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.

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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

There are always discrepancies between design models and the actual physical systems or phenomena that they model. Regardless of their source, such perturbations can degrade the performance of otherwise optimal designs. This article discusses a design strategy for models with bounded perturbations. In comparison to other robust formulations, the resulting procedure performs data regularization as opposed to de-regularization. Applications in state-space estimation and adaptive filtering are discussed.

State-space estimation with uncertain models

Many optimization, inference and learning tasks can be accomplished efficiently by means of decentralized processing algorithms where the network topology (i.e., the graph) plays a critical role in enabling the interactions among neighboring nodes. There is a large body of literature examining the effect of the graph structure on the performance of decentralized processing strategies. In this article, we examine the inverse problem and consider the reverse question: How much information does observing the behavior at the nodes of a graph convey about the underlying topology? For large-scale networks, the difficulty in addressing such inverse problems is compounded by the fact that usually only a limited fraction of the nodes can be probed, giving rise to a second important question: Despite the presence of unobserved nodes, can partial observations still be sufficient to discover the graph linking the probed nodes? The article surveys recent advances on this challenging learning problem and related questions.

Graph Learning Under Partial Observability

The present invention provides a method for predicting channel power fading in a wireless communications system. This prediction method estimates the channel power fading via oversampling of the received and transmitted powers. The prediction method is then combined with several proposed structures for closed loop power control. The resulting structures result in improved performance in wireless communications systems.

Reducing power control errors in wireless communication system

In a previous study, we proposed an adaptive sigma delta modulator with an improved dynamic range. The modulator adapts the step size of the quantizer from estimates of the quantizer input instead of the modulator input. In this study, we conduct an error variance analysis of the new modulator and derive expression for the SNR. The derived expression shows that the SNR is independent of the input signal strength, which supports the simulation results.

Ali H. Sayed

Papers

State-space estimation with uncertain models

Graph Learning Under Partial Observability

Reducing power control errors in wireless communication system

SNR performance of an adaptive sigma delta modulator

3. State-Space Models in Krein Space