Three-point vertices in Landau-gauge Yang-Mills theory

Vertices are of central importance for constructing QCD bound states out of the individual constituents of the theory, i.e. quarks and gluons. In particular, the determination of three-point vertices is crucial in nonperturbative investigations of QCD. We use numerical simulations of lattice gauge theory to obtain results for the 3-point vertices in Landau-gauge SU(2) Yang-Mills theory in three and four space-time dimensions for various kinematic configurations. In all cases considered, the ghost-gluon vertex is found to be essentially tree-level-like, while the three-gluon vertex is suppressed at intermediate momenta. For the smallest physical momenta, reachable only in three dimensions, we find that some of the three-gluon-vertex tensor structures change sign.

4-{2-[4-(Dimethylamino)phenyl]ethylidene}benzonitrile

In the crystal of the title compound, C(17)H(16)N(2), molecules are linked by C-H center dot center dot center dot N hydrogen bonds, forming rings of graph-set motifs R(2)(1) (6) and R(2)(2) (10). The title molecule is close to planar, with a dihedral angle between the aromatic rings of 0.6 (1)degrees. Torsion angles confirm a conformational trans structure.

N-(4-chlorophenyl)maleimide

In the title compound, C10H6ClNO2, the dihedral angle between the benzene and maleimide rings is 47.54 (9)degrees. Molecules form centrosymmetric dimers through C-H center dot center dot center dot O hydrogen bonds, resulting in rings of graph- set motif R2 2(8) and chains in the [100] direction. Molecules are also linked by C-H center dot center dot center dot Cl hydrogen bonds along [001]. In this same direction, molecules are connected to other neighbouring molecules by C-H center dot center dot center dot O hydrogen bonds, forming edge- fused R-4(4)(24) rings.

On the k-restricted structure ratio in planar and outerplanar graphs

A planar k-restricted structure is a simple graph whose blocks are planar and each has at most k vertices. Planar k-restricted structures are used by approximation algorithms for Maximum Weight Planar Subgraph, which motivates this work. The planar k-restricted ratio is the infimum, over simple planar graphs H, of the ratio of the number of edges in a maximum k-restricted structure subgraph of H to the number edges of H. We prove that, as k tends to infinity, the planar k-restricted ratio tends to 1/2. The same result holds for the weighted version. Our results are based on analyzing the analogous ratios for outerplanar and weighted outerplanar graphs. Here both ratios tend to 1 as k goes to infinity, and we provide good estimates of the rates of convergence, showing that they differ in the weighted from the unweighted case.

An algorithmic Friedman-Pippenger theorem on tree embeddings and applications

An (n, d)-expander is a graph G = (V, E) such that for every X subset of V with vertical bar X vertical bar <= 2n - 2 we have vertical bar Gamma(G)(X) vertical bar >= (d + 1) vertical bar X vertical bar. A tree T is small if it has at most n vertices and has maximum degree at most d. Friedman and Pippenger (1987) proved that any ( n; d)- expander contains every small tree. However, their elegant proof does not seem to yield an efficient algorithm for obtaining the tree. In this paper, we give an alternative result that does admit a polynomial time algorithm for finding the immersion of any small tree in subgraphs G of (N, D, lambda)-graphs Lambda, as long as G contains a positive fraction of the edges of Lambda and lambda/D is small enough. In several applications of the Friedman-Pippenger theorem, including the ones in the original paper of those authors, the (n, d)-expander G is a subgraph of an (N, D, lambda)-graph as above. Therefore, our result suffices to provide efficient algorithms for such previously non-constructive applications. As an example, we discuss a recent result of Alon, Krivelevich, and Sudakov (2007) concerning embedding nearly spanning bounded degree trees, the proof of which makes use of the Friedman-Pippenger theorem. We shall also show a construction inspired on Wigderson-Zuckerman expander graphs for which any sufficiently dense subgraph contains all trees of sizes and maximum degrees achieving essentially optimal parameters. Our algorithmic approach is based on a reduction of the tree embedding problem to a certain on-line matching problem for bipartite graphs, solved by Aggarwal et al. (1996).

