There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or $N$-way array. Decompositions of higher-order tensors (i.e., $N$-way arrays with $N \geq 3$) have applications in psycho-metrics, chemometrics, signal processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, and elsewhere. Two particular tensor decompositions can be considered to be higher-order extensions of the matrix singular value decomposition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum of rank-one tensors, and the Tucker decomposition is a higher-order form of principal component analysis. There are many other tensor decompositions, including INDSCAL, PARAFAC2, CANDELINC, DEDICOM, and PARATUCK2 as well as nonnegative variants of all of the above. The N-way Toolbox, Tensor Toolbox, and Multilinear Engine are examples of software packages for working with tensors.

/pdf/tensor-decompositions-and-applications-46vl2ih5gn.pdf

Tensor Decompositions and Applications

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Statistics for Spatial Data.

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Table Of Integrals Series And Products

Inspired by bacterial motility, we propose an algorithm for adaptation over networks with mobile nodes. The nodes have limited abilities and they are allowed to cooperate with their neighbors to optimize a common objective function. In contrast to traditional adaptation formulations, an important consideration in this work is the fact that the nodes do not know the form of the cost function beforehand. The nodes can only sense variations in the values of the objective function as they diffuse through the space, such as sensing the variation in the concentration of nutrients in the environment. We propose a technique for the nodes to pick the search vector as a linear combination of the neighbors' last steps, by attempting to maximize the nutritional gradient. The procedure enables information to flow from “information-rich” nodes to the other nodes.

Bio-inspired cooperative optimization with application to bacteria motility

An l 2 -stable feedback structure for nonlinear adaptive filtering and identification

This paper addresses the problem of adaptive channel tracking and equalization for multi-input multi-output (MIMO) time-variant frequency-selective channels. A finite-length minimum-mean-squared-error decision-feedback equalizer (MMSE-DFE) performs the equalization task, while a Kalman filter tracks the MIMO channel, which models the corrupting effects of inter-symbol interference (ISI), inter-user interference (IUI), and noise. The Kalman tracking is aided by previous hard decisions produced by the DFE, with a decision delay /spl Delta/>0, which causes the Kalman filter to track the channel with a delay. A channel prediction module bridges the time gap between the channel estimates produced by the Kalman filter and those needed for the DFE adaptation. The proposed algorithm offers good tracking behavior for multi-user fading ISI channels at the expense of higher complexity.

/pdf/adaptive-multi-input-multi-output-fading-channel-2156znxfnh.pdf

Adaptive multi-input multi-output fading channel equalization using Kalman estimation

We consider the problem of decentralized clustering and estimation over multitask networks, where agents infer and track different models of interest The agents do not know beforehand which model is generating their own data They also do not know which agents in their neighborhood belong to the same cluster We propose a decentralized clustering algorithm aimed at identifying and forming clusters of agents of similar objectives, and at guiding cooperation to enhance the inference performance One key feature of the proposed technique is the integration of the learning and clustering tasks into a single strategy We analyze the performance of the procedure and show that the error probabilities of types I and II decay exponentially to zero with the step-size parameter While links between agents following different objectives are ignored in the clustering process, we nevertheless show how to exploit these links to relay critical information across the network for enhanced performance Simulation results illustrate the performance of the proposed method in comparison to other useful techniques

Decentralized Clustering and Linking by Networked Agents

We propose and study an adaptive delta modulator that has improved SNR performance and robustness in tracking highly varying signals. The step-size adaptation used in this modulator is based on information about the absolute value of the quantizer input. The modulator is shown to be free of zero-input limit cycles and is BIBO stable.

Ali H. Sayed

Papers

Bio-inspired cooperative optimization with application to bacteria motility

An l 2 -stable feedback structure for nonlinear adaptive filtering and identification

Adaptive multi-input multi-output fading channel equalization using Kalman estimation

Decentralized Clustering and Linking by Networked Agents

A stable adaptive structure for delta modulation with improved performance