Optimal network topologies: Expanders, Cages, Ramanujan graphs, Entangled networks and all that

We report on some recent developments in the search for optimal network topologies. First we review some basic concepts on spectral graph theory, including adjacency and Laplacian matrices, and paying special attention to the topological implications of having large spectral gaps. We also introduce related concepts as ``expanders'', Ramanujan, and Cage graphs. Afterwards, we discuss two different dynamical feautures of networks: synchronizability and flow of random walkers and so that they are optimized if the corresponding Laplacian matrix have a large spectral gap. From this, we show, by developing a numerical optimization algorithm that maximum synchronizability and fast random walk spreading are obtained for a particular type of extremely homogeneous regular networks, with long loops and poor modular structure, that we call entangled networks. These turn out to be related to Ramanujan and Cage graphs. We argue also that these graphs are very good finite-size approximations to Bethe lattices, and provide almost or almost optimal solutions to many other problems as, for instance, searchability in the presence of congestion or performance of neural networks. Finally, we study how these results are modified when studying dynamical processes controlled by a normalized (weighted and directed) dynamics; much more heterogeneous graphs are optimal in this case. Finally, a critical discussion of the limitations and possible extensions of this work is presented.Comment: 17 pages. 11 figures. Small corrections and a new reference. Accepted for pub. in JSTA

Random walks and diffusion on networks

Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including diffusion, interactions, and opinions among humans and animals; and can be used to extract information about important entities or dense groups of entities in a network. Random walks have been studied for many decades on both regular lattices and (especially in the last couple of decades) on networks with a variety of structures. In the present article, we survey the theory and applications of random walks on networks, restricting ourselves to simple cases of single and non-adaptive random walkers. We distinguish three main types of random walks: discrete-time random walks, node-centric continuous-time random walks, and edge-centric continuous-time random walks. We first briefly survey random walks on a line, and then we consider random walks on various types of networks. We extensively discuss applications of random walks, including ranking of nodes (e.g., PageRank), community detection, respondent-driven sampling, and opinion models such as voter models

Energy-Economical Heuristically Based Control of Compass Gait Walking on Stochastically Varying Terrain

Investigation uses simulation to explore the inherent tradeoffs ofcontrolling high-speed and highly robust walking robots while minimizing energy consumption. Using a novel controller which optimizes robustness, energy economy, and speed of a simulated robot on rough terrain, the user can adjust their priorities between these three outcome measures and systematically generate a performance curveassessing the tradeoffs associated with these metrics

Energy-Economical Heuristically Based Control of Compass Gait Walking on Stochastically Varying Terrain

Investigation uses simulation to explore the inherent tradeoffs ofcontrolling high-speed and highly robust walking robots while minimizing energy consumption. Using a novel controller which optimizes robustness, energy economy, and speed of a simulated robot on rough terrain, the user can adjust their priorities between these three outcome measures and systematically generate a performance curveassessing the tradeoffs associated with these metrics

Change blindness: eradication of gestalt strategies

Arrays of eight, texture-defined rectangles were used as stimuli in a one-shot change blindness (CB) task where there was a 50% chance that one rectangle would change orientation between two successive presentations separated by an interval. CB was eliminated by cueing the target rectangle in the first stimulus, reduced by cueing in the interval and unaffected by cueing in the second presentation. This supports the idea that a representation was formed that persisted through the interval before being 'overwritten' by the second presentation (Landman et al, 2003 Vision Research 43149–164]. Another possibility is that participants used some kind of grouping or Gestalt strategy. To test this we changed the spatial position of the rectangles in the second presentation by shifting them along imaginary spokes (by ±1 degree) emanating from the central fixation point. There was no significant difference seen in performance between this and the standard task [F(1,4)=2.565, p=0.185]. This may suggest two things: (i) Gestalt grouping is not used as a strategy in these tasks, and (ii) it gives further weight to the argument that objects may be stored and retrieved from a pre-attentional store during this task

Using MapReduce Streaming for Distributed Life Simulation on the Cloud

Distributed software simulations are indispensable in the study of large-scale life models but often require the use of technically complex lower-level distributed computing frameworks, such as MPI. We propose to overcome the complexity challenge by applying the emerging MapReduce (MR) model to distributed life simulations and by running such simulations on the cloud. Technically, we design optimized MR streaming algorithms for discrete and continuous versions of Conway’s life according to a general MR streaming pattern. We chose life because it is simple enough as a testbed for MR’s applicability to a-life simulations and general enough to make our results applicable to various lattice-based a-life models. We implement and empirically evaluate our algorithms’ performance on Amazon’s Elastic MR cloud. Our experiments demonstrate that a single MR optimization technique called strip partitioning can reduce the execution time of continuous life simulations by 64%. To the best of our knowledge, we are the first to propose and evaluate MR streaming algorithms for lattice-based simulations. Our algorithms can serve as prototypes in the development of novel MR simulation algorithms for large-scale lattice-based a-life models.https://digitalcommons.chapman.edu/scs_books/1014/thumbnail.jp

