Search results for " Mathematics"
showing 10 items of 10797 documents
Stability of stationary solutions in models of the Calvin cycle
2017
Abstract In this paper results are obtained concerning the number of positive stationary solutions in simple models of the Calvin cycle of photosynthesis and the stability of these solutions. It is proved that there are open sets of parameters in the model of Zhu et al. (2009) for which there exist two positive stationary solutions. There are never more than two isolated positive stationary solutions but under certain explicit special conditions on the parameters there is a whole continuum of positive stationary solutions. It is also shown that in the set of parameter values for which two isolated positive stationary solutions exist there is an open subset where one of the solutions is asym…
A study on time discretization and adaptive mesh refinement methods for the simulation of cancer invasion: The urokinase model
2016
In the present work we investigate a model that describes the chemotactically and proteolytically driven tissue invasion by cancer cells. The model is a system of advection-reaction-diffusion equations that takes into account the role of the serine protease urokinase-type plasminogen activator. The analytical and numerical study of such a system constitutes a challenge due to the merging, emerging, and traveling concentrations that the solutions exhibit. Classical numerical methods applied to this system necessitate very fine discretization grids to resolve these dynamics in an accurate way. To reduce the computational cost without sacrificing the accuracy of the solution, we apply adaptive…
Parallel algorithms for large-scale biological sequence alignment on Xeon-Phi based clusters
2016
Computing alignments between two or more sequences are common operations frequently performed in computational molecular biology. The continuing growth of biological sequence databases establishes the need for their efficient parallel implementation on modern accelerators. This paper presents new approaches to high performance biological sequence database scanning with the Smith-Waterman algorithm and the first stage of progressive multiple sequence alignment based on the ClustalW heuristic on a Xeon Phi-based compute cluster. Our approach uses a three-level parallelization scheme to take full advantage of the compute power available on this type of architecture; i.e. cluster-level data par…
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 ¨
Preventive and Therapeutic Role of Muscle Contraction Against Chronic Diseases.
2016
Background: Due to the continuing increase of the elderly population in the western countries, the prevalence of the main chronic diseases (obesity, type 2 diabetes and related metabolic disorders, arterial hypertension, vascular damage due to atherosclerotic process, cancer, chronic obstructive pulmonary disease, neurodegenerative diseases, chronic kidney disease, immune-mediated diseases) is increasing. There is incontrovertible evidence that regular physical activity contributes to the primary and secondary prevention of several chronic diseases and is associated with a reduced risk of premature death. Methods: In this review the most prevalent chronic pathologic conditions are discussed…
Bacteria classification using minimal absent words
2017
Bacteria classification has been deeply investigated with different tools for many purposes, such as early diagnosis, metagenomics, phylogenetics. Classification methods based on ribosomal DNA sequences are considered a reference in this area. We present a new classificatier for bacteria species based on a dissimilarity measure of purely combinatorial nature. This measure is based on the notion of Minimal Absent Words, a combinatorial definition that recently found applications in bioinformatics. We can therefore incorporate this measure into a probabilistic neural network in order to classify bacteria species. Our approach is motivated by the fact that there is a vast literature on the com…
A solution of the minimum-time velocity planning problem based on lattice theory
2018
For a vehicle on an assigned path, we find the minimum-time speed law that satisfies kinematic and dynamic constraints, related to maximum speed and maximum tangential and transversal acceleration. We present a necessary and sufficient condition for the feasibility of the problem and a simple operator, based on the solution of two ordinary differential equations, which computes the optimal solution. Theoretically, we show that the problem feasible set, if not empty, is a lattice, whose supremum element corresponds to the optimal solution.
Networks Describing Dynamical Systems
2018
Abstract We consider systems of ordinary differential equations that arise in the theory of gene regulatory networks. These systems can be of arbitrary size but of definite structure that depends on the choice of regulatory matrices. Attractors play the decisive role in behaviour of elements of such systems. We study the structure of simple attractors that consist of a number of critical points for several choices of regulatory matrices.
Discovering unbounded unions of regular pattern languages from positive examples
1996
The problem of learning unions of certain pattern languages from positive examples is considered. We restrict to the regular patterns, i.e., patterns where each variable symbol can appear only once, and to the substring patterns, which is a subclass of regular patterns of the type xαy, where x and y are variables and α is a string of constant symbols. We present an algorithm that, given a set of strings, finds a good collection of patterns covering this set. The notion of a ‘good covering’ is defined as the most probable collection of patterns likely to be present in the examples, assuming a simple probabilistic model, or equivalently using the Minimum Description Length (MDL) principle. Ou…
DNA combinatorial messages and Epigenomics: The case of chromatin organization and nucleosome occupancy in eukaryotic genomes
2019
Abstract Epigenomics is the study of modifications on the genetic material of a cell that do not depend on changes in the DNA sequence, since those latter involve specific proteins around which DNA wraps. The end result is that Epigenomic changes have a fundamental role in the proper working of each cell in Eukaryotic organisms. A particularly important part of Epigenomics concentrates on the study of chromatin, that is, a fiber composed of a DNA-protein complex and very characterizing of Eukaryotes. Understanding how chromatin is assembled and how it changes is fundamental for Biology. In more than thirty years of research in this area, Mathematics and Theoretical Computer Science have gai…