A Two-Player Game of Life

We present a new extension of Conway's game of life for two players, which we call p2life. P2life allows one of two types of token, black or white, to inhabit a cell, and adds competitive elements into the birth and survival rules of the original game. We solve the mean-field equation for p2life and determine by simulation that the asymptotic density of p2life approaches 0.0362.Comment: 7 pages, 3 figure

Sampling properties of directed networks

For many real-world networks only a small "sampled" version of the original network may be investigated; those results are then used to draw conclusions about the actual system. Variants of breadth-first search (BFS) sampling, which are based on epidemic processes, are widely used. Although it is well established that BFS sampling fails, in most cases, to capture the IN-component(s) of directed networks, a description of the effects of BFS sampling on other topological properties are all but absent from the literature. To systematically study the effects of sampling biases on directed networks, we compare BFS sampling to random sampling on complete large-scale directed networks. We present new results and a thorough analysis of the topological properties of seven different complete directed networks (prior to sampling), including three versions of Wikipedia, three different sources of sampled World Wide Web data, and an Internet-based social network. We detail the differences that sampling method and coverage can make to the structural properties of sampled versions of these seven networks. Most notably, we find that sampling method and coverage affect both the bow-tie structure, as well as the number and structure of strongly connected components in sampled networks. In addition, at low sampling coverage (i.e. less than 40%), the values of average degree, variance of out-degree, degree auto-correlation, and link reciprocity are overestimated by 30% or more in BFS-sampled networks, and only attain values within 10% of the corresponding values in the complete networks when sampling coverage is in excess of 65%. These results may cause us to rethink what we know about the structure, function, and evolution of real-world directed networks.Comment: 21 pages, 11 figure

On Abelian Multi-Chern-Simons Field Theories

In this paper a class of multi-Chern-Simons field theories which is relevant to the statistical mechanics of polymer systems is investigated. Motivated by the problems which one encounters in the treatment of these theories, a general procedure is presented to eliminate the Chern-Simons fields from their action. In this way it has been possible to derive an expression of the partition function of topologically linked polymers which depends explicitly on the topological numbers and does not have intractable nonlocal terms as it happened in previous approaches. The new formulation of multi-Chern-Simons field theories is then used to remove and clarify some inconsistencies and ambiguities which apparently affect field theoretical models of topologically linked polymers. Finally, the limit of disentangled polymers is discussed.Comment: 18 pages, plain LaTe

Efficient Representation of Multidimensional Data over Hierarchical Domains

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-46049-9_19[Abstract] We consider the problem of representing multidimensional data where the domain of each dimension is organized hierarchically, and the queries require summary information at a different node in the hierarchy of each dimension. This is the typical case of OLAP databases. A basic approach is to represent each hierarchy as a one-dimensional line and recast the queries as multidimensional range queries. This approach can be implemented compactly by generalizing to more dimensions the k2k2 -treap, a compact representation of two-dimensional points that allows for efficient summarization queries along generic ranges. Instead, we propose a more flexible generalization, which instead of a generic quadtree-like partition of the space, follows the domain hierarchies across each dimension to organize the partitioning. The resulting structure is much more efficient than a generic multidimensional structure, since queries are resolved by aggregating much fewer nodes of the tree.Ministerio de Economía, Industria y Competitividad; TIN2013-46238-C4-3-RMinisterio de Economía, Industria y Competitividad; IDI-20141259Ministerio de Economía, Industria y Competitividad; ITC-20151305Ministerio de Economía y Competitividad; ITC-20151247Xunta de Galicia; GRC2013/053Chile.Fondo Nacional de Desarrollo Científico y Tecnológico; 1-140796COST. IC130

A flexible and efficient template format for circular consensus sequencing and SNP detection

A novel template design for single-molecule sequencing is introduced, a structure we refer to as a SMRTbell™ template. This structure consists of a double-stranded portion, containing the insert of interest, and a single-stranded hairpin loop on either end, which provides a site for primer binding. Structurally, this format resembles a linear double-stranded molecule, and yet it is topologically circular. When placed into a single-molecule sequencing reaction, the SMRTbell template format enables a consensus sequence to be obtained from multiple passes on a single molecule. Furthermore, this consensus sequence is obtained from both the sense and antisense strands of the insert region. In this article, we present a universal method for constructing these templates, as well as an application of their use. We demonstrate the generation of high-quality consensus accuracy from single molecules, as well as the use of SMRTbell templates in the identification of rare sequence variants

