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During outbreaks of serious infectious diseases many individuals closely follow media reports of the outbreak and take steps, including self-isolation, to protect themselves from infection and possibly death. Self-isolation can take many forms including restricting local and long-distance travel, using face masks, and choosing to receive a vaccine. We use mathematical modeling to show that public health agencies working together with the media can significantly decrease the severity of an outbreak by providing timely and accurate accounts of the numbers of new infections and deaths. Our model also shows that although providing such information beginning as early as possible is best, even starting to provide it well into the course of an outbreak can significantly reduce the severity of the outbreak. We illustrate our results with a simulated outbreak of Ebola Hemorrhagic Fever in the town of Huntington, West Virginia (population about 50, 000)., Comment: This paper has been withdrawn by the authors due to required major revisions

Thomas Schelling developed an influential demographic model that illustrated 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. Individuals in Schelling's model cities are divided into two groups of equal number and each individual is 'happy' or 'unhappy' when the number of similar neighbors cross a simple threshold. In this manuscript we consider natural extensions of Schelling's original model to allow the two groups have different sizes and to allow different notions of happiness of an individual. We observe that differences in aggregation patterns of majority and minority groups are highly sensitive to the happiness threshold; for low threshold, the differences are small, and when the threshold is raised, striking new patterns emerge. We also observe that when individuals strongly prefer to live integrated neighborhoods, the final states exhibit a new tessellated-like structure., Comment: 19 pages, 10 figures

Although the existence of robust inverted biomass pyramids seem paradoxical, they have been observed in planktonic communities, and more recently, in pristine coral reefs. Understanding the underlying mechanisms which produce inverted biomass pyramids provides new ecological insights, and for coral reefs, may help mitigate or restore damaged reefs. We present three classes of predator-prey models which elucidate mechanisms that generate robust inverted biomass pyramids. The first class of models exploits well-mixing of predators and prey, the second class has a refuge (with explicit size) for the prey to hide, and the third class incorporates the immigration of prey. Our models indicate that inverted biomass pyramids occur when the prey growth rate, prey carrying capacity, biomass conversion efficiency, the predator life span, or the immigration rate of prey fish is sufficiently large. In the second class, we discuss three hypotheses on how refuge size can impact the amount of prey available to predators. By explicitly incorporating a refuge size, these can more realistically model predator-prey interactions than refgue models with implicit refuge size., Comment: 24 page, 2 figures

Until recently, the only examples of inverted biomass pyramids have been in freshwater and marine planktonic communities. In 2002 and 2008 investigators documented inverted biomass pyramids for nearly pristine coral reef ecosystems within the NW Hawaiian islands and the Line Islands, where apex predator abundance comprises up to 85% of the fish biomass. We build a new refuge based predator-prey model to study the fish biomass structure at coral reefs and investigate the effect of fishing on biomass pyramids. Utilizing realistic life history parameters of coral reef fish, our model exhibits a stable inverted biomass pyramid. Since the predators and prey are not well mixed, our model does not incorporate homogeneous mixing and the inverted biomass pyramid is a consequence of the refuge. Understanding predator-prey dynamics in nearly pristine conditions provides a more realistic historical framework for comparison with fished reefs. Finally, we show that fishing transforms the inverted biomass pyramid to be bottom heavy., Comment: 24 pages, 4 figures

We prove topological transitivity for the Weil Petersson geodesic flow for two-dimensional moduli spaces of hyperbolic structures. Our proof follows a new approach that exploits the density of singular unit tangent vectors, the geometry of cusps and convexity properties of negative curvature. We also show that the Weil Petersson geodesic flow has: horseshoes, invariant sets with positive topological entropy, and that there are infinitely many hyperbolic closed geodesics, whose number grows exponentially in length. Furthermore, we note that the volume entropy is infinite.

Thomas Schelling proposed an influential 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. Aggregation relates to individuals coming together to form groups and global aggregation corresponds to segregation. Many authors assumed that the segregation which Schelling observed in simulations on very small cities persists for larger, realistic size cities. We devise new measures 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.

The protection of data transmitted over the space-link is an issue of growing importance also for civilian space missions. Through the Consultative Committee for Space Data Systems (CCSDS), space agencies have reacted to this need by specifying the Space Data-Link Layer Security (SDLS) protocol which provides confidentiality and integrity services for the CCSDS Telemetry (TM), Telecommand (TC) and Advanced Orbiting Services (AOS) space data-link protocols. This paper describes the approach of the CCSDS SDLS working group to specify and execute the necessary interoperability tests. It first details the individual SDLS implementations that have been produced by ESA, NASA, and CNES and then the overall architecture that allows the interoperability tests between them. The paper reports on the results of the interoperability tests and identifies relevant aspects for the evolution of the test environment.