On Counting Triangles through Edge Sampling in Large Dynamic Graphs

Traditional frameworks for dynamic graphs have relied on processing only the stream of edges added into or deleted from an evolving graph, but not any additional related information such as the degrees or neighbor lists of nodes incident to the edges. In this paper, we propose a new edge sampling framework for big-graph analytics in dynamic graphs which enhances the traditional model by enabling the use of additional related information. To demonstrate the advantages of this framework, we present a new sampling algorithm, called Edge Sample and Discard (ESD). It generates an unbiased estimate of the total number of triangles, which can be continuously updated in response to both edge additions and deletions. We provide a comparative analysis of the performance of ESD against two current state-of-the-art algorithms in terms of accuracy and complexity. The results of the experiments performed on real graphs show that, with the help of the neighborhood information of the sampled edges, the accuracy achieved by our algorithm is substantially better. We also characterize the impact of properties of the graph on the performance of our algorithm by testing on several Barabasi-Albert graphs.Comment: A short version of this article appeared in Proceedings of the 2017 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2017

Relationship between intact HIV-1 proviruses in circulating CD4+ T cells and rebound viruses emerging during treatment interruption.

Combination antiretroviral therapy controls but does not cure HIV-1 infection because a small fraction of cells harbor latent viruses that can produce rebound viremia when therapy is interrupted. The circulating latent virus reservoir has been documented by a variety of methods, most prominently by viral outgrowth assays (VOAs) in which CD4+ T cells are activated to produce virus in vitro, or more recently by amplifying proviral near full-length (NFL) sequences from DNA. Analysis of samples obtained in clinical studies in which individuals underwent analytical treatment interruption (ATI), showed little if any overlap between circulating latent viruses obtained from outgrowth cultures and rebound viruses from plasma. To determine whether intact proviruses amplified from DNA are more closely related to rebound viruses than those obtained from VOAs, we assayed 12 individuals who underwent ATI after infusion of a combination of two monoclonal anti-HIV-1 antibodies. A total of 435 intact proviruses obtained by NFL sequencing were compared with 650 latent viruses from VOAs and 246 plasma rebound viruses. Although, intact NFL and outgrowth culture sequences showed similar levels of stability and diversity with 39% overlap, the size of the reservoir estimated from NFL sequencing was larger than and did not correlate with VOAs. Finally, intact proviruses documented by NFL sequencing showed no sequence overlap with rebound viruses; however, they appear to contribute to recombinant viruses found in plasma during rebound

Stability of Ca-montmorillonite hydrates: A computer simulation study

Classic simulations are used to study interlayer structure, swelling curves, and stability of Ca-montmorillonite hydrates. For this purpose, NPzzT$ and MuPzzT ensembles are sampled for ground level and given burial conditions. For ground level conditions, a double layer hydrate having 15.0 A of basal spacing is the predominant state for relative vapor pressures (p/po) ranging in 0.6-1.0. A triple hydrate counting on 17.9 A of interlaminar distance was also found stable for p/po=1.0. For low vapor pressures, the system may produce a less hydrated but still double layer state with 13.5 A or even a single layer hydrate with 12.2 A of interlaminar distance. This depends on the established initial conditions. On the other hand, the effect of burial conditions is two sided. It was found that it enhances dehydration for all vapor pressures except for saturation, where swelling is promoted.Comment: 8 pages, 9 figure

Streaming Property Testing of Visibly Pushdown Languages

In the context of language recognition, we demonstrate the superiority of streaming property testers against streaming algorithms and property testers, when they are not combined. Initiated by Feigenbaum et al., a streaming property tester is a streaming algorithm recognizing a language under the property testing approximation: it must distinguish inputs of the language from those that are $\varepsilon$-far from it, while using the smallest possible memory (rather than limiting its number of input queries). Our main result is a streaming $\varepsilon$-property tester for visibly pushdown languages (VPL) with one-sided error using memory space $\mathrm{poly}((\log n) / \varepsilon)$. This constructions relies on a (non-streaming) property tester for weighted regular languages based on a previous tester by Alon et al. We provide a simple application of this tester for streaming testing special cases of instances of VPL that are already hard for both streaming algorithms and property testers. Our main algorithm is a combination of an original simulation of visibly pushdown automata using a stack with small height but possible items of linear size. In a second step, those items are replaced by small sketches. Those sketches relies on a notion of suffix-sampling we introduce. This sampling is the key idea connecting our streaming tester algorithm to property testers.Comment: 23 pages. Major modifications in the presentatio