arXiv subjects

Mason A. Porter

Publications and source records attributed to Mason A. Porter.

At least 145 records · Page 8Linked to original sources

arXiv2016

Quasi-Centralized Limit Order Books

A quasi-centralized limit order book (QCLOB) is a limit order book (LOB) in which financial institutions can only access the trading opportunities offered by counterparties with whom they possess sufficient bilateral credit. We perform an empirical analysis of a recent, high-quality data set from a large electronic trading platform that utilizes QCLOBs to facilitate trade. We find many significant differences between our results and those widely reported for other LOBs. We also uncover a remarkable empirical universality: although the distributions describing order flow and market state vary considerably across days, a simple, linear rescaling causes them to collapse onto a single curve. Motivated by this finding, we propose a semi-parametric model of order flow and market state in a QCLOB on a single trading day. Our model provides similar performance to that of parametric curve-fitting techniques, while being simpler to compute and faster to implement.

q-fin.TR↗

arXiv2016

Eigenvector-Based Centrality Measures for Temporal Networks

Numerous centrality measures have been developed to quantify the importances of nodes in time-independent networks, and many of them can be expressed as the leading eigenvector of some matrix. With the increasing availability of network data that changes in time, it is important to extend such eigenvector-based centrality measures to time-dependent networks. In this paper, we introduce a principled generalization of network centrality measures that is valid for any eigenvector-based centrality. We consider a temporal network with N nodes as a sequence of T layers that describe the network during different time windows, and we couple centrality matrices for the layers into a supra-centrality matrix of size NTxNT whose dominant eigenvector gives the centrality of each node i at each time t. We refer to this eigenvector and its components as a joint centrality, as it reflects the importances of both the node i and the time layer t. We also introduce the concepts of marginal and conditional centralities, which facilitate the study of centrality trajectories over time. We find that the strength of coupling between layers is important for determining multiscale properties of centrality, such as localization phenomena and the time scale of centrality changes. In the strong-coupling regime, we derive expressions for time-averaged centralities, which are given by the zeroth-order terms of a singular perturbation expansion. We also study first-order terms to obtain first-order-mover scores, which concisely describe the magnitude of nodes' centrality changes over time. As examples, we apply our method to three empirical temporal networks: the United States Ph.D. exchange in mathematics, costarring relationships among top-billed actors during the Golden Age of Hollywood, and citations of decisions from the United States Supreme Court.

physics.soc-ph↗

arXiv2016

The Topological "Shape" of Brexit

Persistent homology is a method from computational algebraic topology that can be used to study the "shape" of data. We illustrate two filtrations --- the weight rank clique filtration and the Vietoris--Rips (VR) filtration --- that are commonly used in persistent homology, and we apply these filtrations to a pair of data sets that are both related to the 2016 European Union "Brexit" referendum in the United Kingdom. These examples consider a topical situation and give useful illustrations of the strengths and weaknesses of these methods.

cs.CG↗

arXiv2016

Scattering of Waves by Impurities in Precompressed Granular Chains

We study scattering of waves by impurities in strongly precompressed granular chains. We explore the linear scattering of plane waves and identify a closed-form expression for the reflection and transmission coefficients for the scattering of the waves from both a single impurity and a double impurity. For single-impurity chains, we show that, within the transmission band of the host granular chain, high-frequency waves are strongly attenuated (such that the transmission coefficient vanishes as the wavenumber $k\rightarrow \pmπ$), whereas low-frequency waves are well-transmitted through the impurity. For double-impurity chains, we identify a resonance --- enabling full transmission at a particular frequency --- in a manner that is analogous to the Ramsauer--Townsend (RT) resonance from quantum physics. We also demonstrate that one can tune the frequency of the RT resonance to any value in the pass band of the host chain. We corroborate our theoretical predictions both numerically and experimentally, and we directly observe complete transmission for frequencies close to the RT resonance frequency. Finally, we show how this RT resonance can lead to the existence of reflectionless modes even in granular chains (including disordered ones) with multiple double impurities.

nlin.PS↗

arXiv2016

A Local Perspective on Community Structure in Multilayer Networks

The analysis of multilayer networks is among the most active areas of network science, and there are now several methods to detect dense "communities" of nodes in multilayer networks. One way to define a community is as a set of nodes that trap a diffusion-like dynamical process (usually a random walk) for a long time. In this view, communities are sets of nodes that create bottlenecks to the spreading of a dynamical process on a network. We analyze the local behavior of different random walks on multiplex networks (which are multilayer networks in which different layers correspond to different types of edges) and show that they have very different bottlenecks that hence correspond to rather different notions of what it means for a set of nodes to be a good community. This has direct implications for the behavior of community-detection methods that are based on these random walks.

