arXiv subjects

Gourab Ghoshal

Publications and source records attributed to Gourab Ghoshal.

At least 55 records · Page 3Linked to original sources

arXiv2019

Impact of temporal scales and recurrent mobility patterns on the unfolding of epidemics

Human mobility plays a key role on the transformation of local disease outbreaks into global pandemics. Thus, the inclusion of human movements into epidemic models has become mandatory for understanding current epidemic episodes and to design efficient prevention policies. Following this challenge, here we develop a Markovian framework which enables to address the impact of recurrent mobility patterns on the epidemic onset at different temporal scales. This formalism is validated by comparing their predictions with results from mechanistic simulations. The fair agreement between both theory and simulations enables to get an analytical expression for the epidemic threshold which captures the critical conditions triggering epidemic outbreaks. Finally, by performing an exhaustive analysis of this epidemic threshold, we reveal that the impact of tuning human mobility on the emergence of diseases is strongly affected by the temporal scales associated to both epidemiological and mobility processes.

physics.soc-ph↗

arXiv2019

Uncovering the role of spatial constraints in the differences and similarities between physical and virtual mobility

The recent availability of digital traces from Information and Communications Technologies (ICT) has facilitated the study of both individual- and population-level movement with unprecedented spatiotemporal resolution, enabling us to better understand a plethora of socioeconomic processes such as urbanization, transportation, impact on the environment and epidemic spreading to name a few. Using empirical spatiotemporal trends, several mobility models have been proposed to explain the observed regularities in human movement. With the advent of the World Wide Web, a new type of virtual mobility has emerged that has begun to supplant many traditional facets of human activity. Here we conduct a systematic analysis of physical and virtual movement, uncovering both similarities and differences in their statistical patterns. The differences manifest themselves primarily in the temporal regime, as a signature of the spatial and economic constraints inherent in physical movement, features that are predominantly absent in the virtual space. We demonstrate that once one moves to the time-independent space of events, i.e the sequences of visited locations, these differences vanish, and the statistical patterns of physical and virtual mobility are identical. The observed similarity in navigating these markedly different domains point towards a common mechanism governing the movement patterns, a feature we describe through a Metropolis-Hastings type optimization model, where individuals navigate locations through decision-making processes resembling a cost-benefit analysis of the utility of locations. In contrast to existing phenomenological models of mobility, we show that our model can reproduce the commonalities in the empirically observed statistics with minimal input.

physics.soc-ph↗

arXiv2019

Turing patterns mediated by network topology in homogeneous active systems

Mechanisms of pattern formation---of which the Turing instability is an archetype---constitute an important class of dynamical processes occurring in biological, ecological and chemical systems. Recently, it has been shown that the Turing instability can induce pattern formation in discrete media such as complex networks, opening up the intriguing possibility of exploring it as a generative mechanism in a plethora of socioeconomic contexts. Yet, much remains to be understood in terms of the precise connection between network topology and its role in inducing the patterns. Here, we present a general mathematical description of a two-species reaction-diffusion process occurring on different flavors of network topology. The dynamical equations are of the predator-prey class, that while traditionally used to model species population, has also been used to model competition between antagonistic ideas in social systems. We demonstrate that the Turing instability can be induced in any network topology, by tuning the diffusion of the competing species, or by altering network connectivity. The extent to which the emergent patterns reflect topological properties is determined by a complex interplay between the diffusion coefficients and the localization properties of the eigenvectors of the graph Laplacian. We find that networks with large degree fluctuations tend to have stable patterns over the space of initial perturbations, whereas patterns in more homogenous networks are purely stochastic.

cond-mat.dis-nn↗

arXiv2018

From the betweenness centrality in street networks to structural invariants in random planar graphs

We demonstrate that the distribution of betweenness centrality (BC), a global structural metric based on network flow, is an invariant quantity in most planar graphs. We confirm this invariance through an empirical analysis of street networks from 97 of the most populous cities worldwide, at scales significantly larger than previous studies. We also find that the BC distribution is robust to major alterations in the network, including significant changes to its topology and edge weight structure, indicating that the only relevant factors shaping the distribution are the number of nodes and edges as well as the constraint of planarity. Through simulations of random planar graph models and analytical calculations on Cayley trees, this invariance is demonstrated to be a consequence of a bimodal regime consisting of an underlying tree structure for high BC nodes, and a low BC regime arising from the presence of loops providing local path alternatives. Furthermore, the high BC nodes display a non-trivial spatial dependence, with increasing spatial correlation as a function of the number of edges, leading them to cluster around the barycenter at large densities. Our results suggest that the spatial distribution of the BC is a more accurate discriminator when comparing patterns across cities. Moreover, the BC being a static predictor of congestion in planar graphs, the observed invariance and spatial dependence has practical implications for infrastructural and biological networks. In particular, for the case of street networks, as long as planarity is conserved, bottlenecks continue to persist, and the effect of planned interventions to alleviate structural congestion will be limited primarily to load redistribution, a feature confirmed by analyzing 200 years of data for central Paris.

