### Session A4: Human Mobility: The Statistical Physics of When, Where, and How

 Monday, March 15, 2010 8:00AM - 8:36AM A4.00001: Communities, boundaries and symmetries - Hidden structures in multi-scale human mobilty networks Invited Speaker: Dirk Brockmann Geographical boundaries are key determinants of various spatially extended dynamical phenomena. Examples are migration dynamics of species, the spread of infectious diseases, bioinvasive processes, and the spatial evolution of language. I will give an overview of a set of research projects that address the organizational units encoded in multi-scale human mobility networks. I will show how these networks can be employed to introduce, define and quantify large scale communities and their boundaries that only partially coincide with administrative and political ones. I will show how common modularity measures can be used to identify these structures and will discuss an alternative approach based on a new notion of distance in human mobility. I will conclude with a discussion of the discovery of novel symmetries in multi-scale mobility networks an point out a new coordinate system for representing complex mobility networks. Monday, March 15, 2010 8:36AM - 9:12AM A4.00002: Multiscale mobility networks and the large scale spreading of infectious diseases Invited Speaker: Alessandro Vespignani Among the realistic ingredients to be considered in the computational modeling of infectious diseases, human mobility represents a crucial challenge both on the theoretical side and in view of the limited availability of empirical data. In order to study the interplay between small-scale commuting flows and long-range airline traffic in shaping the spatio-temporal pattern of a global epidemic we {\em i)} analyze mobility data from $29$ countries around the world and find a gravity model able to provide a global description of commuting patterns up to $300$ kms; {\em ii)} integrate in a worldwide structured metapopulation epidemic model a time-scale separation technique for evaluating the force of infection due to multiscale mobility processes in the disease dynamics. Commuting flows are found, on average, to be one order of magnitude larger than airline flows. However, their introduction into the worldwide model shows that the large scale pattern of the simulated epidemic exhibits only small variations with respect to the baseline case where only airline traffic is considered. The presence of short range mobility increases however the synchronization of subpopulations in close proximity and affects the epidemic behavior at the periphery of the airline transportation infrastructure. The present approach outlines the possibility for the definition of layered computational approaches where different modeling assumptions and granularities can be used consistently in a unifying multi-scale framework. Monday, March 15, 2010 9:12AM - 9:48AM A4.00003: Modelling large scale human activity in San Francisco Invited Speaker: Marta Gonzalez Diverse group of people with a wide variety of schedules, activities and travel needs compose our cities nowadays. This represents a big challenge for modeling travel behaviors in urban environments; those models are of crucial interest for a wide variety of applications such as traffic forecasting, spreading of viruses, or measuring human exposure to air pollutants. The traditional means to obtain knowledge about travel behavior is limited to surveys on travel journeys. The obtained information is based in questionnaires that are usually costly to implement and with intrinsic limitations to cover large number of individuals and some problems of reliability. Using mobile phone data, we explore the basic characteristics of a model of human travel: The distribution of agents is proportional to the population density of a given region, and each agent has a characteristic trajectory size contain information on frequency of visits to different locations. Additionally we use a complementary data set given by smart subway fare cards offering us information about the exact time of each passenger getting in or getting out of the subway station and the coordinates of it. This allows us to uncover the temporal aspects of the mobility. Since we have the actual time and place of individual's origin and destination we can understand the temporal patterns in each visited location with further details. Integrating two described data set we provide a dynamical model of human travels that incorporates different aspects observed empirically. Monday, March 15, 2010 9:48AM - 10:24AM A4.00004: Big Data, Global Development, and Complex Social Systems Invited Speaker: Nathan Eagle Petabytes of data about human movements, transactions, and communication patterns are continuously being generated by everyday technologies such as mobile phones and credit cards. This unprecedented volume of information facilitates a novel set of research questions applicable to a wide range of development issues. In collaboration with the mobile phone, internet, and credit card industries, my colleagues and I are aggregating and analyzing behavioral data from over 250 million people from North and South America, Europe, Asia and Africa. I will discuss a selection of projects arising from these collaborations that involve inferring behavioral dynamics on a broad spectrum of scales; from risky behavior in a group of MIT freshman to population-level behavioral signatures, including cholera outbreaks in Rwanda and wealth in the UK. Access to the movement patterns of the majority of mobile phones in East Africa also facilitates realistic models of disease transmission as well as slum formations. This vast volume of data requires new analytical tools - we are developing a range of large-scale network analysis and machine learning algorithms that we hope will provide deeper insight into human behavior. However, ultimately our goal is to determine how we can use these insights to actively improve the lives of the billions of people who generate this data and the societies in which they live. Monday, March 15, 2010 10:24AM - 11:00AM A4.00005: Beller Lectureship Talk: Levy Flights and Walks in Nature Invited Speaker: Joseph Klafter Levy flights are Markovian random processes whose underlying jump length distribution exhibits the long-tailed form. Their probability density in a homogeneous environment is defined through the characteristic function, an immediate consequence being the divergence of the variance. As such, Levy flights are a natural generalization of Gaussian diffusion processes ensuing from the generalized central limit theorem. Despite this seemingly simple definition and their widespread field of applications, Levy processes are far from being completely understood. Here, we review recent work on Levy flights concerning the particular behavior of processes with diverging jump length distributions in regard to some of the fundamental properties of stochastic processes. In particular, we explore the behavior of Levy flights in external potentials, finding distinct multimodality of the probability density function and finite variance in steeper than harmonic potentials. We proceed to show that Levy flights display a universality in the first passage behavior, contradicting the naive result obtained from the method of images; moreover, for Levy flights, the first arrival turns out to differ from the problem of first passage. Next, we address the barrier crossing of Levy flights and show that the exponential survival behavior known from classical Kramers theory is preserved, while the activation behavior of the associated rate becomes non-Arrhenius. Finally, we explore the long-standing complication that Levy flights are `pathological' in the sense that their variance diverges, while the mass of the diffusing particle is non-zero and should therefore have a finite maximum velocity: We show that dissipative nonlinear friction in the dynamics causes a truncation of the Levy stable density of the velocity distribution. This leads to a new understanding of the physical nature of Levy flight processes as an approximation to a multitude of anomalous random processes.