Mathematics, Department of

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A Bounded Consistency Theorem for Strong Summabilities

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
1989
Abstract: 

The study of R-type summability methods is continued in this paper byshowing that two such methods are identical on the bounded portion of the strongsummability field associated with the methods. It is shown that this “boundedconsistency” applies for many non-matrix methods as well as for regular matrix methods.

Document type: 
Article

A Weak Invariance Principle and Asymptotic Stability for Evolution Equations with Bounded Generators

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
1995
Abstract: 

If V is a Lyapunov function of an equation du/dt u’ Zu in a Banach space thenasymptotic stability of an equilibrium point may be easily proved if it is known that sup(V’) < 0 onsufficiently small spheres centered at the equilibrium point. In this paper weak asymptotic stability isproved for a bounded infinitesimal generator Z under a weaker assumption V’ < 0 (which aloneimplies ordinary stability only) if some observability condition, involving Z and the Frechet derivativeof V’, is satisfied. The proof is based on an extension of LaSalle’s invariance principle, which yieldsconvergence in a weak topology and uses a strongly continuous Lyapunov funcdon. The theory isillustrated with an example of an integro-differential equation of interest in the theory of chemicalprocesses. In this case strong asymptotic stability is deduced from the weak one and explicit sufficientconditions for stability are given. In the case of a normal infinitesimal generator Z in a Hilbertspace, strong asymptotic stability is proved under the following assumptions Z* + Z is weaklynegative definite and Ker Z 0 }. The proof is based on spectral theory.

Document type: 
Article
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On Approximation of Functions and Their Derivatives by Quasi-Hermite Interpolation

Author: 
Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
1996
Abstract: 

In this paper, we consider the simultaneous approximation of the derivatives of thefunctions by the corresponding derivatives of qua.si-Hcrmite interpolation based on the zeros of (1z2)p,(z) (where p,(x)is a Lcgcndrc polynomial). The corresponding approximation degrees are given.It is shown that this matrix of nodes is almost optimal

Document type: 
Article

Modelling Desert Dune Fields Based on Discrete Dynamics

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
2002
Abstract: 

A mathematical formulation is developed to model the dynamics of sand dunes. The physical processes display strong non-linearity that has been taken into account in the model. When assessing the success of such a model in capturing physical features we monitor morphology, dune growth, dune migration and spatial patterns within a dune field. Following recent advances, the proposed model is based on a discrete lattice dynamics approach with new features taken into account which reflect physically observed mechanisms.

Document type: 
Article

Continuum Model of the Two-Component Becker-Döring Equations

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
2004
Abstract: 

The process of collision between particles is a subject of interest in many fields of physics, astronomy, polymer physics, atmospheric physics, and colloid chemistry. If two types of particles are allowed to participate in the cluster coalescence, then the time evolution of the cluster distribution has been described by an infinite system of ordinary differential equations. In this paper, we describe the model with a second-order two-dimensional partial differential equation, as a continuum model.

Document type: 
Article

Minmax Strongly Connected Subgraphs with Node Penalties

Author: 
Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
2005
Abstract: 

We propose an O(min{m+nlogn,mlog∗n}) to find a minmax strongly connected spanningsubgraph of a digraph with n nodes and m arcs. A generalization of this problemcalled theminmax strongly connected subgraph problem with node penalties is also considered.An O(mlogn) algorithm is proposed to solve this general problem. We also discussways to improve the average complexity of this algorithm.

Document type: 
Article

BRASERO: A Resource for Benchmarking RNA Secondary Structure Comparison Algorithms

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
2012
Abstract: 

The pairwise comparison of RNA secondary structures is a fundamental problem, with direct application in mining databases for annotating putative noncoding RNA candidates in newly sequenced genomes. An increasing number of software tools are available for comparing RNA secondary structures, based on different models (such as ordered trees or forests, arc annotated sequences, and multilevel trees) and computational principles (edit distance, alignment). We describe here the website BRASERO that offers tools for evaluating such software tools on real and synthetic datasets.

