Search

A Transparent game is a game-theoretic setting that takes action visibility into account. In each round, depending on the relative timing of their actions, players have a certain probability to see their partner’s choice before making their own decision. This probability is determined by the level of transparency. At the two extremes, a game with zero transparency is equivalent to the classical simultaneous game, and a game with maximal transparency corresponds to a sequential game. Despite the prevalence of intermediate transparency in many everyday interactions such scenarios have not been sufficiently studied. Here we consider a transparent iterated Prisoner’s dilemma (iPD) and use evolutionary simulations to investigate how and why the success of various strategies changes with the level of transparency. We demonstrate that non-zero transparency greatly reduces the set of successful memory-one strategies compared to the simultaneous iPD. For low and moderate transparency the classical “Win – Stay, Lose – Shift” (WSLS) strategy is the only evolutionary successful strategy. For high transparency all strategies are evolutionary unstable in the sense that they can be easily counteracted, and, finally, for maximal transparency a novel “Leader-Follower” strategy outperforms WSLS. Our results provide a partial explanation for the fact that the strategies proposed for the simultaneous iPD are rarely observed in nature, where high levels of transparency are common.

Real-world agents, such as humans, animals and robots, observe each other during interactions and choose their own actions taking the partners’ ongoing behaviour into account. Yet, classical game theory assumes that players act either strictly sequentially or strictly simultaneously (without knowing the choices of each other). To account for action visibility and provide a more realistic model of interactions under time constraints, we introduce a new game-theoretic setting called transparent game, where each player has a certain probability to observe the choice of the partner before deciding on its own action. Using evolutionary simulations, we demonstrate that even a small probability of seeing the partner’s choice before one’s own decision substantially changes evolutionary successful strategies. Action visibility enhances cooperation in a Bach-or-Stravinsky game, but disrupts cooperation in a more competitive iterated Prisoner’s Dilemma. In both games, strategies based on the “Win–stay, lose–shift” and “Tit-for-tat” principles are predominant for moderate transparency, while for high transparency strategies of “Leader-Follower” type emerge. Our results have implications for studies of human and animal social behaviour, especially for the analysis of dyadic and group interactions.

A central problem in biomedical imaging is the automated segmentation of images for further quantitative analysis. Recently, fully convolutional neural networks, such as the U-Net, were applied successfully in a variety of segmentation tasks. A downside of this approach is the requirement for a large amount of well-prepared training samples, consisting of image - ground truth mask pairs. Since training data must be created by hand for each experiment, this task can be very costly and time-consuming. Here, we present a segmentation method based on cycle consistent generative adversarial networks, which can be trained even in absence of prepared image - mask pairs. We show that it successfully performs image segmentation tasks on samples with substantial defects and even generalizes well to different tissue types.

Temporally disordered systems frequently exhibit complex intermittent dynamics accompanied by aging and weak ergodicity breaking. Here, we analyze the response behavior of temporally disordered dynamical processes by employing a functional representation. We find that the linear response to an external perturbation is history-dependent and explicitly calculate the response function for a sub-diffusive tracer particle confined in a harmonic potential. Our results demonstrate that the linear response function inherits the aging and weakly ergodic properties of the process, which has crucial implications for the interpretation of experimental measurements.

Spatial heterogeneity of a host population of mobile agents has been shown to be a crucial determinant of many aspects of disease dynamics, ranging from the proliferation of diseases to their persistence and to vaccination strategies. In addition, the importance of regional and structural differences grows in our modern world. Little is known, though, about the consequences when traits of a disease vary regionally. In this paper, we study the effect of a spatially varying per capita infection rate on the behaviour of livestock diseases. We show that the prevalence of an infectious livestock disease in a community of animals can paradoxically decrease owing to transport connections to other communities in which the risk of infection is higher. We study the consequences for the design of livestock transportation restriction measures and establish exact criteria to discriminate those connections that increase the level of infection in the community from those that decrease it.

