arXiv subjects

Mason A. Porter

Publications and source records attributed to Mason A. Porter.

At least 181 records · Page 10Linked to original sources

arXiv2013

Robust Detection of Dynamic Community Structure in Networks

We describe techniques for the robust detection of community structure in some classes of time-dependent networks. Specifically, we consider the use of statistical null models for facilitating the principled identification of structural modules in semi-decomposable systems. Null models play an important role both in the optimization of quality functions such as modularity and in the subsequent assessment of the statistical validity of identified community structure. We examine the sensitivity of such methods to model parameters and show how comparisons to null models can help identify system scales. By considering a large number of optimizations, we quantify the variance of network diagnostics over optimizations (`optimization variance') and over randomizations of network structure (`randomization variance'). Because the modularity quality function typically has a large number of nearly-degenerate local optima for networks constructed using real data, we develop a method to construct representative partitions that uses a null model to correct for statistical noise in sets of partitions. To illustrate our results, we employ ensembles of time-dependent networks extracted from both nonlinear oscillators and empirical neuroscience data.

physics.data-an↗

arXiv2013

Core-Periphery Structure in Networks

Intermediate-scale (or `meso-scale') structures in networks have received considerable attention, as the algorithmic detection of such structures makes it possible to discover network features that are not apparent either at the local scale of nodes and edges or at the global scale of summary statistics. Numerous types of meso-scale structures can occur in networks, but investigations of such features have focused predominantly on the identification and study of community structure. In this paper, we develop a new method to investigate the meso-scale feature known as core-periphery structure, which entails identifying densely-connected core nodes and sparsely-connected periphery nodes. In contrast to communities, the nodes in a core are also reasonably well-connected to those in the periphery. Our new method of computing core-periphery structure can identify multiple cores in a network and takes different possible cores into account. We illustrate the differences between our method and several existing methods for identifying which nodes belong to a core, and we use our technique to examine core-periphery structure in examples of friendship, collaboration, transportation, and voting networks.

cs.SI↗

arXiv2013

Limit Order Books

Limit order books (LOBs) match buyers and sellers in more than half of the world's financial markets. This survey highlights the insights that have emerged from the wealth of empirical and theoretical studies of LOBs. We examine the findings reported by statistical analyses of historical LOB data and discuss how several LOB models provide insight into certain aspects of the mechanism. We also illustrate that many such models poorly resemble real LOBs and that several well-established empirical facts have yet to be reproduced satisfactorily. Finally, we identify several key unresolved questions about LOBs.

q-fin.TR↗

arXiv2013

Two-Particle Circular Billiards Versus Randomly Perturbed One-Particle Circular Billiards

We study a two-particle circular billiard containing two finite-size circular particles that collide elastically with the billiard boundary and with each other. Such a two-particle circular billiard provides a clean example of an "intermittent" system. This billiard system behaves chaotically, but the time scale on which chaos manifests can become arbitrarily long as the sizes of the confined particles become smaller. The finite-time dynamics of this system depends on the relative frequencies of (chaotic) particle-particle collisions versus (integrable) particle-boundary collisions, and investigating these dynamics is computationally intensive because of the long time scales involved. To help improve understanding of such two-particle dynamics, we compare the results of diagnostics used to measure chaotic dynamics for a two-particle circular billiard with those computed for two types of one-particle circular billiards in which a confined particle undergoes random perturbations. Importantly, such one-particle approximations are much less computationally demanding than the original two-particle system, and we expect them to yield reasonable estimates of the extent of chaotic behavior in the two-particle system when the sizes of confined particles are small. Our computations of recurrence-rate coefficients, finite-time Lyapunov exponents, and autocorrelation coefficients support this hypothesis and suggest that studying randomly perturbed one-particle billiards has the potential to yield insights into the aggregate properties of two-particle billiards, which are difficult to investigate directly without enormous computation times (especially when the sizes of the confined particles are small).