physics.soc-ph↗

arXiv2018

Buildup of Speaking Skills in an Online Learning Community: A Network-Analytic Exploration

In this study, we explore peer-interaction effects in online networks on speaking skill development. In particular, we present an evidence for gradual buildup of skills in a small-group setting that has not been reported in the literature. We introduce a novel dataset of six online communities consisting of 158 participants focusing on improving their speaking skills. They video-record speeches for 5 prompts in 10 days and exchange comments and performance-ratings with their peers. We ask (i) whether the participants' ratings are affected by their interaction patterns with peers, and (ii) whether there is any gradual buildup of speaking skills in the communities towards homogeneity. To analyze the data, we employ tools from the emerging field of Graph Signal Processing (GSP). GSP enjoys a distinction from Social Network Analysis in that the latter is concerned primarily with the connection structures of graphs, while the former studies signals on top of graphs. We study the performance ratings of the participants as graph signals atop underlying interaction topologies. Total variation analysis of the graph signals show that the participants' rating differences decrease with time (slope=-0.04, p<0.01), while average ratings increase (slope=0.07, p<0.05)--thereby gradually building up the ratings towards community-wide homogeneity. We provide evidence for peer-influence through a prediction formulation. Our consensus-based prediction model outperforms baseline network-agnostic regression models by about 23% in predicting performance ratings. This, in turn, shows that participants' ratings are affected by their peers' ratings and the associated interaction patterns, corroborating previous findings. Then, we formulate a consensus-based diffusion model that captures these observations of peer-influence from our analyses.

cs.SI↗

arXiv2017

Human Mobility: Models and Applications

Recent years have witnessed an explosion of extensive geolocated datasets related to human movement, enabling scientists to quantitatively study individual and collective mobility patterns, and to generate models that can capture and reproduce the spatiotemporal structures and regularities in human trajectories. The study of human mobility is especially important for applications such as estimating migratory flows, traffic forecasting, urban planning, and epidemic modeling. In this survey, we review the approaches developed to reproduce various mobility patterns, with the main focus on recent developments. This review can be used both as an introduction to the fundamental modeling principles of human mobility, and as a collection of technical methods applicable to specific mobility-related problems. The review organizes the subject by differentiating between individual and population mobility and also between short-range and long-range mobility. Throughout the text the description of the theory is intertwined with real-world applications.

physics.soc-ph↗

arXiv2017

Morphology of travel routes and the organization of cities

The city is a complex system that evolves through its inherent social and economic interactions. Mediating the movements of people and resources, urban street networks offer a spatial footprint of these activities; consequently their structural characteristics have been of great interest in the literature. In comparison, relatively limited attention has been devoted to the interplay between street structure and its functional usage, i.e., the movement patterns of people and resources. To address this, we study the shape of 472,040 spatiotemporally optimized travel routes in the 92 most populated cities in the world. The routes are sampled in a geographically unbiased way such that their properties can be mapped on to each city, with their summary statistics capturing mesoscale connectivity patterns representing the complete space of possible movement in cities. The collective morphology of routes exhibits a directional bias that could be described as influenced by the attractive (or repulsive) forces resulting from congestion, accessibility and travel demand that relate to various socioeconomic factors. To capture this feature, we propose a simple metric, inness, that maps this force field. An analysis of the morphological patterns of individual cities reveals structural and socioeconomic commonalities among cities with similar inness patterns, in particular that they cluster into groups that are correlated with their size and putative stage of urban development as measured by a series of socioeconomic and infrastructural indicators. Our results lend weight to the insight that levels of urban socioeconomic development are intrinsically tied to increasing physical connectivity and diversity of road hierarchies.

physics.soc-ph↗

arXiv2017

Semi-Automated & Collaborative Online Training Module For Improving Communication Skills

This paper presents a description and evaluation of the ROC Speak system, a platform that allows ubiquitous access to communication skills training. ROC Speak (available at rocspeak.com) enables anyone to go to a website, record a video, and receive feedback on smile intensity, body movement, volume modulation, filler word usage, unique word usage, word cloud of the spoken words, in addition to overall assessment and subjective comments by peers. Peer comments are automatically ranked and sorted for usefulness and sentiment (i.e., positive vs. negative). We evaluated the system with a diverse group of 56 online participants for a 10-day period. Participants submitted responses to career oriented prompts every other day. The participants were randomly split into two groups: 1) treatment - full feedback from the ROC Speak system; 2) control - written feedback from online peers. When judged by peers (p<.001) and independent raters (p<.05), participants from the treatment group demonstrated statistically significant improvement in overall speaking skills rating while the control group did not. Furthermore, in terms of speaking attributes, treatment group showed an improvement in friendliness (p<.001), vocal variety (p<.05) and articulation (p<.01).

