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Independent Set (independent + set)
Selected AbstractsIndependent sets of maximal size in tensor powers of vertex-transitive graphsJOURNAL OF GRAPH THEORY, Issue 4 2009Cheng Yeaw Ku Abstract Let G be a connected, nonbipartite vertex-transitive graph. We prove that if the only independent sets of maximal cardinality in the tensor product G × G are the preimages of the independent sets of maximal cardinality in G under projections, then the same holds for all finite tensor powers of G, thus providing an affirmative answer to a question raised by Larose and Tardif (J Graph Theory 40(3) (2002), 162,171). © 2009 Wiley Periodicals, Inc. J Graph Theory 60: 295-301, 2009 [source] Selecting discriminant function models for predicting the expected richness of aquatic macroinvertebratesFRESHWATER BIOLOGY, Issue 2 2006JOHN VAN SICKLE Summary 1. The predictive modelling approach to bioassessment estimates the macroinvertebrate assemblage expected at a stream site if it were in a minimally disturbed reference condition. The difference between expected and observed assemblages then measures the departure of the site from reference condition. 2. Most predictive models employ site classification, followed by discriminant function (DF) modelling, to predict the expected assemblage from a suite of environmental variables. Stepwise DF analysis is normally used to choose a single subset of DF predictor variables with a high accuracy for classifying sites. An alternative is to screen all possible combinations of predictor variables, in order to identify several ,best' subsets that yield good overall performance of the predictive model. 3. We applied best-subsets DF analysis to assemblage and environmental data from 199 reference sites in Oregon, U.S.A. Two sets of 66 best DF models containing between one and 14 predictor variables (that is, having model orders from one to 14) were developed, for five-group and 11-group site classifications. 4. Resubstitution classification accuracy of the DF models increased consistently with model order, but cross-validated classification accuracy did not improve beyond seventh or eighth-order models, suggesting that the larger models were overfitted. 5. Overall predictive model performance at model training sites, measured by the root-mean-squared error of the observed/expected species richness ratio, also improved steadily with DF model order. But high-order DF models usually performed poorly at an independent set of validation sites, another sign of model overfitting. 6. Models selected by stepwise DF analysis showed evidence of overfitting and were outperformed by several of the best-subsets models. 7. The group separation strength of a DF model, as measured by Wilks',, was more strongly correlated with overall predictive model performance at training sites than was DF classification accuracy. 8. Our results suggest improved strategies for developing reliable, parsimonious predictive models. We emphasise the value of independent validation data for obtaining a realistic picture of model performance. We also recommend assessing not just one or two, but several, candidate models based on their overall performance as well as the performance of their DF component. 9. We provide links to our free software for stepwise and best-subsets DF analysis. [source] Association study between kynurenine 3-monooxygenase gene and schizophrenia in the Japanese populationGENES, BRAIN AND BEHAVIOR, Issue 4 2006N. Aoyama Several lines of evidence suggest that metabolic changes in the kynurenic acid (KYNA) pathway are related to the etiology of schizophrenia. The inhibitor of kynurenine 3-monooxygenase (KMO) is known to increase KYNA levels, and the KMO gene is located in the chromosome region associated with schizophrenia, 1q42-q44. Single-marker and haplotype analyses for 6-tag single nucleotide polymorphisms (SNPs) of KMO were performed (cases = 465, controls = 440). Significant association of rs2275163 with schizophrenia was observed by single-marker comparisons (P = 0.032) and haplotype analysis including this SNP (P = 0.0049). Significant association of rs2275163 and haplotype was not replicated using a second, independent set of samples (cases = 480, controls = 448) (P = 0.706 and P = 0.689, respectively). These results suggest that the KMO is unlikely to be related to the development of schizophrenia in Japanese. [source] Identification of genes with abnormal expression changes in acute myeloid leukemiaGENES, CHROMOSOMES AND CANCER, Issue 1 2008Derek L. Stirewalt Acute myeloid leukemia (AML) is one of the most common and deadly forms of hematopoietic malignancies. We hypothesized that microarray studies could identify previously unrecognized expression changes that occur only in AML blasts. We were particularly interested in those genes with increased expression in AML, believing that these genes may be potential therapeutic targets. To test this hypothesis, we compared gene expression profiles between normal hematopoietic cells from 38 