Modelling and engineering artificial burnt-bridge ratchet molecular motors

Nature has evolved many mechanisms for achieving directed motion on the subcellular level. The burnt-bridge ratchet (BBR) is one mechanism used to accomplish superdiffusive motion over long distances via the successive cleavage of surface-bound energy-rich substrate sites. The BBR mechanism is utilized throughout Nature: it can be found in bacteria, plants, mammals, arthropods (for example Crustaceans and Cheliceratans), as well as non-life forms such as influenza. Motivated to understand how fundamental engineering principles alter BBR kinetics, we have built both computer models and synthetic experimental systems to understand BBR kinetics. By exploring the dynamics of BBRs through simulation we find that their motor-like properties are highly dependent on the number of catalytic legs, the distance that the legs can reach from the central hub, and the hub topology. We further explore how design features in the underlying landscape affect BBR dynamics. We find that reducing the landscape from two- to one-dimensional increases superdiffusivity but leads to a loss in processivity. We also find that landscape elasticity affects all motor-like dynamical properties of BBRs: there are different optimal stiffnesses for distinct dynamical characteristics. For a spherical-hub BBR, speed, processivity, and persistence length are optimized at high, intermediate and soft stiffnesses, respectively, while rolling is also optimized at a high surface stiffness. Towards our development of a novel micron-sized protein-based BBR in the lab, we develop a new surface chemistry passivation technique and apply it to the surface of nanowires, turning an array of waveguiding nanowires into a high-throughput biosensing assay. In a separate assay, our protein-based BBR, which we call the lawnmower, is implemented in two dimensions on glass cover slips prepared with our surface chemistry (which serves as the lawn). We find the lawnmower dynamics reproduce key observations found in other similar systems, such as saltatory motion and broadly varying anomalously diffusive behaviour. The successful implementation of the lawnmower marks the first demonstration of an artificial protein-based molecular motor

Provision Quality-of-Service Controlled Content Distribution in Vehicular Ad Hoc Networks

By equipping vehicles with the on-board wireless facility, the newly emerged vehicular networking targets to provision the broadband serves to vehicles. As such, a variety of novel and exciting applications can be provided to vehicular users to enhance their road safety and travel comfort, and finally raise a complete change to their on-road life. As the content distribution and media/video streaming, such as Youtube, Netflix, nowadays have become the most popular Internet applications, to enable the efficient content distribution and audio/video streaming services is thus of the paramount importance to the success of the vehicular networking. This, however, is fraught with fundamental challenges due to the distinguished natures of vehicular networking. On one hand, the vehicular communication is challenged by the spotty and volatile wireless connections caused by the high mobility of vehicles. This makes the download performance of connections very unstable and dramatically change over time, which directly threats to the on-top media applications. On the other hand, a vehicular network typically involves an extremely large-scale node population (e.g., hundreds or thousandths of vehicles in a region) with intense spatial and temporal variations across the network geometry at different times. This dictates any designs to be scalable and fully distributed which should not only be resilient to the network dynamics, but also provide the guaranteed quality-of-service (QoS) to users. The purpose of this dissertation is to address the challenges of the vehicular networking imposed by its intrinsic dynamic and large-scale natures, and build the efficient, scalable and, more importantly, practical systems to enable the cost-effective and QoS guaranteed content distribution and media streaming services to vehicular users. Note that to effective- ly deliver the content from the remote Internet to in-motion vehicles, it typically involves three parts as: 1.) an infrastructure grid of gateways which behave as the data depots or injection points of Internet contents and services to vehicles, 2.) protocol at gateways which schedules the bandwidth resource at gateways and coordinates the parallel transmissions to different vehicles, and 3.) the end-system control mechanism at receivers which adapts the receiver’s content download/playback strategy based on the available network throughput to provide users with the desired service experience. With above three parts in mind, the entire research work in this dissertation casts a systematic view to address each part in one topic with: 1.) design of large-scale cost-effective content distribution infrastructure, 2.) MAC (media access control) performance evaluation and channel time scheduling, and 3.) receiver adaptation and adaptive playout in dynamic download environment. In specific, in the first topic, we propose a practical solution to form a large-scale and cost-effective content distribution infrastructure in the city. We argue that a large-scale infrastructure with the dedicated resources, including storage, computing and communication capacity, is necessary for the vehicular network to become an alternative of 3G/4G cellular network as the dominating approach of ubiquitous content distribution and data services to vehicles. On addressing this issue, we propose a fully distributed scheme to form a large-scale infrastructure by the contributions of individual entities in the city, such as grocery stores, movie theaters, etc. That is to say, the installation and maintenance costs are shared by many individuals. In this topic, we explain the design rationale on how to motivate individuals to contribute, and specify the detailed design of the system, which is embodied with distributed protocols and performance evaluation. The second topic investigates on the MAC throughput performance of the vehicle-to- infrastructure (V2I) communications when vehicles drive through RSUs, namely drive-thru Internet. Note that with a large-scale population of fast-motion nodes contending the chan- nel for transmissions, the MAC performance determines the achievable nodal throughput and is crucial to the on-top applications. In this topic, using a simple yet accurate Marko- vian model, we first show the impacts of mobility (characterized by node velocity and moving directions) on the nodal and system throughput performance, respectively. Based on this analysis, we then propose three enhancement schemes to timely adjust the MAC parameters in tune with the vehicle mobility to achieve the maximal the system throughput. The last topic investigates on the end-system design to deliver the user desired media streaming services in the vehicular environment. In specific, the vehicular communications are notoriously known for the intermittent connectivity and dramatically varying throughput. Video streaming on top of vehicular networks therefore inevitably suffers from the severe network dynamics, resulting in the frequent jerkiness or even freezing video playback. To address this issue, an analytical model is first developed to unveil the impacts of network dynamics on the resultant video performance to users in terms of video start-up delay and smoothness of playback. Based on the analysis, the adaptive playout buffer mechanism is developed to adapt the video playback strategy at receivers towards the user-defined video quality. The proposals developed in the three topics are validated with the extensive and high fidelity simulations. We believe that our analysis developed in the dissertation can provide insightful lights on understanding the fundamental performance of the vehicular content distribution networks from the aspects of session-level download performance in urban vehicular networks (topic 1), MAC throughput performance (topic 2), and user perceived media quality (topic 3). The protocols developed in the three topics, respectively, offer practical and efficient solutions to build and optimize the vehicular content distribution networks