cs.HC↗

arXiv2014

Effects of intrinsic noise on a cubic autocatalytic reaction diffusion system

Starting from our recent chemical master equation derivation of the model of an autocatalytic reaction-diffusion chemical system with reactions $U+2V {\stackrel {λ_0}{\rightarrow}}~ 3 V;$ and $V {\stackrel μ{\rightarrow}}~P$, $U {\stackrel ν{\rightarrow}}~ Q$, we determine the effects of intrinsic noise on the momentum-space behavior of its kinetic parameters and chemical concentrations. We demonstrate that the intrinsic noise induces $n \rightarrow n$ molecular interaction processes with $n \geq 4$, where $n$ is the number of molecules participating of type $U$ or $V$. The momentum dependences of the reaction rates are driven by the fact that the autocatalytic reaction (inelastic scattering) is renormalized through the existence of an arbitrary number of intermediate elastic scatterings, which can also be interpreted as the creation and subsequent decay of a three body composite state $σ= ϕ_u ϕ_v^2$, where $ϕ_i$ corresponds to the fields representing the densities of $U$ and $V$. Finally, we discuss the difference between representing $σ$ as a composite or an elementary particle (molecule) with its own kinetic parameters. In one dimension we find that while they show markedly different behavior in the short spatio-temporal scale, high momentum (UV) limit, they are formally equivalent in the large spatio-temporal scale, low momentum (IR) regime. On the other hand in two dimensions and greater, due to the effects of fluctuations, there is no way to experimentally distinguish between a fundamental and composite $σ$. Thus in this regime $σ$ behave as an entity unto itself suggesting that it can be effectively treated as an independent chemical species.

cond-mat.stat-mech↗

arXiv2013

Composite Bound States and Broken U(1) symmetry in the Chemical Master Equation derivation of the Gray-Scott Model

We give a first principles derivation of the stochastic partial differential equations that describe the chemical reactions of the Gray-Scott model (GS): $U+2V {\stackrel λ{\rightarrow}} 3 V;$ and $V {\stackrel μ{\rightarrow}} P$, $U {\stackrel ν{\rightarrow}} Q$, with a constant feed rate for $U$. We find that the conservation of probability ensured by the chemical master equation leads to a modification of the usual differential equations for the GS model which now involves two composite fields and also intrinsic noise terms. One of the composites is $ψ_1 = ϕ_v^2$, where $ < ϕ_v >_η = v$ is the concentration of the species $V$ and the averaging is over the internal noise $η_{u,v,ψ_1}$. The second composite field is the product of three fields $ χ= λϕ_u ϕ_v^2$ and requires a noise source to ensure probability conservation. A third composite $ψ_2 = ϕ_{u} ϕ_{v}$ can be also be identified from the noise-induced reactions. The Hamiltonian that governs the time evolution of the many-body wave function, associated with the master equation, has a broken U(1) symmetry related to particle number conservation. By expanding around the (broken symmetry) zero energy solution of the Hamiltonian (by performing a Doi shift) one obtains from our path integral formulation the usual reaction diffusion equation, at the classical level. The Langevin equations that are derived from the chemical master equation have multiplicative noise sources for the density fields $ϕ_u, ϕ_v, χ$ that induce higher order processes such as $n \rightarrow n$ scattering for $n > 3$. The amplitude of the noise acting on $ ϕ_v$ is itself stochastic in nature.

cond-mat.stat-mech↗

arXiv2013

Parametric pattern selection in a reaction-diffusion model

We compare spot patterns generated by Turing mechanisms with those generated by replication cascades, in a model one-dimensional reaction-diffusion system. We determine the stability region of spot solutions in parameter space as a function of a natural control parameter (feed-rate) where degenerate patterns with different numbers of spots coexist for a fixed feed-rate. While it is possible to generate identical patterns via both mechanisms, we show that replication cascades lead to a wider choice of pattern profiles that can be selected through a tuning of the feed-rate, exploiting hysteresis and directionality effects of the different pattern pathways.