healthy donors and leukemic blasts from 26 AML patients. Normal hematopoietic samples included CD34+ selected cells (N = 18), unselected bone marrows (N = 10), and unselected peripheral bloods (N = 10). Twenty genes displayed AML-specific expression changes that were not found in the normal hematopoietic cells. Subsequent analyses using microarray data from 285 additional AML patients confirmed expression changes for 13 of the 20 genes. Seven genes (BIK, CCNA1, FUT4, IL3RA, HOMER3, JAG1, WT1) displayed increased expression in AML, while 6 genes (ALDHA1A, PELO, PLXNC1, PRUNE, SERPINB9, TRIB2) displayed decreased expression. Quantitative RT/PCR studies for the 7 over-expressed genes were performed in an independent set of 9 normal and 21 pediatric AML samples. All 7 over-expressed genes displayed an increased expression in the AML samples compared to normals. Three of the 7 over-expressed genes (WT1, CCNA1, and IL3RA) have already been linked to leukemogenesis and/or AML prognosis, while little is known about the role of the other 4 over-expressed genes in AML. Future studies will determine their potential role in leukemogenesis and their clinical significance. This article contains Supplementary Material available at http://www.interscience.wiley.com/jpages/1045-2257/suppmat. © 2007 Wiley-Liss, Inc. [source] Upregulation of the tumor suppressor gene menin in hepatocellular carcinomas and its significance in fibrogenesis,HEPATOLOGY, Issue 5 2006Pierre J. Zindy The molecular mechanisms underlying the progression of cirrhosis toward hepatocellular carcinoma were investigated by a combination of DNA microarray analysis and literature data mining. By using a microarray screening of suppression subtractive hybridization cDNA libraries, we first analyzed genes differentially expressed in tumor and nontumor livers with cirrhosis from 15 patients with hepatocellular carcinomas. Seventy-four genes were similarly recovered in tumor (57.8% of differentially expressed genes) and adjacent nontumor tissues (64% of differentially expressed genes) compared with histologically normal livers. Gene ontology analyses revealed that downregulated genes (n = 35) were mostly associated with hepatic functions. Upregulated genes (n = 39) included both known genes associated with extracellular matrix remodeling, cell communication, metabolism, and post-transcriptional regulation gene (e.g., ZFP36L1), as well as the tumor suppressor gene menin (multiple endocrine neoplasia type 1; MEN1). MEN1 was further identified as an important node of a regulatory network graph that integrated array data with array-independent literature mining. Upregulation of MEN1 in tumor was confirmed in an independent set of samples and associated with tumor size (P = .016). In the underlying liver with cirrhosis, increased steady-state MEN1 mRNA levels were correlated with those of collagen ,2(I) mRNA (P < .01). In addition, MEN1 expression was associated with hepatic stellate cell activation during fibrogenesis and involved in transforming growth factor beta (TGF-,),dependent collagen ,2(I) regulation. In conclusion, menin is a key regulator of gene networks that are activated in fibrogenesis associated with hepatocellular carcinoma through the modulation of TGF-, response. (HEPATOLOGY 2006;44:1296,1307.) [source] A new distributed approximation algorithm for constructing minimum connected dominating set in wireless ad hoc networksINTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS, Issue 8 2005Bo Gao Abstract In recent years, constructing a virtual backbone by nodes in a connected dominating set (CDS) has been proposed to improve the performance of ad hoc wireless networks. In general, a dominating set satisfies that every vertex in the graph is either in the set or adjacent to a vertex in the set. A CDS is a dominating set that also induces a connected sub-graph. However, finding the minimum connected dominating set (MCDS) is a well-known NP-hard problem in graph theory. Approximation algorithms for MCDS have been proposed in the literature. Most of these algorithms suffer from a poor approximation ratio, and from high time complexity and message complexity. In this paper, we present a new distributed approximation algorithm that constructs a MCDS for wireless ad hoc networks based on a maximal independent set (MIS). Our algorithm, which is fully localized, has a constant approximation ratio, and O(n) time and O(n) message complexity. In this algorithm, each node only requires the knowledge of its one-hop neighbours and there is only one shortest path connecting two dominators that are at most three hops away. We not only give theoretical performance analysis for our algorithm, but also conduct extensive simulation to compare our algorithm with other algorithms in the literature. Simulation results and theoretical analysis show that our algorithm has better efficiency and performance than others. Copyright © 2005 John Wiley & Sons, Ltd. [source] A constructive approach for the lower bounds on the Ramsey numbers R (s, t)JOURNAL OF GRAPH