Showing papers in "Physical Review E in 2009"

Community detection algorithms: a comparative analysis.

Abstract: Uncovering the community structure exhibited by real networks is a crucial step toward an understanding of complex systems that goes beyond the local organization of their constituents. Many algorithms have been proposed so far, but none of them has been subjected to strict tests to evaluate their performance. Most of the sporadic tests performed so far involved small networks with known community structure and/or artificial graphs with a simplified structure, which is very uncommon in real systems. Here we test several methods against a recently introduced class of benchmark graphs, with heterogeneous distributions of degree and community size. The methods are also tested against the benchmark by Girvan and Newman [Proc. Natl. Acad. Sci. U.S.A. 99, 7821 (2002)] and on random graphs. As a result of our analysis, three recent algorithms introduced by Rosvall and Bergstrom [Proc. Natl. Acad. Sci. U.S.A. 104, 7327 (2007); Proc. Natl. Acad. Sci. U.S.A. 105, 1118 (2008)], Blondel et al. [J. Stat. Mech.: Theory Exp. (2008), P10008], and Ronhovde and Nussinov [Phys. Rev. E 80, 016109 (2009)] have an excellent performance, with the additional advantage of low computational complexity, which enables one to analyze large systems.

Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities.

Abstract: Many complex networks display a mesoscopic structure with groups of nodes sharing many links with the other nodes in their group and comparatively few with nodes of different groups. This feature is known as community structure and encodes precious information about the organization and the function of the nodes. Many algorithms have been proposed but it is not yet clear how they should be tested. Recently we have proposed a general class of undirected and unweighted benchmark graphs, with heterogeneous distributions of node degree and community size. An increasing attention has been recently devoted to develop algorithms able to consider the direction and the weight of the links, which require suitable benchmark graphs for testing. In this paper we extend the basic ideas behind our previous benchmark to generate directed and weighted networks with built-in community structure. We also consider the possibility that nodes belong to more communities, a feature occurring in real systems, such as social networks. As a practical application, we show how modularity optimization performs on our benchmark.

Pore-network extraction from micro-computerized-tomography images

Abstract: Network models that represent the void space of a rock by a lattice of pores connected by throats can predict relative permeability once the pore geometry and wettability are known. Micro-computerized-tomography scanning provides a three-dimensional image of the pore space. However, these images cannot be directly input into network models. In this paper a modified maximal ball algorithm, extending the work of Silin and Patzek [D. Silin and T. Patzek, Physica A 371, 336 (2006)], is developed to extract simplified networks of pores and throats with parametrized geometry and interconnectivity from images of the pore space. The parameters of the pore networks, such as coordination number, and pore and throat size distributions are computed and compared to benchmark data from networks extracted by other methods, experimental data, and direct computation of permeability and formation factor on the underlying images. Good agreement is reached in most cases allowing networks derived from a wide variety of rock types to be used for predictive modeling.

Rogue waves and rational solutions of the nonlinear Schrödinger equation

Abstract: We present a method for finding the hierarchy of rational solutions of the self-focusing nonlinear Schrodinger equation and present explicit forms for these solutions from first to fourth order. We also explain their relation to the highest amplitude part of a field that starts with a plane wave perturbed by random small amplitude radiation waves. Our work can elucidate the appearance of rogue waves in the deep ocean and can be applied to the observation of rogue light pulse waves in optical fibers.

Line graphs, link partitions, and overlapping communities.

Abstract: In this paper, we use a partition of the links of a network in order to uncover its community structure. This approach allows for communities to overlap at nodes so that nodes may be in more than one community. We do this by making a node partition of the line graph of the original network. In this way we show that any algorithm that produces a partition of nodes can be used to produce a partition of links. We discuss the role of the degree heterogeneity and propose a weighted version of the line graph in order to account for this.

Similarity index based on local paths for link prediction of complex networks.

Abstract: Predictions of missing links of incomplete networks, such as protein-protein interaction networks or very likely but not yet existent links in evolutionary networks like friendship networks in web society, can be considered as a guideline for further experiments or valuable information for web users. In this paper, we present a local path index to estimate the likelihood of the existence of a link between two nodes. We propose a network model with controllable density and noise strength in generating links, as well as collect data of six real networks. Extensive numerical simulations on both modeled networks and real networks demonstrated the high effectiveness and efficiency of the local path index compared with two well-known and widely used indices: the common neighbors and the Katz index. Indeed, the local path index provides competitively accurate predictions as the Katz index while requires much less CPU time and memory space than the Katz index, which is therefore a strong candidate for potential practical applications in data mining of huge-size networks.

