arXiv subjects

Peter Sheridan Dodds

Publications and source records attributed to Peter Sheridan Dodds.

At least 109 records · Page 6Linked to original sources

arXiv2015

Direct, physically motivated derivation of triggering probabilities for spreading processes on generalized random networks

We derive a general expression for the probability of global spreading starting from a single infected seed for contagion processes acting on generalized, correlated random networks. We employ a simple probabilistic argument that encodes the spreading mechanism in an intuitive, physical fashion. We use our approach to directly and systematically obtain triggering probabilities for contagion processes acting on a collection of random network families including bipartite random networks. We find the contagion condition, the location of the phase transition into an endemic state, from an expansion about the disease-free state.

cond-mat.dis-nn↗

arXiv2015

Constructing a taxonomy of fine-grained human movement and activity motifs through social media

Profiting from the emergence of web-scale social data sets, numerous recent studies have systematically explored human mobility patterns over large populations and large time scales. Relatively little attention, however, has been paid to mobility and activity over smaller time-scales, such as a day. Here, we use Twitter to identify people's frequently visited locations along with their likely activities as a function of time of day and day of week, capitalizing on both the content and geolocation of messages. We subsequently characterize people's transition pattern motifs and demonstrate that spatial information is encoded in word choice.

physics.soc-ph↗

arXiv2015

Zipf's law holds for phrases, not words

With Zipf's law being originally and most famously observed for word frequency, it is surprisingly limited in its applicability to human language, holding over no more than three to four orders of magnitude before hitting a clear break in scaling. Here, building on the simple observation that phrases of one or more words comprise the most coherent units of meaning in language, we show empirically that Zipf's law for phrases extends over as many as nine orders of rank magnitude. In doing so, we develop a principled and scalable statistical mechanical method of random text partitioning, which opens up a rich frontier of rigorous text analysis via a rank ordering of mixed length phrases.

cs.CL↗

arXiv2015

Text mixing shapes the anatomy of rank-frequency distributions: A modern Zipfian mechanics for natural language

Natural languages are full of rules and exceptions. One of the most famous quantitative rules is Zipf's law which states that the frequency of occurrence of a word is approximately inversely proportional to its rank. Though this `law' of ranks has been found to hold across disparate texts and forms of data, analyses of increasingly large corpora over the last 15 years have revealed the existence of two scaling regimes. These regimes have thus far been explained by a hypothesis suggesting a separability of languages into core and non-core lexica. Here, we present and defend an alternative hypothesis, that the two scaling regimes result from the act of aggregating texts. We observe that text mixing leads to an effective decay of word introduction, which we show provides accurate predictions of the location and severity of breaks in scaling. Upon examining large corpora from 10 languages in the Project Gutenberg eBooks collection (eBooks), we find emphatic empirical support for the universality of our claim.

cs.CL↗

arXiv2014

An Evolutionary Algorithm Approach to Link Prediction in Dynamic Social Networks

Many real world, complex phenomena have underlying structures of evolving networks where nodes and links are added and removed over time. A central scientific challenge is the description and explanation of network dynamics, with a key test being the prediction of short and long term changes. For the problem of short-term link prediction, existing methods attempt to determine neighborhood metrics that correlate with the appearance of a link in the next observation period. Recent work has suggested that the incorporation of topological features and node attributes can improve link prediction. We provide an approach to predicting future links by applying the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) to optimize weights which are used in a linear combination of sixteen neighborhood and node similarity indices. We examine a large dynamic social network with over $10^6$ nodes (Twitter reciprocal reply networks), both as a test of our general method and as a problem of scientific interest in itself. Our method exhibits fast convergence and high levels of precision for the top twenty predicted links. Based on our findings, we suggest possible factors which may be driving the evolution of Twitter reciprocal reply networks.

physics.soc-ph↗

arXiv2014

Estimation of global network statistics from incomplete data

Complex networks underlie an enormous variety of social, biological, physical, and virtual systems. A profound complication for the science of complex networks is that in most cases, observing all nodes and all network interactions is impossible. Previous work addressing the impacts of partial network data is surprisingly limited, focuses primarily on missing nodes, and suggests that network statistics derived from subsampled data are not suitable estimators for the same network statistics describing the overall network topology. We generate scaling methods to predict true network statistics, including the degree distribution, from only partial knowledge of nodes, links, or weights. Our methods are transparent and do not assume a known generating process for the network, thus enabling prediction of network statistics for a wide variety of applications. We validate analytical results on four simulated network classes and empirical data sets of various sizes. We perform subsampling experiments by varying proportions of sampled data and demonstrate that our scaling methods can provide very good estimates of true network statistics while acknowledging limits. Lastly, we apply our techniques to a set of rich and evolving large-scale social networks, Twitter reply networks. Based on 100 million tweets, we use our scaling techniques to propose a statistical characterization of the Twitter Interactome from September 2008 to November 2008. Our treatment allows us to find support for Dunbar's hypothesis in detecting an upper threshold for the number of active social contacts that individuals maintain over the course of one week.

