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Bacteria can form a great variety of spatially heterogeneous cell density patterns, ranging from simple concentric rings to dynamical spiral waves appearing in growing colonies. These pattern formation phenomena are important as they…
This paper investigates the symmetry properties of basins of attraction and their boundaries in equivariant dynamical systems. While the symmetry groups of compact attractors are well understood, the corresponding analysis for non-compact…
The paper is grown from the lecture course "Metric projective geometry" which I hold at the summer school "Finsler geometry with applications" at Karlovassi, Samos, in 2014, and at the workshop before the 8th seminar on Geometry and…
Over the past decade, the techniques of topological data analysis (TDA) have grown into prominence to describe the shape of data. In recent years, there has been increasing interest in developing statistical methods and in particular…
In systems as diverse as migrating mammals to road traffic, crowding acts to inhibit efficient collective movement. Bacteria, however, are observed to move in very dense groups containing billions of individuals without causing the gridlock…
The orbit problem is at the heart of symmetry reduction methods for model checking concurrent systems. It asks whether two given configurations in a concurrent system (represented as finite strings over some finite alphabet) are in the same…
Time-distance helioseismology is a set of powerful tools to study features below the Sun's surface. Inverse methods are needed to interpret time-distance measurements, with many examples in the literature. However, techniques that utilize a…
Diffusion models represent a class of generative models that produce data by denoising a sample corrupted by white noise. Despite the success of diffusion models in computer vision, audio synthesis, and point cloud generation, so far they…
More than ever, today we are left with the abundance of molecular data outpaced by the advancements of the phylogenomic methods. Especially in the case of presence of many genes over a set of species under the phylogeny question, more…
Two parameter families of plane conics are called nets of conics. There is a natural group action on the vector space of nets of conics, namely the product of the group reparametrizing the underlying plane, and the group reparametrizing the…
Modeling symmetry breaking is essential for understanding the fundamental changes in the behaviors and properties of physical systems, from microscopic particle interactions to macroscopic phenomena like fluid dynamics and cosmic…
Microbiology is the science of microbes, particularly bacteria. Many bacteria are motile: they are capable of self-propulsion. Among these, a significant class execute so-called run-and-tumble motion: they follow a fairly straight path for…
Bayesian phylogenetics is vital for understanding evolutionary dynamics, and requires accurate and efficient approximation of posterior distributions over trees. In this work, we develop a variational Bayesian approach for ultrametric…
In symmetric groups, studies of permutation factorizations or triples of permutations satisfying certain conditions have a long history. One particular interesting case is when two of the involved permutations are long cycles, for which…
When a group acts on a set, it naturally partitions it into orbits, giving rise to orbit problems. These are natural algorithmic problems, as symmetries are central in numerous questions and structures in physics, mathematics, computer…
The distributed genome hypothesis states that the set of genes in a population of bacteria is distributed over all individuals that belong to the specific taxon. It implies that certain genes can be gained and lost from generation to…
Invariance to nuisance transformations is one of the desirable properties of effective representations. We consider transformations that form a \emph{group} and propose an approach based on kernel methods to derive local group invariant…
In this paper we are concerned with the conjecture that, for any set of generators S of the symmetric group of degree n, the word length in terms of S of every permutation is bounded above by a polynomial of n. We prove this conjecture for…
Given a generator set $S$ of the symmetric group ${\rm{Sym}}_n$, every permutation $\pi\in {\rm{Sym}_n}$ is a word (product of elements) of $S$. A positive integer $d(\pi)$ is associated with each $\pi\in{\rm{Sym}_n}$ taking the length of…
In this article we consider the cycle structure of compositions of pairs of involutions in the symmetric group S_n chosen uniformly at random. These can be modeled as modified 2-regular graphs, giving rise to exponential generating…