Drop impact onto a liquid layer of finite thickness: dynamics of the cavity evolution.

Abstract: In the present work experimental, numerical, and theoretical investigations of a normal drop impact onto a liquid film of finite thickness are presented. The dynamics of drop impact on liquid surfaces, the shape of the cavity, the formation and propagation of a capillary wave in the crater, and the residual film thickness on the rigid wall are determined and analyzed. The shape of the crater within the film and the uprising liquid sheet formed upon the impact are observed using a high-speed video system. The effects of various influencing parameters such as drop impact velocity, liquid film thickness and physical properties of the liquids, including viscosity and surface tension, on the time evolution of the crater formation are investigated. Complementary to experiments the direct numerical simulations of the phenomena are performed using an advanced free-surface capturing model based on a two-fluid formulation of the classical volume-of-fluid (VOF) model in the framework of the finite volume numerical method. In this model an additional convective term is introduced into the transport equation for phase fraction, contributing decisively to a sharper interface resolution. Furthermore, an analytical model for the penetration depth of the crater is developed accounting for the liquid inertia, viscosity, gravity, and surface tension. The model agrees well with the experiments at the early times of penetration far from the wall if the impact velocity is high. Finally, a scaling analysis of the residual film thickness on the wall is conducted demonstrating a good agreement with the numerical predictions.

Horizontal visibility graphs: Exact results for random time series

Abstract: networks. This procedure allows us to apply methods of complex network theory for characterizing time series. In this work we present the horizontal visibility algorithm, a geometrically simpler and analytically solvable version of our former algorithm, focusing on the mapping of random series series of independent identically distributed random variables. After presenting some properties of the algorithm, we present exact results on the topological properties of graphs associated with random series, namely, the degree distribution, the clustering coefficient, and the mean path length. We show that the horizontal visibility algorithm stands as a simple method to discriminate randomness in time series since any random series maps to a graph with an exponential degree distribution of the shape Pk=1 /32 /3 k2 , independent of the probability distribution from which the series was generated. Accordingly, visibility graphs with other Pk are related to nonrandom series. Numerical simulations confirm the accuracy of the theorems for finite series. In a second part, we show that the method is able to distinguish chaotic series from independent and identically distributed i.i.d. theory, studying the following situations: i noise-free low-dimensional chaotic series, ii low-dimensional noisy chaotic series, even in the presence of large amounts of noise, and iii high-dimensional chaotic series coupled map lattice, without needs for additional techniques such as surrogate data or noise reduction methods. Finally, heuristic arguments are given to explain the topological properties of chaotic series, and several sequences that are conjectured to be random are analyzed.

Quantum mechanical evolution towards thermal equilibrium.

Abstract: The circumstances under which a system reaches thermal equilibrium, and how to derive this from basic dynamical laws, has been a major question from the very beginning of thermodynamics and statistical mechanics. Despite considerable progress, it remains an open problem. Motivated by this issue, we address the more general question of equilibration. We prove, with virtually full generality, that reaching equilibrium is a universal property of quantum systems: almost any subsystem in interaction with a large enough bath will reach an equilibrium state and remain close to it for almost all times. We also prove several general results about other aspects of thermalization besides equilibration, for example, that the equilibrium state does not depend on the detailed microstate of the bath.

Memristive model of amoeba learning.

Abstract: Recently, it was shown that the amoebalike cell Physarum polycephalum when exposed to a pattern of periodic environmental changes learns and adapts its behavior in anticipation of the next stimulus to come. Here we show that such behavior can be mapped into the response of a simple electronic circuit consisting of a LC contour and a memory-resistor (a memristor) to a train of voltage pulses that mimic environment changes. We also identify a possible biological origin of the memristive behavior in the cell. These biological memory features are likely to occur in other unicellular as well as multicellular organisms, albeit in different forms. Therefore, the above memristive circuit model, which has learning properties, is useful to better understand the origins of primitive intelligence.

Community detection in networks with positive and negative links

Abstract: Detecting communities in complex networks accurately is a prime challenge, preceding further analyses of network characteristics and dynamics. Until now, community detection took into account only positively valued links, while many actual networks also feature negative links. We extend an existing Potts model to incorporate negative links as well, resulting in a method similar to the clustering of signed graphs, as dealt with in social balance theory, but more general. To illustrate our method, we applied it to a network of international alliances and disputes. Using data from 1993-2001, it turns out that the world can be divided into six power blocs similar to Huntington's civilizations, with some notable exceptions.

