Received: September 4, 2005, Revised:February 2, 2008 – c © Springer-Verlag 2008 Abstract. Most epidemic models assume equal mixing among members of a population. An alternative approach is to model a population as a random network in which individuals may have heterogeneous connectivity. This paper builds on previous research by describing the exact dynamical behavior of epidemics as they occu...

In this paper, we propose a new network growth model and its learning algorithm to more precisely model such a real-world growing network as the Web. Unlike the conventional models, we have incorporated directional attachment and community structure for this purpose. We show that the proposed model exhibits a degree distribution with a power-law tail, which is an important characteristic of man...

A new dual-Petrov-Galerkin method is proposed, analyzed and implemented for third and higher odd-order equations using a spectral discretization. The key idea is to use trial functions satisfying the underlying boundary conditions of the differential equations and test functions satisfying the “dual” boundary conditions. The method leads to linear systems which are sparse for problems with cons...

We develop the qualitative theory of the solutions of the McKendrick partial differential equation of population dynamics. We calculate explicitly the weak solutions of the McKendrick equation and of the Lotka renewal integral equation with time and age dependent birth rate. Mortality modulus is considered age dependent. We show the existence of demography cycles. For a population with only one...

The general idea of a stochastic gauge representation is introduced and compared with more traditional phase-space expansions, like the Wigner expansion. Stochastic gauges can be used to obtain an infinite class of positive-definite stochastic time-evolution equations, equivalent to master equations, for many systems including quantum time evolution. The method is illustrated with a variety of ...

For the directed edge preferential attachment network growth model studied by Bollobás et al. (2003) and Krapivsky and Redner (2001), we prove that the joint distribution of in-degree and out-degree has jointly regularly varying tails. Typically the marginal tails of the in-degree distribution and the out-degree distribution have different regular variation indices and so the joint regular vari...

The shape and evolution of firm size distribution has been studied in industrial organization and labor economics. The standard hypothesis of Gibrat’s law of proportionate effect posits that the rate of firm growth is size-independent. We test Gibrat’s law using a new empirical methodology and considering the underinvestigated Brazilian case. Quantile regression is used to estimate the evolutio...

The paper assumes a continuum of two period-lived agents; agents are identical except for the inherited income. Young agents optimally allocate their inherited income between consumption and investment in human capital in a stochastic environment. In the second period they receive a wage proportional to the accumulated human capital and invest in o®spring. Two main results are provided: a low e...

The nucleus is the center of direction and coordination of the cell's metabolic and reproductive activities. In recent years it was found that it is formed by many functionally specialized domains. These subnuclear structures are not surrounded by membranes as the cytoplasmic organelles and their function is mostly not well understood. To obtain insights into the structural organisation of the ...

Distribution of materials (such as enzymes) between the alimentary canal and the blood stream is a complex process involving the factors of synthesis, movement into one or more compartments, and destruction.' An initial attempt to quantitate these events is presented. A theory and methodology are developed and illustrated by preliminary data on the distribution of pepsinogen. The general approa...