A general framework for consistent estimation of charge transport properties via random walks in random environments

A general framework is proposed for the study of the charge transport properties of materials via random walks in random environments (RWRE). The material of interest is modeled by a random environment, and the charge carrier is modeled by a random walker. The framework combines a model for the fast generation of random environments that realistically mimic materials morphology with an algorithm for efficient estimation of key properties of the resulting random walk. The model of the environment makes use of tools from spatial statistics and the theory of random geometric graphs. More precisely, the disordered medium is represented by a random spatial graph with directed edge weights, where the edge weights represent the transition rates of a Markov jump process (MJP) modeling the motion of the random walker. This MJP is a multiscale stochastic process. In the long term, it explores all vertices of the random graph model. In the short term, however, it becomes trapped in small subsets of the state space and makes many transitions in these small regions. This behavior makes efficient estimation of velocity by Monte Carlo simulations a challenging task. Therefore, we use aggregate Monte Carlo (AMC), introduced in [T. Brereton et al., Methodol. Comput. Appl. Probab., 16 (2014), pp. 465-484], for estimating the velocity of a random walker as it passes through a realization of the random environment. In this paper, we prove the strong consistency of the AMC velocity estimator and use this result to conduct a detailed case study, in which we describe the motion of holes in an amorphous mesophase of an organic semiconductor, dicyanovinyl-substituted oligothiophene (DCV4T). In particular, we analyze the effect of system size (i.e., number of molecules) on the velocity of single charge carriers

Learning multifractal structure in large networks

Generating random graphs to model networks has a rich history. In this paper, we analyze and improve upon the multifractal network generator (MFNG) introduced by Palla et al. We provide a new result on the probability of subgraphs existing in graphs generated with MFNG. From this result it follows that we can quickly compute moments of an important set of graph properties, such as the expected number of edges, stars, and cliques. Specifically, we show how to compute these moments in time complexity independent of the size of the graph and the number of recursive levels in the generative model. We leverage this theory to a new method of moments algorithm for fitting large networks to MFNG. Empirically, this new approach effectively simulates properties of several social and information networks. In terms of matching subgraph counts, our method outperforms similar algorithms used with the Stochastic Kronecker Graph model. Furthermore, we present a fast approximation algorithm to generate graph instances following the multi- fractal structure. The approximation scheme is an improvement over previous methods, which ran in time complexity quadratic in the number of vertices. Combined, our method of moments and fast sampling scheme provide the first scalable framework for effectively modeling large networks with MFNG

Dynamic Reconfiguration of Network Topology in Optical Networks

Dynamic reconfiguration of the logical topology of a network is generally used to adjust the shape of the network to adhere to changes in traffic. In this thesis the logical topology reconfiguration problem for a WDM network is combined with the multi-path routing of traffic throughout the network. Changes to the logical topology are made using branch exchanges to minimize the disruption to the network traffic. A Multi-timescale Markov Decision Process (MMDP) model is used to capture the different frequencies of changes to the network topology (slow timescale) and the routing of traffic (fast timescale). Heuristic policies are developed for the slow and fast time scales and rollout is used to improve the performance of the heuristic. To measure the performance of the heuristic and rollout policies, the Model Reference Adaptive Search (MRAS) method is used to find reference topologies that are close to optimal for a given static traffic demand matrix. To implement the MRAS method a random graph generation algorithm is needed. To address this need, a very efficient random graph generation algorithm is developed that competes with existing algorithms in the literature

Generating realistic scaled complex networks

Research on generative models is a central project in the emerging field of network science, and it studies how statistical patterns found in real networks could be generated by formal rules. Output from these generative models is then the basis for designing and evaluating computational methods on networks, and for verification and simulation studies. During the last two decades, a variety of models has been proposed with an ultimate goal of achieving comprehensive realism for the generated networks. In this study, we (a) introduce a new generator, termed ReCoN; (b) explore how ReCoN and some existing models can be fitted to an original network to produce a structurally similar replica, (c) use ReCoN to produce networks much larger than the original exemplar, and finally (d) discuss open problems and promising research directions. In a comparative experimental study, we find that ReCoN is often superior to many other state-of-the-art network generation methods. We argue that ReCoN is a scalable and effective tool for modeling a given network while preserving important properties at both micro- and macroscopic scales, and for scaling the exemplar data by orders of magnitude in size.Comment: 26 pages, 13 figures, extended version, a preliminary version of the paper was presented at the 5th International Workshop on Complex Networks and their Application