TESTING STATISTICAL HYPOTHESIS ON RANDOM TREES AND APPLICATIONS TO THE PROTEIN CLASSIFICATION PROBLEM

Efficient automatic protein classification is of central importance in genomic annotation. As an independent way to check the reliability of the classification, we propose a statistical approach to test if two sets of protein domain sequences coming from two families of the Pfam database are significantly different. We model protein sequences as realizations of Variable Length Markov Chains (VLMC) and we use the context trees as a signature of each protein family. Our approach is based on a Kolmogorov-Smirnov-type goodness-of-fit test proposed by Balding et at. [Limit theorems for sequences of random trees (2008), DOI: 10.1007/s11749-008-0092-z]. The test statistic is a supremum over the space of trees of a function of the two samples; its computation grows, in principle, exponentially fast with the maximal number of nodes of the potential trees. We show how to transform this problem into a max-flow over a related graph which can be solved using a Ford-Fulkerson algorithm in polynomial time on that number. We apply the test to 10 randomly chosen protein domain families from the seed of Pfam-A database (high quality, manually curated families). The test shows that the distributions of context trees coming from different families are significantly different. We emphasize that this is a novel mathematical approach to validate the automatic clustering of sequences in any context. We also study the performance of the test via simulations on Galton-Watson related processes.

An oracle approach for interaction neighborhood estimation in random fields

We consider the problem of interaction neighborhood estimation from the partial observation of a finite number of realizations of a random field. We introduce a model selection rule to choose estimators of conditional probabilities among natural candidates. Our main result is an oracle inequality satisfied by the resulting estimator. We use then this selection rule in a two-step procedure to evaluate the interacting neighborhoods. The selection rule selects a small prior set of possible interacting points and a cutting step remove from this prior set the irrelevant points. We also prove that the Ising models satisfy the assumptions of the main theorems, without restrictions on the temperature, on the structure of the interacting graph or on the range of the interactions. It provides therefore a large class of applications for our results. We give a computationally efficient procedure in these models. We finally show the practical efficiency of our approach in a simulation study.

The Lobel-Komlos-Sos conjecture for trees of diameter 5 and for certain caterpillars

Loebl, Komlos, and Sos conjectured that if at least half the vertices of a graph G have degree at least some k is an element of N, then every tree with at most k edges is a subgraph of G. We prove the conjecture for all trees of diameter at most 5 and for a class of caterpillars. Our result implies a bound on the Ramsey number r( T, T') of trees T, T' from the above classes.

The role of exon shuffling in shaping protein-protein interaction networks

Background: Physical protein-protein interaction (PPI) is a critical phenomenon for the function of most proteins in living organisms and a significant fraction of PPIs are the result of domain-domain interactions. Exon shuffling, intron-mediated recombination of exons from existing genes, is known to have been a major mechanism of domain shuffling in metazoans. Thus, we hypothesized that exon shuffling could have a significant influence in shaping the topology of PPI networks. Results: We tested our hypothesis by compiling exon shuffling and PPI data from six eukaryotic species: Homo sapiens, Mus musculus, Drosophila melanogaster, Caenorhabditis elegans, Cryptococcus neoformans and Arabidopsis thaliana. For all four metazoan species, genes enriched in exon shuffling events presented on average higher vertex degree (number of interacting partners) in PPI networks. Furthermore, we verified that a set of protein domains that are simultaneously promiscuous (known to interact to multiple types of other domains), self-interacting (able to interact with another copy of themselves) and abundant in the genomes presents a stronger signal for exon shuffling. Conclusions: Exon shuffling appears to have been a recurrent mechanism for the emergence of new PPIs along metazoan evolution. In metazoan genomes, exon shuffling also promoted the expansion of some protein domains. We speculate that their promiscuous and self-interacting properties may have been decisive for that expansion.

Morpholin-4-ium morpholine-4-carbodithioate

The title compound, C(4)H(10)NO(+)center dot C(5)H(8)NOS(2)(-), is built up of a morpholinium cation and a dithiocarbamate anion. In the crystal, two structurally independent formula units are linked via N-H center dot center dot center dot S hydrogen bonds, forming an inversion dimer, with graph-set motif R(4)(4)(12).

