Related papers: Group-theoretic models of the inversion process in…
One of the main challenges in Computational Biology is to find the evolutionary distance between two organisms. In the field of comparative genomics, one way to estimate such distance is to find a minimum cost sequence of rearrangements…
Many complex ecosystems, such as those formed by multiple microbial taxa, involve intricate interactions amongst various sub-communities. The most basic relationships are frequently modeled as co-occurrence networks in which the nodes…
We use the mean-bacterial-velocity model to investigate the \textit{irreversibility} of two-dimensional (2D) \textit{bacterial turbulence} and to compare it with its 2D fluid-turbulence counterpart. We carry out extensive direct numerical…
In an oriented graph, the inversion of a subset of vertices X is the operation reversing the direction of every arc with both endpoints in X. Given a graph G, the inversion distance between two orientations G is the minimum number of…
Diffusion Models achieve state-of-the-art performance in generating new samples but lack a low-dimensional latent space that encodes the data into editable features. Inversion-based methods address this by reversing the denoising…
In this paper we present a topological framework for studying signed permutations and their reversal distance. As a result we can give an alternative approach and interpretation of the Hannenhalli-Pevzner formula for the reversal distance…
In this paper, we consider 1D agent-based and kinetic models of aggregation with reversals. In particular, we fit a Gamma distribution to represent the run times in myxobacteria and analyze numerically the importance of non-exponential…
It is shown that square free set theoretic involutive non-degenerate solutions of the Yang-Baxter equation whose associated permutation group (referred to as an involutive Yang-Baxter group) is abelian are retractable in the sense of…
In this paper we consider the multispecies stirring process on the discrete torus. We prove a large deviation principle for the trajectory of the vector of densities of the different species. The technique of proof consists in extending the…
Group theory is extremely successful in characterizing the symmetries in quantum systems, which greatly simplifies and unifies our treatments of quantum systems. Here we introduce the concept of the symmetry for a quantum Boltzmann machine…
Epidemiological models describe the spread of an infectious disease within a population. They capture microscopic details on how the disease is passed on among individuals in various different ways, while making predictions about the state…
Stokes inversion techniques are very powerful methods for obtaining information on the thermodynamic and magnetic properties of solar and stellar atmospheres. In recent years, very sophisticated inversion codes have been developed that are…
First and second fundamental theorems are given for polynomial invariants of a class of pseudo-reflection groups (including the Weyl groups of type $B_n$), under the assumption that the order of the group is invertible in the base field.…
Felsner introduced a cycle reversal, namely the `flip' reversal, for \alpha-orientations (i.e., each vertex admits a prescribed out-degree) of a graph G embedded on the plane and further proved that the set of all the \alpha-orientations of…
In this paper, we introduce plane permutations, i.e. pairs $\mathfrak{p}=(s,\pi)$ where $s$ is an $n$-cycle and $\pi$ is an arbitrary permutation, represented as a two-row array. Accordingly a plane permutation gives rise to three distinct…
In previous works the group inverse of a network obtained by some perturbations, as the deletion of a vertex, the addition of a new vertex, contraction of an edge, etc. is obtained in terms of the group inverse of the original network. In…
If we treat the symmetric group $S_n$ as a probability measure space where each element has measure $1/n!$, then the number of cycles in a permutation becomes a random variable. The Cycle Length Lemma describes the expected values of…
Permutations are usually enumerated by size, but new results can be found by enumerating them by inversions instead, in which case one must restrict one's attention to indecomposable permutations. In the style of the seminal paper by Simion…
Two genomes over the same set of gene families form a canonical pair when each of them has exactly one gene from each family. Different distances of canonical genomes can be derived from a structure called breakpoint graph, which represents…
We uncover connections between maximum likelihood estimation in statistics and norm minimization over a group orbit in invariant theory. We focus on Gaussian transformation families, which include matrix normal models and Gaussian graphical…