We study the dynamical states of a small-world network of recurrently coupled excitable neurons, through both numerical and analytical methods. The dynamics of this system depend mostly on both the number of long-range connections or "shortcuts", and the delay associated with neuronal interactions. We find that persistent activity emerges at low density of shortcuts, and that the system undergo...

This article decomposes total population momentum into two constituent and multiplicative parts: "nonstable" momentum and "stable" momentum. Nonstable momentum depends on deviations between a population's current age distribution and its implied stable age distribution. Stable momentum is a function of deviations between a population's implied stable and stationary age distributions. In general...

where h and g are analytic in D. We call h the analytic part and g the coanalytic part of f . A necessary and sufficient condition for f to be locally univalent and sense preserving in D is that |h z | > |g z | for all z in D see 1 . Let H be the class of functions of the form 1.1 that are harmonic univalent and sense preserving in the unit disk U {z : |z| < 1} for which f 0 fz 0 − 1 0. Then fo...

In this paper we provide the derivation of a super compact pairwise model with only 4 equations in the context of describing susceptible-infected-susceptible (SIS) epidemic dynamics on heterogenous networks. The super compact model is based on a new closure relation that involves not only the average degree but also the second and third moments of the degree distribution. Its derivation uses an...

Data from longitudinal studies may be analyzed both cross-sectionally and longitudinally. Discrepancies between estimates obtained from these analyses pose questions about the validity of cross-sectional estimates of change. In some cases these discrepancies are the result of period effects, cohort effects, or selective dropout. In others, they are the result of incomplete modeling of the proce...

This paper uses a two-sided market model to study if lastmile access providers (ISPs), should charge content providers (CPs), who derive revenue from advertisers, for the right to access ISP’s end-users. We compare two-sided pricing (ISPs could charge CPs for content delivery) with one-sided pricing (neutrality regulations prohibit such charges). Our analysis indicates that number of CPs is low...

We find a formula that relates the Fourier transform of a radial function on R with the Fourier transform of the same function defined on R. This formula enables one to explicitly calculate the Fourier transform of any radial function f(r) in any dimension, provided one knows the Fourier transform of the one-dimensional function t 7→ f(|t|) and the two-dimensional function (x1, x2) 7→ f(|(x1, x...