Detecting network communities by propagating labels under constraints.

Abstract: We investigate the recently proposed label-propagation algorithm (LPA) for identifying network communities. We reformulate the LPA as an equivalent optimization problem, giving an objective function whose maxima correspond to community solutions. By considering properties of the objective function, we identify conceptual and practical drawbacks of the label-propagation approach, most importantly the disparity between increasing the value of the objective function and improving the quality of communities found. To address the drawbacks, we modify the objective function in the optimization problem, producing a variety of algorithms that propagate labels subject to constraints; of particular interest is a variant that maximizes the modularity measure of community quality. Performance properties and implementation details of the proposed algorithms are discussed. Bipartite as well as unipartite networks are considered.

Topology-independent impact of noise on cooperation in spatial public goods games.

Abstract: We study the evolution of cooperation in public goods games on different regular graphs as a function of the noise level underlying strategy adoptions. We focus on the effects that are brought about by different group sizes of public goods games in which individuals participate, revealing that larger groups of players may induce qualitatively different behavior when approaching the deterministic limit of strategy adoption. While by pairwise interactions an intermediate uncertainty by strategy adoptions may ensure optimal conditions for the survival of cooperators at a specific graph topology, larger groups warrant this only in the vicinity of the deterministic limit independently from the underlying graph. These discrepancies are attributed to the indirect linkage of otherwise not directly connected players, which is brought about by joint memberships within the larger groups. Thus, we show that increasing the group size may introduce an effective transition of the interaction topology, and that the latter shapes the noise dependence of the evolution of cooperation in case of pairwise interactions only.

Synchronization transitions on scale-free neuronal networks due to finite information transmission delays.

Abstract: We investigate front propagation and synchronization transitions in dependence on the information transmission delay and coupling strength over scale-free neuronal networks with different average degrees and scaling exponents. As the underlying model of neuronal dynamics, we use the efficient Rulkov map with additive noise. We show that increasing the coupling strength enhances synchronization monotonously, whereas delay plays a more subtle role. In particular, we found that depending on the inherent oscillation frequency of individual neurons, regions of irregular and regular propagating excitatory fronts appear intermittently as the delay increases. These delay-induced synchronization transitions manifest as well-expressed minima in the measure for spatial synchrony, appearing at every multiple of the oscillation frequency. Larger coupling strengths or average degrees can broaden the region of regular propagating fronts by a given information transmission delay and further improve synchronization. These results are robust against variations in system size, intensity of additive noise, and the scaling exponent of the underlying scale-free topology. We argue that fine-tuned information transmission delays are vital for assuring optimally synchronized excitatory fronts on complex neuronal networks and, indeed, they should be seen as important as the coupling strength or the overall density of interneuronal connections. We finally discuss some biological implications of the presented results.

Diffusion of scientific credits and the ranking of scientists

Abstract: Recently, the abundance of digital data is enabling the implementation of graph-based ranking algorithms that provide system level analysis for ranking publications and authors. Here, we take advantage of the entire Physical Review publication archive (1893-2006) to construct authors' networks where weighted edges, as measured from opportunely normalized citation counts, define a proxy for the mechanism of scientific credit transfer. On this network, we define a ranking method based on a diffusion algorithm that mimics the spreading of scientific credits on the network. We compare the results obtained with our algorithm with those obtained by local measures such as the citation count and provide a statistical analysis of the assignment of major career awards in the area of physics. A website where the algorithm is made available to perform customized rank analysis can be found at the address http://www.physauthorsrank.org.

Towards real-time community detection in large networks.

Abstract: The recent boom of large-scale online social networks (OSNs) both enables and necessitates the use of parallelizable and scalable computational techniques for their analysis. We examine the problem of real-time community detection and a recently proposed linear time---$O(m)$ on a network with $m$ edges---label propagation, or ``epidemic'' community detection algorithm. We identify characteristics and drawbacks of the algorithm and extend it by incorporating different heuristics to facilitate reliable and multifunctional real-time community detection. With limited computational resources, we employ the algorithm on OSN data with $1\ifmmode\times\else\texttimes\fi{}{10}^{6}$ nodes and about $58\ifmmode\times\else\texttimes\fi{}{10}^{6}$ directed edges. Experiments and benchmarks reveal that the extended algorithm is not only faster but its community detection accuracy compares favorably over popular modularity-gain optimization algorithms known to suffer from their resolution limits.