physics.soc-ph↗

arXiv2014

Standing Swells Surveyed Showing Surprisingly Stable Solutions for the Lorenz '96 Model

The Lorenz '96 model is an adjustable dimension system of ODEs exhibiting chaotic behavior representative of dynamics observed in the Earth's atmosphere. In the present study, we characterize statistical properties of the chaotic dynamics while varying the degrees of freedom and the forcing. Tuning the dimensionality of the system, we find regions of parameter space with surprising stability in the form of standing waves traveling amongst the slow oscillators. The boundaries of these stable regions fluctuate regularly with the number of slow oscillators. These results demonstrate hidden order in the Lorenz '96 system, strengthening the evidence for its role as a hallmark representative of nonlinear dynamical behavior.

nlin.CD↗

arXiv2014

Dynamical influence processes on networks: General theory and applications to social contagion

We study binary state dynamics on a network where each node acts in response to the average state of its neighborhood. Allowing varying amounts of stochasticity in both the network and node responses, we find different outcomes in random and deterministic versions of the model. In the limit of a large, dense network, however, we show that these dynamics coincide. We construct a general mean field theory for random networks and show this predicts that the dynamics on the network are a smoothed version of the average response function dynamics. Thus, the behavior of the system can range from steady state to chaotic depending on the response functions, network connectivity, and update synchronicity. As a specific example, we model the competing tendencies of imitation and non-conformity by incorporating an off-threshold into standard threshold models of social contagion. In this way we attempt to capture important aspects of fashions and societal trends. We compare our theory to extensive simulations of this "limited imitation contagion" model on Poisson random graphs, finding agreement between the mean-field theory and stochastic simulations.

physics.soc-ph↗

arXiv2014

Human language reveals a universal positivity bias

Using human evaluation of 100,000 words spread across 24 corpora in 10 languages diverse in origin and culture, we present evidence of a deep imprint of human sociality in language, observing that (1) the words of natural human language possess a universal positivity bias; (2) the estimated emotional content of words is consistent between languages under translation; and (3) this positivity bias is strongly independent of frequency of word usage. Alongside these general regularities, we describe inter-language variations in the emotional spectrum of languages which allow us to rank corpora. We also show how our word evaluations can be used to construct physical-like instruments for both real-time and offline measurement of the emotional content of large-scale texts.

physics.soc-ph↗

arXiv2014

Collective Philanthropy: Describing and Modeling the Ecology of Giving

Reflective of income and wealth distributions, philanthropic gifting appears to follow an approximate power-law size distribution as measured by the size of gifts received by individual institutions. We explore the ecology of gifting by analysing data sets of individual gifts for a diverse group of institutions dedicated to education, medicine, art, public support, and religion. We find that the detailed forms of gift-size distributions differ across but are relatively constant within charity categories. We construct a model for how a donor's income affects their giving preferences in different charity categories, offering a mechanistic explanation for variations in institutional gift-size distributions. We discuss how knowledge of gift-sized distributions may be used to assess an institution's gift-giving profile, to help set fundraising goals, and to design an institution-specific giving pyramid.

physics.soc-ph↗

arXiv2013

The Geography of Happiness: Connecting Twitter sentiment and expression, demographics, and objective characteristics of place

We conduct a detailed investigation of correlations between real-time expressions of individuals made across the United States and a wide range of emotional, geographic, demographic, and health characteristics. We do so by combining (1) a massive, geo-tagged data set comprising over 80 million words generated over the course of several recent years on the social network service Twitter and (2) annually-surveyed characteristics of all 50 states and close to 400 urban populations. Among many results, we generate taxonomies of states and cities based on their similarities in word use; estimate the happiness levels of states and cities; correlate highly-resolved demographic characteristics with happiness levels; and connect word choice and message length with urban characteristics such as education levels and obesity rates. Our results show how social media may potentially be used to estimate real-time levels and changes in population-level measures such as obesity rates.

physics.soc-ph↗

arXiv2013

Limited Imitation Contagion on Random Networks: Chaos, Universality, and Unpredictability

