bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the Solution Structure of Nonlinear Hill's Equation II, Local Results
Authors: Mrziglod Thomas 
Published: May 2007

AbstractThe behavior of solution components in W2,P(ℝ) × ℝ of nonlinear Hill's equation near boundary points of the continuous spectrum is discussed in full detail. The starting point of several articles concerned with the study of this solution structure is the existence result of unbounded solution components in a recent paper. The main assumption there is the concentration of the nonlinearity to a compact interval which allows the reduction to an equivalent nonlinear Sturm ‐ Liouville problem with parameter dependent boundary conditions. In particular, this approach makes it possible to analyse the solution structure of the Sturm‐Liouville and the original problem. It turns out in the present article that each solution component consists of a. branch near the bifurcation point. For the behavior of the solution branches of the original problem, the bifurcation direction and order of bifurcation play an important role. Using the corresponding local results, a class of nonlinearities can be constructed such that at each boundary point of the spectrum infinitely many branches bifurcate asymptotically from infinity.
The Triebel ‐ Lizorkin Scale of Function Spaces for the Fourier ‐ Helgason Transform
Authors: Skrzypczak Leszek 
Published: May 2007

AbstractWe define and investigate the Triebel ‐ Lizorkin scale of function spaces F, with 1< p < ∞, 1< q ≤ ∞ for the Fourier‐Helgason transform on symmetric Riemannian manifolds of the noncompact type.
Mixed Crack Type Problem in Anisotropic Elasticity
Authors: Duduchava R. , Natroshvili D. 
Published: May 2007

AbstractThe paper deals with three‐dimensional mixed boundary value problem of the anisotropic elasticity theory when the elastic body under consideration has a cut in the form of an arbitrary non‐closed, two‐dimensional, smooth surface with a smooth boundary: on one side of the cut surface the Dirichlet type condition (i.e., the displacement vector) is given, while on the other side the Neumann type condition (i.e., the stress vector) is prescribed. Applying the potential method and invoking the theory of ΨDEs uniqueness, existence and regularity results are proved in various function spaces. The asymptotic expansion of the solution of the corresponding system of boundary ΨDEs is written.
Some Estimates for Radial Fourier Multiplier Operators with Slowly Decaying Kernels
Authors: Epperson Jay 
Published: May 2007

AbstractWe consider the restriction to radial functions of a class of radial Fourier multiplier operators containing the Bochner‐Riesz multiplier operator. The convolution kernel K(x) of an operator in this class decays too slowly at infinity to be integrable, but has enough oscillation to achieve Lp ‐boundedness for p inside a suitable interval (a, b). We prove boundedness results for the maximal operator Kf(x) = supr>0 rn∣K(r) * f(x)∣ associated with such a kernel. The maximal operator is shown to be weak type bounded at the lower critical index a, restricted weak type bounded at the upper critical index b, and strong type bounded between. This together with our assumptions on K(x) leads to the pointwise convergence result limγ→ γn K(γ·) * f(x) = cf(x) a. e. for radial f ϵ LP(ℝn), a ≥ p > b.
Boundary Integral Operators in Countably Normed Spaces
Authors: Heubr Norbert , Stephan Ernst P. 
Published: May 2007

AbstractWe show the mapping properties of several integral operators acting on polygons within countably normed spaces. The integral operators are the weakly singular single layer potential operator for the Laplacian, the corresponding double layer potential operator and the normal derivatives of these operators. Our analysis of the boundary integral equations in the countably normed spaces is based on Mellin techniques and uses the Mellin symbols of the integral operators. Functions of these countably normed spaces can be approximated very efficiently by splines through the use of well adapted mesh‐refinement and polynomial degree distribution. Therefore the hp‐version of the boundary element method with geometric mesh can be proved to converge exponentially fast for the solutions to those integral equations.
Poisson Lie Groups and Non‐Linear Convexity Theorems
Authors: Hilgert Joachim , Neeb Karl‐Hermann 
Published: May 2007

