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We present an algorithm that can efficiently compute a broad class of inferences for discrete-time imprecise Markov chains, a generalised type of Markov chains that allows one to take into account partially specified probabilities and other…
Labeled infinite trees provide combinatorial interpretations for many integer sequences generated by nested recurrence relations. Typically, such sequences are monotone increasing. Several of these sequences also have straightforward…
Concave mirrors are fundamental optical elements, yet some easily observed behaviors are rarely addressed in standard textbooks, such as the formation of multiple reflected images. Here we investigate self-imaging -- where the observer is…
Power system voltage regulation is crucial to maintain power quality while integrating intermittent renewable resources in distribution grids. However, the system model on the grid edge is often unknown, making it difficult to model…
Deterministic complex networks that use iterative generation algorithms have been found to more closely mirror properties found in real world networks than the traditional uniform random graph models. In this paper we introduce a new,…
The defining property of an artificial physical self-replicating system, such as a self-replicating robot, is that it has the ability to make copies of itself from basic parts. Three questions that immediately arises in the study of such…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
When the network is reconstructed, two types of errors can occur: false positive and false negative errors about the presence or absence of links. In this paper, the influence of these two errors on the vertex degree distribution is…
We give rates of convergence in the strong invariance principle for stationary sequences satisfying some projective criteria. The conditions are expressed in terms of conditional expectations of partial sums of the initial sequence. Our…
We present a recurrence-transience classification for discrete-time Markov chains on manifolds with negative curvature. Our classification depends only on geometric quantities associated to the increments of the chain, defined via the…
The usual setting for learning the structure and parameters of a graphical model assumes the availability of independent samples produced from the corresponding multivariate probability distribution. However, for many models the mixing time…
Unsupervised learning makes manifest the underlying structure of data without curated training and specific problem definitions. However, the inference of relationships between data points is frustrated by the `curse of dimensionality' in…
Repeat proteins are made with tandem copies of similar amino acid stretches that fold into elongated architectures. Due to their symmetry, these proteins constitute excellent model systems to investigate how evolution relates to structure,…
An inversion sequence of length $n$ is an integer sequence $e=e_{1}e_{2}\dots e_{n}$ such that $0\leq e_{i}<i$ for each $i$. Corteel--Martinez--Savage--Weselcouch and Mansour--Shattuck began the study of patterns in inversion sequences,…
Phylogenetic mixture models, in which the sites in sequences undergo different substitution processes along the same or different trees, allow the description of heterogeneous evolutionary processes. As data sets consisting of longer…
The nonnegative inverse eigenvalue problem (NIEP) asks which lists of $n$ complex numbers (counting multiplicity) occur as the eigenvalues of some $n$-by-$n$ entry-wise nonnegative matrix. The NIEP has a long history and is a known hard…
We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly…
The dynamics of coupled intermittent maps is used to model the correlated structure of genomic sequences. The use of intermittent maps, as opposed to other simple chaotic maps, is particularly suited for the production of long range…
We exhibit a one to one correspondence between some universal probabilistic properties of the ordering coordinate of one-dimensional Ising-like models and a class of continuous time random walks. This correspondence provides an new…
In a large class of statistical inverse problems it is necessary to suppose that the transformation that is inverted is known. Although, in many applications, it is unrealistic to make this assumption, the problem is often insoluble without…