Search results for "Computation"
showing 10 items of 7362 documents
A lower bound for the Bloch radius of 𝐾-quasiregular mappings
2004
We give a quantitative proof to Eremenko’s theorem (2000), which extends Bloch’s classical theorem to the class of n n -dimensional K K -quasiregular mappings.
Guaranteed error bounds and local indicators for adaptive solvers using stabilised space–time IgA approximations to parabolic problems
2019
Abstract The paper is concerned with space–time IgA approximations to parabolic initial–boundary value problems. We deduce guaranteed and fully computable error bounds adapted to special features of such type of approximations and investigate their efficiency. The derivation of error estimates is based on the analysis of the corresponding integral identity and exploits purely functional arguments in the maximal parabolic regularity setting. The estimates are valid for any approximation from the admissible (energy) class and do not contain mesh-dependent constants. They provide computable and fully guaranteed error bounds for the norms arising in stabilised space–time approximations. Further…
Models of Computation, Riemann Hypothesis, and Classical Mathematics
1998
Classical mathematics is a source of ideas used by Computer Science since the very first days. Surprisingly, there is still much to be found. Computer scientists, especially, those in Theoretical Computer Science find inspiring ideas both in old notions and results, and in the 20th century mathematics. The latest decades have brought us evidence that computer people will soon study quantum physics and modern biology just to understand what computers are doing.
Knot Theory, Jones Polynomial and Quantum Computing
2005
Knot theory emerged in the nineteenth century for needs of physics and chemistry as these needs were understood those days. After that the interest of physicists and chemists was lost for about a century. Nowadays knot theory has made a comeback. Knot theory and other areas of topology are no more considered as abstract areas of classical mathematics remote from anything of practical interest. They have made deep impact on quantum field theory, quantum computation and complexity of computation.
Span Programs and Quantum Algorithms for st-Connectivity and Claw Detection
2012
We introduce a span program that decides st-connectivity, and generalize the span program to develop quantum algorithms for several graph problems. First, we give an algorithm for st-connectivity that uses O(n d^{1/2}) quantum queries to the n x n adjacency matrix to decide if vertices s and t are connected, under the promise that they either are connected by a path of length at most d, or are disconnected. We also show that if T is a path, a star with two subdivided legs, or a subdivision of a claw, its presence as a subgraph in the input graph G can be detected with O(n) quantum queries to the adjacency matrix. Under the promise that G either contains T as a subgraph or does not contain T…
How to untie G-quadruplex knots and why?
2021
International audience; For over two decades, the prime objective of the chemical biology community studying G-quadruplexes (G4s) has been to use chemicals to interact with and stabilize G4s in cells to obtain mechanistic interpretations. This strategy has been undoubtedly successful, as demonstrated by recent advances. However, these insights have also led to a fundamental rethinking of G4-targeting strategies: due to the prevalence of G4s in the human genome, transcriptome, and ncRNAome (collectively referred to as the G4ome), and their involvement in human diseases, should we continue developing G4-stabilizing ligands or should we invest in designing molecular tools to unfold G4s? Here, …
Results of Numerical Modeling of Blood Flow in the Internal Jugular Vein Exhibiting Different Types of Strictures
2022
The clinical relevance of nozzle-like strictures in upper parts of the internal jugular veins remains unclear. This study was aimed at understanding flow disturbances caused by such stenoses. Computational fluid dynamics software, COMSOL Multiphysics, was used. Two-dimensional computational domain involved stenosis at the beginning of modeled veins, and a flexible valve downstream. The material of the venous valve was considered to be hyperelastic. In the vein models with symmetric 2-leaflets valve without upstream stenosis or with minor 30% stenosis, the flow was undisturbed. In the case of major 60% and 75% upstream stenosis, centerline velocity was positioned asymmetrically, and areas of…
Assessing the impact of copy number variants on miRNA genes in autism by Monte Carlo simulation.
2014
Autism Spectrum Disorders (ASDs) are childhood neurodevelopmental disorders with complex genetic origins. Previous studies have investigated the role of de novo Copy Number Variants (CNVs) and microRNAs as important but distinct etiological factors in ASD. We developed a novel computational procedure to assess the potential pathogenic role of microRNA genes overlapping de novo CNVs in ASD patients. Here we show that for chromosomes # 1, 2 and 22 the actual number of miRNA loci affected by de novo CNVs in patients was found significantly higher than that estimated by Monte Carlo simulation of random CNV events. Out of 24 miRNA genes over-represented in CNVs from these three chromosomes only …
Gentechnik in der Schule
1999
The Fonds of German Chemical Industry (FCI) has produced an instrumental kit named „Blue Genes” which enables High School teachers to perform in their school environment basic experiments of gene analysis and cloning. In particular, the kit contains all necessary equipment and reagents to perform a restriction analysis, and cloning and expression of a bacterial gene.
SMART: Unique splitting-while-merging framework for gene clustering
2014
© 2014 Fa et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Successful clustering algorithms are highly dependent on parameter settings. The clustering performance degrades significantly unless parameters are properly set, and yet, it is difficult to set these parameters a priori. To address this issue, in this paper, we propose a unique splitting-while-merging clustering framework, named "splitting merging awareness tactics" (SMART), which does not require any a priori knowledge of either the number …