AbstractIn this paper we describe how one can derive nonlinear convexity theorems which are similar to Kostant's nonlinear convexity theorem for the Iwasawa decomposition from Hamiltonian actions on Poisson Lie groups. Our results generalize those of LU and Ratiu ([24]) and aim at a unified symplectic framework for the convexity theorem in [32] and the linear convexity theorems for coadjoint orbits of convex type in [15].
Homogeneous Vector Bundles and Koszul Algebras
Authors: Hille Lutz 
Published: May 2007

AbstractLet G be a reductive algebraic group defined over an algebraically closed field of characteristic zero and let P be a parabolic subgroup of G. We consider the category of homogeneous vector bundles over the flag variety G/P. This category is equivalent to a category of representations of a certain infinite quiver with relations by a generalisation of a result in [BK]. We prove that both categories are Koszul precisely when the unipotent radical Pu of P is abelian.
The Shape of the Solution Set for Systems of Interval Linear Equations with Dependent Coefficients
Authors: Alefeld Götz , Kreinovich Vladik , Mayer Günter 
Published: May 2007

AbstractA standard system of interval linear equations is defined by Ax = b, where A is an m × n coefficient matrix with (compact) intervals as entries, and b is an m‐dimensional vector whose components are compact intervals. It is known that for systems of interval linear equations the solution set, i. e., the set of all vectors x for which Ax = b for some A ϵ A and b ϵ b, is a polyhedron.In some cases, it makes sense to consider not all possible A ϵ A and b ϵ b, but only those A and b that satisfy certain linear conditions describing dependencies between the coefficients. For example, if we allow only symmetric matrices A (aij = aji), then the corresponding solution set becomes (in general) piecewise‐quadratic.In this paper, we show that for general dependencies, we can have arbitrary (semi)algebraic sets as projections of solution sets.
Non‐Autonomous Evolution Equations on Nonsmooth Domair
Authors: Mehmeti Felix Ali , Nicaise Serge 
Published: May 2007

AbstractThe solution of a stationary boundary value problem on a domain with conical points has singularities near these points. Here we first consider existence results in appropriate weighted Sobolev spaces in order to incorporate the singularities. We secondly use these results to prove existence, uniqueness and regularity of solutions of non‐autonomous second order evolution equations on such domains.
Use of the Domain Derivative to Prove Symmetry Results in Partial Differential Equations
Authors: Choulli Mourad , Henrot Antoine 
Published: May 2007

AbstractIn this paper we present a different method for proving symmetry results in partial differential equations. The principal idea is to use the classical tool of shape optimization, namely, the differentiation with respect to the domain. The aim is to derive, from an optimality condition, information on the boundary of the domain.
Finite and Infinite Systems of Interacting Diffusions: Cluster Formation and Universality Properties
Authors: Cox John Ted , Greven Andreas , Shiga Tokuzo 
Published: May 2007

AbstractWe study some aspects of the relationship between the long time behaviour of systems with a finite but large number of components and their idealizations with countably many components. The following class of models is considered in detail, which contains examples occuring in population growth and population genetic models.
Some Remarks on Almost and Stable Almost Complex Manifolds
Authors: Dessai Anand 
Published: May 2007

AbstractIn the first part we give necessary and sufficient conditions for the existence of a stable almost complex structure on a 10‐manifold M with H1(M;ℤ) = 0 and no 2‐torsion in H1(M;ℤ) for i = 2,3. Using the Classification Theorem of Donaldson we give a reformulation of the conditions for a 4‐manifold to be almost complex in terms of Betti numbers and the dimension of the ±‐eigenspaces of the intersection form. In the second part we give general conditions for an almost complex manifold to admit infinitely many almost complex structures and apply these to symplectic manifolds, to homogeneous spaces and to complete intersections.
When Do Some Geodesics of the Induced and the Metrical Connection Coincide?
Authors: Dillen Franki , Vrancken Luc 
Published: May 2007

AbstractIn affine differential geometry, three natural connections can be considered, namely the induced connection, the Levi Civita connection of the affine metric and the conjugate connection. Quadrics are characterized by the conditions that all the pre‐geodesies with respect to one of these connections are also pre‐geodesies with respect to the other two connections. In the present paper we describe 3‐dimensional affine hypersurfaces for which some of the geodesies or pre‐geodesies for the different connections coincide.
Multiplicity Results for Second Order Nonlinear Problems with Maximum and Minimum
Authors: Stanêk Svatoslav 
Published: May 2007