cs.SI↗

arXiv2016

Heterogeneity of Global and Local Connectivity in Spatial Network Structures of World Migration

We examine world migration as a social-spatial network of countries connected via movements of people. We assess how multilateral migratory relationships at global, regional, and local scales coexist ("glocalization"), divide ("polarization"), or form an interconnected global system ("globalization"). To do this, we decompose the world migration network (WMN) into communities---sets of countries with denser than expected migration connections---and characterize their pattern of local (i.e., intracommunity) and global (i.e., intercommunity) connectivity. We distinguish community signatures---"cave", "biregional", and "bridging"---with distinct migration patterns, spatial network structures, temporal dynamics, and underlying antecedents. Cave communities are tightly-knit, enduring structures that tend to channel local migration between contiguous countries; biregional communities are likely to merge migration between two distinct geographic regions (e.g., North Africa and Europe); and bridging communities have hub-and-spoke structures that tend to emerge dynamically from globe-spanning movements. We find that world migration is neither globally interconnected nor reproduces the geographic boundaries as drawn on a world map but involves a heterogeneous interplay of global and local tendencies in different network regions. We discuss the implications of our results for the understating of variability in today's transnational mobility patterns and migration opportunities across the globe.

physics.soc-ph↗

arXiv2015

Heterogeneous, Weakly Coupled Map Lattices

Coupled map lattices (CMLs) are often used to study emergent phenomena in nature. It is typically assumed (unrealistically) that each component is described by the same map, and it is important to relax this assumption. In this paper, we characterize periodic orbits and the laminar regime of type-I intermittency in heterogeneous weakly coupled map lattices (HWCMLs). We show that the period of a cycle in an HWCML is preserved for arbitrarily small coupling strengths even when an associated uncoupled oscillator would experience a period-doubling cascade. Our results characterize periodic orbits both near and far from saddle--node bifurcations, and we thereby provide a key step for examining the bifurcation structure of heterogeneous CMLs.

nlin.PS↗

arXiv2015

The Long Memory of Order Flow in the Foreign Exchange Spot Market

We study the long memory of order flow for each of three liquid currency pairs on a large electronic trading platform in the foreign exchange (FX) spot market. Due to the extremely high levels of market activity on the platform, and in contrast to existing empirical studies of other markets, our data enables us to perform statistically stable estimation without needing to aggregate data from different trading days. We find strong evidence of long memory, with a Hurst exponent of approximately 0.7, for each of the three currency pairs and on each trading day in our sample. We repeat our calculations using data that spans different trading days, and we find no significant differences in our results. We test and reject the hypothesis that the apparent long memory of order flow is an artifact caused by structural breaks, in favour of the alternative hypothesis of true long memory. We therefore conclude that the long memory of order flow in the FX spot market is a robust empirical property that persists across daily boundaries.

q-fin.TR↗

arXiv2015

What are essential concepts about networks?

Networks have become increasingly relevant to everyday life as human society has become increasingly connected. Attaining a basic understanding of networks has thus become a necessary form of literacy for people (and for youths in particular). At the NetSci 2014 conference, we initiated a year-long process to develop an educational resource that concisely summarizes essential concepts about networks that can be used by anyone of school age or older. The process involved several brainstorming sessions on one key question: "What should every person living in the 21st century know about networks by the time he/she finishes secondary education?" Different sessions reached diverse participants, which included professional researchers in network science, educators, and high-school students. The generated ideas were connected by the students to construct a concept network. We examined community structure in the concept network to group ideas into a set of important themes, which we refined through discussion into seven essential concepts. The students played a major role in this development process by providing insights and perspectives that were often unrecognized by researchers and educators. The final result, "Network Literacy: Essential Concepts and Core Ideas", is now available as a booklet in several different languages from http://tinyurl.com/networkliteracy .

