Local Statistics of Realizable Vertex Models

We study planar "vertex" models, which are probability measures on edge subsets of a planar graph, satisfying certain constraints at each vertex, examples including dimer model, and 1-2 model, which we will define. We express the local statistics of a large class of vertex models on a finite hexagonal lattice as a linear combination of the local statistics of dimers on the corresponding Fisher graph, with the help of a generalized holographic algorithm. Using an $n\times n$ torus to approximate the periodic infinite graph, we give an explicit integral formula for the free energy and local statistics for configurations of the vertex model on an infinite bi-periodic graph. As an example, we simulate the 1-2 model by the technique of Glauber dynamics

Quadri-tilings of the plane

We introduce {\em quadri-tilings} and show that they are in bijection with dimer models on a {\em family} of graphs $\{R^*\}$ arising from rhombus tilings. Using two height functions, we interpret a sub-family of all quadri-tilings, called {\em triangular quadri-tilings}, as an interface model in dimension 2+2. Assigning "critical" weights to edges of $R^*$, we prove an explicit expression, only depending on the local geometry of the graph $R^*$, for the minimal free energy per fundamental domain Gibbs measure; this solves a conjecture of \cite{Kenyon1}. We also show that when edges of $R^*$ are asymptotically far apart, the probability of their occurrence only depends on this set of edges. Finally, we give an expression for a Gibbs measure on the set of {\em all} triangular quadri-tilings whose marginals are the above Gibbs measures, and conjecture it to be that of minimal free energy per fundamental domain.Comment: Revised version, minor changes. 30 pages, 13 figure

The critical Ising model via Kac-Ward matrices

The Kac-Ward formula allows to compute the Ising partition function on any finite graph G from the determinant of 2^{2g} matrices, where g is the genus of a surface in which G embeds. We show that in the case of isoradially embedded graphs with critical weights, these determinants have quite remarkable properties. First of all, they satisfy some generalized Kramers-Wannier duality: there is an explicit equality relating the determinants associated to a graph and to its dual graph. Also, they are proportional to the determinants of the discrete critical Laplacians on the graph G, exactly when the genus g is zero or one. Finally, they share several formal properties with the Ray-Singer \bar\partial-torsions of the Riemann surface in which G embeds.Comment: 30 pages, 10 figures; added section 4.4 in version

Perceived Social Support from Different Sources and Adolescent Life Satisfaction Across 42 Countries/Regions: The Moderating Role of National-Level Generalized Trust

Although previous research established a positive association between perceived social support and adolescent life satisfaction, little is known about the relative importance of different sources of support for adolescent life satisfaction and cross-country variations in this respect. Using large-scale representative samples from the 2017/18 Health Behaviour in School-aged Children (HBSC) study, this study examined to what extent the association between social support and life satisfaction in early adolescence varied across different social sources and countries. Also, it examined whether cross-country variations are explained by national-level generalized trust, a sociocultural factor that shapes adolescent socialization. National-level data were linked to data from 183,918 early adolescents (Mage = 13.56, SD = 1.63, 52% girls) from 42 European and North American countries/regions obtained from HBSC. Multilevel regression analyses yielded a positive association between support from different sources and life satisfaction. The strongest associations were found for support from families, followed by teachers and classmates, and weakest for support from friends. Associations varied across different countries/regions. National-level trust amplified the association between perceived classmate support and adolescent life satisfaction. The revealed cross-country differences open avenues for future cross-cultural research on explanations for cross-cultural differences in the association between social support from different sources and life satisfaction in early adolescence

Viral population estimation using pyrosequencing

The diversity of virus populations within single infected hosts presents a major difficulty for the natural immune response as well as for vaccine design and antiviral drug therapy. Recently developed pyrophosphate based sequencing technologies (pyrosequencing) can be used for quantifying this diversity by ultra-deep sequencing of virus samples. We present computational methods for the analysis of such sequence data and apply these techniques to pyrosequencing data obtained from HIV populations within patients harboring drug resistant virus strains. Our main result is the estimation of the population structure of the sample from the pyrosequencing reads. This inference is based on a statistical approach to error correction, followed by a combinatorial algorithm for constructing a minimal set of haplotypes that explain the data. Using this set of explaining haplotypes, we apply a statistical model to infer the frequencies of the haplotypes in the population via an EM algorithm. We demonstrate that pyrosequencing reads allow for effective population reconstruction by extensive simulations and by comparison to 165 sequences obtained directly from clonal sequencing of four independent, diverse HIV populations. Thus, pyrosequencing can be used for cost-effective estimation of the structure of virus populations, promising new insights into viral evolutionary dynamics and disease control strategies.Comment: 23 pages, 13 figure

The social relations of health care and household resource allocation in neoliberal Nicaragua

<p>Abstract</p> <p>Background</p> <p>With the transition to neoliberalism, Nicaragua's once-critically acclaimed health care services have substantially diminished. Local level social formations have been under pressure to try to bridge gaps as the state's role in the provision of health care and other vital social services has decreased. This paper presents a case study of how global and national health policies reverberated in the social relations of an extended network of female kin in a rural community during late 2002 - 2003.</p> <p>Methods</p> <p>The qualitative methods used in this ethnographic study included semi-structured interviews completed during bi-weekly visits to 51 households, background interviews with 20 lay and professional health practitioners working in the public and private sectors, and participant-observation conducted in the region's government health centers. Interviews and observational field notes were manually coded and iteratively reviewed to identify and conceptually organize emergent themes. Three households of extended kin were selected from the larger sample to examine as a case study.</p> <p>Results</p> <p>The ongoing erosion of vital services formerly provided by the public sector generated considerable frustration and tension among households, networks of extended kin, and neighbors. As resource allocations for health care seeking and other needs were negotiated within and across households, longstanding ideals of reciprocal exchange persisted, but in conditions of poverty, expectations were often unfulfilled, exposing the tension between the need for social support, versus the increasingly oppositional positioning of social network members as sources of competition for limited resources.</p> <p>Conclusions</p> <p>In compliance with neoliberal structural adjustment policies mandated by multilateral and bilateral agencies, government-provided health care services have been severely restricted in Nicaragua. As the national safety net for health care has been eroded, the viability of local level social formations and their ability to respond to struggles collectively has been put at risk as well. Bi-lateral and multilateral agencies need to take into account local needs and demands, and implement policies in a manner that respects national laws, and protects both the physical and social well-being of individuals.</p