AbstractA functional differential equation of the type where F: C1(J) → L1(J) is a unbounded operator, is considered. Sufficient conditions for the existence of at least two different solutions satisfying boundary conditions min{x(t): t ϵ J} = α, max{x(t): t ϵ J} = β are given.
On the Growth of Convergence Radii for the Eigenvalues of the Mathieu Equation
Authors: Volkmer Hans 
Published: May 2007

AbstractIt is proved that the convergence radii ρn of the eigenvalues of the Mathieu equation satisfy lim inf ρn/n2 > kk′K2 = 2.0418., where the modulus k of the complete elliptic integrals is determined by 2E = K.
On the Surjectivity of the Exponential Function of Solvable Lie Groups
Authors: Wüstner Michael 
Published: May 2007

AbstractFor a solvable Lie group G the surjectivity of the exponential function expG is equivalent to the connectedness of the near‐Cartan subgroups and to the connectedness of the centralizers in a Cartan subgroup of all nilpotent elements in its Lie algebra g. Furthermore, these conditions are satisfied if and only if for all elements g ϵ G there is an x ϵ g with g = expG x in which expG is regular.
The dual method of solving the linear programming problem
Authors: Lemke C. E. 
Published: May 2007

AbstractMany problems in logistics are capable of being formulated as linear programming problems. For example, one such problem is the so‐called transportation problem, which is concerned with obtaining the best way (in the sense of least time, or of least expense, etc.) of shipping stipulated quantities of materials from m origins to n destinations. This paper develops a new computational method of solving general linear programming problems.
Optimal two‐ and three‐stage production schedules with setup times included
Authors: Johnson S. M. 
Published: May 2007

AbstractEach of a collection of items are to be produced on two machines (or stages). Each machine can handle only one item at a time and each item must be processed through machine one and then through machine two. The setup time plus work time for each item for each machine is known. A simple decision rule is obtained in this paper for the optimal scheduling of the production so that the total elapsed time is a minimum. A three‐machine problem is also discussed and solved for a restricted case.
Detection of generic spaced motifs using submotif pattern mining
Authors: Wijaya Edward , Rajaraman Kanagasabai , Yiu Siu-Ming , Sung Wing-Kin 
Published: May 2007

AbstractMotivation: Identification of motifs is one of the critical stages in studying the regulatory interactions of genes. Motifs can have complicated patterns. In particular, spaced motifs, an important class of motifs, consist of several short segments separated by spacers of different lengths. Locating spaced motifs is not trivial. Existing motif-finding algorithms are either designed for monad motifs (short contiguous patterns with some mismatches) or have assumptions on the spacer lengths or can only handle at most two segments. An effective motif finder for generic spaced motifs is highly desirable.Results: This article proposes a novel approach for identifying spaced motifs with any number of spacers of different lengths. We introduce the notion of submotifs to capture the segments in the spaced motif and formulate the motif-finding problem as a frequent submotif mining problem. We provide an algorithm called SPACE to solve the problem. Based on experiments on real biological datasets, synthetic datasets and the motif assessment benchmarks by Tompa et al., we show that our algorithm performs better than existing tools for spaced motifs with improvements in both sensitivity and specificity and for monads, SPACE performs as good as other tools.Availability: The source code is available upon request from the authors.Contact: ksung@comp.nus.edu.sgSupplementary information: Supplementary data are available at Bioinformatics online.
BioDownloader: bioinformatics downloads and updates in a few clicks
Authors: Shapovalov Maxim V. , Canutescu Adrian A. , Dunbrack Roland L. 
Published: May 2007