cs.SI↗

arXiv2015

Superdiffusive Transport and Energy Localization in Disordered Granular Crystals

We study the spreading of initially localized excitations in 1D disordered granular crystals. We thereby investigate localization phenomena in strongly nonlinear systems, which we demonstrate to be fundamentally different from localization in linear and weakly nonlinear systems. We compare wave dynamics in chains with 3 different types of disorder: an uncorrelated (Anderson-like) disorder and 2 types of correlated disorders (random dimer arrangements), and for 2 types of initial conditions: displacement excitations and velocity excitations. For strongly precompressed chains, the dynamics depend strongly on the initial condition. For displacement excitations, the long-time behavior of the second moment $\tilde{m}_2$ has oscillations that depend on the type of disorder, with a complex trend that differs markedly from a power law and which is particularly evident for an Anderson disorder. For velocity excitations, we find a scaling $\tilde{m}_2\sim t^γ$ (for a constant $γ$) for all 3 types of disorder. For weakly precompressed (strongly nonlinear) chains, $\tilde{m}_2$ and the inverse participation ratio $P^{-1}$ satisfy $\tilde{m}_2\sim t^γ$ and $P^{-1}\sim t^{-η}$, and the dynamics is superdiffusive for all examined cases. When precompression is strong, the IPR decreases slowly for all 3 types of disorder, and we observe a partial localization around the core and the leading edge of the wave. For an Anderson disorder, displacement perturbations lead to localization of energy primarily in the core, and velocity perturbations cause the energy to be divided between the core and the leading edge. This localization phenomenon does not occur in the sonic-vacuum regime, which yields the surprising result that the energy is no longer contained in strongly nonlinear waves but instead is spread across many sites. In this regime, the exponents are very similar in all cases.

cond-mat.dis-nn↗

arXiv2015

Numerical Methods for the Computation of the Confluent and Gauss Hypergeometric Functions

The two most commonly used hypergeometric functions are the confluent hypergeometric function and the Gauss hypergeometric function. We review the available techniques for accurate, fast, and reliable computation of these two hypergeometric functions in different parameter and variable regimes. The methods that we investigate include Taylor and asymptotic series computations, Gauss-Jacobi quadrature, numerical solution of differential equations, recurrence relations, and others. We discuss the results of numerical experiments used to determine the best methods, in practice, for each parameter and variable regime considered. We provide 'roadmaps' with our recommendation for which methods should be used in each situation.

math.NA↗

arXiv2015

Structure of Triadic Relations in Multiplex Networks

Recent advances in the study of networked systems have highlighted that our interconnected world is composed of networks that are coupled to each other through different "layers" that each represent one of many possible subsystems or types of interactions. Nevertheless, it is traditional to aggregate multilayer networks into a single weighted network in order to take advantage of existing tools. This is admittedly convenient, but it is also extremely problematic, as important information can be lost as a result. It is therefore important to develop multilayer generalizations of network concepts. In this paper, we analyze triadic relations and generalize the idea of transitivity to multiplex networks. By focusing on triadic relations, which yield the simplest type of transitivity, we generalize the concept and computation of clustering coefficients to multiplex networks. We show how the layered structure of such networks introduces a new degree of freedom that has a fundamental effect on transitivity. We compute multiplex clustering coefficients for several real multiplex networks and illustrate why one must take great care when generalizing standard network concepts to multiplex networks. We also derive analytical expressions for our clustering coefficients for ensemble averages of networks in a family of random multiplex networks. Our analysis illustrates that social networks have a strong tendency to promote redundancy by closing triads at every layer and that they thereby have a different type of multiplex transitivity from transportation networks, which do not exhibit such a tendency. These insights are invisible if one only studies aggregated networks.

physics.soc-ph↗

arXiv2015

Topological data analysis of contagion maps for examining spreading processes on networks

Social and biological contagions are influenced by the spatial embeddedness of networks. Historically, many epidemics spread as a wave across part of the Earth's surface; however, in modern contagions long-range edges -- for example, due to airline transportation or communication media -- allow clusters of a contagion to appear in distant locations. Here we study the spread of contagions on networks through a methodology grounded in topological data analysis and nonlinear dimension reduction. We construct "contagion maps" that use multiple contagions on a network to map the nodes as a point cloud. By analyzing the topology, geometry, and dimensionality of manifold structure in such point clouds, we reveal insights to aid in the modeling, forecast, and control of spreading processes. Our approach highlights contagion maps also as a viable tool for inferring low-dimensional structure in networks.

nlin.AO↗

arXiv2015

Estimating inter-event time distributions from finite observation periods in communication networks

