Recruitment dynamics in adaptive social networks

We model recruitment in adaptive social networks in the presence of birth and death processes. Recruitment is characterized by nodes changing their status to that of the recruiting class as a result of contact with recruiting nodes. Only a susceptible subset of nodes can be recruited. The recruiting individuals may adapt their connections in order to improve recruitment capabilities, thus changing the network structure adaptively. We derive a mean field theory to predict the dependence of the growth threshold of the recruiting class on the adaptation parameter. Furthermore, we investigate the effect of adaptation on the recruitment level, as well as on network topology. The theoretical predictions are compared with direct simulations of the full system. We identify two parameter regimes with qualitatively different bifurcation diagrams depending on whether nodes become susceptible frequently (multiple times in their lifetime) or rarely (much less than once per lifetime)

Twin Families of Bisolitons in Dispersion Managed Systems

We calculate bisoliton solutions using a slowly varying stroboscopic equation. The system is characterized in terms of a single dimensionless parameter. We find two branches of solutions and describe the structure of the tails for the lower branch solutions.Comment: 3 pages 4 figure

Epidemics in Adaptive Social Networks with Temporary Link Deactivation

Disease spread in a society depends on the topology of the network of social contacts. Moreover, individuals may respond to the epidemic by adapting their contacts to reduce the risk of infection, thus changing the network structure and affecting future disease spread. We propose an adaptation mechanism where healthy individuals may choose to temporarily deactivate their contacts with sick individuals, allowing reactivation once both individuals are healthy. We develop a mean-field description of this system and find two distinct regimes: slow network dynamics, where the adaptation mechanism simply reduces the effective number of contacts per individual, and fast network dynamics, where more efficient adaptation reduces the spread of disease by targeting dangerous connections. Analysis of the bifurcation structure is supported by numerical simulations of disease spread on an adaptive network. The system displays a single parameter-dependent stable steady state and non-monotonic dependence of connectivity on link deactivation rate

Effects of Nonlinearity and Disorder in Communication Systems

In this dissertation we present theoretical and experimental investigation of the performance quality of fiber optical communication systems, and find new and inexpansive ways of increasing the rate of theinformation transmission.The first part of this work discuss the two major factors limiting the quality of information channels in the fiber optical communication systems. Using methods of large deviation theory from statisticalphysics, we carry out analytical and numerical study of error statistics in optical communication systems in the presence of the temporal noise from optical amplifiers and the structural disorder of optical fibers. In the slowly varying envelope approximation light propagation through optical fiber is described by Schr\{o}dinger's equation. Signal transmission is impeded by the additive (amplifiers) and multiplicative (birefringence) noise This results in signal distortion that may lead to erroneous interpretation of the signal. System performance is characterized by the probability of error occurrence. Fluctuation of spacial disorder due to changing external factors (temperature, vibrations, etc) leads to fluctuations of error rates. Commonly the distribution of error rates is assumed to be Gaussian. Using the optimal fluctuation method we show that this distribution is in fact lognormal. Sucha distribution has ""fat"" tails implying that the likelihood of system outages is much higher than itwould be in the Gaussian approximation. We present experimental results that provide excellent confirmation of our theoretical predictions.In the second part of this dissertation we present some published work on bisolitons in the dispersion managed systems. Modern communication systems use light pulses to transmit tremendous amounts of information. These systems can be modeled using variations of the Nonlinear Shrodinger Equation where chromatic dispersion and nonlinear effects in the glass fiber are taken into account. The best system performance to date is achieved using dispersion management. We will see how the dispersion management works and how it can be modeled. As you pack information more tightly the interaction between the pulsesbecomes increasingly important. In Fall 2005, experiments in Germany showed that bound pairs of pulses (bisolitons) could propagate significant distances. Through numerical investigation we found parametric bifurcation of bisolitonic solutions, and developed a new iterative method with polynomial correction for the calculation of these solutions. Using these solutions in the signal transmission could increase the transmission rates