THEORY, Issue 3 2004Xu Xiaodong Abstract Graph G is a (k,,p)-graph if G does not contain a complete graph on k vertices Kk, nor an independent set of order p. Given a (k,,p)-graph G and a (k,,q)-graph H, such that G and H contain an induced subgraph isomorphic to some Kk,1 -free graph M, we construct a (k,,p,+,q,,,1)-graph on n(G),+,n(H),+,n(M) vertices. This implies that R,(k,,p,+,q,,,1),,,R,(k,,p),+,R,(k,,q),+,n(M),,,1, where R,(s,,t) is the classical two-color Ramsey number. By applying this construction, and some its generalizations, we improve on 22 lower bounds for R,(s,,t), for various specific values of s and t. In particular, we obtain the following new lower bounds: R,(4,,15) , 153, R,(6,,7) , 111, R,(6,,11) , 253, R,(7,,12) , 416, and R,(8,,13) , 635. Most of the results did not require any use of computer algorithms. © 2004 Wiley Periodicals, Inc. J Graph Theory 47: 231,239, 2004 [source] A new thermodynamic model for clino- and orthoamphiboles in the system Na2O,CaO,FeO,MgO,Al2O3,SiO2,H2O,OJOURNAL OF METAMORPHIC GEOLOGY, Issue 6 2007J. F. A. DIENER Abstract A recent thermodynamic model for the Na,Ca clinoamphiboles in the system Na2O,CaO,FeO,MgO,Al2O3,SiO2,H2O,O (NCFMASHO), is improved, and extended to include cummingtonite,grunerite and the orthoamphiboles, anthophyllite and gedrite. The clinoamphibole model in NCMASH is adopted, but the extension into the FeO- and Fe2O3 -bearing systems is revised to provide thermodynamic consistency and better agreement with natural assemblage data. The new model involves order,disorder of Fe,Mg between the M2, M13 and M4 sites in the amphibole structure, calibrated using the experimental data on site distributions in cummingtonite,grunerite. In the independent set of end-members used to represent the thermodynamics, grunerite (rather than ferroactinolite) is used for FeO, with two ordered Fe,Mg end-members, and magnesioriebeckite (rather than ferritschermakite) is used for Fe2O3. Natural assemblage data for coexisting clinoamphiboles are used to constrain the interaction energies between the various amphibole end-members. For orthamphibole, the assumption is made that the site distributions and the non-ideal formulation is the same as for clinoamphibole. The data set end-members anthophyllite, ferroanthophyllite and gedrite, are used; for the others, they are based on the clinoamphibole end-members, with the necessary adjustments to their enthalpies constrained by natural assemblage data for coexisting clino- and orthoamphiboles. The efficacy of the models is illustrated with P,T grids and various pseudosections, with a particular emphasis on the prediction of mineral assemblages in ferric-bearing systems. [source] Maximum independent set for intervals by divide and conquer with pruningNETWORKS: AN INTERNATIONAL JOURNAL, Issue 2 2007Jack Snoeyink Abstract Suppose a given set of n intervals contains a maximum independent set of k disjoint intervals. This brief note demonstrates that "divide and conquer with pruning" produces an easy, output-sensitive O(n log k)-time algorithm to compute such a maximum independent set. © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 49(2), 158,159 2007 [source] Distance-two interpolation for parallel algebraic multigridNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 2-3 2008Hans De Sterck Abstract Algebraic multigrid (AMG) is one of the most efficient and scalable parallel algorithms for solving sparse linear systems on unstructured grids. However, for large 3D problems, the coarse grids that are normally used in AMG often lead to growing complexity in terms of memory use and execution time per AMG V-cycle. Sparser coarse grids, such as those obtained by the parallel modified independent set (PMIS) coarsening algorithm, remedy this complexity growth but lead to nonscalable AMG convergence factors when traditional distance-one interpolation methods are used. In this paper, we study the scalability of AMG methods that combine PMIS coarse grids with long-distance interpolation methods. AMG performance and scalability are compared for previously introduced interpolation methods as well as new variants of them for a variety of relevant test problems on parallel computers. It is shown that the increased interpolation accuracy largely restores the scalability of AMG convergence factors for PMIS-coarsened grids, and in combination with complexity reducing methods, such as interpolation truncation, one obtains a class of parallel AMG methods that enjoy excellent scalability properties on large parallel computers. Copyright © 2007 John Wiley & Sons, Ltd. [source] Genetic modifiers of the severity of sickle cell anemia identified through a genome-wide association study,AMERICAN JOURNAL OF HEMATOLOGY, Issue 1 2010Paola Sebastiani We conducted a genome-wide association study (GWAS) to discover single nucleotide polymorphisms (SNPs) associated with the severity of sickle cell anemia in 1,265 patients with either "severe" or "mild" disease based on a network model of disease severity. We analyzed data using