Initial Sequence and Comparative Analysis of the Cat Genome

The genome sequence (1.9-fold coverage) of an inbred Abyssinian domestic cat was assembled, mapped, and annotated with a comparative approach that involved cross-reference to annotated genome assemblies of six mammals (human, chimpanzee, mouse, rat, dog, and cow). The results resolved chromosomal positions for 663,480 contigs, 20,285 putative feline gene orthologs, and 133,499 conserved sequence blocks (CSBs). Additional annotated features include repetitive elements, endogenous retroviral sequences, nuclear mitochondrial (numt) sequences, micro-RNAs, and evolutionary breakpoints that suggest historic balancing of translocation and inversion incidences in distinct mammalian lineages. Large numbers of single nucleotide polymorphisms (SNPs), deletion insertion polymorphisms (DIPs), and short tandem repeats (STRs), suitable for linkage or association studies were characterized in the context of long stretches of chromosome homozygosity. In spite of the light coverage capturing ∼65% of euchromatin sequence from the cat genome, these comparative insights shed new light on the tempo and mode of gene/genome evolution in mammals, promise several research applications for the cat, and also illustrate that a comparative approach using more deeply covered mammals provides an informative, preliminary annotation of a light (1.9-fold) coverage mammal genome sequence

Multichromosomal median and halving problems under different genomic distances

<p>Abstract</p> <p>Background</p> <p>Genome median and genome halving are combinatorial optimization problems that aim at reconstructing ancestral genomes as well as the evolutionary events leading from the ancestor to extant species. Exploring complexity issues is a first step towards devising efficient algorithms. The complexity of the median problem for unichromosomal genomes (permutations) has been settled for both the breakpoint distance and the reversal distance. Although the multichromosomal case has often been assumed to be a simple generalization of the unichromosomal case, it is also a relaxation so that complexity in this context does not follow from existing results, and is open for all distances.</p> <p>Results</p> <p>We settle here the complexity of several genome median and halving problems, including a surprising polynomial result for the breakpoint median and guided halving problems in genomes with circular and linear chromosomes, showing that the multichromosomal problem is actually easier than the unichromosomal problem. Still other variants of these problems are NP-complete, including the DCJ double distance problem, previously mentioned as an open question. We list the remaining open problems.</p> <p>Conclusion</p> <p>This theoretical study clears up a wide swathe of the algorithmical study of genome rearrangements with multiple multichromosomal genomes.</p

Screening synteny blocks in pairwise genome comparisons through integer programming

<p>Abstract</p> <p>Background</p> <p>It is difficult to accurately interpret chromosomal correspondences such as true orthology and paralogy due to significant divergence of genomes from a common ancestor. Analyses are particularly problematic among lineages that have repeatedly experienced whole genome duplication (WGD) events. To compare multiple "subgenomes" derived from genome duplications, we need to relax the traditional requirements of "one-to-one" syntenic matchings of genomic regions in order to reflect "one-to-many" or more generally "many-to-many" matchings. However this relaxation may result in the identification of synteny blocks that are derived from ancient shared WGDs that are not of interest. For many downstream analyses, we need to eliminate weak, low scoring alignments from pairwise genome comparisons. Our goal is to objectively select subset of synteny blocks whose total scores are maximized while respecting the duplication history of the genomes in comparison. We call this "quota-based" screening of synteny blocks in order to appropriately fill a quota of syntenic relationships within one genome or between two genomes having WGD events.</p> <p>Results</p> <p>We have formulated the synteny block screening as an optimization problem known as "Binary Integer Programming" (BIP), which is solved using existing linear programming solvers. The computer program QUOTA-ALIGN performs this task by creating a clear objective function that maximizes the compatible set of synteny blocks under given constraints on overlaps and depths (corresponding to the duplication history in respective genomes). Such a procedure is useful for any pairwise synteny alignments, but is most useful in lineages affected by multiple WGDs, like plants or fish lineages. For example, there should be a 1:2 ploidy relationship between genome A and B if genome B had an independent WGD subsequent to the divergence of the two genomes. We show through simulations and real examples using plant genomes in the rosid superorder that the quota-based screening can eliminate ambiguous synteny blocks and focus on specific genomic evolutionary events, like the divergence of lineages (in cross-species comparisons) and the most recent WGD (in self comparisons).</p> <p>Conclusions</p> <p>The QUOTA-ALIGN algorithm screens a set of synteny blocks to retain only those compatible with a user specified ploidy relationship between two genomes. These blocks, in turn, may be used for additional downstream analyses such as identifying true orthologous regions in interspecific comparisons. There are two major contributions of QUOTA-ALIGN: 1) reducing the block screening task to a BIP problem, which is novel; 2) providing an efficient software pipeline starting from all-against-all BLAST to the screened synteny blocks with dot plot visualizations. Python codes and full documentations are publicly available <url>http://github.com/tanghaibao/quota-alignment</url>. QUOTA-ALIGN program is also integrated as a major component in SynMap <url>http://genomevolution.com/CoGe/SynMap.pl</url>, offering easier access to thousands of genomes for non-programmers.</p