Document type: 
Article

A Methodological Framework for the Reconstruction of Contiguous Regions of Ancestral Genomes and Its Application to Mammalian Genomes

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
2008-11
Abstract: 

The reconstruction of ancestral genome architectures and gene orders from homologies between extant species is a long-standing problem, considered by both cytogeneticists and bioinformaticians. A comparison of the two approaches was recently investigated and discussed in a series of papers, sometimes with diverging points of view regarding the performance of these two approaches. We describe a general methodological framework for reconstructing ancestral genome segments from conserved syntenies in extant genomes. We show that this problem, from a computational point of view, is naturally related to physical mapping of chromosomes and benefits from using combinatorial tools developed in this scope. We develop this framework into a new reconstruction method considering conserved gene clusters with similar gene content, mimicking principles used in most cytogenetic studies, although on a different kind of data. We implement and apply it to datasets of mammalian genomes. We perform intensive theoretical and experimental comparisons with other bioinformatics methods for ancestral genome segments reconstruction. We show that the method that we propose is stable and reliable: it gives convergent results using several kinds of data at different levels of resolution, and all predicted ancestral regions are well supported. The results come eventually very close to cytogenetics studies. It suggests that the comparison of methods for ancestral genome reconstruction should include the algorithmic aspects of the methods as well as the disciplinary differences in data aquisition.

Document type: 
Article
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Wavelength Isolation Sequence Design

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
2013-05
Abstract: 

A recent paper by Jedwab and Wodlinger renewed interest in aproblem of multislit spectrometer design rst proposed by Golay in1951 but subsequently forgotten. It is shown that Golay's formulationof the problem in terms of 0/1 binary sequences is unduly restrictive.By relaxing the restrictions, in nitely many spectrometer designs sat-isfying all the original physical criteria can be found. Three construc-tions for such spectrometer designs are presented, involving Golombrulers and variants. These constructions explain all nontrivial exam-ples involving at most 26 slits.

Document type: 
Article

Consistency-Based Detection of Potential Tumor-Specific Deletions in Matched Normal/Tumor Genomes

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
2011
Abstract: 

Background: Structural variations in human genomes, such as insertions, deletion, or rearrangements, play animportant role in cancer development. Next-Generation Sequencing technologies have been central in providingways to detect such variations. Most existing methods however are limited to the analysis of a single genome, and itis only recently that the comparison of closely related genomes has been considered. In particular, a few recentworks considered the analysis of data sets obtained by sequencing both tumor and healthy tissues of the samecancer patient. In that context, the goal is to detect variations that are specific to exactly one of the genomes, forexample to differentiate between patient-specific and tumor-specific variations. This is a difficult task, especially whenfacing the additional challenge of the possible contamination of healthy tissues by tumor cells and conversely.Results: In the current work, we analyzed a data set of paired-end short-reads, obtained by sequencing tumortissues and healthy tissues, both from the same cancer patient. Based on a combinatorial notion of conflictbetween deletions, we show that in the tumor data, more deletions are predicted than there could actually be in adiploid genome. In contrast, the predictions for the data from normal tissues are almost conflict-free. We designedand applied a method, specific to the analysis of such pooled and contaminated data sets, to detect potentialtumor-specific deletions. Our method takes the deletion calls from both data sets and assigns reads from themixed tumor/normal data to the normal one with the goal to minimize the number of reads that need to bediscarded to obtain a set of conflict-free deletion clusters. We observed that, on the specific data set we analyze,only a very small fraction of the reads needs to be discarded to obtain a set of consistent deletions.Conclusions: We present a framework based on a rigorous definition of consistency between deletions and theassumption that the tumor sample also contains normal cells. A combined analysis of both data sets based on thismodel allowed a consistent explanation of almost all data, providing a detailed picture of candidate patient- andtumor-specific deletions.

Document type: 
Article