identical observational units. A series of recent works have studied scenarios in which this assumption is violated under terms such as ``Unlabeled…
Two strings are considered to have parameterized matching when there exists a bijection of the parameterized alphabet onto itself such that it transforms one string to another. Parameterized matching has application in software duplication…
The two strands of a DNA molecule with a repetitive sequence can pair into many different basepairing patterns. For perfectly periodic sequences, early bulk experiments of Poerschke indicate the existence of a sliding process, permitting…
We study very simple sorting algorithms based on a probabilistic comparator model. In our model, errors in comparing two elements are due to (1) the energy or effort put in the comparison and (2) the difference between the compared…
We study the problem of similarity detection by sequence alignment with gaps, using a recently established theoretical framework based on the morphology of alignment paths. Alignments of sequences without mutual correlations are found to…
State aggregation aims to reduce the computational complexity of solving Markov Decision Processes (MDPs) while preserving the performance of the original system. A fundamental challenge lies in optimizing policies within the aggregated, or…
At present, there have been suggested two types of physical mechanism that may facilitate preferential pairing between DNA molecules, with identical or similar base pair texts, without separation of base pairs. One solely relies on base…
Network reconstruction consists in determining the unobserved pairwise couplings between $N$ nodes given only observational data on the resulting behavior that is conditioned on those couplings -- typically a time-series or independent…
Stein's method of exchangeable pairs is examined through five examples in relation to Poisson and normal distribution approximation. In particular, in the case where the exchangeable pair is constructed from a reversible Markov chain, we…
Base pair mismatch can relieve mechanical stress in highly strained DNA molecules, but how it affects their kinetic stability is not known. Using single-molecule Fluorescence Resonance Energy Transfer (FRET), we measured the lifetimes of…
In the analysis of Markov chains and processes, it is sometimes convenient to replace an unbounded state space with a "truncated" bounded state space. When such a replacement is made, one often wants to know whether the equilibrium behavior…
A variety of selection-mutation models for DNA (or RNA) sequences, well known in molecular evolution, can be translated into a model of coupled Ising quantum chains. This correspondence is used to investigate the genetic variability and…
Let $({\mathcal{T}}_{*t})$ be a predual quantum Markov semigroup acting on the full 2 x 2 matrix algebra and having an absorbing pure state. We prove that for any initial state $\omega$, the net of orthogonal measures representing the net…
RNA motifs typically consist of short, modular patterns that include base pairs formed within and between modules. Estimating the abundance of these patterns is of fundamental importance for assessing the statistical significance of matches…
Large-scale multiple testing tasks often exhibit dependence, and leveraging the dependence between individual tests is still one challenging and important problem in statistics. With recent advances in graphical models, it is feasible to…
We establish a simple variance inequality for U-statistics whose underlying sequence of random variables is an ergodic Markov Chain. The constants in this inequality are explicit and depend on computable bounds on the mixing rate of the…
This paper gives a method for computing distributions associated with patterns in the state sequence of a hidden Markov model, conditional on observing all or part of the observation sequence. Probabilities are computed for very general…
The first paper in this series introduced a \emph{short-to-long mixing} condition that captures mean-field GOE/GUE edge universality in the supercritical sparsity regime, for symmetric/Hermitian random matrices with independent entries and…