Abstract
Summary: There are many ftp or http servers storing data required for biological research. While some download applications are available, there is no user-friendly download application with a graphical interface specifically designed and adapted to meet the requirements of bioinformatics. BioDownloader is a program for downloading and updating files from ftp and http servers. It is optimized to work robustly with large numbers of files. It allows the selective retrieval of only the required files (batch downloads, multiple file masks, ls-lR file parsing, recursive search, recent updates, etc.). BioDownloader has a built-in repository containing the settings for common bioinformatics file-synchronization needs, including the Protein Data Bank (PDB) and National Center for Biotechnology Information (NCBI) databases. It can post-process downloaded files, including archive extraction and file conversions.
Availability: The program can be installed from http://dunbrack.fccc.edu/BioDownloader. The software is freely available for both non-commercial and commercial users under the BSD license.
Contact: Roland.Dunbrack@fccc.edu
A Markov random field model for network-based analysis of genomic data
Authors: Wei Zhi , Li Hongzhe 
Published: May 2007

AbstractMotivation: A central problem in genomic research is the identification of genes and pathways involved in diseases and other biological processes. The genes identified or the univariate test statistics are often linked to known biological pathways through gene set enrichment analysis in order to identify the pathways involved. However, most of the procedures for identifying differentially expressed (DE) genes do not utilize the known pathway information in the phase of identifying such genes. In this article, we develop a Markov random field (MRF)-based method for identifying genes and subnetworks that are related to diseases. Such a procedure models the dependency of the DE patterns of genes on the networks using a local discrete MRF model.Results: Simulation studies indicated that the method is quite effective in identifying genes and subnetworks that are related to disease and has higher sensitivity and lower false discovery rates than the commonly used procedures that do not use the pathway structure information. Applications to two breast cancer microarray gene expression datasets identified several subnetworks on several of the KEGG transcriptional pathways that are related to breast cancer recurrence or survival due to breast cancer.Conclusions: The proposed MRF-based model efficiently utilizes the known pathway structures in identifying the DE genes and the subnetworks that might be related to phenotype. As more biological networks are identified and documented in databases, the proposed method should find more applications in identifying the subnetworks that are related to diseases and other biological processes.Contact: hongzhe@mail.med.upenn.edu or hli@cceb.upenn.edu
Genomix: a method for combining gene-finders' predictions, which uses evolutionary conservation of sequence and intron–exon structure
Authors: Coghlan Avril , Durbin Richard 
Published: May 2007

AbstractMotivation: Correct gene predictions are crucial for most analyses of genomes. However, in the absence of transcript data, gene prediction is still challenging. One way to improve gene-finding accuracy in such genomes is to combine the exons predicted by several gene-finders, so that gene-finders that make uncorrelated errors can correct each other.Results: We present a method for combining gene-finders called Genomix. Genomix selects the predicted exons that are best conserved within and/or between species in terms of sequence and intron–exon structure, and combines them into a gene structure. Genomix was used to combine predictions from four gene-finders for Caenorhabditis elegans, by selecting the predicted exons that are best conserved with C.briggsae and C.remanei. On a set of ∼1500 confirmed C.elegans genes, Genomix increased the exon-level specificity by 10.1% and sensitivity by 2.7% compared to the best input gene-finder.Availability: Scripts and Supplementary Material can be found at http://www.sanger.ac.uk/Software/analysis/genomixContact: alc@sanger.ac.ukSupplementary information: Supplementary data are available at Bioinformatics online.
Weighted rank aggregation of cluster validation measures: a Monte Carlo cross-entropy approach
Authors: Pihur Vasyl , Datta Susmita , Datta Somnath 
Published: May 2007

Abstract
Motivation: Biologists often employ clustering techniques in the explorative phase of microarray data analysis to discover relevant biological groupings. Given the availability of numerous clustering algorithms in the machine-learning literature, an user might want to select one that performs the best for his/her data set or application. While various validation measures have been proposed over the years to judge the quality of clusters produced by a given clustering algorithm including their biological relevance, unfortunately, a given clustering algorithm can perform poorly under one validation measure while outperforming many other algorithms under another validation measure. A manual synthesis of results from multiple validation measures is nearly impossible in practice, especially, when a large number of clustering algorithms are to be compared using several measures. An automated and objective way of reconciling the rankings is needed.
Results: Using a Monte Carlo cross-entropy algorithm, we successfully combine the ranks of a set of clustering algorithms under consideration via a weighted aggregation that optimizes a distance criterion. The proposed weighted rank aggregation allows for a far more objective and automated assessment of clustering results than a simple visual inspection. We illustrate our procedure using one simulated as well as three real gene expression data sets from various platforms where we rank a total of eleven clustering algorithms using a combined examination of 10 different validation measures. The aggregate rankings were found for a given number of clusters k and also for an entire range of k.
Availability: R code for all validation measures and rank aggregation is available from the authors upon request.
Contact: somnath.datta@louisville.edu
Supplementary information: Supplementary information are available at http://www.somnathdatta.org/Supp/RankCluster/supp.htm.
Incorporating prior knowledge of predictors into penalized classifiers with multiple penalty terms
Authors: Tai Feng , Pan Wei 
Published: May 2007

