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The scope of this paper is generative modeling through diffusion processes. An approach falling within this paradigm is the work of Song et al. (2021), which relies on a time-reversal argument to construct a diffusion process targeting the…
The search for similarity and dissimilarity measures on phylogenetic trees has been motivated by the computation of consensus trees, the search by similarity in phylogenetic databases, and the assessment of clustering results in…
We study the problem of transformation inversion on general Lie groups: a datum is transformed by an unknown group element, and the goal is to recover an inverse transformation that maps it back to the original data distribution. Such…
Determining crystal symmetry from powder X-ray diffraction is a central problem in materials characterization, yet multiple space groups can produce indistinguishable patterns, making automated classification difficult. We show that…
Suppose a finite set $X$ is repeatedly transformed by a sequence of permutations of a certain type acting on an initial element $x$ to produce a final state $y$. We investigate how 'different' the resulting state $y'$ to $y$ can be if a…
V. Levenshtein first proposed the sequence reconstruction problem in 2001. This problem studies the model where the same sequence from some set is transmitted over multiple channels, and the decoder receives the different outputs. Assume…
Understanding the space of probability measures on a metric space equipped with a Wasserstein distance is one of the fundamental questions in mathematical analysis. The Wasserstein metric has received a lot of attention in the machine…
Group testing is a method of identifying infected patients by performing tests on a pool of specimens collected from patients. For the case in which the test returns a false result with finite probability, we propose Bayesian inference and…
Computational asymmetry, i.e., the discrepancy between the complexity of transformations and the complexity of their inverses, is at the core of one-way transformations. We introduce a computational asymmetry function that measures the…
We investigate the number of inverted repeats observed in 37 complete genomes of bacteria. The number of inverted repeats observed is much higher than expected using Markovian models of DNA sequences in most of the eubacteria. By using the…
We report molecular dynamics simulations of the segregation of two overlapping chains in cylindrical confinement. We find that the entropic repulsion between the chains can be sufficiently strong to cause segregation on a time scale that is…
Motivated by Bourque and Pevzner's simulation study of the parsimony method for studying genome rearrangement, Berestycki and Durrett used techniques from random graph theory to prove that the minimum parsimony distance after iterating the…
Several cycle lexicographical orders are found to describe the relative likelihood of elements of the random walks on the symmetric group generated by the conjugacy classes of transpositions, 3-cycles, and n-cycles. Spectral analysis finds…
We study how the dynamic equilibrium of the reversible protein-protein binding network in yeast Saccharomyces cerevisiae responds to large changes in abundances of individual proteins. The magnitude of shifts between free and bound…
In this paper, we use the Bayesian inversion approach to study the data assimilation problem for a family of tumor growth models described by porous-medium type equations. The models contain uncertain parameters and are indexed by a…
Crossing symmetry asserts that particles are indistinguishable from anti-particles traveling back in time. In quantum field theory, this statement translates to the long-standing conjecture that probabilities for observing the two scenarios…
Temporal evolution of a clonal bacterial population is modelled taking into account reversible mutation and selection mechanisms. For the mutation model, an efficient algorithm is proposed to verify whether experimental data can be…
Motile cells often explore natural environments characterized by a high degree of structural complexity. Moreover cell motility is also intrinsically noisy due to spontaneous random reorientation and speed fluctuations. This interplay of…
We prove existence of the large deviation principle, with a proper convex rate function, for the distribution of the renormalized distance from the origin of a random walk on a free product of finitely generated groups. As a consequence, we…
Controlling the phases of matter is a challenge that spans from condensed materials to biological systems. Here, by imposing a geometric boundary condition, we study controlled collective motion of Escherichia coli bacteria. A circular…