Modeling Epidemic Spread in Synthetic Populations - Virtual Plagues in Massively Multiplayer Online Games

A virtual plague is a process in which a behavior-affecting property spreads among characters in a Massively Multiplayer Online Game (MMOG). The MMOG individuals constitute a synthetic population, and the game can be seen as a form of interactive executable model for studying disease spread, albeit of a very special kind. To a game developer maintaining an MMOG, recognizing, monitoring, and ultimately controlling a virtual plague is important, regardless of how it was initiated. The prospect of using tools, methods and theory from the field of epidemiology to do this seems natural and appealing. We will address the feasibility of such a prospect, first by considering some basic measures used in epidemiology, then by pointing out the differences between real world epidemics and virtual plagues. We also suggest directions for MMOG developer control through epidemiological modeling. Our aim is understanding the properties of virtual plagues, rather than trying to eliminate them or mitigate their effects, as would be in the case of real infectious disease.Comment: Accepted for presentation at Digital Games Research Association (DiGRA) conference in Tokyo in September 2007. All comments to the authors (mail addresses are in the paper) are welcom

Relative geometric assembly and mapping cones, Part I: The geometric model and applications

Inspired by an analytic construction of Chang, Weinberger and Yu, we define an assembly map in relative geometric $K$-homology. The properties of the geometric assembly map are studied using a variety of index theoretic tools (e.g., the localized index and higher Atiyah-Patodi-Singer index theory). As an application we obtain a vanishing result in the context of manifolds with boundary and positive scalar curvature; this result is also inspired and connected to work of Chang, Weinberger and Yu. Furthermore, we use results of Wahl to show that rational injectivity of the relative assembly map implies homotopy invariance of the relative higher signatures of a manifold with boundary.Comment: 37 pages. Accepted in Journal of Topolog

The Discrete Nonlinear Schr\"odinger equation - 20 Years on

We review work on the Discrete Nonlinear Schr\"odinger (DNLS) equation over the last two decades.Comment: 24 pages, 1 figure, Proceedings of the conference on "Localization and Energy Transfer in Nonlinear Systems", June 17-21, 2002, San Lorenzo de El Escorial, Madrid, Spain; to be published by World Scientifi

Relative geometric assembly and mapping cones, Part II: Chern characters and the Novikov property

We study Chern characters and the assembly mapping for free actions using the framework of geometric $K$-homology. The focus is on the relative groups associated with a group homomorphism $\phi:\Gamma_1\to \Gamma_2$ along with applications to Novikov type properties. In particular, we prove a relative strong Novikov property for homomorphisms of hyperbolic groups and a relative strong $\ell^1$-Novikov property for polynomially bounded homomorphisms of groups with polynomially bounded cohomology in \C. As a corollary, relative higher signatures on a manifold with boundary $W$, with $\pi_1(\partial W)\to \pi_1(W)$ belonging to the class above, are homotopy invariant.Comment: 32 pages, accepted in M\"unster Journal of Mathematic

The first use of Fulton's K for assessing and comparing the conditions of inter-tidal fish populations

Fulton's K condition factor was applied, for the first time, to inter-tidal specimens of the shanny (Lipophrys pholis) and long-spined scorpion fish (Taurulus bubalis) from two English rocky shore and two Welsh rocky shore sites during summer 2010 and winter 2011. As both species contribute to the diet of commercial species such as cod (Gadus morhua) and near-threatened species such as the European otter (Lutra lutra), their condition may affect that of these predators. Fulton's K found that inter-tidal Welsh fish maintained a ‘good’ condition between seasons, whereas the inter-tidal English fish were in a poorer condition during winter. Although condition also changed amongst the sites on each coast, further studies are needed into fish morphologies, environmental parameters, prey availabilities and abundances, and fish specimen sex and maturities

Synaptic shot noise and conductance fluctuations affect the membrane voltage with equal significance

The subthresholdmembranevoltage of a neuron in active cortical tissue is a fluctuating quantity with a distribution that reflects the firing statistics of the presynaptic population. It was recently found that conductancebased synaptic drive can lead to distributions with a significant skew. Here it is demonstrated that the underlying shot noise caused by Poissonian spike arrival also skews the membrane distribution, but in the opposite sense. Using a perturbative method, we analyze the effects of shot noise on the distribution of synaptic conductances and calculate the consequent voltage distribution. To first order in the perturbation theory, the voltage distribution is a gaussian modulated by a prefactor that captures the skew. The gaussian component is identical to distributions derived using current-based models with an effective membrane time constant. The well-known effective-time-constant approximation can therefore be identified as the leading-order solution to the full conductance-based model. The higher-order modulatory prefactor containing the skew comprises terms due to both shot noise and conductance fluctuations. The diffusion approximation misses these shot-noise effects implying that analytical approaches such as the Fokker-Planck equation or simulation with filtered white noise cannot be used to improve on the gaussian approximation. It is further demonstrated that quantities used for fitting theory to experiment, such as the voltage mean and variance, are robust against these non-Gaussian effects. The effective-time-constant approximation is therefore relevant to experiment and provides a simple analytic base on which other pertinent biological details may be added

Numerical Calculation of Bessel Functions

A new computational procedure is offered to provide simple, accurate and flexible methods for using modern computers to give numerical evaluations of the various Bessel functions. The Trapezoidal Rule, applied to suitable integral representations, may become the method of choice for evaluation of the many Special Functions of mathematical physics.Comment: 10 page