single SNP analysis and a novel SNP set enrichment analysis (SSEA) developed to discover clusters of associated SNPs. Single SNP analysis discovered 40 SNPs that were strongly associated with sickle cell severity (odds for association >1,000); of the 32 that we could analyze in an independent set of 163 patients, five replicated, eight showed consistent effects although failed to reach statistical significance, whereas 19 did not show any convincing association. Among the replicated associations are SNPs in KCNK6 a K+ channel gene. SSEA identified 27 genes with a strong enrichment of significant SNPs (P < 10,6); 20 were replicated with varying degrees of confidence. Among the novel findings identified by SSEA is the telomere length regulator gene TNKS. These studies are the first to use GWAS to understand the genetic diversity that accounts the phenotypic heterogeneity sickle cell anemia as estimated by an integrated model of severity. Additional validation, resequencing, and functional studies to understand the biology and reveal mechanisms by which candidate genes might have their effects are the future goals of this work. Am. J. Hematol., 2010. © 2009 Wiley-Liss, Inc. [source] Sampling independent sets in the discrete torus,RANDOM STRUCTURES AND ALGORITHMS, Issue 3 2008David GalvinArticle first published online: 27 MAY 200 Abstract The even discrete torus is the graph TL,d on vertex set {0,,,L , 1}d (with L even) in which two vertices are adjacent if they differ on exactly one coordinate and differ by 1(modL) on that coordinate. The hard-core measure with activity , on TL,d is the probability distribution ,, on the independent sets (sets of vertices spanning no edges) of TL,d in which an independent set I is chosen with probability proportional to ,|I|. This distribution occurs naturally in problems from statistical physics and the study of communication networks. We study Glauber dynamics, a single-site update Markov chain on the set of independent sets of TL,d whose stationary distribution is ,,. We show that for , = ,(d,1/4 log 3/4d) and d sufficiently large the convergence to stationarity is (essentially) exponentially slow in Ld,1. This improves a result of Borgs, Chayes, Frieze, Kim, Tetali, Vigoda, and Vu (Proceedings of the IEEE FOCS (1999), 218,229) 5 who had shown slow mixing of Glauber dynamics for , growing exponentially with d. Our proof, which extends to ,-local chains (chains which alter the state of at most a proportion , of the vertices in each step) for suitable ,, closely follows the conductance argument of Borgs et al., 5 adding to it some combinatorial enumeration methods that are modifications of those used by Galvin and Kahn (Combinatorics, Probability and Computing 13 (2004), 137,164) 12 to show that the hard-core model with parameter , on the integer lattice ,d exhibits phase coexistence for , = ,(d,1/4 log 3/4d). The discrete even torus is a bipartite graph, with partition classes , (consisting of those vertices the sum of whose coordinates is even) and . Our result can be expressed combinatorially as the statement that for each sufficiently large ,, there is a ,(,) > 0 such that if I is an independent set chosen according to ,,, then the probability that ,I ,,|,|I ,, is at most ,(,)Ld is exponentially small in Ld,1. In particular, we obtain the combinatorial result that for all , > 0 the probability that a uniformly chosen independent set from TL,d satisfies ,I ,,|,|I ,,, (.25 - ,)Ld is exponentially small in Ld,1. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008 [source] Maximum weight independent sets and matchings in sparse random graphs.RANDOM STRUCTURES AND ALGORITHMS, Issue 1 2006Exact results using the local weak convergence method Let G(n,c/n) and Gr(n) be an n -node sparse random graph and a sparse random r -regular graph, respectively, and let I(n,r) and I(n,c) be the sizes of the largest independent set in G(n,c/n) and Gr(n). The asymptotic value of I(n,c)/n as n , ,, can be computed using the Karp-Sipser algorithm when c , e. For random cubic graphs, r = 3, it is only known that .432 , lim infnI(n,3)/n , lim supnI(n,3)/n , .4591 with high probability (w.h.p.) as n , ,, as shown in Frieze and Suen [Random Structures Algorithms 5 (1994), 649,664] and Bollabas [European J Combin 1 (1980), 311,316], respectively. In this paper we assume in addition that the nodes of the graph are equipped with nonnegative weights, independently generated according to some common distribution, and we consider instead the maximum weight of an independent set. Surprisingly, we discover that for certain weight distributions, the limit limnI(n,c)/n can be computed exactly even when c > e, and limnI(n,r)/n can be computed exactly for some r , 1. For example, when the weights are exponentially distributed with parameter 1, limnI(n,2e)/n , .5517, and limnI(n,3)/n , .6077. Our results are established using the recently developed local weak convergence method further reduced to a certain local optimality property exhibited by the models we consider. We extend our results to maximum weight matchings in G(n,c/n) and Gr(n). For the case of exponential distributions, we compute the corresponding limits for every c > 0 and every r , 2. