Towards random uniform sampling of bipartite graphs with given degree sequence

In this paper we consider a simple Markov chain for bipartite graphs with given degree sequence on $n$ vertices. We show that the mixing time of this Markov chain is bounded above by a polynomial in $n$ in case of {\em semi-regular} degree sequence. The novelty of our approach lays in the construction of the canonical paths in Sinclair's method.Comment: 47 pages, submitted for publication. In this version we explain explicitly our main contribution and corrected a serious flaw in the cycle decompositio

Towards random uniform sampling of bipartite graphs with given degree sequence

In this paper we consider a simple Markov chain for bipartite graphs with given degree sequence on n vertices. We show that the mixing time of this Markov chain is bounded above by a polynomial in n in case of half-regular degree sequence. The novelty of our approach lies in the construction of the multicommodity flow in Sinclair's method

Metabolic network visualization eliminating node redundance and preserving metabolic pathways

<p>Abstract</p> <p>Background</p> <p>The tools that are available to draw and to manipulate the representations of metabolism are usually restricted to metabolic pathways. This limitation becomes problematic when studying processes that span several pathways. The various attempts that have been made to draw genome-scale metabolic networks are confronted with two shortcomings: 1- they do not use contextual information which leads to dense, hard to interpret drawings, 2- they impose to fit to very constrained standards, which implies, in particular, duplicating nodes making topological analysis considerably more difficult.</p> <p>Results</p> <p>We propose a method, called MetaViz, which enables to draw a genome-scale metabolic network and that also takes into account its structuration into pathways. This method consists in two steps: a clustering step which addresses the pathway overlapping problem and a drawing step which consists in drawing the clustered graph and each cluster.</p> <p>Conclusion</p> <p>The method we propose is original and addresses new drawing issues arising from the no-duplication constraint. We do not propose a single drawing but rather several alternative ways of presenting metabolism depending on the pathway on which one wishes to focus. We believe that this provides a valuable tool to explore the pathway structure of metabolism.</p

Hummingbird diversity, abundance, and feeding interactions across three floral communities on Mount Totumas, Chiriquí, Panamá

(Trochilidae) are a large Neotropical bird family of nectar-feeders that have evolved as pollinators of many Neotropical plants. Interactions between hummingbirds and plants form mutualistic networks that may change in structure over environmental and anthropogenic gradients. While the unique dynamics of hummingbird diversity and floral interactions have been studied throughout the Neotropics, differing drivers between locations emphasizes the need for further local research. This deficit is especially crucial in biodiverse and understudied locations like the Western Highlands of Panamá. In this study, I investigated how hummingbird diversity, abundance, and floral interactions differed between Cloud Forest, Garden, and Oak Forest on Mount Totumas, Chiriquí Highlands, Panamá. I quantified and compared hummingbird richness, Shannon diversity, abundance, floral density, and floral visitation during three days of replicate point counts in each site. Additionally, I constructed quantitative hummingbird-plant networks, computed standard network indices, and compared hummingbird specialization at a species-level. Across study sites, I made 548 observations of 14 hummingbird species, and observed 4533 hummingbird visits to 35 plant species. Hummingbird richness was highest in the Garden, while Shannon diversity was slightly higher in the Cloud Forest. Hummingbird relative abundance, floral density, and visitation rates were significantly higher in the Garden site, and decreased in Cloud Forest and Oak Forest. Linear models suggest that floral density predicts hummingbird abundance and richness, suggesting that high floral density in the Garden likely attracts hummingbirds. While not representative of a complete elevational gradient, hummingbird diversity decreased at the higher elevation Oak Forest site. The study area hummingbird-plant network was speciose, with the Garden contributing more species and interactions than the forest sites. Across sites, nestedness (wNODF) and connectance (C) were lower than expected by null models, while network-level specialization (H2’) and modularity (Q) were higher. Network-level specialization was higher in the forest sites than in the Garden, possibly indicating hummingbird foraging flexibility in human-impacted landscapes. Hummingbird species specialization (d’) varied on a species-specific level between sites, and was not significantly predicted by hummingbird body length, bill length, or bill curvature. While there are clearly structural differences in hummingbird-plant interactions between sites, further study over the entire year is essential to fully describe hummingbird dynamics at Mount Totumas