nlin.PS↗

arXiv2013

Internal composite bound states in deterministic reaction diffusion models

By identifying potential composite states that occur in the Sel'kov-Gray-Scott (GS) model, we show that it can be considered as an effective theory at large spatio-temporal scales, arising from a more \textit{fundamental} theory (which treats these composite states as fundamental chemical species obeying the diffusion equation) relevant at shorter spatio-temporal scales. When simulations in the latter model are performed as a function of a parameter $M = λ^{-1}$, the generated spatial patterns evolve at late times into those of the GS model at large $M$, implying that the composites follow their own unique dynamics at short scales. This separation of scales is an example of \textit{dynamical} decoupling in reaction diffusion systems.

cond-mat.stat-mech↗

arXiv2013

Urban characteristics attributable to density-driven tie formation

Motivated by empirical evidence on the interplay between geography, population density and societal interaction, we propose a generative process for the evolution of social structure in cities. Our analytical and simulation results predict both super-linear scaling of social tie density and information flow as a function of the population. We demonstrate that our model provides a robust and accurate fit for the dependency of city characteristics with city size, ranging from individual-level dyadic interactions (number of acquaintances, volume of communication) to population-level variables (contagious disease rates, patenting activity, economic productivity and crime) without the need to appeal to modularity, specialization, or hierarchy.

physics.soc-ph↗

arXiv2009

Hypergraph topological quantities for tagged social networks

Recent years have witnessed the emergence of a new class of social networks, that require us to move beyond previously employed representations of complex graph structures. A notable example is that of the folksonomy, an online process where users collaboratively employ tags to resources to impart structure to an otherwise undifferentiated database. In a recent paper[1] we proposed a mathematical model that represents these structures as tripartite hypergraphs and defined basic topological quantities of interest. In this paper we extend our model by defining additional quantities such as edge distributions, vertex similarity and correlations as well as clustering. We then empirically measure these quantities on two real life folksonomies, the popular online photo sharing site Flickr and the bookmarking site CiteULike. We find that these systems share similar qualitative features with the majority of complex networks that have been previously studied. We propose that the quantities and methodology described here can be used as a standard tool in measuring the structure of tagged networks.

physics.soc-ph↗

arXiv2009

Random hypergraphs and their applications

In the last few years we have witnessed the emergence, primarily in on-line 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 which 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 on-line photography web site 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.

physics.soc-ph↗

arXiv2008

The diplomat's dilemma: Maximal power for minimal effort in social networks

Closeness is a global measure of centrality in networks, and a proxy for how influential actors are in social networks. In most network models, and many empirical networks, closeness is strongly correlated with degree. However, in social networks there is a cost of maintaining social ties. This leads to a situation (that can occur in the professional social networks of executives, lobbyists, diplomats and so on) where agents have the conflicting objectives of aiming for centrality while simultaneously keeping the degree low. We investigate this situation in an adaptive network-evolution model where agents optimize their positions in the network following individual strategies, and using only local information. The strategies are also optimized, based on the success of the agent and its neighbors. We measure and describe the time evolution of the network and the agents' strategies.

physics.soc-ph↗

arXiv2008

Preservation of network Degree Distributions from non-uniform failures

There has been a considerable amount of interest in recent years on the robustness of networks to failures. Many previous studies have concentrated on the effects of node and edge removals on the connectivity structure of a static network; the networks are considered to be static in the sense that no compensatory measures are allowed for recovery of the original structure. Real world networks such as the world wide web, however, are not static and experience a considerable amount of turnover, where nodes and edges are both added and deleted. Considering degree-based node removals, we examine the possibility of preserving networks from these types of disruptions. We recover the original degree distribution by allowing the network to react to the attack by introducing new nodes and attaching their edges via specially tailored schemes. We focus particularly on the case of non-uniform failures, a subject that has received little attention in the context of evolving networks. Using a combination of analytical techniques and numerical simulations, we demonstrate how to preserve the exact degree distribution of the studied networks from various forms of attack.

cond-mat.stat-mech↗

arXiv2007

Bicomponents and the robustness of networks to failure

A common definition of a robust connection between two nodes in a network such as a communication network is that there should be at least two independent paths connecting them, so that the failure of no single node in the network causes them to become disconnected. This definition leads us naturally to consider bicomponents, subnetworks in which every node has a robust connection of this kind to every other. Here we study bicomponents in both real and model networks using a combination of exact analytic techniques and numerical methods. We show that standard network models predict there to be essentially no small bicomponents in most networks, but there may be a giant bicomponent, whose presence coincides with the presence of the ordinary giant component, and we find that real networks seem by and large to follow this pattern, although there are some interesting exceptions. We study the size of the giant bicomponent as nodes in the network fail, using a specially developed computer algorithm based on data trees, and find in some cases that our networks are quite robust to failure, with large bicomponents persisting until almost all vertices have been removed.

cond-mat.stat-mech↗