AbstractMotivation: In the context of sample (e.g. tumor) classifications with microarray gene expression data, many methods have been proposed. However, almost all the methods ignore existing biological knowledge and treat all the genes equally a priori. On the other hand, because some genes have been identified by previous studies to have biological functions or to be involved in pathways related to the outcome (e.g. cancer), incorporating this type of prior knowledge into a classifier can potentially improve both the predictive performance and interpretability of the resulting model.Results: We propose a simple and general framework to incorporate such prior knowledge into building a penalized classifier. As two concrete examples, we apply the idea to two penalized classifiers, nearest shrunken centroids (also called PAM) and penalized partial least squares (PPLS). Instead of treating all the genes equally a priori as in standard penalized methods, we group the genes according to their functional associations based on existing biological knowledge or data, and adopt group-specific penalty terms and penalization parameters. Simulated and real data examples demonstrate that, if prior knowledge on gene grouping is indeed informative, our new methods perform better than the two standard penalized methods, yielding higher predictive accuracy and screening out more irrelevant genes.Contact: weip@biostat.umn.edu
Improving the efficacy of trastuzumab in breast cancer
Authors: Suzuki Eiji , Toi Masakazu 
Published: May 2007

Although overexpression of human epidermal growth factor receptor 2 (HER2) protein, amplification of the gene or both are associated with poor prognosis in breast cancer, trastuzumab has clearly provided clinical benefits in metastatic breast cancer, adjuvant treatment settings and primary systemic therapy. However, even in those HER2 overexpressors, the majority of patients who achieve an initial response generally acquire resistance within 1 year. Therefore, it is critical to elucidate the mechanism of resistance and to search for better combination treatments with chemotherapeutic agents or other novel modalities. Here, we discuss both clinical and preclinical data regarding these issues. (Cancer Sci 2007; 98: 767–771)
Association of maternal fat and alcohol intake with maternal and umbilical hormone levels and birth weight
Authors: Nagata Chisato , Iwasa Shinichi , Shiraki Makoto , Sahashi Yukari , Shimizu Hiroyuki 
Published: May 2007

High levels of estrogen during pregnancy have been hypothesized to increase the risk of breast cancer in offspring. Some studies have reported a positive association of estrogen level during pregnancy with fetal size, which has been linked to the subsequent risk of breast cancer in offspring. We examined whether maternal diet, including fat and alcohol intake, was associated with hormone levels during pregnancy, as well as with birth weight. The concentrations of estradiol, estriol, and testosterone were measured in the maternal serum and umbilical cord blood of 189 women during pregnancy and at delivery. Intakes of fat, alcohol, and other nutrients were assessed by 5‐day diet records at approximately the 29th week of pregnancy before blood sampling. Intake of polyunsaturated fatty acids was moderately but significantly positively correlated with the umbilical cord estriol level (r = 0.17, P = 0.03) after controlling for covariates. The positive association between intake of polyunsaturated fatty acids and birth weight was of borderline significance (r = 0.14, P = 0.06). Intake of long‐chain n‐3 fatty acids was significantly inversely correlated with the umbilical cord estradiol and testosterone levels (r = –0.18, P = 0.02 and r = –0.24, P = 0.002, respectively). Alcohol intake was significantly positively correlated with the maternal estradiol level in the 29th week of pregnancy (r = 0.19, P = 0.01), but was unrelated to birth weight. Estrogen level during pregnancy may be regulated by dietary polyunsaturated fatty acids and mediate their effects on fetal growth. (Cancer Sci 2007; 98: 869–873)