Efficient and exact sampling of simple graphs with given arbitrary degree sequence

Uniform sampling from graphical realizations of a given degree sequence is a fundamental component in simulation-based measurements of network observables, with applications ranging from epidemics, through social networks to Internet modeling. Existing graph sampling methods are either link-swap based (Markov-Chain Monte Carlo algorithms) or stub-matching based (the Configuration Model). Both types are ill-controlled, with typically unknown mixing times for link-swap methods and uncontrolled rejections for the Configuration Model. Here we propose an efficient, polynomial time algorithm that generates statistically independent graph samples with a given, arbitrary, degree sequence. The algorithm provides a weight associated with each sample, allowing the observable to be measured either uniformly over the graph ensemble, or, alternatively, with a desired distribution. Unlike other algorithms, this method always produces a sample, without back-tracking or rejections. Using a central limit theorem-based reasoning, we argue, that for large N, and for degree sequences admitting many realizations, the sample weights are expected to have a lognormal distribution. As examples, we apply our algorithm to generate networks with degree sequences drawn from power-law distributions and from binomial distributions.Comment: 8 pages, 3 figure

The formation of physician patient sharing networks in medicare: Exploring the effect of hospital affiliation

This study explores the forces that drive the formation of physician patient sharing networks. In particular, I examine the degree to which hospital affiliation drives physicians\u27 sharing of Medicare patients. Using a revealed preference framework where observed network links are taken to be pairwise stable, I estimate the physicians\u27 pair‐specific values using a tetrad maximum score estimator that is robust to the presence of unobserved physician specific characteristics. I also control for a number of potentially confounding patient sharing channels, such as (a) common physician group or hospital system affiliation, (b) physician homophily, (c) knowledge complementarity, (d) patient side considerations related to both geographic proximity and insurance network participation, and (e) spillover from other collaborations. Focusing on the Chicago hospital referral region, I find that shared hospital affiliation accounts for 36.5% of the average pair‐specific utility from a link. Implications for reducing care fragmentation are discussed

The anatomical distance of functional connections predicts brain network topology in health and schizophrenia.

The human brain is a topologically complex network embedded in anatomical space. Here, we systematically explored relationships between functional connectivity, complex network topology, and anatomical (Euclidean) distance between connected brain regions, in the resting-state functional magnetic resonance imaging brain networks of 20 healthy volunteers and 19 patients with childhood-onset schizophrenia (COS). Normal between-subject differences in average distance of connected edges in brain graphs were strongly associated with variation in topological properties of functional networks. In addition, a club or subset of connector hubs was identified, in lateral temporal, parietal, dorsal prefrontal, and medial prefrontal/cingulate cortical regions. In COS, there was reduced strength of functional connectivity over short distances especially, and therefore, global mean connection distance of thresholded graphs was significantly greater than normal. As predicted from relationships between spatial and topological properties of normal networks, this disorder-related proportional increase in connection distance was associated with reduced clustering and modularity and increased global efficiency of COS networks. Between-group differences in connection distance were localized specifically to connector hubs of multimodal association cortex. In relation to the neurodevelopmental pathogenesis of schizophrenia, we argue that the data are consistent with the interpretation that spatial and topological disturbances of functional network organization could arise from excessive "pruning" of short-distance functional connections in schizophrenia.PEV is supported by the Medical Research Council (grant number MR/K020706/1). This work was supported by the Neuroscience in Psychiatry Network (NSPN) which is funded by a Wellcome Trust strategy award to the University of Cambridge and University College London. ETB is employed half-time by the University of Cambridge and half-time by GlaxoSmithKline; he holds stock in GSK.This is the final published version. It first appeared at http://onlinelibrary.wiley.com/doi/10.1111/jcpp.12365/full

Techniques for Complex Analysis of Contemporary Data

Contemporary data objects are typically complex, semi-structured, or unstructured at all. Besides, objects are also related to form a network. In such a situation, data analysis requires not only the traditional attribute-based access but also access based on similarity as well as data mining operations. Though tools for such operations do exist, they usually specialise in operation and are available for specialized data structures supported by specific computer system environments. In contrary, advance analyses are obtained by application of several elementary access operations which in turn requires expert knowledge in multiple areas. In this paper, we propose a unification platform for various data analytical operators specified as a general-purpose analytical system ADAMiSS. An extensible data-mining and similarity-based set of operators over a common versatile data structure allow the recursive application of heterogeneous operations, thus allowing the definition of complex analytical processes, necessary to solve the contemporary analytical tasks. As a proof-of-concept, we present results that were obtained by our prototype implementation on two real-world data collections: the Twitter Higg's boson and the Kosarak datasets

