/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

The resampling algorithm of Moser & Tardos is a powerful approach to develop versions of the Lovasz Local Lemma. We develop a partial resampling approach motivated by this methodology: when a bad event holds, we resample an appropriately-random subset of the set of variables that define this event, rather than the entire set as in Moser & Tardos. This leads to several improved algorithmic applications in scheduling, graph transversals, packet routing etc. For instance, we improve the approximation ratio of a generalized D-dimensional scheduling problem studied by Azar & Epstein from O(D) to O(log D/ log log D), and settle a conjecture of Szabo & Tardos on graph transversals asymptotically.

The Moser-Tardos Framework with Partial Resampling

We present a new general upper bound on the number of examples required to estimate all of the expectations of a set of random variables uniformly well. The quality of the estimates is measured using a variant of the relative error proposed by Haussler and Pollard. We also show that our bound is within a constant factor of the best possible. Our upper bound implies improved bounds on the sample complexity of learning according to Haussler’s decision theoretic model. ∗A preliminary version of this work appeared in the Proceedings of the Eleventh Annual ACM-SIAM Symposium on Discrete Algorithms, 2000. †Part of this work was done while this author was at the School of Computing of the National University of Singapore.

/pdf/improved-bounds-on-the-sample-complexity-of-learning-3i43zgf48j.pdf

Improved bounds on the sample complexity of learning

The PAC learning of rectangles has been studied because they have been found experimentally to yield excellent hypotheses for several applied learning problems. Also, pseudorandom sets for rectangles have been actively studied recently because (i) they are a subproblem common to the derandomization of depth-2 (DNF) circuits and derandomizing randomized logspace, and (ii) they approximate the distribution ofnindependent multivalued random variables. We present improved upper bounds for a class of such problems of “approximating” high-dimensional rectangles that arise in PAC learning and pseudo- randomness.

Approximating Hyper-Rectangles

The Lovasz local lemma (LLL) is a powerful tool that is increasingly playing a valuable role in computer science. The original lemma was nonconstructive; a breakthrough of Beck and its generalizations (due to Alon and Molloy and Reed) have led to constructive versions. However, these methods do not capture some classes of applications of the LLL. We make progress on this by providing algorithmic approaches to two families of applications of the LLL. The first provides constructive versions of certain applications of an extension of the LLL (modeling, e.g., hypergraph-partitioning and low-congestion routing problems); the second provides new algorithmic results on constructing disjoint paths in graphs. Our results can also be seen as constructive upper bounds on the integrality gap of certain packing problems. One common theme of our work is a "gradual rounding" approach.

New Algorithmic Aspects of the Local Lemma with Applications to Routing and Partitioning

We present improved approximation algorithms in stochastic optimization. We prove that the multistage stochastic versions of covering integer programs (such as set cover and vertex cover) admit essentially the same approximation algorithms as their standard (nonstochastic) counterparts; this improves upon work of Swamy and Shmoys which shows an approximability that depends multiplicatively on the number of stages. We also present approximation algorithms for facility location and some of its variants in the 2-stage recourse model, improving on previous approximation guarantees. We give a 2.2975-approximation algorithm in the standard polynomial-scenario model and an algorithm with an expected per-scenario 2.4957-approximation guarantee, which is applicable to the more general black-box distribution model.

Aravind Srinivasan

Papers

The Moser-Tardos Framework with Partial Resampling

Improved bounds on the sample complexity of learning

Approximating Hyper-Rectangles

New Algorithmic Aspects of the Local Lemma with Applications to Routing and Partitioning

Approximation Algorithms for Stochastic and Risk-Averse Optimization