Related papers: Matrix and graph representations of vine copula st…
We investigate hierarchical structure in various complex systems according to Minimum Spanning Tree methods. Firstly, we investigate stock markets where the graphis obtained from the matrix of correlations coefficient computed between all…
A randomized algorithm for computing a data sparse representation of a given rank structured matrix $A$ (a.k.a. an $H$-matrix) is presented. The algorithm draws on the randomized singular value decomposition (RSVD), and operates under the…
Topologically constrained genome-like polymers often double-fold into tree-like configurations, which can be modelled on the level of folded (ring) polymers or on the level of the underlying random trees. For both descriptions, we have…
There is a profound connection between copositive matrices and graph theory. Copositive matrices provide a powerful tool for formulating and solving various challenging graph-related problems. Conversely, graph theory provides a rich set of…
Combining a set of phylogenetic trees into a single phylogenetic network that explains all of them is a fundamental challenge in evolutionary studies. Existing methods are computationally expensive and can either handle only small numbers…
Simplified vine copulas are flexible tools over standard multivariate distributions for modeling and understanding different dependence properties in high-dimensional data. Their conditional distributions are of utmost importance, from…
Undirected graphs can be used to describe matrix variate distributions. In this paper, we develop new methods for estimating the graphical structures and underlying parameters, namely, the row and column covariance and inverse covariance…
This paper considers 1-string representations of planar graphs that are order-preserving in the sense that the order of crossings along the curve representing vertex $v$ is the same as the order of edges in the clockwise order around $v$ in…
The recovery of network structure from experimental data is a basic and fundamental problem. Unfortunately, experimental data often do not directly reveal structure due to inherent limitations such as imprecision in timing or other…
Tree Containment is a fundamental problem in phylogenetics useful for verifying a proposed phylogenetic network, representing the evolutionary history of certain species. Tree Containment asks whether the given phylogenetic tree (for…
We consider algorithms with access to an unknown matrix $M\in\mathbb{F}^{n \times d}$ via matrix-vector products, namely, the algorithm chooses vectors $\mathbf{v}^1, \ldots, \mathbf{v}^q$, and observes $M\mathbf{v}^1,\ldots,…
We consider the problem of uniformly generating a spanning tree, of a connected undirected graph. This process is useful to compute statistics, namely for phylogenetic trees. We describe a Markov chain for producing these trees. For cycle…
We automatically verify the crucial steps in the original proof of correctness of an algorithm which, given a geometric graph satisfying certain additional properties removes edges in a systematic way for producing a connected graph in…
A graph theoretic approach is proposed for object shape representation in a hierarchical compositional architecture called Compositional Hierarchy of Parts (CHOP). In the proposed approach, vocabulary learning is performed using a hybrid…
The forest matrix plays a crucial role in network science, opinion dynamics, and machine learning, offering deep insights into the structure of and dynamics on networks. In this paper, we study the problem of querying entries of the forest…
In a confluence of combinatorics and geometry, simultaneous representations provide a way to realize combinatorial objects that share common structure. A standard case in the study of simultaneous representations is the sunflower case where…
The transmission of a vertex in a connected graph is the sum of distances from that vertex to all the other vertices. A connected graph is transmission irregular if any two distinct vertices have different transmissions. We present an…
In phylogenetics, evolution is traditionally represented in a tree-like manner. However, phylogenetic networks can be more appropriate for representing evolutionary events such as hybridization, horizontal gene transfer, and others. In…
In this paper the main results in arXiv:0901.3179v3, related to the matrix representation of polynomial maps, are restated in traditional way of linear algebra assuming that variable vectors are presented as column vectors. Some new results…
Visualization of the adjacency matrix enables us to capture macroscopic features of a network when the matrix elements are aligned properly. Community structure, a network consisting of several densely connected components, is a…