Bethe-Peierls approximation and the inverse Ising model

We apply the Bethe-Peierls approximation to the problem of the inverse Ising model and show how the linear response relation leads to a simple method to reconstruct couplings and fields of the Ising model. This reconstruction is exact on tree graphs, yet its computational expense is comparable to other mean-field methods. We compare the performance of this method to the independent-pair, naive mean- field, Thouless-Anderson-Palmer approximations, the Sessak-Monasson expansion, and susceptibility propagation in the Cayley tree, SK-model and random graph with fixed connectivity. At low temperatures, Bethe reconstruction outperforms all these methods, while at high temperatures it is comparable to the best method available so far (Sessak-Monasson). The relationship between Bethe reconstruction and other mean- field methods is discussed

Genome-wide linkage analysis of inguinal hernia in pigs using affected sib pairs

BACKGROUND: Inguinal and scrotal hernias are of great concern to pig producers, and lead to poor animal welfare and severe economic loss. Selection against these conditions is highly preferable, but at this time no gene, Quantitative Trait Loci (QTL), or mode of inheritance has been identified in pigs or in any other species. Therefore, a complete genome scan was performed in order to identify genomic regions affecting inguinal and scrotal hernias in pigs. Records from seedstock breeding farms were collected. No clinical examinations were executed on the pigs and there was therefore no distinction between inguinal and scrotal hernias. The genome scan utilised affected sib pairs (ASP), and the data was analysed using both an ASP test based on Non-parametric Linkage (NPL) analysis, and a Transmission Disequilibrium Test (TDT). RESULTS: Significant QTLs (p < 0.01) were detected on 8 out of 19 porcine chromosomes. The most promising QTLs, however, were detected in SSC1, SSC2, SSC5, SSC6, SSC15, SSC17 and SSCX; all of these regions showed either statistical significance with both statistical methods, or convincing significance with one of the methods. Haplotypes from these suggestive QTL regions were constructed and analysed with TDT. Of these, six different haplotypes were found to be differently transmitted (p < 0.01) to healthy and affected pigs. The most interesting result was one haplotype on SSC5 that was found to be transmitted to hernia pigs with four times higher frequency than to healthy pigs (p < 0.00005). CONCLUSION: For the first time in any species, a genome scan has revealed suggestive QTLs for inguinal and scrotal hernias. While this study permitted the detection of chromosomal regions only, it is interesting to note that several promising candidate genes, including INSL3, MIS, and CGRP, are located within the highly significant QTL regions. Further studies are required in order to narrow down the suggestive QTL regions, investigate the candidate genes, and to confirm the suggestive QTLs in other populations. The haplotype associated with inguinal and scrotal hernias may help in achieving selection against the disorder

Design and Synthesis of Heterocyclic Cations for Specific DNA Recognition: From AT-Rich to Mixed-Base-Pair DNA Sequences

The compounds synthesized in this research were designed with the goal of establishing a new paradigm for mixed-base-pair DNA sequence-specific recognition. The design scheme starts with a cell-permeable heterocyclic cation that binds to AT base pair sites in the DNA minor groove. Modifications were introduced in the original compound to include an Hbond accepting group to specifically recognize the G-NH that projects into the minor groove. Therefore, a series of heterocyclic cations substituted with an azabenzimidazole ring has been designed and synthesized for mixed-base-pair DNA recognition. The most successful compound, 12a, had an azabenzimidazole to recognize G and additional modifications for general minor groove interactions. It binds to the DNA site −AAAGTTT− more strongly than the −AAATTT− site without GC and indicates the design success. Structural modifications of 12a generally weakened binding. The interactions of the new compound with a variety of DNA sequences with and without GC base pairs were evaluated by thermal melting analysis, circular dichroism, fluorescence emission spectroscopy, surface plasmon resonance, and molecular modeling