91,746 research outputs found

    Local properties on the remainders of the topological groups

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    When does a topological group GG have a Hausdorff compactification bGbG with a remainder belonging to a given class of spaces? In this paper, we mainly improve some results of A.V. Arhangel'ski\v{\i} and C. Liu's. Let GG be a non-locally compact topological group and bGbG be a compactification of GG. The following facts are established: (1) If bG∖GbG\setminus G has a locally a point-countable pp-metabase and π\pi-character of bG∖GbG\setminus G is countable, then GG and bGbG are separable and metrizable; (2) If bG∖GbG\setminus G has locally a δθ\delta\theta-base, then GG and bGbG are separable and metrizable; (3) If bG∖GbG\setminus G has locally a quasi-GδG_{\delta}-diagonal, then GG and bGbG are separable and metrizable. Finally, we give a partial answer for a question, which was posed by C. Liu in \cite{LC}.Comment: 10pages (replace

    Deep SimNets

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    We present a deep layered architecture that generalizes convolutional neural networks (ConvNets). The architecture, called SimNets, is driven by two operators: (i) a similarity function that generalizes inner-product, and (ii) a log-mean-exp function called MEX that generalizes maximum and average. The two operators applied in succession give rise to a standard neuron but in "feature space". The feature spaces realized by SimNets depend on the choice of the similarity operator. The simplest setting, which corresponds to a convolution, realizes the feature space of the Exponential kernel, while other settings realize feature spaces of more powerful kernels (Generalized Gaussian, which includes as special cases RBF and Laplacian), or even dynamically learned feature spaces (Generalized Multiple Kernel Learning). As a result, the SimNet contains a higher abstraction level compared to a traditional ConvNet. We argue that enhanced expressiveness is important when the networks are small due to run-time constraints (such as those imposed by mobile applications). Empirical evaluation validates the superior expressiveness of SimNets, showing a significant gain in accuracy over ConvNets when computational resources at run-time are limited. We also show that in large-scale settings, where computational complexity is less of a concern, the additional capacity of SimNets can be controlled with proper regularization, yielding accuracies comparable to state of the art ConvNets

    Satisfaction Equilibrium: A General Framework for QoS Provisioning in Self-Configuring Networks

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    This paper is concerned with the concept of equilibrium and quality of service (QoS) provisioning in self-configuring wireless networks with non-cooperative radio devices (RD). In contrast with the Nash equilibrium (NE), where RDs are interested in selfishly maximizing its QoS, we present a concept of equilibrium, named satisfaction equilibrium (SE), where RDs are interested only in guaranteing a minimum QoS. We provide the conditions for the existence and the uniqueness of the SE. Later, in order to provide an equilibrium selection framework for the SE, we introduce the concept of effort or cost of satisfaction, for instance, in terms of transmit power levels, constellation sizes, etc. Using the idea of effort, the set of efficient SE (ESE) is defined. At the ESE, transmitters satisfy their minimum QoS incurring in the lowest effort. We prove that contrary to the (generalized) NE, at least one ESE always exists whenever the network is able to simultaneously support the individual QoS requests. Finally, we provide a fully decentralized algorithm to allow self-configuring networks to converge to one of the SE relying only on local information.Comment: Accepted for publication in Globecom 201
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