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The effects of error propagation in the reproduction of diploid organisms are studied within the populational genetics framework of the quasispecies model. The dependence of the error threshold on the dominance parameter is fully investigated. In particular, it is shown that dominance can protect the wild-type alleles from the error catastrophe. The analysis is restricted to a diploid analogue of the single-peaked landscape.
This paper shows how to determine all the unidimensional two-state cellular automaton rules of a given number of inputs which conserve the number of active sites. These rules have to satisfy a necessary and sufficient condition. If the active sites are viewed as cells occupied by identical particles, these cellular automaton rules represent evolution operators of systems of identical interacting particles whose total number is conserved. Some of these rules, which allow motion in both directions, mimic ensembles of one-dimensional pseudo-random walkers. Numerical evidence indicates that the corresponding stochastic processes might be non-Gaussian.
We consider a particle in the over-damped regime at zero temperature under the influence of a sawtooth potential and of a noisy force, which is correlated in time. A current occurs, even if the mean of the noisy force vanishes. We calculate the stationary probability distribution and the stationary current. We discuss, how these items depend on the characteristic parameters of the underlying stochastic process. A formal expansion of the current around the white-noise limit not always gives the correct asymptotic behaviour. We improve the expansion for some simple but representative cases.
The benefits of a recently proposed method to approximate hard optimization problems are demonstrated on the graph partitioning problem. The performance of this new method, called Extremal Optimization, is compared to Simulated Annealing in extensive numerical simulations. While generally a complex (NP-hard) problem, the optimization of the graph partitions is particularly difficult for sparse graphs with average connectivities near the percolation threshold. At this threshold, the relative error of Simulated Annealing for large graphs is found to diverge relative to Extremal Optimization at equalized runtime. On the other hand, Extremal Optimization, based on the extremal dynamics of self-organized critical systems, reproduces known results about optimal partitions at this critical point quite well.
We study a mixed population of adaptive agents with small and large memories, competing in a minority game. If the agents are sufficiently adaptive, we find that the average winnings per agent can exceed that obtainable in the corresponding pure populations. In contrast to the pure population, the average success rate of the large-memory agents can be greater than 50 percent. The present results are not reproduced if the agents are fed a random history, thereby demonstrating the importance of memory in this system.
We investigate the polarization fluctuations caused by quantum noise in quantum well vertical cavity surface emitting lasers (VCSELs). Langevin equations are derived on the basis of a generalized rate equation model in which the influence of competing gain-loss and frequency anisotropies is included. This reveals how the anisotropies and the quantum well confinement effects shape the correlations and the magnitude of fluctuations in ellipticity and in polarization direction. According to our results all parameters used in the rate equations may be obtained experimentally from precise time resolved measurements of the intensity and polarization fluctuations in the emitted laser light. To clarify the effects of anisotropies and of quantum well confinement on the laser process in VCSELs we therefore propose time resolved measurements of the polarization fluctuations in the laser light. In particular, such measurements allow to distinguish the effects of frequency anisotropy and of gain-loss anisotropy and would provide data on the spin relaxation rate in the quantum well structure during cw operation as well as representing a new way of experimentally determinig the linewidth enhancement factor alpha.
We present quantum Maxwell-Bloch equations (QMBE) for spatially inhomogeneous semiconductor laser devices. The QMBE are derived from fully quantum mechanical operator dynamics describing the interaction of the light field with the quantum states of the electrons and the holes near the band gap. By taking into account field-field correlations and field-dipole correlations, the QMBE include quantum noise effects which cause spontaneous emission and amplified spontaneous emission. In particular, the source of spontaneous emission is obtained by factorizing the dipole-dipole correlations into a product of electron and hole densities. The QMBE are formulated for general devices, for edge emitting lasers and for vertical cavity surface emitting lasers, providing a starting point for the detailed analysis of spatial coherence in the near field and far field patterns of such laser diodes. Analytical expressions are given for the spectra of gain and spontaneous emission described by the QMBE. These results are applied to the case of a broad area laser, for which the frequency and carrier density dependent spontaneous emission factor beta and the evolution of the far field pattern near threshold are derived.
One of the main results in canonical quantum gravity is the introduction of spin network states as a basis on the space of kinematical states. To arrive at the physical state space of the theory though we need to understand the dynamics of the quantum gravitational states. To this aim we study a model in which we allow for the spins, labeling the edges of spin networks, to change according to simple rules. The gauge invariance of the theory, restricting the possible values for the spins, induces propagating modes of spin changes. We investigate these modes under various assumptions about the parameters of the model.