nlin.CD↗

arXiv2013

Dark Solitary Waves in a Class of Collisionally Inhomogeneous Bose-Einstein Condensates

We study the structure, stability, and dynamics of dark solitary waves in parabolically trapped, collisionally inhomogeneous Bose-Einstein condensates (BECs) with spatially periodic variations of the scattering length. This collisional inhomogeneity yields a nonlinear lattice, which we tune from a small-amplitude, approximately sinusoidal structure to a periodic sequence of densely spaced spikes. We start by investigating time-independent inhomogeneities, and we subsequently examine the dynamical response when one starts with a collisionally homogeneous BEC and then switches on an inhomogeneity either adiabatically or nonadiabatically. Using Bogoliubov-de Gennes linearization as well as direct numerical simulations of the Gross-Pitaevskii equation, we observe dark solitary waves, which can become unstable through oscillatory or exponential instabilities. We find a critical wavelength of the nonlinear lattice that is comparable to the healing length. Near this value, the fundamental eigenmode responsible for the stability of the dark solitary wave changes its direction of movement as a function of the strength of the nonlinearity. When it increases, it collides with other eigenmodes, leading to oscillatory instabilities; when it decreases, it collides with the origin and becomes imaginary, illustrating that the instability mechanism is fundamentally different in wide-well versus narrow-well lattices. When starting from a collisionally homogeneous setup and switching on inhomogeneities, we find that dark solitary waves are preserved generically for aligned lattices. We briefly examine the time scales for the onset of solitary-wave oscillations in this scenario.

nlin.PS↗

arXiv2013

Teach Network Science to Teenagers

We discuss our outreach efforts to introduce school students to network science and explain why networks researchers should be involved in such outreach activities. We provide overviews of modules that we have designed for these efforts, comment on our successes and failures, and illustrate the potentially enormous impact of such outreach efforts.

physics.ed-ph↗

arXiv2013

Multi-Stage Complex Contagions

The spread of ideas across a social network can be studied using complex contagion models, in which agents are activated by contact with multiple activated neighbors. The investigation of complex contagions can provide crucial insights into social influence and behavior-adoption cascades on networks. In this paper, we introduce a model of a multi-stage complex contagion on networks. Agents at different stages --- which could, for example, represent differing levels of support for a social movement or differing levels of commitment to a certain product or idea --- exert different amounts of influence on their neighbors. We demonstrate that the presence of even one additional stage introduces novel dynamical behavior, including interplay between multiple cascades, that cannot occur in single-stage contagion models. We find that cascades --- and hence collective action --- can be driven not only by high-stage influencers but also by low-stage influencers.

cs.SI↗

arXiv2012

Multislice Modularity Optimization in Community Detection and Image Segmentation

Because networks can be used to represent many complex systems, they have attracted considerable attention in physics, computer science, sociology, and many other disciplines. One of the most important areas of network science is the algorithmic detection of cohesive groups (i.e., "communities") of nodes. In this paper, we algorithmically detect communities in social networks and image data by optimizing multislice modularity. A key advantage of modularity optimization is that it does not require prior knowledge of the number or sizes of communities, and it is capable of finding network partitions that are composed of communities of different sizes. By optimizing multislice modularity and subsequently calculating diagnostics on the resulting network partitions, it is thereby possible to obtain information about network structure across multiple system scales. We illustrate this method on data from both social networks and images, and we find that optimization of multislice modularity performs well on these two tasks without the need for extensive problem-specific adaptation. However, improving the computational speed of this method remains a challenging open problem.

cs.SI↗

arXiv2012

Geosocial Graph-Based Community Detection

We apply spectral clustering and multislice modularity optimization to a Los Angeles Police Department field interview card data set. To detect communities (i.e., cohesive groups of vertices), we use both geographic and social information about stops involving street gang members in the LAPD district of Hollenbeck. We then compare the algorithmically detected communities with known gang identifications and argue that discrepancies are due to sparsity of social connections in the data as well as complex underlying sociological factors that blur distinctions between communities.

