Elephants can always remember: Exact long-range memory effects in a non-Markovian random walk

We consider a discrete-time random walk where the random increment at time step $t$ depends on the full history of the process. We calculate exactly the mean and variance of the position and discuss its dependence on the initial condition and on the memory parameter $p$. At a critical value $p_c^{(1)}=1/2$ where memory effects vanish there is a transition from a weakly localized regime (where the walker returns to its starting point) to an escape regime. Inside the escape regime there is a second critical value where the random walk becomes superdiffusive. The probability distribution is shown to be governed by a non-Markovian Fokker-Planck equation with hopping rates that depend both on time and on the starting position of the walk. On large scales the memory organizes itself into an effective harmonic oscillator potential for the random walker with a time-dependent spring constant $k = (2p-1)/t$. The solution of this problem is a Gaussian distribution with time-dependent mean and variance which both depend on the initiation of the process.Comment: 10 page

Stability of Localized Wave Fronts in Bistable Systems

Localized wave fronts are a fundamental feature of biological systems from cell biology to ecology. Here, we study a broad class of bistable models subject to self-activation, degradation, and spatially inhomogeneous activating agents. We determine the conditions under which wave-front localization is possible and analyze the stability thereof with respect to extrinsic perturbations and internal noise. It is found that stability is enhanced upon regulating a positional signal and, surprisingly, also for a low degree of binding cooperativity. We further show a contrasting impact of self-activation to the stability of these two sources of destabilization. DOI: 10.1103/PhysRevLett.110.03810

Vision Zero Oregon

Vision Zero Oregon (VZO) is a street safety philosophy that aims to create streets where no one will be killed or seriously injured. Vision Zero Oregon prioritizes road safety above all else. Every life is worth more than an increase in speeds or road capacity for vehicles. Achieving Vision Zero Oregon goals will require a shift in the focus of policy, laws and enforcement, and the formation of a new relationship between residents and their streets, and revolution in the way transportation departments operate their streets. This project takes on one part of this complex topic, focusing on community interest, involvement, and influence in the transportation system of a neighborhood. The goal is to turn resident interest into activism, and empower a population to support the innovative changes necessary to decisively improve safety. Please visit the website at: http://www.visionzerooregon.org/. This project was conducted under the supervision of Sumner Sharpe and Ellen Bassett

The Role of Alternative Testing Strategies in Environmental Risk Assessment of Engineered Nanomaterials

Within toxicology there is a pressure to find new test systems to replace, reduce and refine animal testing. In nanoecotoxicology this raises a number of questions

Relationship between a Non-Markovian Process and Fokker-Planck Equation

We demonstrate the equivalence of a Non--Markovian evolution equation with a linear memory--coupling and a Fokker--Planck equation (FPE). In case the feedback term offers a direct and permanent coupling of the current probability density to an initial distribution, the corresponding FPE offers a non-trivial drift term depending itself on the diffusion parameter. As the consequence the deterministic part of the underlying Langevin equation is likewise determined by the noise strength of the stochastic part. This memory induced stochastic behavior is discussed for different initial distributions. The analytical calculations are supported by numerical results.Comment: 14 pages, 17 figure