Multidirectional sweeping preconditioners with non-overlapping checkerboard domain decomposition for Helmholtz problems

This paper explores a family of generalized sweeping preconditioners for Helmholtz problems with non-overlapping checkerboard partition of the computational domain. The domain decomposition procedure relies on high-order transmission conditions and cross-point treatments, which cannot scale without an efficient preconditioning technique when the number of subdomains increases. With the proposed approach, existing sweeping preconditioners, such as the symmetric Gauss-Seidel and parallel double sweep preconditioners, can be applied to checkerboard partitions with different sweeping directions (e.g. horizontal and diagonal). Several directions can be combined thanks to the flexible version of GMRES, allowing for the rapid transfer of information in the different zones of the computational domain, then accelerating the convergence of the final iterative solution procedure. Several two-dimensional finite element results are proposed to study and to compare the sweeping preconditioners, and to illustrate the performance on cases of increasing complexity

Colorectal cancer stages transcriptome analysis

Colorectal cancer (CRC) is the third most common cancer and the second leading cause of cancer-related deaths in the United States. The purpose of this study was to evaluate the gene expression differences in different stages of CRC. Gene expression data on 433 CRC patient samples were obtained from The Cancer Genome Atlas (TCGA). Gene expression differences were evaluated across CRC stages using linear regression. Genes with p 0.001 in expression differences were evaluated further in principal component analysis and genes with p 0.0001 were evaluated further in gene set enrichment analysis. A total of 377 patients with gene expression data in 20,532 genes were included in the final analysis. The numbers of patients in stage I through IV were 59, 147, 116 and 55, respectively. NEK4 gene, which encodes for NIMA related kinase 4, was differentially expressed across the four stages of CRC. The stage I patients had the highest expression of NEK4 genes, while the stage IV patients had the lowest expressions (p = 9*10−6 ). Ten other genes (RNF34, HIST3H2BB, NUDT6, LRCh4, GLB1L, HIST2H4A, TMEM79, AMIGO2, C20orf135 and SPSB3) had p value of 0.0001 in the differential expression analysis. Principal component analysis indicated that the patients from the 4 clinical stages do not appear to have distinct gene expression pattern. Network-based and pathway-based gene set enrichment analyses showed that these 11 genes map to multiple pathways such as meiotic synapsis and packaging of telomere ends, etc. Ten of these 11 genes were linked to Gene Ontology terms such as nucleosome, DNA packaging complex and protein-DNA interactions. The protein complex-based gene set analysis showed that four genes were involved in H2AX complex II. This study identified a small number of genes that might be associated with clinical stages of CRC. Our analysis was not able to find a molecular basis for the current clinical staging for CRC based on the gene expression patterns

Fuzzy Measures and Integrals as Aggregation Operators: Solving the Commensurability Problem

The aim of this paper is to shed some light on the use of fuzzy measures and integrals as aggregation operators in multicriteria decision making. These techniques have been widely used on an ad hoc basis, but with no axiomatization

Interval-Based Multicriteria Decision Making

The aim of this paper is to show how non-additive measures and intervals can be combined in order to provide a simple and accurate approach to multi-criteria decision making problems. We construct an interval-based Choquet integral in order to derive preferences over a set of multidimensional alternatives. Preferences are no longer real number comparisons, but interval comparisons, which is not straightforward to interpret. In this paper, we propose strategies of choice, and explain how we can integrate additional information – such as probabilities – to intervals, so as to ease the choice

The optimality of non-additive approaches for portfolio selection

The selection of assets in which to invest money is of critical importance in the finance industry, and is rendered very treacherous because of the inherent market fluctuations, and the connections with the Economy, and major world events. Because of the high dimensionality of the problem of selecting an optimal portfolio (in the financial sense of, a portfolio outperforming other portfolios), and the large amount of data available, intelligent systems (e.g. artificial intelligence techniques, machine learning approaches) are a natural approach to tackle this problem, from a computational standpoint. Numerous techniques have been developed to combine the values of return, risk, and other characteristics of an asset. However, the majority of techniques that have been used to construct a portfolio, tend to ignore dependencies among the characteristics of an asset. Moreover, most of the techniques assume that all available data are precise, which is not the case since, for instance, the expected return of an asset is a prediction of future behavior. To address these drawbacks, it was proposed in Magoc, Modave, Ceberio, and Kreinovich (2009) to use non-additive (or fuzzy) methods. Fuzzy methods outperformed other techniques, at least in the case of the Shanghai market, where full disclosure of information is assumed. In this paper, we give an intuition why fuzzy approach performs very well in this particular finance problem

An Interval-valued, 2-additive Choquet Integral for Multicriteria Decision Making

The aim of this paper is to show how fuzzy measures and intervals can be combined in order to provide a simple and accurate practical solution to multi-criteria decision making problems. More specifically, we construct an interval-based Choquet integral in order to derive preferences over a set of multidimensional alternatives

Decision making for robust resilient systems

Robust and resilient interconnected structures rely on decision prWWK ur es, bothunder uncerzQQK8 and multicrPNWBQz In decisionunder uncerzQQK7B we aim at finding a scorPB prWB7 ur e to deterKzE an optimal decision without prho knowledge on the actual state of theworWQ In multicrEP87P decision making, the state of theworW is known but we aim at r anking alterNUQWzE definedover a multidimensional set.Ther efor e, thepr oblem is to find anappr opr8U aggr egation prWPN ur e. In pr actical applications, we have to deal with decisionpr oblemswher e the state of thewor7 is not known, and thealterWQzEPW ar e multidimensional. It is well known that thepr obabilityappr oach to thesepr oblem leads to par adoxes, that ar er elated to independence pr operWWQ required on the preferences. Thi