Search results for "Discrete Mathematics"
showing 10 items of 1728 documents
Variable neighborhood descent for the incremental graph drawing
2017
Abstract Graphs are used to represent reality in several areas of knowledge. Drawings of graphs have many applications, from project scheduling to software diagrams. The main quality desired for drawings of graphs is readability, and crossing reduction is a fundamental aesthetic criterion for a good representation of a graph. In this paper we target the edge crossing reduction in the context of incremental graph drawing, in which we want to preserve the layout of a graph over successive drawings. We propose a hybrid method based on the GRASP (Greedy Randomized Adaptive Search Procedure) and VND (Variable Neighborhood Descent) methodologies and compare it with previous methods via simulation.
On the minimal number of singular fibers with non-compact Jacobians for families of curves over P1
2016
Abstract Let f : X → P 1 be a non-isotrivial family of semi-stable curves of genus g ≥ 1 defined over an algebraically closed field k. Denote by s nc the number of the singular fibers whose Jacobians are non-compact. We prove that s nc ≥ 5 if k = C and g ≥ 5 ; we also prove that s nc ≥ 4 if char ( k ) > 0 and the relative Jacobian of f is non-smooth.
Measuring spectrally-resolved information transfer.
2020
Information transfer, measured by transfer entropy, is a key component of distributed computation. It is therefore important to understand the pattern of information transfer in order to unravel the distributed computational algorithms of a system. Since in many natural systems distributed computation is thought to rely on rhythmic processes a frequency resolved measure of information transfer is highly desirable. Here, we present a novel algorithm, and its efficient implementation, to identify separately frequencies sending and receiving information in a network. Our approach relies on the invertible maximum overlap discrete wavelet transform (MODWT) for the creation of surrogate data in t…
Identifying Prognostic SNPs in Clinical Cohorts: Complementing Univariate Analyses by Resampling and Multivariable Modeling
2016
Clinical cohorts with time-to-event endpoints are increasingly characterized by measurements of a number of single nucleotide polymorphisms that is by a magnitude larger than the number of measurements typically considered at the gene level. At the same time, the size of clinical cohorts often is still limited, calling for novel analysis strategies for identifying potentially prognostic SNPs that can help to better characterize disease processes. We propose such a strategy, drawing on univariate testing ideas from epidemiological case-controls studies on the one hand, and multivariable regression techniques as developed for gene expression data on the other hand. In particular, we focus on …
Generalized Molecular Descriptors Derived From Event-Based Discrete Derivative.
2016
In the present study, a generalized approach for molecular structure characterization is introduced, based on the relation frequency matrix (F) representation of the molecular graph and the subsequent calculation of the corresponding discrete derivative (finite difference) over a pair of elements (atoms). In earlier publications (22- 24), an unique event, named connected subgraphs, (based on the Kier-Hall's subgraphs) was systematically employed for the computation of the matrix F. The present report is a generalization of this notion, in which eleven additional events are introduced, classified in three categories, namely, topological (terminal paths, vertex path incidence, quantum subgrap…
KnotGenome: a server to analyze entanglements of chromosomes.
2018
Abstract The KnotGenome server enables the topological analysis of chromosome model data using three-dimensional coordinate files of chromosomes as input. In particular, it detects prime and composite knots in single chromosomes, and links between chromosomes. The knotting complexity of the chromosome is presented in the form of a matrix diagram that reveals the knot type of the entire polynucleotide chain and of each of its subchains. Links are determined by means of the Gaussian linking integral and the HOMFLY-PT polynomial. Entangled chromosomes are presented graphically in an intuitive way. It is also possible to relax structure with short molecular dynamics runs before the analysis. Kn…
New Approach of Controlling Cardiac Alternans
2018
The alternans of the cardiac action potential duration is a pathological rhythm. It is considered to be relating to the onset of ventricular fibrillation and sudden cardiac death. It is well known that, the predictive control is among the control methods that use the chaos to stabilize the unstable fixed point. Firstly, we show that alternans (or period-2 orbit) can be suppressed temporally by the predictive control of the periodic state of the system. Secondly, we determine an estimation of the size of a restricted attraction's basin of the unstable equilibrium point representing the unstable regular rhythm stabilized by the control. This result allows the application of predictive control…
Two-Stage Bayesian Approach for GWAS With Known Genealogy
2019
Genome-wide association studies (GWAS) aim to assess relationships between single nucleotide polymorphisms (SNPs) and diseases. They are one of the most popular problems in genetics, and have some peculiarities given the large number of SNPs compared to the number of subjects in the study. Individuals might not be independent, especially in animal breeding studies or genetic diseases in isolated populations with highly inbred individuals. We propose a family-based GWAS model in a two-stage approach comprising a dimension reduction and a subsequent model selection. The first stage, in which the genetic relatedness between the subjects is taken into account, selects the promising SNPs. The se…
Natural visibility graphs for diagnosing attention deficit hyperactivity disorder (ADHD)
2016
“NOTICE: this is the author’s version of a work that was accepted for publication in Electronic Notes in Discrete Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Electronic Notes in Discrete Mathematics, [Volume 54, October 2016, Pages 337-342] DOI 10.1016/j.endm.2016.09.058 ¨
Packing colorings of subcubic outerplanar graphs
2018
Given a graph $G$ and a nondecreasing sequence $S=(s_1,\ldots,s_k)$ of positive integers, the mapping $c:V(G)\longrightarrow \{1,\ldots,k\}$ is called an $S$-packing coloring of $G$ if for any two distinct vertices $x$ and $y$ in $c^{-1}(i)$, the distance between $x$ and $y$ is greater than $s_i$. The smallest integer $k$ such that there exists a $(1,2,\ldots,k)$-packing coloring of a graph $G$ is called the packing chromatic number of $G$, denoted $\chi_{\rho}(G)$. The question of boundedness of the packing chromatic number in the class of subcubic (planar) graphs was investigated in several earlier papers; recently it was established that the invariant is unbounded in the class of all sub…