We obtain the exact solution for the Burgers equation with a time dependent forcing, which depends linearly on the spatial coordinate. For the case of a stochastic time dependence an exact expression for the joint probability distribution for the velocity fields at multiple spatial points is obtained. A connection with stretched vortices in hydrodynamic flows is discussed., Comment: 10 pages

Dynamical processes exhibiting non-Poissonian kinetics with nonexponential waiting times are frequently encountered in nature. Examples are biochemical processes like gene transcription which are known to involve multiple intermediate steps. However, often a second process, obeying Poissonian statistics, affects the first one simultaneously, such as the degradation of mRNA in the above example. The aim of the present article is to provide a concise treatment of such random systems which are affected by regular and non-Poissonian kinetics at the same time. We derive the governing master equation and provide a controlled approximation scheme for this equation. The simplest approximation leads to generalized reaction rate equations. For a simple model of gene transcription we solve the resulting equation and show how the time evolution is influenced significantly by the type of waiting time distribution assumed for the non-Poissonian process.

We introduce a population model for species under cyclic competition. This model allows individuals to coexist and interact on single cells while migration takes place between adjacent cells. In contrast to the model introduced by Reichenbach, Mobilia, and Frey [Reichenbach, Mobilia, and Frey, Nature (London) 448, 1046 (2007)], we find that the emergence of spirals results in an ambiguous behavior regarding the stability of coexistence. The typical time until extinction exhibits, however, a qualitatively opposite dependence on the newly introduced nonunit carrying capacity in the spiraling and the nonspiraling regimes. This allows us to determine a critical mobility that marks the onset of this spiraling state sharply. In contrast, we demonstrate that the conventional finite size stability analysis with respect to spatial size is of limited use for identifying the onset of the spiraling regime.

We present a model of stochastic molecular transport in spiny dendrites. In this model the molecules perform a random walk between the spines that trap the walkers. If the molecules interact with each other inside the spines the trapping time in each spine depends on the number of molecules in the respective trap. The corresponding mathematical problem has non-trivial solutions even in the absence of external disorder due to self-organization phenomenon. We obtain the stationary distributions of the number of walkers in the traps for different kinds of on-site interactions between the walkers. We analyze how birth and death processes of the random walkers affect these distributions. We apply this model to describe the dynamics of the PSD-95 proteins in spiny dendrites. PSD-95 is the most abundant molecule in the post-synaptic density (PSD) located in the spines. It is observed that these molecules have high turnover rates and that neighboring spines are constantly exchanging individual molecules. We propose that the geometry of individual PSD-95 clusters determines the dependence of trapping times on the number of molecules inside the trap and thus can vary from spine to spine. Furthermore, we suggest that activity-dependent reorganization of the PSD-95 cluster can lead to synaptic plasticity in a form of long-term potentiation (LTP). In the model this is achieved by spine specific activity-dependent ubiquitinization of PSD-95 molecules, which transiently reduces the amount of PSD-95 in the spine but change the geometry of the PSD-95 cluster in such a way that self-organization process results in the overall increase of the number of PSD-95 molecules associated with LTP. We also show that such a dynamics of the PSD-95 molecules can set up the conditions for anomalous diffusive transport inside spiny dendrites and predict the distribution of the PSD sizes which has features of both exponential and Poisson distributions.

We consider the motion of particles which are scattered by randomly distributed obstacles. In between scattering events the particles move uniformly. The governing master equation is obtained by mapping the problem onto a master equation which was previously devised for the description of anomalous diffusion of particles with inertia [R. Friedrich, Phys. Rev. Lett. 96, 230601 (2006)]. We show that for a scale-free distance distribution of scatterers a time-fractional master equation arises. The corresponding diffusion equation which exhibits a power-law diffusion coefficient is solved in d dimensions via the method of subordination.

Humboldt University, Newtonstr. 15,D-12489 Berlin, Germany(Dated: September 8, 2008)We formulate the generalized master equation for a class of continuous time random walks in thepresence of a prescribed deterministic evolution between successive transitions. This formulation isexemplified by means of an advection-diffusion and a jump-diffusion scheme. Based on this masterequation, we also derive reaction-diffusion equations for subdiffusive chemical species, using a meanfield approximation.

Employing the generalized master equation proposed in [R. Friedrich et al., Phys. Rev. Lett. 96, 230601 (2006)], we derive a kinetic equation for a random kick model. For a particular choice of the time evolution kernel, a fractional master equation is obtained, which can be related to a Levy walk. In one dimension, we use this model to describe a stochastic Lorentz gas with an annealed disorder. Exact moment relations are obtained in Laplace space, and the long-time behavior of the moments is discussed. The results are compared to those of related models.

