Schelling's Segregation Model: Parameters, scaling, and aggregation

Thomas Schelling proposed a simple spatial model to illustrate how, even with relatively mild assumptions on each individual's nearest neighbor preferences, an integrated city would likely unravel to a segregated city, even if all individuals prefer integration. This agent based lattice model has become quite influential amongst social scientists, demographers, and economists. Aggregation relates to individuals coming together to form groups and Schelling equated global aggregation with segregation. Many authors assumed that the segregation which Schelling observed in simulations on very small cities persists for larger, realistic size cities. We describe how different measures could be used to quantify the segregation and unlock its dependence on city size, disparate neighbor comfortability threshold, and population density. We identify distinct scales of global aggregation, and show that the striking global aggregation Schelling observed is strictly a small city phenomenon. We also discover several scaling laws for the aggregation measures. Along the way we prove that as the Schelling model evolves, the total perimeter of the interface between the different agents decreases, which provides a useful analytical tool to study the evolution.clusters, segregation, simulation, statistics

A Conceptual Framework for Studying the Sources of Variation in Program Effects

Evaluations of public programs in many fields reveal that (1) different types of programs (or different versions of the same program) vary in their effectiveness, (2) a program that is effective for one group of people might not be effective for other groups of people, and (3) a program that is effective in one set of circumstances may not be effective in other circumstances. This paper presents a conceptual framework for research on such variation in program effects and the sources of this variation. The framework is intended to help researchers -- both those who focus mainly on studying program implementation and those who focus mainly on estimating program effects -- see how their respective pieces fit together in a way that helps to identify factors that explain variation in program effects and thereby support more systematic data collection on these factors. The ultimate goal of the framework is to enable researchers to offer better guidance to policymakers and program operators on the conditions and practices that are associated with larger and more positive effects

The SIR model and the Foundations of Public Health

We introduce and analyze a basic transmission model for a directly transmitted infectious disease. The model consists of a system of three coupled non-linear ordinary differential equations which does not possess an explicit formula solution. However, simple tools from calculus allow us to extract a great deal of information about the solutions. Along the way we illustrate how this simple model helps to lay a theoretical foundation for public health interventions and how several cornerstones of public health required such a model to illuminate

Publishing structural genomics results continued: the SSGCID Special Issue

Editoria

Occurrence and core-envelope structure of 1--4x Earth-size planets around Sun-like stars

Small planets, 1-4x the size of Earth, are extremely common around Sun-like stars, and surprisingly so, as they are missing in our solar system. Recent detections have yielded enough information about this class of exoplanets to begin characterizing their occurrence rates, orbits, masses, densities, and internal structures. The Kepler mission finds the smallest planets to be most common, as 26% of Sun-like stars have small, 1-2 R_e planets with orbital periods under 100 days, and 11% have 1-2 R_e planets that receive 1-4x the incident stellar flux that warms our Earth. These Earth-size planets are sprinkled uniformly with orbital distance (logarithmically) out to 0.4 AU, and probably beyond. Mass measurements for 33 transiting planets of 1-4 R_e show that the smallest of them, R < 1.5 R_e, have the density expected for rocky planets. Their densities increase with increasing radius, likely caused by gravitational compression. Including solar system planets yields a relation: rho = 2.32 + 3.19 R/R_e [g/cc]. Larger planets, in the radius range 1.5-4.0 R_e, have densities that decline with increasing radius, revealing increasing amounts of low-density material in an envelope surrounding a rocky core, befitting the appellation "mini-Neptunes." Planets of ~1.5 R_e have the highest densities, averaging near 10 g/cc. The gas giant planets occur preferentially around stars that are rich in heavy elements, while rocky planets occur around stars having a range of heavy element abundances. One explanation is that the fast formation of rocky cores in protoplanetary disks enriched in heavy elements permits the gravitational accumulation of gas before it vanishes, forming giant planets. But models of the formation of 1-4 R_e planets remain uncertain. Defining habitable zones remains difficult, without benefit of either detections of life elsewhere or an understanding of life's biochemical origins.Comment: 11 pages, 6 figures, accepted for publication Proc. Natl. Acad. Sc

Controlling viral outbreaks: Quantitative strategies

Preparing for and responding to outbreaks of serious livestock infectious diseases are critical measures to safeguard animal health, public health, and food supply. Almost all of the current control strategies are empirical, and mass culling or “stamping out” is frequently the principal strategy for controlling epidemics. However, there are ethical, ecological, and economic reasons to consider less drastic control strategies. Here we use modeling to quantitatively study the efficacy of different control measures for viral outbreaks, where the infectiousness, transmissibility and death rate of animals commonly depends on their viral load. We develop a broad theoretical framework for exploring and understanding this heterogeneity. The model includes both direct transmission from infectious animals and indirect transmission from an environmental reservoir. We then incorporate a large variety of control measures, including vaccination, antivirals, isolation, environmental disinfection, and several forms of culling, which may result in fewer culled animals. We provide explicit formulae for the basic reproduction number, R0, for each intervention and for combinations. We evaluate the control methods for a realistic simulated outbreak of low pathogenic avian influenza on a mid-sized turkey farm. In this simulated outbreak, culling results in more total dead birds and dramatically more when culling all of the infected birds

Get the News Out Loudly and Quickly: Modeling the Influence of the Media on Limiting Infectious Disease

During outbreaks of infectious diseases with high morbidity and mortality, individuals closely follow media reports of the outbreak. Many will attempt to minimize contacts with other individuals in order to protect themselves from infection and possibly death. This process is called social distancing. Social distancing strategies include restricting socializing and travel, and using barrier protections. We use modeling to show that for short-term outbreaks, social distancing can have a large influence on reducing outbreak morbidity and mortality. In particular, public health agencies working together with the media can significantly reduce the severity of an outbreak by providing timely accounts of new infections and deaths. Our models show that the most effective strategy to reduce infections is to provide this information as early as possible, though providing it well into the course of the outbreak can still have a significant effect. However, our models for long-term outbreaks indicate that reporting historic infection data can result in more infections than with no reporting at all. We examine three types of media influence and we illustrate the media influence with a simulated outbreak of a generic emerging infectious disease in a small city. Social distancing can never be complete; however, for a spectrum of outbreaks, we show that leaving isolation (stopping applying social distancing measures) for up to 4 hours each day has modest effect on the overall morbidity and mortality

Pulsating waves in nonlinear magnetoconvection

Numerical experiments on compressible magnetoconvection reveal a new type of periodic oscillation, associated with alternating streaming motion. Analogous behaviour in a Boussinesq fluid is constrained by extra symmetry. A low-order model confirms that these pulsating waves appear via a pitchfork-Hopf-gluing bifurcation sequence from the steady state