An Analysis of the Influence of Graph Theory When Preparing for Programming Contests

[EN] The subject known as Programming Contests in the Bachelor's Degree in Computer Engineering course focuses on solving programming problems frequently met within contests such as the Southwest Europe Regional Contest (SWERC). In order to solve these problems one first needs to model the problem correctly, find the ideal solution, and then be able to program it without making any mistakes in a very short period of time. Leading multinationals such as Google, Apple, IBM, Facebook and Microsoft place a very high value on these abilities when selecting candidates for posts in their companies. In this communication we present some preliminary results of an analysis of the interaction between two optional subjects in the Computer Science Degree course: Programming Contests (PC) and Graphs, Models and Applications (GMA). The results of this analysis enabled us to make changes to some of the contents in GMA in order to better prepare the students to deal with the challenges they have to face in programming contests.This project was funded by the Vicerrectorado de Estudios y Calidad Academica of the Universitat Politecnica de Valencia. PIME-B08: Modelos de la Teoria de Grafos aplicados a problemas de competiciones de programacion.Jordan-Lluch, C.; Gomez, J.; Conejero, JA. (2017). An Analysis of the Influence of Graph Theory When Preparing for Programming Contests. Mathematics. 5(1):1-11. doi:10.3390/math5010008S1115

Hierarchically embedded interaction networks represent a missing link in the study of behavioral and community ecology

Because genes and phenotypes are embedded within individuals, and individuals within populations, interactions within one level of biological organization are inherently linked to interactors at others. Here, we expand the network paradigm to consider that nodes can be embedded within other nodes, and connections (edges) between nodes at one level of organization form "bridges" for connections between nodes embedded within them. Such hierarchically embedded networks highlight two central properties of biological systems: 1) processes occurring across multiple levels of organization shape connections among biological units at any given level of organization and 2) ecological effects occurring at a given level of organization can propagate up or down to additional levels. Explicitly considering the embedded structure of evolutionary and ecological networks can capture otherwise hidden feedbacks and generate new insights into key biological phenomena, ultimately promoting a broader understanding of interactions in evolutionary theory. Lay Summary: Interactions are ubiquitous across biological systems. Modeling their consequences requires capturing how units are organized across biological scales: gene and protein interactions shape phenotypic traits within individuals, individuals are embedded within populations, populations within communities, and communities within ecosystems. Doing so reveals how indirect connections among units arise from the structure of connections at higher or lower levels of organization, and how effects at one level of the network propagate across neighboring levels.Peer reviewe

Graph multicoloring reduction methods and application to McDiarmid-Reed's Conjecture

A $(a,b)$-coloring of a graph $G$ associates to each vertex a set of $b$ colors from a set of $a$ colors in such a way that the color-sets of adjacent vertices are disjoints. We define general reduction tools for $(a,b)$-coloring of graphs for $2\le a/b\le 3$. In particular, we prove necessary and sufficient conditions for the existence of a $(a,b)$-coloring of a path with prescribed color-sets on its end-vertices. Other more complex $(a,b)$-colorability reductions are presented. The utility of these tools is exemplified on finite triangle-free induced subgraphs of the triangular lattice. Computations on millions of such graphs generated randomly show that our tools allow to find (in linear time) a $(9,4)$-coloring for each of them. Although there remain few graphs for which our tools are not sufficient for finding a $(9,4)$-coloring, we believe that pursuing our method can lead to a solution of the conjecture of McDiarmid-Reed.Comment: 27 page

Stochastic Minority on Graphs

Cellular automata have been mainly studied on very regular graphs carrying the cells (like lines or grids) and under synchronous dynamics (all cells update simultaneously). In this paper we study how the asynchronism and the topology of cells act upon the dynamics of the classical Minority rule. Beyond its apparent simplicity, this rule yields complex behaviors which are clearly linked to the structure of the graph carrying the cells