Related papers: Splitting pairs and the number of clusters generat…
We consider heteroclinic networks between $n \in \mathbb{N}$ nodes where the only connections are those linking each node to its two subsequent neighbouring ones. Using a construction method where all nodes are placed in a single…
Motivated by group-project distribution, we introduce and study stable matching under the constraint of applicants needing to share a location to be matched with the same institute, which we call the Location-Restricted Stable Matching…
It is well known that the joint probability density of the eigenvalues of Gaussian ensembles of random matrices may be interpreted as a Coulomb gas. We review these classical results for hermitian and complex random matrices, with special…
We propose that the Standard Model is coupled to a sector with an enormous landscape of vacua, where only the dimensionful parameters--the vacuum energy and Higgs masses--are finely "scanned" from one vacuum to another, while dimensionless…
Although geographic isolation has been shown to play a key role in promoting reproductive isolation, it is now believed that speciation can also happen in sympatry and with considerable gene flow. Here we present a model of sympatric…
The topology of gene expression space for a set of 12 cancer types is studied by means of an entropy-like magnitude, which allows the characterization of the regions occupied by tumor and normal samples. The comparison indicates that the…
Subspace clustering is the problem of clustering data points into a union of low-dimensional linear/affine subspaces. It is the mathematical abstraction of many important problems in computer vision, image processing and machine learning. A…
The inability to produce two perfect copies of an unknown state is inherently linked with the inability to produce maximal entanglement between multiple spins. Despite this, there is no quantitative link between how much entanglement can be…
This paper discusses the split feasibility problem with polynomials. The sets are semi-algebraic, defined by polynomial inequalities. They can be either convex or nonconvex, either feasible or infeasible. We give semidefinite relaxations…
Real-world physical systems are inherently complex, often involving the coupling of multiple physics, making their simulation both highly valuable and challenging. Many mainstream approaches face challenges when dealing with decoupled data.…
Darwinian evolution is driven by random mutations, genetic recombination (gene shuffling) and selection that favors genotypes with high fitness. For systems where each genotype can be represented as a bitstring of length $L$, an overview of…
In this paper, we consider classic randomized low diameter decomposition procedures for planar graphs that obtain connected clusters which are cohesive in that close-by pairs of nodes are assigned to the same cluster with high probability.…
Identifying drivers of complex traits from the noisy signals of genetic variation obtained from high throughput genome sequencing technologies is a central challenge faced by human geneticists today. We hypothesize that the variants…
Using the notion of compatibility between Poisson brackets and cluster structures in the coordinate rings of simple Lie groups, Gekhtman Shapiro and Vainshtein conjectured a correspondence between the two. Poisson Lie groups are classified…
We construct Lie algebras of vector fields on universal bundles $\mathcal{E}^2_{N,0}$ of symmetric squares of hyperelliptic curves of genus $g=1,2,\dots$, where $g=\left[\frac{N-1}{2}\right], \ N=3,4,\ldots$. For each of these Lie algebras,…
Genomic regions (or loci) displaying outstanding correlation with some environmental variables are likely to be under selection and this is the rationale of recent methods of identifying selected loci and retrieving functional information…
There is no proof yet of convergence of Genetic Algorithms. We do not supply it too. Instead, we present some thoughts and arguments to convince the Reader, that Genetic Algorithms are essentially bound for success. For this purpose, we…
Phylogenetic inference can potentially result in a more accurate tree using data from multiple loci. However, if the loci are incongruent--due to events such as incomplete lineage sorting or horizontal gene transfer--it can be misleading to…
A classical view of speciation is that reproductive isolation arises as a by-product of genetic divergence. Here, individual-based simulations are used to evaluate whether the mechanisms implied by this view may result in rapid speciation…
Efficient embedding virtual clusters in physical network is a challenging problem. In this paper we consider a scenario where physical network has a structure of a balanced tree. This assumption is justified by many real- world…