BDDC and FETI-DP under Minimalist Assumptions

The FETI-DP, BDDC and P-FETI-DP preconditioners are derived in a particulary simple abstract form. It is shown that their properties can be obtained from only on a very small set of algebraic assumptions. The presentation is purely algebraic and it does not use any particular definition of method components, such as substructures and coarse degrees of freedom. It is then shown that P-FETI-DP and BDDC are in fact the same. The FETI-DP and the BDDC preconditioned operators are of the same algebraic form, and the standard condition number bound carries over to arbitrary abstract operators of this form. The equality of eigenvalues of BDDC and FETI-DP also holds in the minimalist abstract setting. The abstract framework is explained on a standard substructuring example.Comment: 11 pages, 1 figure, also available at http://www-math.cudenver.edu/ccm/reports

Clustering of nonstationary data streams: a survey of fuzzy partitional methods

YesData streams have arisen as a relevant research topic during the past decade. They are real‐time, incremental in nature, temporally ordered, massive, contain outliers, and the objects in a data stream may evolve over time (concept drift). Clustering is often one of the earliest and most important steps in the streaming data analysis workflow. A comprehensive literature is available about stream data clustering; however, less attention is devoted to the fuzzy clustering approach, even though the nonstationary nature of many data streams makes it especially appealing. This survey discusses relevant data stream clustering algorithms focusing mainly on fuzzy methods, including their treatment of outliers and concept drift and shift.Ministero dell‘Istruzione, dell‘Universitá e della Ricerca

Distinct gene loci control the host response to influenza H1N1 virus infection in a time-dependent manner

<p>Abstract</p> <p>Background</p> <p>There is strong but mostly circumstantial evidence that genetic factors modulate the severity of influenza infection in humans. Using genetically diverse but fully inbred strains of mice it has been shown that host sequence variants have a strong influence on the severity of influenza A disease progression. In particular, C57BL/6J, the most widely used mouse strain in biomedical research, is comparatively resistant. In contrast, DBA/2J is highly susceptible.</p> <p>Results</p> <p>To map regions of the genome responsible for differences in influenza susceptibility, we infected a family of 53 BXD-type lines derived from a cross between C57BL/6J and DBA/2J strains with influenza A virus (PR8, H1N1). We monitored body weight, survival, and mean time to death for 13 days after infection. <it>Qivr5</it> (quantitative trait for influenza virus resistance on chromosome 5) was the largest and most significant QTL for weight loss. The effect of <it>Qivr5</it> was detectable on day 2 post infection, but was most pronounced on days 5 and 6. Survival rate mapped to <it>Qivr5</it>, but additionally revealed a second significant locus on chromosome 19 (<it>Qivr19</it>). Analysis of mean time to death affirmed both <it>Qivr5</it> and <it>Qivr19</it>. In addition, we observed several regions of the genome with suggestive linkage. There are potentially complex combinatorial interactions of the parental alleles among loci. Analysis of multiple gene expression data sets and sequence variants in these strains highlights about 30 strong candidate genes across all loci that may control influenza A susceptibility and resistance.</p> <p>Conclusions</p> <p>We have mapped influenza susceptibility loci to chromosomes 2, 5, 16, 17, and 19. Body weight and survival loci have a time-dependent profile that presumably reflects the temporal dynamic of the response to infection. We highlight candidate genes in the respective intervals and review their possible biological function during infection.</p

Planktonic Aggregates as Hotspots for Heterotrophic Diazotrophy: The Plot Thickens

Biological dinitrogen (N-2) fixation is performed solely by specialized bacteria and archaea termed diazotrophs, introducing new reactive nitrogen into aquatic environments. Conventionally, phototrophic cyanobacteria are considered the major diazotrophs in aquatic environments. However, accumulating evidence indicates that diverse non-cyanobacterial diazotrophs (NCDs) inhabit a wide range of aquatic ecosystems, including temperate and polar latitudes, coastal environments and the deep ocean. NCDs are thus suspected to impact global nitrogen cycling decisively, yet their ecological and quantitative importance remain unknown. Here we review recent molecular and biogeochemical evidence demonstrating that pelagic NCDs inhabit and thrive especially on aggregates in diverse aquatic ecosystems. Aggregates are characterized by reduced-oxygen microzones, high C:N ratio (above Redfield) and high availability of labile carbon as compared to the ambient water. We argue that planktonic aggregates are important loci for energetically-expensive N-2 fixation by NCDs and propose a conceptual framework for aggregate-associated N-2 fixation. Future studies on aggregate-associated diazotrophy, using novel methodological approaches, are encouraged to address the ecological relevance of NCDs for nitrogen cycling in aquatic environments

Multispace and Multilevel BDDC

BDDC method is the most advanced method from the Balancing family of iterative substructuring methods for the solution of large systems of linear algebraic equations arising from discretization of elliptic boundary value problems. In the case of many substructures, solving the coarse problem exactly becomes a bottleneck. Since the coarse problem in BDDC has the same structure as the original problem, it is straightforward to apply the BDDC method recursively to solve the coarse problem only approximately. In this paper, we formulate a new family of abstract Multispace BDDC methods and give condition number bounds from the abstract additive Schwarz preconditioning theory. The Multilevel BDDC is then treated as a special case of the Multispace BDDC and abstract multilevel condition number bounds are given. The abstract bounds yield polylogarithmic condition number bounds for an arbitrary fixed number of levels and scalar elliptic problems discretized by finite elements in two and three spatial dimensions. Numerical experiments confirm the theory.Comment: 26 pages, 3 figures, 2 tables, 20 references. Formal changes onl

On the Nodal Count Statistics for Separable Systems in any Dimension

We consider the statistics of the number of nodal domains aka nodal counts for eigenfunctions of separable wave equations in arbitrary dimension. We give an explicit expression for the limiting distribution of normalised nodal counts and analyse some of its universal properties. Our results are illustrated by detailed discussion of simple examples and numerical nodal count distributions.Comment: 21 pages, 4 figure

A new urban freight distribution scheme and an optimization methodology for reducing its overall cost

The paper refers to an innovative urban freight distribution scheme, aimed at reducing the externalities connected with the freight delivery process. Both packages destined to commercial activities and to end consumers (e-commerce) are taken into account. Each package is characterized by an address and dimensions. In the proposed transport system, freight is firstly delivered to the UDC on the border of urban areas through trucks or trains which perform the long distance transport. After, freight is reorganized and consolidated into load units, i.e. the FURBOT boxes, according to packages dimensions and to the addresses of receivers. Each box is addressed to a temporary unloading bay and it is delivered there by a FURBOT vehicle. The receivers are in charge of collecting their packages in the related unloading bays where they have been delivered. The paper concerns a methodology for optimizing this freight transport system's performances. The overall methodology receives in input the actual freight demand and the road network, and finds the transport system parameters (number of required FURBOT boxes, their temporary unloading bay, the FURBOT fleet dimension and the FURBOT vehicle routing) that minimize the system overall cost. The overall cost is a sum of the users' cost, which depends on the distance they have to walk for collecting their packages in the FURBOT box, and of the operator's cost, which depends on the number of required boxes, the total distance travelled by the FURBOT vehicles and the required number of FURBOT vehicles. The overall procedure has been applied to the case study of Barreiro old town, a suburb of Lisbon, Portugal