Reshetikhin's Formula for the Jones Polynomial of a Link: Feynman diagrams and Milnor's Linking Numbers

We use Feynman diagrams to prove a formula for the Jones polynomial of a link derived recently by N.~Reshetikhin. This formula presents the colored Jones polynomial as an integral over the coadjoint orbits corresponding to the representations assigned to the link components. The large $k$ limit of the integral can be calculated with the help of the stationary phase approximation. The Feynman rules allow us to express the phase in terms of integrals over the manifold and the link components. Its stationary points correspond to flat connections in the link complement. We conjecture a relation between the dominant part of the phase and Milnor's linking numbers. We check it explicitly for the triple and quartic numbers by comparing their expression through the Massey product with Feynman diagram integrals.Comment: 33 pages, 11 figure

Seismic pounding mitigation by using viscous and viscoelastic dampers

This paper examines the effects of viscous and viscoelastic dampers as an efficient technique for seismic pounding mitigation. To aim that, 15 steel frame models with different numbers of stories and bays and also with different types of ductility were analyzed under 10 different earthquake records for assigned values of link damping and stiffness and the most suitable values of damper parameters (damping and stiffness) are presented. Moreover, it is demonstrated that viscous dampers can perform as efficiently as viscoelastic alternative with a more economical aspect for pounding mitigation purposes.Keywords: Adjacent buildings;Viscous and Viscoelastic links;Separation distance;Poundingmitigatio

Robust Principal Component Analysis for Compositional Tables

A data table which is arranged according to two factors can often be considered as a compositional table. An example is the number of unemployed people, split according to gender and age classes. Analyzed as compositions, the relevant information would consist of ratios between different cells of such a table. This is particularly useful when analyzing several compositional tables jointly, where the absolute numbers are in very different ranges, e.g. if unemployment data are considered from different countries. Within the framework of the logratio methodology, compositional tables can be decomposed into independent and interactive parts, and orthonormal coordinates can be assigned to these parts. However, these coordinates usually require some prior knowledge about the data, and they are not easy to handle for exploring the relationships between the given factors. Here we propose a special choice of coordinates with a direct relation to centered logratio (clr) coefficients, which are particularly useful for an interpretation in terms of the original cells of the tables. With these coordinates, robust principal component analysis (PCA) is performed for dimension reduction, allowing to investigate the relationships between the factors. The link between orthonormal coordinates and clr coefficients enables to apply robust PCA, which would otherwise suffer from the singularity of clr coefficients.Comment: 20 pages, 2 figure

Cloning, analysis and functional annotation of expressed sequence tags from the Earthworm Eisenia fetida

<p>Abstract</p> <p>Background</p> <p><it>Eisenia fetida</it>, commonly known as red wiggler or compost worm, belongs to the Lumbricidae family of the Annelida phylum. Little is known about its genome sequence although it has been extensively used as a test organism in terrestrial ecotoxicology. In order to understand its gene expression response to environmental contaminants, we cloned 4032 cDNAs or expressed sequence tags (ESTs) from two <it>E. fetida </it>libraries enriched with genes responsive to ten ordnance related compounds using suppressive subtractive hybridization-PCR.</p> <p>Results</p> <p>A total of 3144 good quality ESTs (GenBank dbEST accession number <ext-link ext-link-type="gen" ext-link-id="EH669363">EH669363</ext-link>–<ext-link ext-link-type="gen" ext-link-id="EH672369">EH672369</ext-link> and <ext-link ext-link-type="gen" ext-link-id="EL515444">EL515444</ext-link>–<ext-link ext-link-type="gen" ext-link-id="EL515580">EL515580</ext-link>) were obtained from the raw clone sequences after cleaning. Clustering analysis yielded 2231 unique sequences including 448 contigs (from 1361 ESTs) and 1783 singletons. Comparative genomic analysis showed that 743 or 33% of the unique sequences shared high similarity with existing genes in the GenBank nr database. Provisional function annotation assigned 830 Gene Ontology terms to 517 unique sequences based on their homology with the annotated genomes of four model organisms <it>Drosophila melanogaster</it>, <it>Mus musculus</it>, <it>Saccharomyces cerevisiae</it>, and <it>Caenorhabditis elegans</it>. Seven percent of the unique sequences were further mapped to 99 Kyoto Encyclopedia of Genes and Genomes pathways based on their matching Enzyme Commission numbers. All the information is stored and retrievable at a highly performed, web-based and user-friendly relational database called EST model database or ESTMD version 2.</p> <p>Conclusion</p> <p>The ESTMD containing the sequence and annotation information of 4032 <it>E. fetida </it>ESTs is publicly accessible at <url>http://mcbc.usm.edu/estmd/</url>.</p

How pairs of partners emerge in an initially fully connected society

A social group is represented by a graph, where each pair of nodes is connected by two oppositely directed links. At the beginning, a given amount $p(i)$ of resources is assigned randomly to each node $i$. Also, each link $r(i,j)$ is initially represented by a random positive value, which means the percentage of resources of node $i$ which is offered to node $j$. Initially then, the graph is fully connected, i.e. all non-diagonal matrix elements $r(i,j)$ are different from zero. During the simulation, the amounts of resources $p(i)$ change according to the balance equation. Also, nodes reorganise their activity with time, going to give more resources to those which give them more. This is the rule of varying the coefficients $r(i,j)$. The result is that after some transient time, only some pairs $(m,n)$ of nodes survive with non-zero $p(m)$ and $p(n)$, each pair with symmetric and positive $r(m,n)=r(n,m)$. Other coefficients $r(m,i\ne n)$ vanish. Unpaired nodes remain with no resources, i.e. their $p(i)=0$, and they cease to be active, as they have nothing to offer. The percentage of survivors (i.e. those with with $p(i)$ positive) increases with the velocity of varying the numbers $r(i,j)$, and it slightly decreases with the size of the group. The picture and the results can be interpreted as a description of a social algorithm leading to marriages.Comment: 7 pages, 3 figure