A diverse variety of processes --- including recurrent disease episodes, neuron firing, and communication patterns among humans --- can be described using inter-event time (IET) distributions. Many such processes are ongoing, although event sequences are only available during a finite observation window. Because the observation time window is more likely to begin or end during long IETs than during short ones, the analysis of such data is susceptible to a bias induced by the finite observation period. In this paper, we illustrate how this length bias is born and how it can be corrected without assuming any particular shape for the IET distribution. To do this, we model event sequences using stationary renewal processes, and we formulate simple heuristics for determining the severity of the bias. To illustrate our results, we focus on the example of empirical communication networks, which are temporal networks that are constructed from communication events. The IET distributions of such systems guide efforts to build models of human behavior, and the variance of IETs is very important for estimating the spreading rate of information in networks of temporal interactions. We analyze several well-known data sets from the literature, and we find that the resulting bias can lead to systematic underestimates of the variance in the IET distributions and that correcting for the bias can lead to qualitatively different results for the tails of the IET distributions.

physics.soc-ph↗

arXiv2015

MuxViz: A Tool for Multilayer Analysis and Visualization of Networks

Multilayer relationships among entities and information about entities must be accompanied by the means to analyze, visualize, and obtain insights from such data. We present open-source software (muxViz) that contains a collection of algorithms for the analysis of multilayer networks, which are an important way to represent a large variety of complex systems throughout science and engineering. We demonstrate the ability of muxViz to analyze and interactively visualize multilayer data using empirical genetic, neuronal, and transportation networks. Our software is available at https://github.com/manlius/muxViz.

physics.soc-ph↗

arXiv2015

Information measures and cognitive limits in multilayer navigation

Cities and their transportation systems become increasingly complex and multimodal as they grow, and it is natural to wonder if it is possible to quantitatively characterize our difficulty to navigate in them and whether such navigation exceeds our cognitive limits. A transition between different searching strategies for navigating in metropolitan maps has been observed for large, complex metropolitan networks. This evidence suggests the existence of another limit associated to the cognitive overload and caused by large amounts of information to process. In this light, we analyzed the world's 15 largest metropolitan networks and estimated the information limit for determining a trip in a transportation system to be on the order of 8 bits. Similar to the "Dunbar number," which represents a limit to the size of an individual's friendship circle, our cognitive limit suggests that maps should not consist of more than about $250$ connections points to be easily readable. We also show that including connections with other transportation modes dramatically increases the information needed to navigate in multilayer transportation networks: in large cities such as New York, Paris, and Tokyo, more than $80\%$ of trips are above the 8-bit limit. Multimodal transportation systems in large cities have thus already exceeded human cognitive limits and consequently the traditional view of navigation in cities has to be revised substantially.

physics.soc-ph↗

arXiv2015

Dynamical Systems on Networks: A Tutorial

We give a tutorial for the study of dynamical systems on networks. We focus especially on "simple" situations that are tractable analytically, because they can be very insightful and provide useful springboards for the study of more complicated scenarios. We briefly motivate why examining dynamical systems on networks is interesting and important, and we then give several fascinating examples and discuss some theoretical results. We also briefly discuss dynamical systems on dynamical (i.e., time-dependent) networks, overview software implementations, and give an outlook on the field.

nlin.AO↗

arXiv2015

Extraction of Force-Chain Network Architecture in Granular Materials Using Community Detection

Force chains form heterogeneous physical structures that can constrain the mechanical stability and acoustic transmission of granular media. However, despite their relevance for predicting bulk properties of materials, there is no agreement on a quantitative description of force chains. Consequently, it is difficult to compare the force-chain structures in different materials or experimental conditions. To address this challenge, we treat granular materials as spatially-embedded networks in which the nodes (particles) are connected by weighted edges that represent contact forces. We use techniques from community detection, which is a type of clustering, to find sets of closely connected particles. By using a geographical null model that is constrained by the particles' contact network, we extract chain-like structures that are reminiscent of force chains. We propose three diagnostics to measure these chain-like structures, and we demonstrate the utility of these diagnostics for identifying and characterizing classes of force-chain network architectures in various materials. To illustrate our methods, we describe how force-chain architecture depends on pressure for two very different types of packings: (1) ones derived from laboratory experiments and (2) ones derived from idealized, numerically-generated frictionless packings. By resolving individual force chains, we quantify statistical properties of force-chain shape and strength, which are potentially crucial diagnostics of bulk properties (including material stability). These methods facilitate quantitative comparisons between different particulate systems, regardless of whether they are measured experimentally or numerically.

cond-mat.soft↗