We study a family of binary state, socially-inspired contagion models which incorporate imitation limited by an aversion to complete conformity. We uncover rich behavior in our models whether operating with either probabilistic or deterministic individual response functions on both dynamic and fixed random networks. In particular, we find significant variation in the limiting behavior of a population's infected fraction, ranging from steady-state to chaotic. We show that period doubling arises as we increase the average node degree, and that the universality class of this well known route to chaos depends on the interaction structure of random networks rather than the microscopic behavior of individual nodes. We find that increasing the fixedness of the system tends to stabilize the infected fraction, yet disjoint, multiple equilibria are possible depending solely on the choice of the initially infected node.

nlin.CD↗

arXiv2012

Twitter reciprocal reply networks exhibit assortativity with respect to happiness

The advent of social media has provided an extraordinary, if imperfect, 'big data' window into the form and evolution of social networks. Based on nearly 40 million message pairs posted to Twitter between September 2008 and February 2009, we construct and examine the revealed social network structure and dynamics over the time scales of days, weeks, and months. At the level of user behavior, we employ our recently developed hedonometric analysis methods to investigate patterns of sentiment expression. We find users' average happiness scores to be positively and significantly correlated with those of users one, two, and three links away. We strengthen our analysis by proposing and using a null model to test the effect of network topology on the assortativity of happiness. We also find evidence that more well connected users write happier status updates, with a transition occurring around Dunbar's number. More generally, our work provides evidence of a social sub-network structure within Twitter and raises several methodological points of interest with regard to social network reconstructions.

cs.SI↗

arXiv2012

Positivity of the English language

Over the last million years, human language has emerged and evolved as a fundamental instrument of social communication and semiotic representation. People use language in part to convey emotional information, leading to the central and contingent questions: (1) What is the emotional spectrum of natural language? and (2) Are natural languages neutrally, positively, or negatively biased? Here, we report that the human-perceived positivity of over 10,000 of the most frequently used English words exhibits a clear positive bias. More deeply, we characterize and quantify distributions of word positivity for four large and distinct corpora, demonstrating that their form is broadly invariant with respect to frequency of word use.

physics.soc-ph↗

arXiv2011

Temporal patterns of happiness and information in a global social network: Hedonometrics and Twitter

Individual happiness is a fundamental societal metric. Normally measured through self-report, happiness has often been indirectly characterized and overshadowed by more readily quantifiable economic indicators such as gross domestic product. Here, we examine expressions made on the online, global microblog and social networking service Twitter, uncovering and explaining temporal variations in happiness and information levels over timescales ranging from hours to years. Our data set comprises over 46 billion words contained in nearly 4.6 billion expressions posted over a 33 month span by over 63 million unique users. In measuring happiness, we use a real-time, remote-sensing, non-invasive, text-based approach---a kind of hedonometer. In building our metric, made available with this paper, we conducted a survey to obtain happiness evaluations of over 10,000 individual words, representing a tenfold size improvement over similar existing word sets. Rather than being ad hoc, our word list is chosen solely by frequency of usage and we show how a highly robust metric can be constructed and defended.

physics.soc-ph↗

arXiv2011

Exact solutions for social and biological contagion models on mixed directed and undirected, degree-correlated random networks

We derive analytic expressions for the possibility, probability, and expected size of global spreading events starting from a single infected seed for a broad collection of contagion processes acting on random networks with both directed and undirected edges and arbitrary degree-degree correlations. Our work extends previous theoretical developments for the undirected case, and we provide numerical support for our findings by investigating an example class of networks for which we are able to obtain closed-form expressions.

physics.soc-ph↗

arXiv2011

Direct, physically-motivated derivation of the contagion condition for spreading processes on generalized random networks

For a broad range single-seed contagion processes acting on generalized random networks, we derive a unifying analytic expression for the possibility of global spreading events in a straightforward, physically intuitive fashion. Our reasoning lays bare a direct mechanical understanding of an archetypal spreading phenomena that is not evident in circuitous extant mathematical approaches.

cond-mat.dis-nn↗

arXiv2009

On the optimal form of branching supply and collection networks

For the problem of efficiently supplying material to a spatial region from a single source, we present a simple scaling argument based on branching network volume minimization that identifies limits to the scaling of sink density. We discuss implications for two fundamental and unresolved problems in organismal biology and geomorphology: how basal metabolism scales with body size for homeotherms and the scaling of drainage basin shape on eroding landscapes.

nlin.PS↗