Algorithms to Measure Diversity and Clustering in Social Networks through Dot Product Graphs

Social networks are often analyzed through a graph model of the network. The dot product model assumes that two individuals are connected in the social network if their attributes or opinions are similar. In the model, a d-dimensional vector a v represents the extent to which individual v has each of a set of d attributes or opinions. Then two individuals u and v are assumed to be friends, that is, they are connected in the graph model, if and only if a u · a v  ≥ t, for some fixed, positive threshold t. The resulting graph is called a d-dot product graph.. We consider two measures for diversity and clustering in social networks by using a d-dot product graph model for the network. Diversity is measured through the size of the largest independent set of the graph, and clustering is measured through the size of the largest clique. We obtain a tight result for the diversity problem, namely that it is polynomial-time solvable for d = 2, but NP-complete for d ≥ 3. We show that the clustering problem is polynomial-time solvable for d = 2. To our knowledge, these results are also the first on the computational complexity of combinatorial optimization problems on dot product graphs. We also consider the situation when two individuals are connected if their preferences are not opposite. This leads to a variant of the standard dot product graph model by taking the threshold t to be zero. We prove in this case that the diversity problem is polynomial-time solvable for any fixed d

Estimates of present and future flood risk in the conterminous United States

Past attempts to estimate rainfall-driven flood risk across the US either have incomplete coverage, coarse resolution or use overly simplified models of the flooding process. In this paper, we use a new 30m resolution model of the entire conterminous US with a 2D representation of flood physics to produce estimates of flood hazard, which match to within 90% accuracy the skill of local models built with detailed data. These flood depths are combined with exposure datasets of commensurate resolution to calculate current and future flood risk. Our data show that the total US population exposed to serious flooding is 2.6–3.1 times higher than previous estimates, and that nearly 41 million Americans live within the 1% annual exceedance probability floodplain (compared to only 13 million when calculated using FEMA flood maps). We find that population and GDP growth alone are expected to lead to significant future increases in exposure, and this change may be exacerbated in the future by climate change

Approximate affine linear relationship between L1 norm objective functional values and L2 norm constraint bounds

For an optimization problem with an norm objective function subject to an norm inequality constraint, this paper shows that there is an approximately linear relationship between the norm objective functional values and the norm specifications. This relationship is verified through the use of random and real world industrial data. The obtained results can be employed for 1) estimating the norm output objective functional value without solving the optimization problem numerically; 2) providing an insight for defining the norm specification in which a simple method is proposed in this paper; and 3) testing whether the obtained solutions are the globally optimal solutions or not. These advantages are demonstrated via the use of random data

Fine-Scale Mapping of the 4q24 Locus Identifies Two Independent Loci Associated with Breast Cancer Risk

Background: A recent association study identified a common variant (rs9790517) at 4q24 to be associated with breast cancer risk. Independent association signals and potential functional variants in this locus have not been explored. Methods: We conducted a fine-mapping analysis in 55,540 breast cancer cases and 51,168 controls from the Breast Cancer Association Consortium. Results: Conditional analyses identified two independent association signals among women of European ancestry, represented by rs9790517 [conditional P = 2.51 × 10−4; OR, 1.04; 95% confidence interval (CI), 1.02–1.07] and rs77928427 (P = 1.86 × 10−4; OR, 1.04; 95% CI, 1.02–1.07). Functional annotation using data from the Encyclopedia of DNA Elements (ENCODE) project revealed two putative functional variants, rs62331150 and rs73838678 in linkage disequilibrium (LD) with rs9790517 (r2 ≥ 0.90) residing in the active promoter or enhancer, respectively, of the nearest gene, TET2. Both variants are located in DNase I hypersensitivity and transcription factor–binding sites. Using data from both The Cancer Genome Atlas (TCGA) and Molecular Taxonomy of Breast Cancer International Consortium (METABRIC), we showed that rs62331150 was associated with level of expression of TET2 in breast normal and tumor tissue. Conclusion: Our study identified two independent association signals at 4q24 in relation to breast cancer risk and suggested that observed association in this locus may be mediated through the regulation of TET2. Impact: Fine-mapping study with large sample size warranted for identification of independent loci for breast cancer risk

