Adaptive walks and extreme value theory

We study biological evolution in a high-dimensional genotype space in the regime of rare mutations and strong selection. The population performs an uphill walk which terminates at local fitness maxima. Assigning fitness randomly to genotypes, we show that the mean walk length is logarithmic in the number of initially available beneficial mutations, with a prefactor determined by the tail of the fitness distribution. This result is derived analytically in a simplified setting where the mutational neighborhood is fixed during the adaptive process, and confirmed by numerical simulations.     

Anomalous transport and diffusion phenomena induced by biharmonic forces in deformable potential systems

We study transport properties of an inertial Brownian motor which moves in a deformable Remoissenet-Peyrad periodic potential and is subjected to both a static bias force and time periodic driving biharmonic force. By modifying the shape of the potential, the anomalous transport is identified for a particular set of the system parameters. For a particular potential shape, the mean velocity of a particle is modified by going from negative to positive values according to the external bias force. These features also depend on both the biharmonic parameter and the phase-lag of two signals. A remarkable transition of the negative velocity depending on the shape of the potential is observed. We also focus on the efficiency of the motor and discuss velocity fluctuation. In addition, within selected system parameters, different types of diffusion particle such as subdiffusion, superdiffusion, normal diffusion, ballistic diffusion, hyperdiffusion and dispersionless transport phenomena are generated in the system.     

Anomalous diffusion and continuum percolation

Anomalous diffusion for continuum percolation is simulated by considering systems of randomly distributed circles and spheres. Universal behavior is obtained for the case of equal local conductances and nonuniversal behavior for diverging distributions of the local conductances. Diffusion in the continuum has a behavior consistent with that of other transport properties in the continuum. In addition, the results suggest that different algorithms for diffusion, which differ only in the random walker sitting times, are equivalent.     

Anomalous deterministic transport

We present a series of results on deterministic transport in chaotic system, obtained in the framework of periodic orbits theory. The emphasis is on intermittent systems, where deviations from complete chaos may induce anomalies on the asymptotic moments' growth.     

反常扩散与分数阶对流-扩散方程

反常扩散现象在自然界和社会系统中广泛存在.考虑了扩散过程的时间相关和时空相关性，用非局域性的处理方法，在传统的二阶对流 扩散方程基础上，得到了分数阶对流 扩散方程，以此方程来描述反常扩散.在此方程中，弥散项和对时间的导数为分数阶导数所代替.由此分数阶对流 扩散方程，对传统的费克扩散定律进行推广，得到了广义的分数费克扩散定律，分数费克扩散定律说明某时刻空间中某点的流量不仅与其领域内的浓度梯度有关，而且与整个空间中其他不同点的粒子浓度、浓度变化的历史，甚至初始时刻的浓度有关.讨论了方程的解——分数稳定分布，并由此说明了扩散运动的平均平方位移是运移时间的非线性函数. 关键词： 扩散 分数阶微积分 稳定分布（Lévy分布） 费克扩散定律     

Anomalous diffusion and fractional stable distributions

A new set of distributions, called fractional stable distributions, is described. A subset of this set is represented by stable laws, while its particular case is the Gaussian distribution. These distributions arise as solutions to fractional-order partial differential equations that represent a generalization of the ordinary diffusion equation to the case of anomalous diffusion. The properties of multidimensional fractional stable densities are described, their expressions in terms of special functions are presented, and physical problems that lead to these densities are discussed.     

Anomalous transport and quantum-classical correspondence

We present evidence that anomalous transport in the classical standard map results in strong enhancement of fluctuations in the localization length of quasienergy states in the corresponding quantum dynamics. This generic effect occurs even far from the semiclassical limit and reflects the interplay of local and global quantum suppression mechanisms of classically chaotic dynamics. Possible experimental scenarios are also discussed.     

Anomalous diffusion in silo drainage

The silo discharge process is studied by molecular dynamics simulations. The development of the velocity profile and the probability density function for the displacements in the horizontal and vertical axis are obtained. The PDFs obtained at the beginning of the discharge reveal non-Gaussian statistics and superdiffusive behaviors. When the stationary flow is developed, the PDFs at shorter temporal scales are non-Gaussian too. For big orifices a well-defined transition between ballistic and diffusive regime is observed. In the case of a small outlet orifice, no well-defined transition is observed. We use a nonlinear diffusion equation introduced in the framework of non-extensive thermodynamics in order to describe the movements of the grains. The solution of this equation gives a well-defined relationship (γ= 2/(3-q)) between the anomalous diffusion exponent γ and the entropic parameter q introduced by the non-extensive formalism to fit the PDF of the fluctuations.     

Value-at-risk estimation with wavelet-based extreme value theory: Evidence from emerging markets

This paper introduces wavelet-based extreme value theory (EVT) for univariate value-at-risk estimation. Wavelets and EVT are combined for volatility forecasting to estimate a hybrid model. In the first stage, wavelets are used as a threshold in generalized Pareto distribution, and in the second stage, EVT is applied with a wavelet-based threshold. This new model is applied to two major emerging stock markets: the Istanbul Stock Exchange (ISE) and the Budapest Stock Exchange (BUX). The relative performance of wavelet-based EVT is benchmarked against the Riskmetrics-EWMA, ARMA-GARCH, generalized Pareto distribution, and conditional generalized Pareto distribution models. The empirical results show that the wavelet-based extreme value theory increases predictive performance of financial forecasting according to number of violations and tail-loss tests. The superior forecasting performance of the wavelet-based EVT model is also consistent with Basel II requirements, and this new model can be used by financial institutions as well.     