Gel-Electrophoresis and Diffusion of Ring-Shaped DNA

A model for the motion of ring-shaped DNA in a gel is introduced and studied by numerical simulations and a mean-field approximation. The ring motion is mediated by finger-shaped loops (hernias) that move in an amoeba-like fashion around the gel obstructions. This constitutes an extension of previous reptation tube treatments. It is shown that tension is essential for describing the dynamics in the presence of hernias. It is included in the model as long range interactions over stretched DNA regions. The mobility of ring-shaped DNA is found to saturate much as in the well-studied case of linear DNA. Experiments in polymer gels, however, show that the mobility drops exponentially with the DNA ring size. This is commonly attributed to dangling-ends in the gel that can impale the ring. The predictions of the present model are expected to apply to artificial 2D obstacle arrays (W.D. Volkmuth, R.H. Austin, Nature 358,600 (1992)) which have no dangling-ends. In the zero-field case an exact solution of the model steady-state is obtained, and quantities such as the average ring size are calculated. An approximate treatment of the ring dynamics is given, and the diffusion coefficient is derived. The model is also discussed in the context of spontaneous symmetry breaking in one dimension.Comment: 8 figures, LaTeX, Phys. Rev. E - in pres

An introduction to Graph Data Management

A graph database is a database where the data structures for the schema and/or instances are modeled as a (labeled)(directed) graph or generalizations of it, and where querying is expressed by graph-oriented operations and type constructors. In this article we present the basic notions of graph databases, give an historical overview of its main development, and study the main current systems that implement them

A straightforward multiallelic significance test for the Hardy-Weinberg equilibrium law

Much forensic inference based upon DNA evidence is made assuming Hardy-Weinberg Equilibrium (HWE) for the genetic loci being used. Several statistical tests to detect and measure deviation from HWE have been devised, and their limitations become more obvious when testing for deviation within multiallelic DNA loci. The most popular methods-Chi-square and Likelihood-ratio tests-are based on asymptotic results and cannot guarantee a good performance in the presence of low frequency genotypes. Since the parameter space dimension increases at a quadratic rate on the number of alleles, some authors suggest applying sequential methods, where the multiallelic case is reformulated as a sequence of “biallelic” tests. However, in this approach it is not obvious how to assess the general evidence of the original hypothesis; nor is it clear how to establish the significance level for its acceptance/rejection. In this work, we introduce a straightforward method for the multiallelic HWE test, which overcomes the aforementioned issues of sequential methods. The core theory for the proposed method is given by the Full Bayesian Significance Test (FBST), an intuitive Bayesian approach which does not assign positive probabilities to zero measure sets when testing sharp hypotheses. We compare FBST performance to Chi-square, Likelihood-ratio and Markov chain tests, in three numerical experiments. The results suggest that FBST is a robust and high performance method for the HWE test, even in the presence of several alleles and small sample sizes

On the Use of Variance per Genotype as a Tool to Identify Quantitative Trait Interaction Effects: A Report from the Women's Genome Health Study

Testing for genetic effects on mean values of a quantitative trait has been a very successful strategy. However, most studies to date have not explored genetic effects on the variance of quantitative traits as a relevant consequence of genetic variation. In this report, we demonstrate that, under plausible scenarios of genetic interaction, the variance of a quantitative trait is expected to differ among the three possible genotypes of a biallelic SNP. Leveraging this observation with Levene's test of equality of variance, we propose a novel method to prioritize SNPs for subsequent gene–gene and gene–environment testing. This method has the advantageous characteristic that the interacting covariate need not be known or measured for a SNP to be prioritized. Using simulations, we show that this method has increased power over exhaustive search under certain conditions. We further investigate the utility of variance per genotype by examining data from the Women's Genome Health Study. Using this dataset, we identify new interactions between the LEPR SNP rs12753193 and body mass index in the prediction of C-reactive protein levels, between the ICAM1 SNP rs1799969 and smoking in the prediction of soluble ICAM-1 levels, and between the PNPLA3 SNP rs738409 and body mass index in the prediction of soluble ICAM-1 levels. These results demonstrate the utility of our approach and provide novel genetic insight into the relationship among obesity, smoking, and inflammation