Zooterapia amazônica: uso de gordura de sucuri ( Eunectes murinus ) como cicatrizante natural

Zootherapy (the use of the therapeutic potential of animals) is at least 6,000 years old, and has been kept active throughout generations until modern days. Animal fat is commonly used in the zootherapeutic folk medicine from South America, specially the green anaconda's fat, which is widely promoted as a natural medicine to treat wounds, even though there is no scientific evidence showing its efficacy. In this study we compared the total healing time and the proportional daily reduction of dorsal epithelial incisions in adult male Wistar rats treated with nitrofural (a commercial cicatrizing ointment) and with anaconda fat. We applied the treatments every two days and measured the incision diameter daily, during ten consecutive days. Differences among the groups in the total healing time and in the proportional daily reduction of the incision consistently showed that the fat-based treatment resulted in a faster healing process compared to the commercial ointment tested. The literature suggests that the efficacy of animal fat on healing may be primarily related to the presence of fatty acids, which have been widely demonstrated to be important for biochemical reactions involved in healing processes. Our findings are widely socially relevant, considering that traditional Amazonian communities that use anaconda fat in folk medicine do not have easy access to pharmacies and hospitals.Práticas ancestrais de zooterapia (uso das potencialidades terapêuticas da fauna) existem há pelo menos 6000 anos, e têm sido mantidas ao longo de gerações até os tempos modernos. Gordura de animais é comumente utilizada na zooterapia tradicional da América do Sul, e a gordura de serpentes sucuris é amplamente comercializada como cicatrizante natural, embora não existam evidências científicas que mostrem sua eficácia terapêutica. Neste estudo comparamos o tempo de cicatrização epitelial total e a redução proporcional diária de uma incisão dorsal em ratos Wistar machos adultos, entre um grupo controle, um grupo tratado com nitrofural (uma pomada cicatrizante comercial) e um grupo tratado com gordura de sucuri. Nós aplicamos os tratamentos a cada dois dias e medimos o diâmetro da incisão diariamente por dez dias consecutivos. Diferenças entre os grupos no tempo de cicatrização total e na redução proporcional diária da incisão consistentemente mostraram que gordura de sucuri teve ação cicatrizante mais eficiente que a pomada comercial testada. A literatura sugere que a eficácia de gordura animal em processos de cicatrização pode estar principalmente relacionada à presença de ácidos graxos, os quais têm sido amplamente demonstrados como importantes para reações bioquímicas envolvidas em processos de cicatrização. Os resultados têm ampla relevância social, considerando que as comunidades tradicionais amazônicas que utilizam a gordura de sucuris como zooterápico não têm acesso fácil a farmácias e hospitais

Bifurcation Analysis of Genetically Engineered Pacemaking in Mammalian Heart

Genetically engineered pacemaking in ventricular cells has been achieved by down-regulation of the time independent inward rectifying current (IK1), or insertion of the hyperpolarisation-activated funny current (If). We analyse the membrane system (i.e. ionic concentrations clamped) of an epicardial Luo-Rudy dynamic cell model using continuation algorithms with the maximum conductance (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{g}$$\end{document}) of IK1 and If as bifurcation parameters. Pacemaker activity can be induced either via Hopf or homoclinic bifurcations. As \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{g}$$\end{document}K1 is decreased by ≈74%, autorhythmicity emerged via a homoclinic bifurcation, i.e., the periodicity first appear with infinitely large periods. In contrast, the insertion of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{g}$$\end{document}f induced periodicity via a subcritical Hopf bifurcation at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{g}$$\end{document}f≈ 0.25 mSμF−1. Stable autorhythmic action potentials occurred at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{g}$$\end{document}f > 0.329 mSμF−1