Node-Depth Encoding and Multiobjective Evolutionary Algorithm Applied to Large-Scale Distribution System Reconfiguration

The power loss reduction in distribution systems (DSs) is a nonlinear and multiobjective problem. Service restoration in DSs is even computationally hard since it additionally requires a solution in real-time. Both DS problems are computationally complex. For large-scale networks, the usual problem formulation has thousands of constraint equations. The node-depth encoding (NDE) enables a modeling of DSs problems that eliminates several constraint equations from the usual formulation, making the problem solution simpler. On the other hand, a multiobjective evolutionary algorithm (EA) based on subpopulation tables adequately models several objectives and constraints, enabling a better exploration of the search space. The combination of the multiobjective EA with NDE (MEAN) results in the proposed approach for solving DSs problems for large-scale networks. Simulation results have shown the MEAN is able to find adequate restoration plans for a real DS with 3860 buses and 632 switches in a running time of 0.68 s. Moreover, the MEAN has shown a sublinear running time in function of the system size. Tests with networks ranging from 632 to 5166 switches indicate that the MEAN can find network configurations corresponding to a power loss reduction of 27.64% for very large networks requiring relatively low running time.

Assembling a consistent set of sentences in relational probabilistic logic with stochastic independence

We examine the representation of judgements of stochastic independence in probabilistic logics. We focus on a relational logic where (i) judgements of stochastic independence are encoded by directed acyclic graphs, and (ii) probabilistic assessments are flexible in the sense that they are not required to specify a single probability measure. We discuss issues of knowledge representation and inference that arise from our particular combination of graphs, stochastic independence, logical formulas and probabilistic assessments. (C) 2007 Elsevier B.V. All rights reserved.

Probabilistic logic with independence

This paper investigates probabilistic logics endowed with independence relations. We review propositional probabilistic languages without and with independence. We then consider graph-theoretic representations for propositional probabilistic logic with independence; complexity is analyzed, algorithms are derived, and examples are discussed. Finally, we examine a restricted first-order probabilistic logic that generalizes relational Bayesian networks. (c) 2007 Elsevier Inc. All rights reserved.

Exploring the random genesis of co-occurrence networks

Using the network random generation models from Gustedt (2009)[23], we simulate and analyze several characteristics (such as the number of components, the degree distribution and the clustering coefficient) of the generated networks. This is done for a variety of distributions (fixed value, Bernoulli, Poisson, binomial) that are used to control the parameters of the generation process. These parameters are in particular the size of newly appearing sets of objects, the number of contexts in which new elements appear initially, the number of objects that are shared with `parent` contexts, and, the time period inside which a context may serve as a parent context (aging). The results show that these models allow to fine-tune the generation process such that the graphs adopt properties as can be found in real world graphs. (C) 2011 Elsevier B.V. All rights reserved.

Characterization of electrical penetration graphs of the Asian citrus psyllid, Diaphorina citri, in sweet orange seedlings

Detailed information on probing behavior of the Asian citrus psyllid, Diaphorina citri Kuwayama (Hemiptera: Psyllidae), is critical for understanding the transmission process of phloem-limited bacteria (Candidatus Liberibacter spp.) associated with citrus `huanglongbing` by this vector. In this study, we investigated stylet penetration activities of D. citri on seedlings of Citrus sinensis (L.) Osbeck cv. Pera (Rutaceae) by using the electrical penetration graph (EPG-DC system) technique. EPG waveforms were described based on amplitude, frequency, voltage level, and electrical origin of the observed traces during stylet penetration into plant tissues. The main waveforms were correlated with histological observations of salivary sheath termini in plant tissues, to determine the putative location of stylet tips. The behavioral activities were also inferred based on waveform similarities in relation to other Sternorrhyncha, particularly aphids and whiteflies. In addition, we correlated the occurrence of specific waveforms with the acquisition of the phloem-limited bacterium Ca. Liberibacter asiaticus by D. citri. The occurrence of a G-like xylem sap ingestion waveform in starved and unstarved psyllids was also compared. By analyzing 8-h EPGs of adult females, five waveforms were described: (C) salivary sheath secretion and other stylet pathway activities; (D) first contact with phloem (distinct from other waveforms reported for Sternorrhyncha); (E1) putative salivation in phloem sieve tubes; (E2) phloem sap ingestion; and (G) probably xylem sap ingestion. Diaphorina citri initiates a probe with stylet pathway through epidermis and parenchyma (C). Interestingly, no potential drops were observed during the stylet pathway phase, as are usually recorded in aphids and other Sternorrhyncha. Once in C, D. citri shows a higher propensity to return to non-probing than to start a phloem or xylem phase. Several probes are usually observed before the phloem phase; waveform D is observed upon phloem contact, always immediately followed by E1. After E1, D. citri either returns to pathway activity (C) or starts phloem sap ingestion, which was the longest activity observed.