On the generalized diffusion theory of current transport in isotype heterojunctions

Summary The generalized diffusion theory of current transport inn-n isotype heterojunctions enunciated previously has been extended to the realistic case of there being two different electron mobilities in the two semiconductors forming then-n heterojunction. This extended theory too reduces to the diffusion theory of current in metal-semiconductor contacts under the appropriate limiting conditions in the same way as the previous theory does. The current-voltage characteristics forn-n heterojunctions according to this extended theory would be different from those according to the previous theory if the values of all the parameters involved such as Λ _nn C, ψ_D1, ψ_D2,V ₁,V ₂, etc. could be calculated rigorously. However, utilizing the values of some parameters such as Λ _nn andC calculated by means of approximate expressions derived under these limiting conditions, one would evaluate current-voltage characteristics that are the same as in the previous theory. A single curve representing the current-voltage characteristic of any particularn-n isotype heterojunction can also be plotted by using a formula derived previously under zero-current conditions, in conjunction with the appropriate expressions derived in the present paper. In appendix B an alternative expression for the current density in an-n isotype heterojunction is also derived in the framework of the generalized diffusion theory.

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Riassunto La teoria della diffusione generalizzata del transporto di corrente nelle eterogiunzioni di isotropin-n enunciata in precedenza è stata estesa al caso realistico in cui vi sono due diverse mobilità di elettroni nei due semiconduttori che formano l'eterogiunzionen-n, Anche questa teoria estesa si riduce alla teoria di diffusione della corrente nei contatti dei semiconduttori metallici nelle condizioni limitanti appropriate nello stesso modo della teoria precedente. Le caratteristiche del voltaggio di corrente per le eterogiunzioni n-n secondo questa teoria estesa sarebbero differenti da quelle secondo la teoria precedente se i valori di tutti i parametri coinvolti come Λ _nn ,C, ψ_D1, ψ_D2,V ₁,V ₂, ecc. potessero essere calcolati rigorosamente. Comunque, utilizzando i valori di alcuni parametri come Λ _nn eC calcolati per mezzo di espressioni approssimate dedotte in queste condizioni limitanti, si valuterebbero le caratteristiche del voltaggio di corrente uguali a quelle delle teoria precedente. Si può anche tracciare una singola curva rappresentante la caratteristica del voltaggio di corrente di ogni particolare eterogiunzione di isotopin-n usando una formula dedotta precedentemente in condizioni di corrente zero, assieme alle espressioni appropriate dedotte in questo lavoro. Nell'appendice B si deduce anche un'espressione alternativa per la densità di corrente in un'eterogiunzione di isotopin-n nel modello della teoria della diffusione generalizzata.

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Рэзюме Обобщенная теория диффузэии для переноса тока в n-n гетеропереходе, развитая ранее, обобщается на реалистический случай, когде в двук полупроводниках, образующих n-n гетеропереход, электроны имеют две различные подвижности. Предложенная обобщенная теииая теория сводится к теории диффузии для тока в контакте металл-полупроводник при определенных ограничивающих условиях, как и в случае предыдущей теории. Вольт-амперная характеристика для n-n гетероперереходов, согласно предлагаемой обобщенной теории, будет отличаться от вольт-амперной характеристики предыдущей теории, если все парамеры теории Λ _nn , С, ψ_D1, ψ_D2,V ₁,V ₂ и т.д, могут быть вычислены строго. Однако, используя для некоторых параметров, таких как Λ _nn и С, приближенные выражения, вычисленные в рамках вышеуказанных ограничивающих условий, получаются вольт-амперные характеристики, совпадающие с результатами предыдущей теории. Приводятся кривые для вольт-амперных характеристик для любого n-n гетероперехода. В Приложении П в рамках обобщенной теории диффузии выводится альтернативное выражение для плотности тока в n-n гетеропереходе.

     

Anomalous diffusion in branched elliptical structure

Diffusion in narrow curved channels with dead-ends as in extracellular space in the biological tissues, e.g., brain, tumors, muscles, etc. is a geometrically induced complex diffusion and is relevant to different kinds of biological, physical, and chemical systems. In this paper, we study the effects of geometry and confinement on the diffusion process in an elliptical comb-like structure and analyze its statistical properties. The ellipse domain whose boundary has the polar equation $rho left( theta right)=frac{b}{sqrt {1-e^{2}cos^{2}theta } }$ with $0相似文献   

Anomalous diffusion in living yeast cells

The viscoelastic properties of the cytoplasm of living yeast cells were investigated by studying the motion of lipid granules naturally occurring in the cytoplasm. A large frequency range of observation was obtained by a combination of video-based and laser-based tracking methods. At time scales from 10(-4) to 10(2) s, the granules typically perform subdiffusive motion with characteristics different from previous measurements in living cells. This subdiffusive behavior is thought to be due to the presence of polymer networks and membranous structures in the cytoplasm. Consistent with this hypothesis, we observe that the motion becomes less subdiffusive upon actin disruption.