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

This paper proposes a globally distributed synchronization algorithm for wireless sensor networks. In the proposed scheme, there is a master node that controls the network synchronization and the other sensors periodically broadcast synchronization pulses; they also monitor different frequency channels in an effort to overcome the effect of channel fading.

A distributed broadcasting time-synchronization scheme for wireless sensor networks

In this paper we investigate the self-organization and cognitive abilities of adaptive networks when the individual agents are allowed to move in pursuit of an objective. The network as a whole acts as an adaptive entity with localized processing and is able to respond to stimuli in real-time. We apply the ensuing model to the foraging behavior of fish schools in search of food sources and reproduce their ability to move in remarkable coherence.

Mobile adaptive networks with self-organization abilities

In distributed inference, local cooperation among network nodes can be exploited to enhance the performance of each individual agent, but a challenging requirement for networks operating in dynamic real-world environments is that of adaptation. The interplay between these two fundamental aspects of cooperation and adaptation has been investigated in recent years in the context of estimation problems. Less explored in the literature is the case of detection, which is our focus. Capitalizing on the powerful tool of large deviations analysis, we show how to design and characterize the performance of diffusion strategies that reconcile both needs of adaptation and detection in decentralized systems.

Large deviations analysis of adaptive distributed detection

We propose a distributed least-mean squares (LMS) procedure based on a diffusion strategy for localization and tracking of mobile terminals in cellular networks. In the proposed algorithm, collaborating base stations measure two sets of parameters, namely, the received signal strength (RSS) and the signal propagation time (SPT) to estimate mobile locations. The proposed algorithm has a simple operational structure, offers agile tracking performance and helps the network to save energy and radio resources by benefiting from its decentralized and adaptive signal processing features.

Diffusion LMS localization and tracking algorithm for wireless cellular networks

In this paper, half- and full-duplex relay processing matrices and source-destination beamforming vectors are jointly optimized based on a minimum mean-square-error (MMSE) formulation under inequality constraints on the transmit power of the source and the relays. Through BER simulations, we illustrate that the full-duplex method performs better than the half-duplex method in various signalto-noise ratio (SNR) scenarios, and it can be a promising candidate for future relay networks.

Ali H. Sayed

Papers

A distributed broadcasting time-synchronization scheme for wireless sensor networks

Mobile adaptive networks with self-organization abilities

Large deviations analysis of adaptive distributed detection

Diffusion LMS localization and tracking algorithm for wireless cellular networks

Design of half- and full-duplex relay systems based on the MMSE formulation