Ergodic properties of fractional Brownian-Langevin motion

Abstract: We investigate the time average mean-square displacement $\overline{{\ensuremath{\delta}}^{2}}\mathbf{(}x(t)\mathbf{)}={\ensuremath{\int}}_{0}^{t\ensuremath{-}\ensuremath{\Delta}}{[x({t}^{\ensuremath{'}}+\ensuremath{\Delta})\ensuremath{-}x({t}^{\ensuremath{'}})]}^{2}d{t}^{\ensuremath{'}}∕(t\ensuremath{-}\ensuremath{\Delta})$ for fractional Brownian-Langevin motion where $x(t)$ is the stochastic trajectory and $\ensuremath{\Delta}$ is the lag time. Unlike the previously investigated continuous-time random-walk model, $\overline{{\ensuremath{\delta}}^{2}}$ converges to the ensemble average $⟨{x}^{2}⟩\ensuremath{\sim}{t}^{2H}$ in the long measurement time limit. The convergence to ergodic behavior is slow, however, and surprisingly the Hurst exponent $H=\frac{3}{4}$ marks the critical point of the speed of convergence. When $Hl\frac{3}{4}$, the ergodicity breaking parameter ${E}_{B}={\mathbf{[}⟨[\overline{{\ensuremath{\delta}}^{2}}\mathbf{(}x(t)\mathbf{)}\mathbf{]}}^{2}⟩\ensuremath{-}{⟨\overline{{\ensuremath{\delta}}^{2}}\mathbf{(}x(t)\mathbf{)}⟩}^{2}\mathbf{]}/{⟨\overline{{\ensuremath{\delta}}^{2}}\mathbf{(}x(t)\mathbf{)}⟩}^{2}\ensuremath{\sim}k(H)\ensuremath{\Delta}{t}^{\ensuremath{-}1}$, when $H=\frac{3}{4}$, ${E}_{B}\ensuremath{\sim}(\frac{9}{16})(\mathrm{ln}\phantom{\rule{0.2em}{0ex}}t)\ensuremath{\Delta}{t}^{\ensuremath{-}1}$, and when $\frac{3}{4}lHl1$, ${E}_{B}\ensuremath{\sim}k(H){\ensuremath{\Delta}}^{4\ensuremath{-}4H}{t}^{4H\ensuremath{-}4}$. In the ballistic limit $H\ensuremath{\rightarrow}1$ ergodicity is broken and ${E}_{B}\ensuremath{\sim}2$. The critical point $H=\frac{3}{4}$ is marked by the divergence of the coefficient $k(H)$. Fractional Brownian motion as a model for recent experiments of subdiffusion of mRNA in the cell is briefly discussed, and a comparison with the continuous-time random-walk model is made.

Characterizing the human mobility pattern in a large street network

Abstract: Previous studies demonstrated empirically that human mobility exhibits Levy flight behavior. However, our knowledge of the mechanisms governing this Levy flight behavior remains limited. Here we analyze over 72,000 people's moving trajectories, obtained from 50 taxicabs during a six-month period in a large street network, and illustrate that the human mobility pattern, or the Levy flight behavior, is mainly attributed to the underlying street network. In other words, the goal-directed nature of human movement has little effect on the overall traffic distribution. We further simulate the mobility of a large number of random walkers and find that (1) the simulated random walkers can reproduce the same human mobility pattern, and (2) the simulated mobility rate of the random walkers correlates pretty well (an R square up to 0.87) with the observed human mobility rate.

Effect of cholesterol on structural and mechanical properties of membranes depends on lipid chain saturation

Abstract: The effects of cholesterol on membrane bending modulus K(C), membrane thickness D(HH), the partial and apparent areas of cholesterol and lipid, and the order parameter S(xray) are shown to depend upon the number of saturated hydrocarbon chains in the lipid molecules. Particularly striking is the result that up to 40% cholesterol does not increase the bending modulus K(C) of membranes composed of phosphatidylcholine lipids with two cis monounsaturated chains, although it does have the expected stiffening effect on membranes composed of lipids with two saturated chains. The B fluctuational modulus in the smectic liquid crystal theory is obtained and used to discuss the interactions between bilayers. Our K(C) results motivate a theory of elastic moduli in the high cholesterol limit and they challenge the relevance of universality concepts. Although most of our results were obtained at 30 degrees C , additional data at other temperatures to allow consideration of a reduced temperature variable do not support universality for the effect of cholesterol on all lipid bilayers. If the concept of universality is to be valid, different numbers of saturated chains must be considered to create different universality classes. The above experimental results were obtained from analysis of x-ray scattering in the low angle and wide angle regions.

