2017, Schumacher, P., Mayr, S.G., Rauschenbach, B.

Germanium thin films were deposited by Pulsed Laser Deposition (PLD) onto single crystal Ge (100) and Si (100) substrates with a native oxide film on the surface. The topography of the surface was investigated by Atomic Force Microscopy (AFM) to evaluate the scaling behavior of the surface roughness of amorphous and polycrystalline Ge films grown on substrates with different roughnesses. Roughness evolution was interpreted within the framework of stochastic rate equations for thin film growth. Here the Kardar-Parisi-Zhang equation was used to describe the smoothening process. Additionally, a roughening regime was observed in which 3-dimensional growth occurred. Diffusion of the deposited Ge adatoms controlled the growth of the amorphous Ge thin films. The growth of polycrystalline thin Ge films was dominated by diffusion processes only in the initial stage of the growth.

2021, Eid, Shereif, Rocha, Ana Paula, Steels, Luc, Herik, Jaap van den

After we describe the waiting queue problem, we identify a partially observable 2n+1-player voting game with only one pivotal player; the player at the n-1 order. Given the simplest rule of heterogeneity presented in this paper, we show that for any infinite sequential voting game of size 2n+1, a power index of size n is a good approximation of the power index at infinity, and it is difficult to achieve. Moreover, we show that the collective utility value of a coalition for a partially observable anonymous game given an equal distribution of weights is n²+n. This formula is developed for infinite sequential anonymous games using a stochastic process that yields a utility function in terms of the probability of the sequence and voting outcome of the coalition. Evidence from Wikidata editing sequences is presented and the results are compared for 10 coalitions.

2018, Yuan, M., Wang, W., Luo, X., Ge, C., Li, L., Kurths, J., Zhao, W.

The paper addresses the issue of synchronization of memristive bidirectional associative memory neural networks (MBAMNNs) with mixed time-varying delays and stochastic perturbation via a sampled-data controller. First, we propose a new model of MBAMNNs with mixed time-varying delays. In the proposed approach, the mixed delays include time-varying distributed delays and discrete delays. Second, we design a new method of sampled-data control for the stochastic MBAMNNs. Traditional control methods lack the capability of reflecting variable synaptic weights. In this paper, the methods are carefully designed to confirm the synchronization processes are suitable for the feather of the memristor. Third, sufficient criteria guaranteeing the synchronization of the systems are derived based on the derive-response concept. Finally, the effectiveness of the proposed mechanism is validated with numerical experiments.

2017, Deuschel, Jean-Dominique, Friz, Peter K., Maurelli, Mario, Slowik, Martin

We establish a Sanov type large deviation principle for an ensemble of interacting Brownian rough paths. As application a large deviations for the (-layer, enhanced) empirical measure of weakly interacting diffusions is obtained. This in turn implies a propagation of chaos result in a space of rough paths and allows for a robust analysis of the particle system and its McKean–Vlasov type limit, as shown in two corollaries.

2017, Botta, N., Jansson, P., Ionescu, C., Christiansen, D.R., Brady, E.

We present a computer-checked generic implementation for solving finite-horizon sequential decision problems. This is a wide class of problems, including inter-temporal optimizations, knapsack, optimal bracketing, scheduling, etc. The implementation can handle time-step dependent control and state spaces, and monadic representations of uncertainty (such as stochastic, non-deterministic, fuzzy, or combinations thereof). This level of genericity is achievable in a programming language with dependent types (we have used both Idris and Agda). Dependent types are also the means that allow us to obtain a formalization and computer-checked proof of the central component of our implementation: Bellman’s principle of optimality and the associated backwards induction algorithm. The formalization clarifies certain aspects of backwards induction and, by making explicit notions such as viability and reachability, can serve as a starting point for a theory of controllability of monadic dynamical systems, commonly encountered in, e.g., climate impact research.