cs.SI↗

arXiv2012

Dynamic Network Centrality Summarizes Learning in the Human Brain

We study functional activity in the human brain using functional Magnetic Resonance Imaging and recently developed tools from network science. The data arise from the performance of a simple behavioural motor learning task. Unsupervised clustering of subjects with respect to similarity of network activity measured over three days of practice produces significant evidence of `learning', in the sense that subjects typically move between clusters (of subjects whose dynamics are similar) as time progresses. However, the high dimensionality and time-dependent nature of the data makes it difficult to explain which brain regions are driving this distinction. Using network centrality measures that respect the arrow of time, we express the data in an extremely compact form that characterizes the aggregate activity of each brain region in each experiment using a single coefficient, while reproducing information about learning that was discovered using the full data set. This compact summary allows key brain regions contributing to centrality to be visualized and interpreted. We thereby provide a proof of principle for the use of recently proposed dynamic centrality measures on temporal network data in neuroscience.

q-bio.NC↗

arXiv2012

The Influence of Network Topology on Sound Propagation in Granular Materials

Granular materials, whose features range from the particle scale to the force-chain scale to the bulk scale, are usually modeled as either particulate or continuum materials. In contrast with either of these approaches, network representations are natural for the simultaneous examination of microscopic, mesoscopic, and macroscopic features. In this paper, we treat granular materials as spatially-embedded networks in which the nodes (particles) are connected by weighted edges obtained from contact forces. We test a variety of network measures for their utility in helping to describe sound propagation in granular networks and find that network diagnostics can be used to probe particle-, curve-, domain-, and system-scale structures in granular media. In particular, diagnostics of meso-scale network structure are reproducible across experiments, are correlated with sound propagation in this medium, and can be used to identify potentially interesting size scales. We also demonstrate that the sensitivity of network diagnostics depends on the phase of sound propagation. In the injection phase, the signal propagates systemically, as indicated by correlations with the network diagnostic of global efficiency. In the scattering phase, however, the signal is better predicted by meso-scale community structure, suggesting that the acoustic signal scatters over local geographic neighborhoods. Collectively, our results demonstrate how the force network of a granular system is imprinted on transmitted waves.

cond-mat.soft↗

arXiv2012

Taxonomies of Networks

The study of networks has grown into a substantial interdisciplinary endeavour that encompasses myriad disciplines in the natural, social, and information sciences. Here we introduce a framework for constructing taxonomies of networks based on their structural similarities. These networks can arise from any of numerous sources: they can be empirical or synthetic, they can arise from multiple realizations of a single process, empirical or synthetic, or they can represent entirely different systems in different disciplines. Since the mesoscopic properties of networks are hypothesized to be important for network function, we base our comparisons on summaries of network community structures. While we use a specific method for uncovering network communities, much of the introduced framework is independent of that choice. After introducing the framework, we apply it to construct a taxonomy for 746 individual networks and demonstrate that our approach usefully identifies similar networks. We also construct taxonomies within individual categories of networks, and in each case we expose non-trivial structure. For example we create taxonomies for similarity networks constructed from both political voting data and financial data. We also construct network taxonomies to compare the social structures of 100 Facebook networks and the growth structures produced by different types of fungi.

physics.data-an↗

arXiv2012

The Extraordinary SVD

The singular value decomposition (SVD) is a popular matrix factorization that has been used widely in applications ever since an efficient algorithm for its computation was developed in the 1970s. In recent years, the SVD has become even more prominent due to a surge in applications and increased computational memory and speed. To illustrate the vitality of the SVD in data analysis, we highlight three of its lesser-known yet fascinating applications: the SVD can be used to characterize political positions of Congressmen, measure the growth rate of crystals in igneous rock, and examine entanglement in quantum computation. We also discuss higher-dimensional generalizations of the SVD, which have become increasingly crucial with the newfound wealth of multidimensional data and have launched new research initiatives in both theoretical and applied mathematics. With its bountiful theory and applications, the SVD is truly extraordinary.