Exact results for the Kuramoto model with a bimodal frequency distribution.

Abstract: We analyze a large system of globally coupled phase oscillators whose natural frequencies are bimodally distributed. The dynamics of this system has been the subject of long-standing interest. In 1984 Kuramoto proposed several conjectures about its behavior; ten years later, Crawford obtained the first analytical results by means of a local center manifold calculation. Nevertheless, many questions have remained open, especially about the possibility of global bifurcations. Here we derive the system's stability diagram for the special case where the bimodal distribution consists of two equally weighted Lorentzians. Using an ansatz recently discovered by Ott and Antonsen, we show that in this case the infinite-dimensional problem reduces exactly to a flow in four dimensions. Depending on the parameters and initial conditions, the long-term dynamics evolves to one of three states: incoherence, where all the oscillators are desynchronized; partial synchrony, where a macroscopic group of phase-locked oscillators coexists with a sea of desynchronized ones; and a standing wave state, where two counter-rotating groups of phase-locked oscillators emerge. Analytical results are presented for the bifurcation boundaries between these states. Similar results are also obtained for the case in which the bimodal distribution is given by the sum of two Gaussians.

Entropy measures for networks: toward an information theory of complex topologies.

Abstract: The quantification of the complexity of networks is, today, a fundamental problem in the physics of complex systems. A possible roadmap to solve the problem is via extending key concepts of information theory to networks. In this Rapid Communication we propose how to define the Shannon entropy of a network ensemble and how it relates to the Gibbs and von Neumann entropies of network ensembles. The quantities we introduce here will play a crucial role for the formulation of null models of networks through maximum-entropy arguments and will contribute to inference problems emerging in the field of complex networks.

World-trade web: Topological properties, dynamics, and evolution

Abstract: This paper studies the statistical properties of the web of import-export relationships among world countries using a weighted-network approach. We analyze how the distributions of the most important network statistics measuring connectivity, assortativity, clustering, and centrality have coevolved over time. We show that all node-statistic distributions and their correlation structure have remained surprisingly stable in the last 20 years—and are likely to do so in the future. Conversely, the distribution of positive link weights is slowly moving from a log-normal density towards a power law. We also characterize the autoregressive properties of network-statistics dynamics. We find that network-statistics growth rates are well-proxied by fat-tailed densities like the Laplace or the asymmetric exponential power. Finally, we find that all our results are reasonably robust to a few alternative, economically meaningful, weighting schemes.

Multiresolution community detection for megascale networks by information-based replica correlations.

Abstract: We use a Potts model community detection algorithm to accurately and quantitatively evaluate the hierarchical or multiresolution structure of a graph. Our multiresolution algorithm calculates correlations among multiple copies ("replicas") of the same graph over a range of resolutions. Significant multiresolution structures are identified by strongly correlated replicas. The average normalized mutual information, the variation in information, and other measures, in principle, give a quantitative estimate of the "best" resolutions and indicate the relative strength of the structures in the graph. Because the method is based on information comparisons, it can, in principle, be used with any community detection model that can examine multiple resolutions. Our approach may be extended to other optimization problems. As a local measure, our Potts model avoids the "resolution limit" that affects other popular models. With this model, our community detection algorithm has an accuracy that ranks among the best of currently available methods. Using it, we can examine graphs over 40 x10;{6} nodes and more than 1 x10;{9} edges. We further report that the multiresolution variant of our algorithm can solve systems of at least 200 000 nodes and 10 x 10;{6} edges on a single processor with exceptionally high accuracy. For typical cases, we find a superlinear scaling O(L1.3) for community detection and O(L1.3 log N) for the multiresolution algorithm, where L is the number of edges and N is the number of nodes in the system.

Reconstruction algorithm for single-particle diffraction imaging experiments.

Abstract: We introduce the EMC algorithm for reconstructing a particle's three-dimensional (3D) diffraction intensity from very many photon shot-noise limited two-dimensional measurements, when the particle orientation in each measurement is unknown. The algorithm combines a maximization step (M) of the intensity's likelihood function, with expansion (E) and compression (C) steps that map the 3D intensity model to a redundant tomographic representation and back again. After a few iterations of the EMC update rule, the reconstructed intensity is given to the difference-map algorithm for reconstruction of the particle contrast. We demonstrate reconstructions with simulated data and investigate the effects of particle complexity, number of measurements, and the number of photons per measurement. The relatively transparent scaling behavior of our algorithm provides an estimate of the data processing resources required for future single-particle imaging experiments.

