102,507 research outputs found

    A Geometric Theorem for Network Design

    Get PDF
    Consider an infinite square grid G. How many discs of given radius r, centered at the vertices of G, are required, in the worst case, to completely cover an arbitrary disc of radius r placed on the plane? We show that this number is an integer in the set {3,4,5,6} whose value depends on the ratio of r to the grid spacing. One application of this result is to design facility location algorithms with constant approximation factors. Another application is to determine if a grid network design, where facilities are placed on a regular grid in a way that each potential customer is within a reasonably small radius around the facility, is cost effective in comparison to a nongrid design. This can be relevant to determine a cost effective design for base station placement in a wireless network

    A Model of an Oscillatory Neural Network with Multilevel Neurons for Pattern Recognition and Computing

    Full text link
    The current study uses a novel method of multilevel neurons and high order synchronization effects described by a family of special metrics, for pattern recognition in an oscillatory neural network (ONN). The output oscillator (neuron) of the network has multilevel variations in its synchronization value with the reference oscillator, and allows classification of an input pattern into a set of classes. The ONN model is implemented on thermally-coupled vanadium dioxide oscillators. The ONN is trained by the simulated annealing algorithm for selection of the network parameters. The results demonstrate that ONN is capable of classifying 512 visual patterns (as a cell array 3 * 3, distributed by symmetry into 102 classes) into a set of classes with a maximum number of elements up to fourteen. The classification capability of the network depends on the interior noise level and synchronization effectiveness parameter. The model allows for designing multilevel output cascades of neural networks with high net data throughput. The presented method can be applied in ONNs with various coupling mechanisms and oscillator topology.Comment: 26 pages, 24 figure

    Isomorphism Checking for Symmetry Reduction

    Get PDF
    In this paper, we show how isomorphism checking can be used as an effective technique for symmetry reduction. Reduced state spaces are equivalent to the original ones under a strong notion of bisimilarity which preserves the multiplicity of outgoing transitions, and therefore also preserves stochastic temporal logics. We have implemented this in a setting where states are arbitrary graphs. Since no efficiently computable canonical representation is known for arbitrary graphs modulo isomorphism, we define an isomorphism-predicting hash function on the basis of an existing partition refinement algorithm. As an example, we report a factorial state space reduction on a model of an ad-hoc network connectivity protocol

    Forcing neurocontrollers to exploit sensory symmetry through hard-wired modularity in the game of Cellz

    Get PDF
    Several attempts have been made in the past to construct encoding schemes that allow modularity to emerge in evolving systems, but success is limited. We believe that in order to create successful and scalable encodings for emerging modularity, we first need to explore the benefits of different types of modularity by hard-wiring these into evolvable systems. In this paper we explore different ways of exploiting sensory symmetry inherent in the agent in the simple game Cellz by evolving symmetrically identical modules. It is concluded that significant increases in both speed of evolution and final fitness can be achieved relative to monolithic controllers. Furthermore, we show that a simple function approximation task that exhibits sensory symmetry can be used as a quick approximate measure of the utility of an encoding scheme for the more complex game-playing task
    corecore