/pdf/scalable-molecular-dynamics-with-namd-3j7xyc70g4.pdf

Scalable Molecular Dynamics with NAMD

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

The mapping of large-scale human movements is important for urban planning, traffic forecasting and epidemic prevention. Work in animals had suggested that their foraging might be explained in terms of a random walk, a mathematical rendition of a series of random steps, or a Levy flight, a random walk punctuated by occasional larger steps. The role of Levy statistics in animal behaviour is much debated — as explained in an accompanying News Feature — but the idea of extending it to human behaviour was boosted by a report in 2006 of Levy flight-like patterns in human movement tracked via dollar bills. A new human study, based on tracking the trajectory of 100,000 cell-phone users for six months, reveals behaviour close to a Levy pattern, but deviating from it as individual trajectories show a high degree of temporal and spatial regularity: work and other commitments mean we are not as free to roam as a foraging animal. But by correcting the data to accommodate individual variation, simple and predictable patterns in human travel begin to emerge. The cover photo (by Cesar Hidalgo) captures human mobility in New York's Grand Central Station. This study used a sample of 100,000 mobile phone users whose trajectory was tracked for six months to study human mobility patterns. Displacements across all users suggest behaviour close to the Levy-flight-like pattern observed previously based on the motion of marked dollar bills, but with a cutoff in the distribution. The origin of the Levy patterns observed in the aggregate data appears to be population heterogeneity and not Levy patterns at the level of the individual. Despite their importance for urban planning1, traffic forecasting2 and the spread of biological3,4,5 and mobile viruses6, our understanding of the basic laws governing human motion remains limited owing to the lack of tools to monitor the time-resolved location of individuals. Here we study the trajectory of 100,000 anonymized mobile phone users whose position is tracked for a six-month period. We find that, in contrast with the random trajectories predicted by the prevailing Levy flight and random walk models7, human trajectories show a high degree of temporal and spatial regularity, each individual being characterized by a time-independent characteristic travel distance and a significant probability to return to a few highly frequented locations. After correcting for differences in travel distances and the inherent anisotropy of each trajectory, the individual travel patterns collapse into a single spatial probability distribution, indicating that, despite the diversity of their travel history, humans follow simple reproducible patterns. This inherent similarity in travel patterns could impact all phenomena driven by human mobility, from epidemic prevention to emergency response, urban planning and agent-based modelling.

/pdf/understanding-individual-human-mobility-patterns-3k1tyob274.pdf

Understanding individual human mobility patterns

We present Tor, a circuit-based low-latency anonymous communication service. This second-generation Onion Routing system addresses limitations in the original design by adding perfect forward secrecy, congestion control, directory servers, integrity checking, configurable exit policies, and a practical design for location-hidden services via rendezvous points. Tor works on the real-world Internet, requires no special privileges or kernel modifications, requires little synchronization or coordination between nodes, and provides a reasonable tradeoff between anonymity, usability, and efficiency. We briefly describe our experiences with an international network of more than 30 nodes. We close with a list of open problems in anonymous communication.

/pdf/tor-the-second-generation-onion-router-2qfrg0ppqb.pdf

Tor: the second-generation onion router

NetworkX is a Python language package for exploration and analysis of networks and network algorithms. The core package provides data structures for representing many types of networks, or graphs, including simple graphs, directed graphs, and graphs with parallel edges and self-loops. The nodes in NetworkX graphs can be any (hashable) Python object and edges can contain arbitrary data; this flexibility makes NetworkX ideal for representing networks found in many dierent scientific fields. In addition to the basic data structures many graph algorithms are implemented for calculating network properties and structure measures: shortest paths, betweenness centrality, clustering, and degree distribution and many more. NetworkX can read and write various graph formats for easy exchange with existing data, and provides generators for many classic graphs and popular graph models, such as the Erdos-Renyi, Small World, and Barabasi-Albert models. The ease-of-use and flexibility of the Python programming language together with connection to the SciPy tools make NetworkX a powerful tool for scientific computations. We discuss some of our recent work studying synchronization of coupled oscillators to demonstrate how NetworkX enables research in the field of computational networks.

