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High-order cumulant tensors carry information about statistics of non-normally distributed multivariate data. In this work we present a new efficient algorithm for calculation of cumulants of arbitrary orders in a sliding window for data streams. We show that this algorithm offers substantial speedups of cumulant updates compared with the current solutions. The proposed algorithm can be used for processing on-line high-frequency multivariate data and can find applications, e.g., in on-line signal filtering and classification of data streams. To present an application of this algorithm, we propose an estimator of non-Gaussianity of a data stream based on the norms of high order cumulant tensors. We show how to detect the transition from Gaussian distributed data to non-Gaussian ones in a data stream. In order to achieve high implementation efficiency of operations on super-symmetric tensors, such as cumulant tensors, we employ a block structure to store and calculate only one hyper-pyramid part of such tensors.
In recent years elastic optical networks have been perceived as a prospective choice for future optical networks due to better adjustment and utilization of optical resources than is the case with traditional wavelength division multiplexing networks. In the paper we investigate the elastic architecture as the communication network for distributed data centers. We address the problems of optimization of routing and spectrum assignment for large-scale computing systems based on an elastic optical architecture; particularly, we concentrate on anycast user to data center traffic optimization. We assume that computational resources of data centers are limited. For this offline problems we formulate the integer linear programming model and propose a few heuristics, including a meta-heuristic algorithm based on a tabu search method. We report computational results, presenting the quality of approximate solutions and efficiency of the proposed heuristics, and we also analyze and compare some data center allocation scenarios.
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