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006 [source] Endothelial Gene Expression in Kidney Transplants with Alloantibody Indicates Antibody-Mediated Damage Despite Lack of C4d StainingAMERICAN JOURNAL OF TRANSPLANTATION, Issue 10 2009Banu Sis Anti-HLA alloantibody is a risk factor for graft loss, but does not indicate which kidneys are experiencing antibody-mediated rejection (ABMR). C4d staining in biopsies is specific for ABMR but insensitive. We hypothesized that altered expression of endothelial genes due to alloantibody acting on the microcirculation would be sensitive indicator of ABMR. We identified 119 endothelial-associated transcripts (ENDATs) from literature, and studied their expression by microarrays in 173 renal allograft biopsies for cause. Mean ENDAT expression was increased in all rejection but was higher in ABMR than in T-cell-mediated rejection and correlated with histopathologic lesions of ABMR, and alloantibody. Many individual ENDATs were increased in ABMR and predicted graft loss. Kidneys with high ENDATs and antibody showed increased lesions of ABMR and worse prognosis in comparison to controls. Only 40% of kidneys with high ENDAT expression and chronic ABMR or graft loss were diagnosed by C4d positivity. High ENDAT expression with antibody predicts graft loss with higher sensitivity (77% vs. 31%) and slightly lower specificity (71% vs. 94%) than C4d. The results were validated in independent set of 82 kidneys. High renal endothelial transcript expression in patients with alloantibody is indicator of active antibody-mediated allograft damage and poor graft outcome. [source] Validation of whole genome linkage-linkage disequilibrium and association results, and identification of markers to predict genetic merit for twinningANIMAL GENETICS, Issue 4 2010C. D. Bierman Summary A previous genome-wide search with a moderate density 10K marker set identified many marker associations with twinning rate, either through single-marker analysis or combined linkage-linkage disequilibrium (LLD; haplotype) analysis. The objective of the current study was to validate putative marker associations using an independent set of phenotypic data. Holstein bulls (n = 921) from 100 paternal half-sib families were genotyped. Twinning rate predicted transmitting abilities were calculated using calving records from 1994 to 1998 (Data I) and 1999 to 2006 (Data II), and the underlying liability scores from threshold model analysis were used as the trait in marker association analyses. The previous analysis used 201 bulls with daughter records in Data I. In the current analysis, this was increased to 434, providing a revised estimate of effect and significance. Bulls with daughter records in Data II totaled 851, and analysis of this data provided the validation of results from analysis of Data I. Single nucleotide polymorphisms (SNPs) were selected to validate previously significant single-marker associations and LLD results. Bulls were genotyped for a total of 306 markers. Nine of 13 LLD regions located on chromosomes 1, 2, 3, 6, 9, 22, 23(2) and 26 were validated, showing significant results for both Data I and II. Association analysis revealed 55 of 174 markers validated, equating to a single-marker validation rate of 31%. Stepwise backward elimination and cross-validation analyses identified 18 SNPs for use in a final reduced marker panel explaining 34% of the genetic variation, and to allow prediction of genetic merit for twinning rate. [source] Assignment of the locus for arachnomelia syndrome to bovine chromosome 23 in Simmental cattleANIMAL GENETICS, Issue 6 2009J. Buitkamp Summary Arachnomelia syndrome is a lethal inherited malformation mainly of the limbs, vertebral column and skull in cattle, which poses a severe impairment to farmers and breeders. Recently, a number of cases of arachnomelia syndrome have occurred in the Simmental breed and some sires with excellent breeding values had been shown to be carriers of the disease. We herein report the genetic mapping of the mutation underlying arachnomelia in cattle. The disease was mapped using a two-stage genome scan. A first round autosomal genome-wide screening using a limited number of cases identified three chromosomal regions with lod-scores > 1. The position of the arachnomelia syndrome locus was identified to be on BTA 23 by genotyping an additional, independent set of animals with markers that provided positive lod-scores in the course of the initial genome-wide screen. Using a denser set of regional microsatellites, the locus could be mapped to a region about 9 cM in length. The most significant linkage signal with arachnomelia syndrome was obtained with marker NRKM-17 (lod-score > 20) using a recessive model. Interestingly, different genes seem to be responsible for the disease in Brown Swiss and Simmental breeds, as arachnomelia syndrome was mapped to a different