/pdf/exploring-network-structure-dynamics-and-function-using-2isdfk9y1h.pdf

Exploring Network Structure, Dynamics, and Function using NetworkX

Low discrepancy sets yield approximate min-wise independent permutation families

In this note, we show that the discrepancy of any family of ‘ permutations of [n] = f1; 2;:::;ng is O( p ‘ logn), improving on the O(‘ logn) bound due to Bohus (Random Structures & Algorithms, 1:215{220, 1990). In the case where ‘ n, we show that the discrepancy is (min f p n log(2‘=n);ng).

http://www.cs.umd.edu/~srin/PDF/disc-unpub.pdf

The discrepancy of permutation families

We present LMS, a protocol for efficient lookup on unstructured networks. Our protocol uses a virtual namespace without imposing specific topologies. It is more efficient than existing lookup protocols for unstructured networks, and thus is an attractive alternative for applications in which the topology cannot be structured as a Distributed Hash Table (DHT). We present analytic bounds for the worst-case performance of LMS. Through detailed simulations (with up to 100,000 nodes), we show that the actual performance on realistic topologies is significantly better. We also show in both simulations and a complete implementation (which includes over five hundred nodes) that our protocol is inherently robust against multiple node failures and can adapt its replication strategy to optimize searches according to a specific heuristic. Moreover, the simulation demonstrates the resilience of LMS to high node turnover rates, and that it can easily adapt to orders of magnitude changes in network size. The overhead incurred by LMS is small, and its performance approaches that of DHTs on networks of similar size

/pdf/efficient-lookup-on-unstructured-topologies-2knt21smoh.pdf

Efficient lookup on unstructured topologies

The Lov\'{a}sz Local Lemma (LLL) is a powerful tool that gives sufficient conditions for avoiding all of a given set of ``bad'' events, with positive probability. A series of results have provided algorithms to efficiently construct structures whose existence is non-constructively guaranteed by the LLL, culminating in the recent breakthrough of Moser \& Tardos. We show that the output distribution of the Moser-Tardos algorithm well-approximates the \emph{conditional LLL-distribution} – the distribution obtained by conditioning on all bad events being avoided. We show how a known bound on the probabilities of events in this distribution can be used for further probabilistic analysis and give new constructive and non-constructive results. We also show that when an LLL application provides a small amount of slack, the number of resamplings of the Moser-Tardos algorithm is nearly linear in the number of underlying independent variables (not events!), and can thus be used to give efficient constructions in cases where the underlying proof applies the LLL to super-polynomially many events. Even in cases where finding a bad event that holds is computationally hard, we show that applying the algorithm to avoid a polynomial-sized ``core'' subset of bad events leads to a desired outcome with high probability. We demonstrate this idea on several applications. We give the first constant-factor approximation algorithm for the Santa Claus problem by making an LLL-based proof of Feige constructive. We provide Monte Carlo algorithms for acyclic edge coloring, non-repetitive graph colorings, and Ramsey-type graphs. In all these applications the algorithm falls directly out of the non-constructive LLL-based proof. Our algorithms are very simple, often provide better bounds than previous algorithms, and are in several cases the first efficient algorithms known. As a second type of application we consider settings beyond the critical dependency threshold of the LLL: avoiding all bad events is impossible in these cases. As the first (even non-constructive) result of this kind, we show that by sampling from the LLL-distribution of a selected smaller core, we can avoid a fraction of bad events that is higher than the expectation. MAX $k$-SAT is an example of this.

New Constructive Aspects of the Lovasz Local Lemma

A basic problem in graphs and hypergraphs is that of finding a large independent set---one of guaranteed size. Understanding the parallel complexity of this and related independent set problems on hypergraphs is a fundamental open issue in parallel computation. Caro and Tuza [J. Graph Theory, 15 (1991), pp. 99--107] have shown a certain lower bound $\alpha_k(H)$ on the size of a maximum independent set in a given k-uniform hypergraph H and have also presented an efficient sequential algorithm to find an independent set of size $\alpha_k(H)$. They also show that $\alpha_k(H)$ is the size of the maximum independent set for various hypergraph families. Here, we show that an RNC algorithm due to Beame and Luby [in Proceedings of the ACM--SIAM Symposium on Discrete Algorithms, 1990, pp. 212--218] finds an independent set of expected size $\alpha_k(H)$ and also derandomizes it for certain special cases. (An intriguing conjecture of Beame and Luby implies that understanding this algorithm better may yield an RNC...

Aravind Srinivasan

Papers

Low discrepancy sets yield approximate min-wise independent permutation families

The discrepancy of permutation families

Efficient lookup on unstructured topologies

New Constructive Aspects of the Lovasz Local Lemma

Finding Large Independent Sets in Graphs and Hypergraphs