Robust transmission stabilization and dynamic switching in broadband hybrid waveguide systems with nonlinear gain and loss

We develop a method for transmission stabilization and robust dynamic switching for colliding optical soliton sequences in broadband waveguide systems with nonlinear gain and loss. The method is based on employing hybrid waveguides, consisting of spans with linear gain and cubic loss, and spans with linear loss, cubic gain, and quintic loss. We show that amplitude dynamics is described by a hybrid Lotka-Volterra (LV) model, and use the model to determine the physical parameter values required for enhanced transmission stabilization and switching. Numerical simulations with the coupled nonlinear Schr\"odinger equations confirm the predictions of the LV model, and show stable transmission over distances larger by an order of magnitude compared with uniform waveguides with linear gain and cubic loss. Moreover, multiple on-off and off-on dynamic switching events are demonstrated over a wide range of soliton amplitudes, showing the superiority of hybrid waveguides compared with static switching in uniform waveguides, considered in earlier studies.Comment: 19 pages, 3 figure

Monte Carlo simulations of pulse propagation in massive multichannel optical fiber communication systems

We study the combined effect of delayed Raman response and bit pattern randomness on pulse propagation in massive multichannel optical fiber communication systems. The propagation is described by a perturbed stochastic nonlinear Schr\"odinger equation, which takes into account changes in pulse amplitude and frequency as well as emission of continuous radiation. We perform extensive numerical simulations with the model, and analyze the dynamics of the frequency moments, the bit-error-rate, and the mutual distribution of amplitude and position. The results of our numerical simulations are in good agreement with theoretical predictions based on the adiabatic perturbation approach.Comment: Submitted to Physical Review E. 8 pages, 5 figure

Mean First Passage Time in Periodic Attractors

The properties of the mean first passage time in a system characterized by multiple periodic attractors are studied. Using a transformation from a high dimensional space to 1D, the problem is reduced to a stochastic process along the path from the fixed point attractor to a saddle point located between two neighboring attractors. It is found that the time to switch between attractors depends on the effective size of the attractors, $\tau$, the noise, $\epsilon$, and the potential difference between the attractor and an adjacent saddle point as: $~T = {c \over \tau} \exp({\tau \over \epsilon} \Delta {\cal{U}})~$; the ratio between the sizes of the two attractors affects $\Delta {\cal{U}}$. The result is obtained analytically for small $\tau$ and confirmed by numerical simulations. Possible implications that may arise from the model and results are discussed.Comment: 14 pages, 3 figures, submitted to journal of physics

Mechanics and dynamics of X-chromosome pairing at X inactivation

At the onset of X-chromosome inactivation, the vital process whereby female mammalian cells equalize X products with respect to males, the X chromosomes are colocalized along their Xic (X-inactivation center) regions. The mechanism inducing recognition and pairing of the X’s remains, though, elusive. Starting from recent discoveries on the molecular factors and on the DNA sequences (the so-called "pairing sites") involved, we dissect the mechanical basis of Xic colocalization by using a statistical physics model. We show that soluble DNA-specific binding molecules, such as those experimentally identified, can be indeed sufficient to induce the spontaneous colocalization of the homologous chromosomes but only when their concentration, or chemical affinity, rises above a threshold value as a consequence of a thermodynamic phase transition. We derive the likelihood of pairing and its probability distribution. Chromosome dynamics has two stages: an initial independent Brownian diffusion followed, after a characteristic time scale, by recognition and pairing. Finally, we investigate the effects of DNA deletion/insertions in the region of pairing sites and compare model predictions to available experimental data

Normal scaling in globally conserved interface-controlled coarsening of fractal clusters

Globally conserved interface-controlled coarsening of fractal clusters exhibits dynamic scale invariance and normal scaling. This is demonstrated by a numerical solution of the Ginzburg-Landau equation with a global conservation law. The sharp-interface limit of this equation is volume preserving motion by mean curvature. The scaled form of the correlation function has a power-law tail accommodating the fractal initial condition. The coarsening length exhibits normal scaling with time. Finally, shrinking of the fractal clusters with time is observed. The difference between global and local conservation is discussed.Comment: 4 pages, 3 eps figure

Game theory of mind

This paper introduces a model of ‘theory of mind’, namely, how we represent the intentions and goals of others to optimise our mutual interactions. We draw on ideas from optimum control and game theory to provide a ‘game theory of mind’. First, we consider the representations of goals in terms of value functions that are prescribed by utility or rewards. Critically, the joint value functions and ensuing behaviour are optimised recursively, under the assumption that I represent your value function, your representation of mine, your representation of my representation of yours, and so on ad infinitum. However, if we assume that the degree of recursion is bounded, then players need to estimate the opponent's degree of recursion (i.e., sophistication) to respond optimally. This induces a problem of inferring the opponent's sophistication, given behavioural exchanges. We show it is possible to deduce whether players make inferences about each other and quantify their sophistication on the basis of choices in sequential games. This rests on comparing generative models of choices with, and without, inference. Model comparison is demonstrated using simulated and real data from a ‘stag-hunt’. Finally, we note that exactly the same sophisticated behaviour can be achieved by optimising the utility function itself (through prosocial utility), producing unsophisticated but apparently altruistic agents. This may be relevant ethologically in hierarchal game theory and coevolution