Percolation and epidemics in random clustered networks.

Abstract: The social networks that infectious diseases spread along are typically clustered. Because of the close relation between percolation and epidemic spread, the behavior of percolation in such networks gives insight into infectious disease dynamics. A number of authors have studied percolation or epidemics in clustered networks, but the networks often contain preferential contacts in high degree nodes. We introduce a class of random clustered networks and a class of random unclustered networks with the same preferential mixing. Percolation in the clustered networks reduces the component sizes and increases the epidemic threshold compared to the unclustered networks.

Local elasticity map and plasticity in a model Lennard-Jones glass.

Abstract: In this work we calculate the local elastic moduli in a weakly polydispersed two-dimensional Lennard-Jones glass undergoing a quasistatic shear deformation at zero temperature. The numerical method uses coarse-grained microscopic expressions for the strain, displacement, and stress fields. This method allows us to calculate the local elasticity tensor and to quantify the deviation from linear elasticity (local Hooke's law) at different coarse-graining scales. From the results a clear picture emerges of an amorphous material with strongly spatially heterogeneous elastic moduli that simultaneously satisfies Hooke's law at scales larger than a characteristic length scale of the order of five interatomic distances. At this scale, the glass appears as a composite material composed of a rigid scaffolding and of soft zones. Only recently calculated in nonhomogeneous materials, the local elastic structure plays a crucial role in the elastoplastic response of the amorphous material. For a small macroscopic shear strain, the structures associated with the nonaffine displacement field appear directly related to the spatial structure of the elastic moduli. Moreover, for a larger macroscopic shear strain we show that zones of low shear modulus concentrate most of the strain in the form of plastic rearrangements. The spatiotemporal evolution of this local elasticity map and its connection with long term dynamical heterogeneity as well as with the plasticity in the material is quantified. The possibility to use this local parameter as a predictor of subsequent local plastic activity is also discussed.

Random hypergraphs and their applications.

Abstract: In the last few years we have witnessed the emergence, primarily in online communities, of new types of social networks that require for their representation more complex graph structures than have been employed in the past. One example is the folksonomy, a tripartite structure of users, resources, and tags—labels collaboratively applied by the users to the resources in order to impart meaningful structure on an otherwise undifferentiated database. Here we propose a mathematical model of such tripartite structures that represents them as random hypergraphs. We show that it is possible to calculate many properties of this model exactly in the limit of large network size and we compare the results against observations of a real folksonomy, that of the online photography website Flickr. We show that in some cases the model matches the properties of the observed network well, while in others there are significant differences, which we find to be attributable to the practice of multiple tagging, i.e., the application by a single user of many tags to one resource or one tag to many resources

Topological analysis of polymeric melts: chain-length effects and fast-converging estimators for entanglement length.

Abstract: Primitive path analyses of entanglements are performed over a wide range of chain lengths for both bead spring and atomistic polyethylene polymer melts. Estimators for the entanglement length N_{e} which operate on results for a single chain length N are shown to produce systematic O(1/N) errors. The mathematical roots of these errors are identified as (a) treating chain ends as entanglements and (b) neglecting non-Gaussian corrections to chain and primitive path dimensions. The prefactors for the O(1/N) errors may be large; in general their magnitude depends both on the polymer model and the method used to obtain primitive paths. We propose, derive, and test new estimators which eliminate these systematic errors using information obtainable from the variation in entanglement characteristics with chain length. The new estimators produce accurate results for N_{e} from marginally entangled systems. Formulas based on direct enumeration of entanglements appear to converge faster and are simpler to apply.

Effects of mobility in a population of prisoner's dilemma players.

Abstract: We address the problem of how the survival of cooperation in a social system depends on the motion of the individuals. Specifically, we study a model in which prisoner's dilemma players are allowed to move in a two-dimensional plane. Our results show that cooperation can survive in such a system provided that both the temptation to defect and the velocity at which agents move are not too high. Moreover, we show that when these conditions are fulfilled, the only asymptotic state of the system is that in which all players are cooperators. Our results might have implications for the design of cooperative strategies in motion coordination and other applications including wireless networks.