32,689 research outputs found

    Generalized closed sets in ditopological texture spaces with application in rough set theory

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    In this paper, the counterparts of generalized open (g-open) and generalized closed (g-closed) sets for ditopological texture spaces are introduced and some of their characterizations are obtained. Some characterizations are presented for generalized bicontinuous difunctions. Also, we introduce new notions of compactness and stability in ditopological texture spaces based on the notion of g-open and g-closed sets. Finally, as an application of g-open and g-closed sets, we generalize the subsystem based denition of rough set theory by using new subsystem, called generalized open sets to dene new types of lower and upper approximation operators, called g-lower and g-upper approximations. These decrease the upper approximation and increase the lower approximation and hence increase the accuracy. Properties of these approximations are studied. An example of multi-valued information systems are given

    Unifying Practical Uncertainty Representations: II. Clouds

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    There exist many simple tools for jointly capturing variability and incomplete information by means of uncertainty representations. Among them are random sets, possibility distributions, probability intervals, and the more recent Ferson's p-boxes and Neumaier's clouds, both defined by pairs of possibility distributions. In the companion paper, we have extensively studied a generalized form of p-box and situated it with respect to other models . This paper focuses on the links between clouds and other representations. Generalized p-boxes are shown to be clouds with comonotonic distributions. In general, clouds cannot always be represented by random sets, in fact not even by 2-monotone (convex) capacities.Comment: 30 pages, 7 figures, Pre-print of journal paper to be published in International Journal of Approximate Reasoning (with expanded section concerning clouds and probability intervals

    Set-valued mapping and Rough Probability

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    In 1982, the theory of rough sets proposed by Pawlak and in 2013, Luay concerned a rough probability by using the notion of Topology. In this paper, we study the rough probability in the stochastic approximation spaces by using set-valued mapping and obtain results on rough expectation, and rough variance.Comment: 9 page

    Learning curves for Gaussian process regression: Approximations and bounds

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    We consider the problem of calculating learning curves (i.e., average generalization performance) of Gaussian processes used for regression. On the basis of a simple expression for the generalization error, in terms of the eigenvalue decomposition of the covariance function, we derive a number of approximation schemes. We identify where these become exact, and compare with existing bounds on learning curves; the new approximations, which can be used for any input space dimension, generally get substantially closer to the truth. We also study possible improvements to our approximations. Finally, we use a simple exactly solvable learning scenario to show that there are limits of principle on the quality of approximations and bounds expressible solely in terms of the eigenvalue spectrum of the covariance function.Comment: 25 pages, 10 figure

    Exploiting Spatial Interference Alignment and Opportunistic Scheduling in the Downlink of Interference Limited Systems

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    In this paper we analyze the performance of single stream and multi-stream spatial multiplexing (SM) systems employing opportunistic scheduling in the presence of interference. In the proposed downlink framework, every active user reports the post-processing signal-to-interference-plus-noise-power-ratio (post-SINR) or the receiver specific mutual information (MI) to its own transmitter using a feedback channel. The combination of scheduling and multi-antenna receiver processing leads to substantial interference suppression gain. Specifically, we show that opportunistic scheduling exploits spatial interference alignment (SIA) property inherent to a multi-user system for effective interference mitigation. We obtain bounds for the outage probability and the sum outage capacity for single stream and multi stream SM employing real or complex encoding for a symmetric interference channel model. The techniques considered in this paper are optimal in different operating regimes. We show that the sum outage capacity can be maximized by reducing the SM rate to a value less than the maximum allowed value. The optimum SM rate depends on the number of interferers and the number of available active users. In particular, we show that the generalized multi-user SM (MU SM) method employing real-valued encoding provides a performance that is either comparable, or significantly higher than that of MU SM employing complex encoding. A combination of analysis and simulation is used to describe the trade-off between the multiplexing rate and sum outage capacity for different antenna configurations
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