location in Brown Swiss. The results provide sufficient information for the development of a genetic test system and also allow the identification of positional candidate genes. [source] Magnetic resonance imaging as a potential surrogate for relapses in multiple sclerosis: A meta-analytic approach,ANNALS OF NEUROLOGY, Issue 3 2009Maria Pia Sormani MscStat Objective The aim of this work was to evaluate whether the treatment effects on magnetic resonance imaging (MRI) markers at the trial level were able to predict the treatment effects on relapse rate in relapsing-remitting multiple sclerosis. Methods We used a pooled analysis of all the published randomized, placebo-controlled clinical trials in relapsing-remitting multiple sclerosis reporting data both on MRI variables and relapses. We extracted data on relapses and on MRI "active" lesions. A regression analysis weighted on trial size and duration was performed to study the relation between the treatment effect on relapses and the treatment effect on MRI lesions. We validated the estimated relation on an independent set of clinical trials satisfying the same inclusion criteria but with a control arm other than placebo. Results A set of 23 randomized, double-blind, placebo-controlled trials in relapsing-remitting multiple sclerosis was identified, for a total of 63 arms, 40 contrasts, and 6,591 patients. A strong correlation was found between the effect on the relapses and the effect on MRI activity. The adjusted R2 value of the weighted regression line was 0.81. The regression equation estimated using the placebo-controlled trials gave a satisfactory prediction of the treatment effect on relapses when applied to the validation set. Interpretation More than 80% of the variance in the effect on relapses between trials is explained by the variance in MRI effects. Smaller and shorter phase II studies based on MRI lesion end points may give indications also on the effect of the treatment on relapse end points. Ann Neurol 2009;65:268,275 [source] Assessment of Protection Systems for Buried Steel Pipelines Endangered by RockfallCOMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 5 2005Bernhard Pichler First, a gravel-based protection system (GBPS) is investigated, that is, a pipeline buried in sandy gravel is considered. To assess the load-carrying behavior of this structure when subjected to rockfall, a finite element (FE) model has been developed. The development and the validation of this structural model are strictly separated, that is, they are based on two physically and statistically independent sets of experiments. Subsequently, scenarios of rockfall onto a gravel-buried steel pipe are analyzed considering different boundary conditions and structural dimensions. Following the conclusions drawn from these numerical analyses, an enhanced protection system (EPS) is proposed. It consists of gravel as an energy-absorbing and impact-damping system and a buried steel plate resting on walls made of concrete representing a load-carrying structural component. The potential and the limitations of both protection systems are discussed in detail. [source] Retrospective selection bias (or the benefit of hindsight)GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2001Francesco Mulargia SUMMARY The complexity of geophysical systems makes modelling them a formidable task, and in many cases research studies are still in the phenomenological stage. In earthquake physics, long timescales and the lack of any natural laboratory restrict research to retrospective analysis of data. Such ,fishing expedition' approaches lead to optimal selection of data, albeit not always consciously. This introduces significant biases, which are capable of falsely representing simple statistical fluctuations as significant anomalies requiring fundamental explanations. This paper identifies three different strategies for discriminating real issues from artefacts generated retrospectively. The first attempts to identify ab initio each optimal choice and account for it. Unfortunately, a satisfactory solution can only be achieved in particular cases. The second strategy acknowledges this difficulty as well as the unavoidable existence of bias, and classifies all ,anomalous' observations as artefacts unless their retrospective probability of occurrence is exceedingly low (for instance, beyond six standard deviations). However, such a strategy is also likely to reject some scientifically important anomalies. The third strategy relies on two separate steps with learning and validation performed on effectively independent sets of data. This approach appears to be preferable in the case of small samples, such as are frequently encountered in geophysics, but the requirement for forward validation implies long waiting times before credible conclusions can be reached. A practical application to pattern recognition, which is the prototype of retrospective ,fishing expeditions', is presented, illustrating that valid conclusions are hard to find. [source] Independent sets of maximal