math.NA↗

arXiv2012

Accuracy of Mean-Field Theory for Dynamics on Real-World Networks

Mean-field analysis is an important tool for understanding dynamics on complex networks. However, surprisingly little attention has been paid to the question of whether mean-field predictions are accurate, and this is particularly true for real-world networks with clustering and modular structure. In this paper, we compare mean-field predictions to numerical simulation results for dynamical processes running on 21 real-world networks and demonstrate that the accuracy of the theory depends not only on the mean degree of the networks but also on the mean first-neighbor degree. We show that mean-field theory can give (unexpectedly) accurate results for certain dynamics on disassortative real-world networks even when the mean degree is as low as 4.

physics.soc-ph↗

arXiv2011

Generalized Master Equations for Non-Poisson Dynamics on Networks

The traditional way of studying temporal networks is to aggregate the dynamics of the edges to create a static weighted network. This implicitly assumes that the edges are governed by Poisson processes, which is not typically the case in empirical temporal networks. Consequently, we examine the effects of non-Poisson inter-event statistics on the dynamics of edges, and we apply the concept of a generalized master equation to the study of continuous-time random walks on networks. We show that the equation reduces to the standard rate equations when the underlying process is Poisson and that the stationary solution is determined by an effective transition matrix whose leading eigenvector is easy to calculate. We discuss the implications of our work for dynamical processes on temporal networks and for the construction of network diagnostics that take into account their nontrivial stochastic nature.

physics.soc-ph↗

arXiv2011

Dynamic reconfiguration of human brain networks during learning

Human learning is a complex phenomenon requiring flexibility to adapt existing brain function and precision in selecting new neurophysiological activities to drive desired behavior. These two attributes -- flexibility and selection -- must operate over multiple temporal scales as performance of a skill changes from being slow and challenging to being fast and automatic. Such selective adaptability is naturally provided by modular structure, which plays a critical role in evolution, development, and optimal network function. Using functional connectivity measurements of brain activity acquired from initial training through mastery of a simple motor skill, we explore the role of modularity in human learning by identifying dynamic changes of modular organization spanning multiple temporal scales. Our results indicate that flexibility, which we measure by the allegiance of nodes to modules, in one experimental session predicts the relative amount of learning in a future session. We also develop a general statistical framework for the identification of modular architectures in evolving systems, which is broadly applicable to disciplines where network adaptability is crucial to the understanding of system performance.

q-bio.NC↗

arXiv2011

Party Polarization in Congress: A Network Science Approach

We measure polarization in the United States Congress using the network science concept of modularity. Modularity provides a conceptually-clear measure of polarization that reveals both the number of relevant groups and the strength of inter-group divisions without making restrictive assumptions about the structure of the party system or the shape of legislator utilities. We show that party influence on Congressional blocs varies widely throughout history, and that existing measures underestimate polarization in periods with weak party structures. We demonstrate that modularity is a significant predictor of changes in majority party and that turnover is more prevalent at medium levels of modularity. We show that two variables related to modularity, called `divisiveness' and `solidarity,' are significant predictors of reelection success for individual House members. Our results suggest that modularity can serve as an early warning of changing group dynamics, which are reflected only later by changes in party labels.

physics.soc-ph↗

arXiv2011

A Mathematical Model for the Dynamics and Synchronization of Cows

We formulate a mathematical model for daily activities of a cow (eating, lying down, and standing) in terms of a piecewise affine dynamical system. We analyze the properties of this bovine dynamical system representing the single animal and develop an exact integrative form as a discrete-time mapping. We then couple multiple cow "oscillators" together to study synchrony and cooperation in cattle herds. We comment on the relevant biology and discuss extensions of our model. With this abstract approach, we not only investigate equations with interesting dynamics but also develop interesting biological predictions. In particular, our model illustrates that it is possible for cows to synchronize \emph{less} when the coupling is increased.

nlin.AO↗