Recent research on the dynamics of certain fluid dynamical instabilities shows that when there is a slow invariant manifold subject to fast timescale instability the dynamics are extremely sensitive to noise. The behaviour of such systems can be described in terms of a one-dimensional map, and previous work has shown how the effect of noise can be modelled by a simple adjustment to the map. Here we undertake an in depth investigation of a particular set of equations, using the methods of stochastic integration. We confirm the prediction of the earlier studies that the noise becomes important when mu|log(epsilon)| = O(1), where mu is the small timescale ratio and εis the noise level. In addition, we present detailed information about the statistics of the solution when the noise is a dominant effect; the analytical results show excellent agreement with numerical simulations.
The dynamics of velocity fluctuations, governed by the one-dimensional Burgers equation, driven by a white-in-time random force with the spatial spectrum $\overline{|f(k)|^2}\proptok^{-1}$, is considered. High-resolution numerical experiments conducted in this work give the energy spectrum $E(k)\propto k^{-β}$ with $β=5/3\pm 0.02$. The observed two-point correlation function $C(k,ω)$ reveals $ω\propto k^z$ with the "dynamical exponent" $z\approx 2/3$. High-order moments of velocity differences show strong intermittency and are dominated by powerful large-scale shocks. The results are compared with predictions of the one-loop renormalized perturbation expansion.
An analytical treatment for the sedimentation rate of disordered suspensions is presented in the context of a resistance problem. From the calculation it is confirmed that the lubrication effect is important in contrast to the suggestion by Brady and Durlofsky (Phys.Fluids Vol.31, 717 (1988)). The calculated sedimentation rate agrees well with the experimental results in all range of the volume fraction.
We have analyzed the Kuramoto-Sivashinsky equation with a stochastic noise term through a dynamic renormalization group calculation. For a system in which the lattice spacing is smaller than the typical wavelength of the linear instability occurring in the system, the large-distance and long-time behavior of this equation is the same as for the Kardar-Parisi-Zhang equation in one and two spatial dimensions. For the $d=2$ case the agreement is only qualitative. On the other hand, when coarse-graining on larger scales the asymptotic flow depends on the initial values of the parameters.
A complete formulation is given of an exact kinetic theory for lattice gases. This kinetic theory makes possible the calculation of corrections to the usual Boltzmann / Chapman-Enskog analysis of lattice gases due to the buildup of correlations. It is shown that renormalized transport coefficients can be calculated perturbatively by summing terms in an infinite series. A diagrammatic notation for the terms in this series is given, in analogy with the diagrammatic expansions of continuum kinetic theory and quantum field theory. A closed-form expression for the coefficients associated with the vertices of these diagrams is given. This method is applied to several standard lattice gases, and the results are shown to correctly predict experimentally observed deviations from the Boltzmann analysis.
The fractal properties of models of randomly placed $n$-dimensional spheres ($n$=1,2,3) are studied using standard techniques for calculating fractal dimensions in empirical data (the box counting and Minkowski-sausage techniques). Using analytical and numerical calculations it is shown that in the regime of low volume fraction occupied by the spheres, apparent fractal behavior is observed for a range of scales between physically relevant cut-offs. The width of this range, typically spanning between one and two orders of magnitude, is in very good agreement with the typical range observed in experimental measurements of fractals. The dimensions are not universal and depend on density. These observations are applicable to spatial, temporal and spectral random structures. Polydispersivity in sphere radii and impenetrability of the spheres (resulting in short range correlations) are also introduced and are found to have little effect on the scaling properties. We thus propose that apparent fractal behavior observed experimentally over a limited range may often have its origin in underlying randomness.
We studied the effects of time correlation of subsequent patterns on the convergence of on-line learning by a feedforward neural network with backpropagation algorithm. By using chaotic time series as sequences of correlated patterns, we found that the unexpected scaling of converging time with learning parameter emerges when time-correlated patterns accelerate learning process.
This paper shows how particle hopping models fit into the context of traffic flow theory. Connections between fluid-dynamical traffic flow models, which derive from the Navier-Stokes-equations, and particle hopping models are shown. In some cases, these connections are exact and have long been established, but have never been viewed in the context of traffic theory. In other cases, critical behavior of traffic jam clusters can be compared to instabilities in the partial differential equations. Finally, it is shown how this leads to a consistent picture of traffic jam dynamics.
Euler turbulence has been experimentally observed to relax to a metaequilibrium state that does not maximize the Boltzmann entropy, but rather seems to minimize enstrophy. We show that a recent generalization of thermodynamics and statistics due to Tsallis is capable of explaining this phenomenon in a natural way. The maximization of the generalized entropy $S_{1/2}$ for this system leads to precisely the same profiles predicted by the Restricted Minimum Enstrophy theory of Huang and Driscoll. This makes possible the construction of a comprehensive thermodynamic description of Euler turbulence.
The characteristic size for spatial structure, that emerges when the bifurcation parameter in model partial differential equations is slowly increased through its critical value, depends logarithmically on the size of added noise. Numerics and analysis are presented for the real Ginzburg-Landau and Swift-Hohenberg equations.