The Arboricity Captures the Complexity of Sampling Edges

In this paper, we revisit the problem of sampling edges in an unknown graph G = (V, E) from a distribution that is (pointwise) almost uniform over E. We consider the case where there is some a priori upper bound on the arboriciy of G. Given query access to a graph G over n vertices and of average degree {d} and arboricity at most alpha, we design an algorithm that performs O(alpha/d * {log^3 n}/epsilon) queries in expectation and returns an edge in the graph such that every edge e in E is sampled with probability (1 +/- epsilon)/m. The algorithm performs two types of queries: degree queries and neighbor queries. We show that the upper bound is tight (up to poly-logarithmic factors and the dependence in epsilon), as Omega(alpha/d) queries are necessary for the easier task of sampling edges from any distribution over E that is close to uniform in total variational distance. We also prove that even if G is a tree (i.e., alpha = 1 so that alpha/d = Theta(1)), Omega({log n}/{loglog n}) queries are necessary to sample an edge from any distribution that is pointwise close to uniform, thus establishing that a poly(log n) factor is necessary for constant alpha. Finally we show how our algorithm can be applied to obtain a new result on approximately counting subgraphs, based on the recent work of Assadi, Kapralov, and Khanna (ITCS, 2019)

The Arboricity Captures the Complexity of Sampling Edges

In this paper, we revisit the problem of sampling edges in an unknown graph $G = (V, E)$ from a distribution that is (pointwise) almost uniform over $E$. We consider the case where there is some a priori upper bound on the arboriciy of $G$. Given query access to a graph $G$ over $n$ vertices and of average degree $d$ and arboricity at most $\alpha$, we design an algorithm that performs $O\!\left(\frac{\alpha}{d} \cdot \frac{\log^3 n}{\varepsilon}\right)$ queries in expectation and returns an edge in the graph such that every edge $e \in E$ is sampled with probability $(1 \pm \varepsilon)/m$. The algorithm performs two types of queries: degree queries and neighbor queries. We show that the upper bound is tight (up to poly-logarithmic factors and the dependence in $\varepsilon$), as $\Omega\!\left(\frac{\alpha}{d} \right)$ queries are necessary for the easier task of sampling edges from any distribution over $E$ that is close to uniform in total variational distance. We also prove that even if $G$ is a tree (i.e., $\alpha = 1$ so that $\frac{\alpha}{d}=\Theta(1)$), $\Omega\left(\frac{\log n}{\log\log n}\right)$ queries are necessary to sample an edge from any distribution that is pointwise close to uniform, thus establishing that a $\mathrm{poly}(\log n)$ factor is necessary for constant $\alpha$. Finally we show how our algorithm can be applied to obtain a new result on approximately counting subgraphs, based on the recent work of Assadi, Kapralov, and Khanna (ITCS, 2019)

The Proteomic Profile of Hereditary Inclusion Body Myopathy

Hereditary inclusion body myopathy (HIBM) is an adult onset, slowly progressive distal and proximal myopathy. Although the causing gene, GNE, encodes for a key enzyme in the biosynthesis of sialic acid, its primary function in HIBM remains unknown. The goal of this study was to unravel new clues on the biological pathways leading to HIBM by proteomic comparison. Muscle cultures and biopsies were analyzed by two dimensional gel electrophoresis (2-DE) and the same biopsy extracts by isobaric tag for relative and absolute quantitation (iTRAQ). Proteins that were differentially expressed in all HIBM specimens versus all controls in each analysis were identified by mass spectrometry. The muscle cultures 2-DE analysis yielded 41 such proteins, while the biopsies 2-DE analysis showed 26 differentially expressed proteins. Out of the 400 proteins identified in biopsies by iTRAQ, 41 showed altered expression. In spite of the different nature of specimens (muscle primary cultures versus muscle biopsies) and of the different methods applied (2D gels versus iTRAQ) the differentially expressed proteins identified in each of the three analyses where related mainly to the same pathways, ubiquitination, stress response and mitochondrial processes, but the most robust cluster (30%) was assigned to cytoskeleton and sarcomere organization. Taken together, these findings indicate a possible novel function of GNE in the muscle filamentous apparatus that could be involved in the pathogenesis of HIBM

Genetic Diversity and Population Parameters of Sea Otters, Enhydra lutris, before Fur Trade Extirpation from 1741–1911

All existing sea otter, Enhydra lutris, populations have suffered at least one historic population bottleneck stemming from the fur trade extirpations of the eighteenth and nineteenth centuries. We examined genetic variation, gene flow, and population structure at five microsatellite loci in samples from five pre-fur trade populations throughout the sea otter's historical range: California, Oregon, Washington, Alaska, and Russia. We then compared those values to genetic diversity and population structure found within five modern sea otter populations throughout their current range: California, Prince William Sound, Amchitka Island, Southeast Alaska and Washington. We found twice the genetic diversity in the pre-fur trade populations when compared to modern sea otters, a level of diversity that was similar to levels that are found in other mammal populations that have not experienced population bottlenecks. Even with the significant loss in genetic diversity modern sea otters have retained historical structure. There was greater gene flow before extirpation than that found among modern sea otter populations but the difference was not statistically significant. The most dramatic effect of pre fur trade population extirpation was the loss of genetic diversity. For long term conservation of these populations increasing gene flow and the maintenance of remnant genetic diversity should be encouraged

Almost Optimal Bounds for Sublinear-Time Sampling of k-Cliques in Bounded Arboricity Graphs

max {(((n?)^(k/2))/n_k)^{1/(k-1)}, (n?^(k-1))/n_k}}), where n is the number of vertices in the graph, and ?^*(?) suppresses dependencies on (log n/?)^O(k). Our upper bound is based on defining a special auxiliary graph H_k, such that sampling edges almost uniformly in H_k translates to sampling k-cliques almost uniformly in the original graph G. We then build on a known edge-sampling algorithm (Eden, Ron and Rosenbaum, ICALP19) to sample edges in H_k. The challenge is simulating queries to H_k while being given query access only to G. Our lower bound follows from a construction of a family of graphs with arboricity ? such that in each graph there are n_k k-cliques, where one of these cliques is "hidden" and hence hard to sample

Improving hygienic environments for infants and young children testing playpens for feasibility and appeal in rural households of Amhara, Ethiopia

This record includes an extended abstract and MP4 presentation. Presented at the 42nd WEDC International Conference