相关论文: Conjugation of reddening sequences and conjugation…
Clustering is the process of finding underlying group structures in data. Although mixture model-based clustering is firmly established in the multivariate case, there is a relative paucity of work on matrix variate distributions and none…
The one-parameter family of second order nonlinear difference equations each of which is given by $$ x_{n-1}x_nx_{n+1}=x_{n-1}+(x_n)^{\beta-1}+x_{n+1} \qquad(\beta\in\mathbb{N}) $$ is explored. Since the equation above is arising from seed…
The evolution model with parallel mutation-selection scheme is solved for the case when selection is accompanied by base substitutions, insertions, and deletions. The fitness is assumed to be either a single-peak function (i.e., having one…
Tandem duplication is an evolutionary process whereby a segment of DNA is replicated and proximally inserted. The different configurations that can arise from this process give rise to some interesting combinatorial questions. Firstly, we…
Although the conjugacy classes of the general linear group are known, it is not obvious (from the canonic form of matrices) that two permutation matrices are similar if and only if they are conjugate as permutations in the symmetric group,…
We describe some configurations of conjugate permutations which may be used as a mathematical model of some genetical processes and crystal growth.
Cluster algebras have recently become an important player in mathematics and physics. In this work, we investigate them through the lens of modern data science, specifically with techniques from network science and machine learning. Network…
In spectral clustering, one defines a similarity matrix for a collection of data points, transforms the matrix to get the Laplacian matrix, finds the eigenvectors of the Laplacian matrix, and obtains a partition of the data using the…
The reconstruction of phylogenies from DNA or protein sequences is a major task of computational evolutionary biology. Common phenomena, notably variations in mutation rates across genomes and incongruences between gene lineage histories,…
The reconstruction of a central tendency `species tree' from a large number of conflicting gene trees is a central problem in systematic biology. Moreover, it becomes particularly problematic when taxon coverage is patchy, so that not all…
We introduce the notion of difference equation defined on a structured set. The symmetry group of the structure determines the set of difference operators. All main notions in the theory of difference equations are introduced as invariants…
We offer elementary proofs for several results in consecutive pattern containment that were previously demonstrated using ideas from cluster method and analytical combinatorics. Furthermore, we establish new general bounds on the growth…
We generalize in this work the properties of the conjugacy of skew tent maps. It is known that the conjugacy $h$ from a skew tent map $g_1$ to $g_2$ is differentiable at a point $x^*$ if and only if there exists left and right limits…
We prove the basic properties of determinantal semi-invariants for presentation spaces over any finite dimensional hereditary algebra over any field. These include the virtual generic decomposition theorem, stability theorem and the…
We extend a conjugacy Theorem of Cartan subalgebras, originally established for symmetrizable Kac-Moody algebras, to the broader context of affine Kac-Moody superalgebras. Along the way, we obtain several results that deepen our…
In this paper we construct an unfolding for $c-$vectors of acyclic sign-skew symmetric matrices and we also prove that the sign-coherence property holds for acyclic sign-skew-symmetric matrices. Then we prove that every acyclic…
We give some basics about homological algebra of difference representations. We consider both the difference-discrete and the difference-rational case. We define the corresponding cohomology theories and show the existence of spectral…
We present a new algorithm to compute initial seeds for cluster structures on categories associated with coordinate rings of open Richardson varieties. This allows us to explicitely determine seeds first considered in Leclerc's 2016…
In this research, we consider a mixture of genome fragments of a certain bacteria set. The problem of mixture separation is studied under the assumption that all the genomes present in the mixture are completely sequenced or are close to…
The sign coherence phenomenon is an important feature of c-vectors in cluster algebras with principal coefficients. In this note, we consider a more general version of c-vectors defined for arbitrary cluster algebras of geometric type and…