Recently a new type of Kramers-Fokker-Planck Equation has been proposed [R. Friedrich et al. Phys. Rev. Lett. {\bf 96}, 230601 (2006)] describing anomalous diffusion in external potentials. In the present paper the explicit cases of a harmonic potential and a velocity-dependend damping are incorporated. Exact relations for moments for these cases are presented and the asymptotic behaviour for long times is discussed. Interestingly the bounding potential and the additional damping by itself lead to a subdiffussive behaviour, while acting together the particle becomes localized for long times., 12 pages, 8 figures

In recent years, several fractional generalizations of the usual Kramers-Fokker-Planck equation have been presented. Using an idea of Fogedby (Fogedby, H. C. Phys. Rev. E 1994, 50, 041103), we show how these equations are related to Langevin equations via the procedure of subordination.

We derive the exact solution for the Burgers equation with a time dependent forcing, which depends linearly on the spatial coordinate. For the case of a stochastic time dependence an exact expression for the joint probability distribution for the velocity fields at multiple spatial points is obtained. We present numerical results for fixed boundary conditions, and analyze the formation of shocks.

Test particle transport in realistic plasma core turbulence (as described by nonlinear gyrokinetics) is investigated, focusing on the question whether and under what conditions the transport may become “anomalous”; i.e. super- or subdiffusive. While in the presence of stochastic fluctuations, the transport always becomes diffusive for large times, coherent flow components such as zonal flows or poloidal drifts can induce non-Gaussian transport over large intermediate time spans. In order to understand the origin of these phenomena, a simple model employing stochastic potentials is used to complement the analysis based on gyrokinetic turbulence simulations.

In order to describe non-Gaussian kinetics in weakly damped systems, the concept of continuous time random walks is extended to particles with finite inertia. One thus obtains a generalized Kramers-Fokker-Planck equation, which retains retardation effects, i.e., nonlocal couplings in time and space. It is shown that despite this complexity, exact solutions of this equation can be given in terms of superpositions of Gaussian distributions with varying variances. In particular, the long-time behavior of the respective low-order moments is calculated.

The anomalous (i.e. non-Gaussian) dynamics of particles subject to a deterministic acceleration and a series of 'random kicks' is studied. Based on an extension of the concept of continuous time random walks to position-velocity space, a new fractional equation of the Kramers-Fokker-Planck type is derived. The associated collision operator necessarily involves a fractional substantial derivative, representing important nonlocal couplings in time and space. For the force-free case, a closed solution is found and discussed., Submitted to Physical Review Letters

Employing the path integral formulation of a broad class of anomalous diffusion processes, we derive the exact relations for the path probability densities of these processes. In particular, we obtain a closed analytical solution for the path probability distribution of a Continuous Time Random Walk (CTRW) process. This solution is given in terms of its waiting time distribution and short time propagator of the corresponding random walk as a solution of a Dyson equation. Applying our analytical solution we derive generalized Feynman?Kac formulae.

Molecules in neurons are in a state far from equilibrium. Therefore their transport properties are strongly affected by fluctuations. We present a model of stochastic molecular transport in neurons which have their synapses located in the spines of a dendrite. In this model we assume that the molecules perform a random walk between the spines that trap the walkers. If the molecules are assumed to interact with each other inside the spines, the trapping time in each spine depends on the number of molecules in the respective trap. The corresponding mathematical problem has non-trivial solutions even in the absence of external disorder due to self-organization phenomena. We obtain the stationary distributions of the number of walkers in the traps for different kinds of on-site interactions between the walkers and furthermore analyze how birth and death processes of the random walkers affect these distributions. We apply this model to describe the dynamics of the PSD-95 proteins in spiny dendrites. PSD-95 is the most abundant molecule in the post-synaptic density (PSD) located in the spines. It is observed that these molecules have high turnover rates and that neighboring spines are constantly exchanging individual molecules. Thus we predict the distribution of PSD-95 cluster sizes that determine the size of the synapse and thus the synaptic strength. Finally, we show that in the model non-equilibrium inter-spine dynamics of PSD-95 molecules can provide the basis for locally controlled synaptic plasticity through activity-dependent ubiquitinization of PSD-95 molecules.