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

An adaptive multi-bit delta and sigma-delta modulation and demodulation technique, wherein a one-bit modulator generates a binary output signal from an analog input signal and a multi-bit adapter for generating a scaling signal for scaling a step-size of the sigma-delta modulator.

Adaptive multi-bit delta and sigma-delta modulation

Decentralized Decision-Making Over Multi-Task Networks

The objective of this interdisciplinary special issue is to highlight the important role of digital signal processing techniques in understanding and mitigating RF/analog circuit impairments. The issue presents 15 papers .

Introduction to the Issue on DSP Techiques for RF/Analog Circuit Impairments

The Kalman filter is the optimal linear least-mean-squares estimator for systems that are described by linear state-space Markovian models [1]. However, when the model is not accurately known, the performance of the filter can deteriorate appreciably. There have been many approaches to robust filtering in the literature (see, e.g., [2]). In [3, 4], frameworks for robust filter designs were discussed that perform regularization as opposed to deregularization. In this paper, we pursue the design of such regularized robust filters for state-delayed systems. We also allow for stochastic uncertainties in the state matrices and deterministic uncertainties for the output matrices and design a robust filter that bounds the state error covariance matrix. Thus consider an n−dimensional state-space model of the form

Ali H. Sayed

Papers

Adaptive multi-bit delta and sigma-delta modulation

Decentralized Decision-Making Over Multi-Task Networks

Introduction to the Issue on DSP Techiques for RF/Analog Circuit Impairments

Regularized Robust Filtering for Discrete Time Uncertain Time-Delayed Stochastic Systems

Guest Editorial Inference and Learning over Networks