Distributed Community Detection in Dynamic Graphs

Inspired by the increasing interest in self-organizing social opportunistic networks, we investigate the problem of distributed detection of unknown communities in dynamic random graphs. As a formal framework, we consider the dynamic version of the well-studied \emph{Planted Bisection Model} \sdG(n,p,q) where the node set $[n]$ of the network is partitioned into two unknown communities and, at every time step, each possible edge $(u,v)$ is active with probability $p$ if both nodes belong to the same community, while it is active with probability $q$ (with $q<<p$) otherwise. We also consider a time-Markovian generalization of this model. We propose a distributed protocol based on the popular \emph{Label Propagation Algorithm} and prove that, when the ratio $p/q$ is larger than $n^{b}$ (for an arbitrarily small constant $b>0$), the protocol finds the right "planted" partition in $O(\log n)$ time even when the snapshots of the dynamic graph are sparse and disconnected (i.e. in the case $p=\Theta(1/n)$).Comment: Version I

A particle system in interaction with a rapidly varying environment: Mean field limits and applications

We study an interacting particle system whose dynamics depends on an interacting random environment. As the number of particles grows large, the transition rate of the particles slows down (perhaps because they share a common resource of fixed capacity). The transition rate of a particle is determined by its state, by the empirical distribution of all the particles and by a rapidly varying environment. The transitions of the environment are determined by the empirical distribution of the particles. We prove the propagation of chaos on the path space of the particles and establish that the limiting trajectory of the empirical measure of the states of the particles satisfies a deterministic differential equation. This deterministic differential equation involves the time averages of the environment process. We apply our results to analyze the performance of communication networks where users access some resources using random distributed multi-access algorithms. For these networks, we show that the environment process corresponds to a process describing the number of clients in a certain loss network, which allows us provide simple and explicit expressions of the network performance.Comment: 31 pages, 2 figure

Convergence speed of unsteady distributed consensus: decay estimate along the settling spanning-trees

Results for estimating the convergence rate of non-stationary distributed consensus algorithms are provided, on the basis of qualitative (mainly topological) as well as basic quantitative information (lower-bounds on the matrix entries). The results appear to be tight in a number of instances and are illustrated through simple as well as more sophisticated examples. The main idea is to follow propagation of information along certain spanning trees which arise in the communication graph.Comment: 27 pages, 5 figure

Efficient Power Allocation Schemes for Hybrid Decode-Amplify-Forward Relay Based Wireless Cooperative Network

Cooperative communication in various wireless domains, such as cellular networks, sensor networks and wireless ad hoc networks, has gained significant interest recently. In cooperative network, relays between the source and the destination, form a virtual MIMO that creates spatial diversity at the destination, which overcomes the fading effect of wireless channels. Such relay assisted schemes have potential to increase the channel capacity and network coverage. Most current research on cooperative communication are focused broadly on efficient protocol design and analysis, resource allocation, relay selection and cross layer optimization. The first part of this research aims at introducing hybrid decode-amplify-forward (HDAF) relaying in a distributed Alamouti coded cooperative network. Performance of such adaptive relaying scheme in terms of symbol error rate (SER), outage probability and average channel capacity is derived theoretically and verified through simulation based study. This work is further extended to a generalized multi HDAF relaying cooperative frame work. Various efficient power allocation schemes such as maximized channel capacity based, minimized SER based and total power minimization based are proposed and their superiority in performance over the existing equal power allocation scheme is demonstrated in the simulation results. Due to the broadcast nature of wireless transmission, information privacy in wireless networks becomes a critical issue. In the context of physical layer security, the role of multi HDAF relaying based cooperative model with control jamming and multiple eavesdroppers is explored in the second part of the research. Performance evaluation parameters such as secrecy rate, secrecy outage and intercept probability are derived theoretically. Further the importance of the proposed power allocation schemes in enhancing the secrecy performance of the network in the presence of multiple eavesdroppers is studied in detail through simulation based study and analysis. For all the proposed power allocation schemes in this research, the optimization problems are defined under total power constraint and are solved using Lagrange multiplier method and also evolutionary algorithms such as Differential evolution and Invasive Weed Optimization are employed. Monte Carlo simulation based study is adopted throughout the research. It is concluded that HDAF relaying based wireless cooperative network with optimal power allocation schemes offers improved and reliable performance compared to conventional amplify forward and decode forward relaying schemes. Above research contributions will be applicable for future generation wireless cooperative networks

Doctor of Philosophy

dissertationAdvances in computer hardware have enabled routine MD simulations of systems with tens of thousands of atoms for up to microseconds (soon milliseconds). The key limiting factor in whether these simulations can advance hypothesis testing in active research is the accuracy of the force fields. In many ways, force fields for RNA are less mature than those for proteins. Yet even the current generation of force fields offers benefits to researchers as we demonstrate with our re-refinement effort on two RNA hairpins. Additionally, our simulation study of the binding of 2-aminobenzimidazole inhibitors to hepatitis C RNA offers a computational perspective on which of the two rather different published structures (one NMR, the other X-ray) is a more reasonable structure for future CADD efforts as well as which free energy methods are suited to these highly charged complexes. Finally, further effort on force field improvement is critical. We demonstrate an effective method to determine quantitative conformational population analysis of small RNAs using enhanced sampling methods. These efforts are allowing us to uncover force field pathologies and quickly test new modifications. In summary, this research serves to strengthen communication between experimental and theoretical methods in order produce mutual benefit

Unifying paradigms of quantum refrigeration: A universal and attainable bound on cooling

Cooling quantum systems is arguably one of the most important thermodynamic tasks connected to modern quantum technologies and an interesting question from a foundational perspective. It is thus of no surprise that many different theoretical cooling schemes have been proposed, differing in the assumed control paradigm and complexity, and operating either in a single cycle or in steady state limits. Working out bounds on quantum cooling has since been a highly context dependent task with multiple answers, with no general result that holds independent of assumptions. In this letter we derive a universal bound for cooling quantum systems in the limit of infinite cycles (or steady state regimes) that is valid for any control paradigm and machine size. The bound only depends on a single parameter of the refrigerator and is theoretically attainable in all control paradigms. For qubit targets we prove that this bound is achievable in a single cycle and by autonomous machines.Comment: 5 + 10 pages, 1 figure. Accepted for publication in PRL. See also the complementing article arXiv:1710.1162

Improving Frequency Estimation under Local Differential Privacy

Local Differential Privacy protocols are stochastic protocols used in data aggregation when individual users do not trust the data aggregator with their private data. In such protocols there is a fundamental tradeoff between user privacy and aggregator utility. In the setting of frequency estimation, established bounds on this tradeoff are either nonquantitative, or far from what is known to be attainable. In this paper, we use information-theoretical methods to significantly improve established bounds. We also show that the new bounds are attainable for binary inputs. Furthermore, our methods lead to improved frequency estimators, which we experimentally show to outperform state-of-the-art methods