size in tensor powers of vertex-transitive graphsJOURNAL OF GRAPH THEORY, Issue 4 2009Cheng Yeaw Ku Abstract Let G be a connected, nonbipartite vertex-transitive graph. We prove that if the only independent sets of maximal cardinality in the tensor product G × G are the preimages of the independent sets of maximal cardinality in G under projections, then the same holds for all finite tensor powers of G, thus providing an affirmative answer to a question raised by Larose and Tardif (J Graph Theory 40(3) (2002), 162,171). © 2009 Wiley Periodicals, Inc. J Graph Theory 60: 295-301, 2009 [source] ARMS: an algebraic recursive multilevel solver for general sparse linear systemsNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 5 2002Y. Saad Abstract This paper presents a general preconditioning method based on a multilevel partial elimination approach. The basic step in constructing the preconditioner is to separate the initial points into two parts. The first part consists of ,block' independent sets, or ,aggregates'. Unknowns of two different aggregates have no coupling between them, but those in the same aggregate may be coupled. The nodes not in the first part constitute what might be called the ,coarse' set. It is natural to call the nodes in the first part ,fine' nodes. The idea of the methods is to form the Schur complement related to the coarse set. This leads to a natural block LU factorization which can be used as a preconditioner for the system. This system is then solved recursively using as preconditioner the factorization that could be obtained from the next level. Iterations between levels are allowed. One interesting aspect of the method is that it provides a common framework for many other techniques. Numerical experiments are reported which indicate that the method can be fairly robust. Copyright © 2002 John Wiley & Sons, Ltd. [source] HLA genes and surnames show a similar genetic structure in Lombardy: Does this reflect part of the history of the region?AMERICAN JOURNAL OF HUMAN BIOLOGY, Issue 3 2007Antonella Lisa Lombardy, in northern Italy, is the most populated and industrialized Italian region. We attempt to study its genetic structure with two independent sets of data: HLA allele frequencies and surnames. According to our results, it is plausible to deduce that ancient history, more than genetic isolation and drift, may have contributed to the present genetic structure of Lombardy. The hypothesis seems to be confirmed by the results of the cluster analysis of the 11 provinces of the region, which was performed using two different types of markers. Both genes and surnames show approximately the same structure. Not only Celts but also ancient Ligurians (and Etruscans) probably shaped the region into the present three clusters in which the 11 provinces appear to be genetically structured. In particular, an ancient historic, archaeological, and linguistic boundary, along the Adda River, seems to be preserved in present-day Lombardy's population structure.Am. J.Hum. Biol. 19:311,318, 2007. © 2007 Wiley-Liss, Inc. [source] Sampling independent sets in the discrete torus,RANDOM STRUCTURES AND ALGORITHMS, Issue 3 2008David GalvinArticle first published online: 27 MAY 200 Abstract The even discrete torus is the graph TL,d on vertex set {0,,,L , 1}d (with L even) in which two vertices are adjacent if they differ on exactly one coordinate and differ by 1(modL) on that coordinate. The hard-core measure with activity , on TL,d is the probability distribution ,, on the independent sets (sets of vertices spanning no edges) of TL,d in which an independent set I is chosen with probability proportional to ,|I|. This distribution occurs naturally in problems from statistical physics and the study of communication networks. We study Glauber dynamics, a single-site update Markov chain on the set of independent sets of TL,d whose stationary distribution is ,,. We show that for , = ,(d,1/4 log 3/4d) and d sufficiently large the convergence to stationarity is (essentially) exponentially slow in Ld,1. This improves a result of Borgs, Chayes, Frieze, Kim, Tetali, Vigoda, and Vu (Proceedings of the IEEE FOCS (1999), 218,229) 5 who had shown slow mixing of Glauber dynamics for , growing exponentially with d. Our proof, which extends to ,-local chains (chains which alter the state of at most a proportion , of the vertices in each step) for suitable ,, closely follows the conductance argument of Borgs et al., 5 adding to it some combinatorial enumeration methods that are modifications of those used by Galvin and Kahn (Combinatorics, Probability and Computing 13 (2004), 137,164) 12 to show that the hard-core model with parameter , on the integer lattice ,d exhibits phase coexistence for , = ,(d,1/4 log 3/4d). The discrete even torus is a bipartite graph, with partition classes , (consisting of those vertices the sum of whose coordinates is even) and . Our result can be expressed combinatorially as the statement that for each sufficiently large ,, there is a ,(,) > 0 such that if I is an independent set chosen according to ,,, then the probability that ,I ,,|,|I ,, is at most ,(,)Ld is exponentially small in Ld,1. In particular, we obtain the combinatorial result that for all , > 0 the probability that a uniformly chosen independent set from TL,d satisfies ,I ,,|,|I ,,, (.25 - ,)Ld is exponentially small in Ld,1. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008 [source] Slow mixing of Glauber dynamics for the hard-core model on regular bipartite graphsRANDOM STRUCTURES AND ALGORITHMS, Issue 4 2006David Galvin Abstract Let , = (V,E) be a finite, d -regular bipartite graph. For any , > 0 let ,, be the probability measure on the independent sets of , in which the set I is chosen with probability proportional to ,|I| (,, is the hard-core measure with activity , on ,). We study the Glauber dynamics, or single-site update Markov chain, whose stationary distribution is ,,. We show that when , is large enough (as a function of d and the expansion of subsets of single-parity of V) then the convergence to stationarity is exponentially slow in |V(,)|. In particular, if , is the d -dimensional hypercube {0,1}d we show that for values of , tending to 0 as d grows, the convergence to stationarity is exponentially slow in the volume of the cube. The proof combines a conductance argument with combinatorial enumeration methods. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006 [source] Maximum weight independent sets and matchings in sparse random graphs.RANDOM STRUCTURES AND ALGORITHMS, Issue 1 2006Exact results using the local weak convergence method Let G(n,c/n) and Gr(n) be an n -node sparse random graph and a sparse random r -regular graph, respectively, and let I(n,r) and I(n,c) be the sizes of the largest independent set in G(n,c/n) and Gr(n). The asymptotic value of I(n,c)/n as n , ,, can be computed using the Karp-Sipser algorithm when c , e. For random cubic graphs, r = 3, it is only known that .432 , lim infnI(n,3)/n , lim supnI(n,3)/n , .4591 with high probability (w.h.p.) as n , ,, as shown in Frieze and Suen [Random Structures Algorithms 5 (1994), 649,664] and Bollabas [European J Combin 1 (1980), 311,316], respectively. In this paper we assume in addition that the nodes of the graph are equipped with nonnegative weights, independently generated according to some common distribution, and we consider instead the maximum weight of an independent set. Surprisingly, we discover that for certain weight distributions, the limit limnI(n,c)/n can be computed exactly even when c > e, and limnI(n,r)/n can be computed exactly for some r , 1. For example, when the weights are exponentially distributed with parameter 1, limnI(n,2e)/n , .5517, and limnI(n,3)/n , .6077. Our results are established using the recently developed local weak convergence method further reduced to a certain local optimality property exhibited by the models we consider. We extend our results to maximum weight matchings in G(n,c/n) and Gr(n). For the case of exponential distributions, we compute the corresponding limits for every c > 0 and every r , 2. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006 [source] The association of a nonsynonymous single-nucleotide polymorphism in TNFAIP3 with systemic lupus erythematosus and rheumatoid arthritis in the Japanese populationARTHRITIS & RHEUMATISM, Issue 2 2010Kenichi Shimane Objective Genome-wide association (GWA) studies in systemic lupus erythematosus (SLE) and rheumatoid arthritis (RA) in Caucasian populations have independently identified risk variants in and near the tumor necrosis factor , (TNF,),induced protein 3 gene (TNFAIP3), which is crucial for the regulation of TNF-mediated signaling and Toll-like receptor signaling. The aim of this study was to assess the role of TNFAIP3 in the development of SLE and RA in Japanese subjects. Methods We selected 2 single-nucleotide polymorphisms (SNPs) from previous GWA studies. Rs2230926 is a nonsynonymous SNP in TNFAIP3 and is associated with SLE, while rs10499194 is an intergenic SNP associated with RA. We then performed 2 independent sets of SLE case,control comparisons (717 patients and 1,362 control subjects) and 3 sets of RA case,control comparisons (3,446 patients and 2,344 control subjects) using Japanese subjects. We genotyped SNPs using TaqMan assays. Results We observed a significant association between rs2230926 and an increased risk of SLE and RA in the Japanese population (for SLE, odds ratio [OR] 1.92, 95% confidence interval [95% CI] 1.53,2.41, P = 1.9 × 10,8; for RA, OR 1.35, 95% CI 1.18,1.56, P = 2.6 × 10,5). The intergenic SNP rs10499194 was also associated with SLE and RA, while the risk allele for RA in Caucasians was protective against the diseases in our population. Conclusion We demonstrated a significant association between the nonsynonymous variant in TNFAIP3 and the risk for SLE and RA in the Japanese population. TNFAIP3, similar to STAT4 and IRF5, may be a common genetic risk factor for SLE and RA that is shared between the Caucasian and Japanese populations. [source] | ||||||||||||||||||||||