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

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In a non-ideal PLL circuit, leakage of the reference signal into the control line produces spurious tones. When the distorted PLL signal is used as a clock signal, it creates spurious tones in the sampled data. Our prior work used a training signal to estimate the distortions and then correct the samples. In this work, we propose an alternative approach that estimates and removes the distortions directly from the sampled data without a training signal. Simulations indicate that the proposed solution is able to reduce the root-mean-square (RMS) sampling errors to about 15% of the original values.

Frequency domain compensation of spurious sidebands in A/D circuits

In a non-ideal PLL circuit, leakage of the reference signal into the control line produces spurious tones. When the distorted PLL signal is used in an analog-to-digital converter (ADC), it creates spurious tones in the sampled data as well. In spectrum sensing applications, the presence of spurious tones can lead to false detection of signals in otherwise empty channels. In a typical spectrum sensing application, there usually exists a Fourier transform block. We propose an algorithm to use this block to estimate the jitter errors from the spurious sidebands and to compensate the distorted samples in the digital domain.

Reducing spurious PLL tones in spectrum sensing architectures

A robust algorithm is developed for jointly controlling the power and rate of flow in a distributed wireless network. The dynamics of the network is modelled as a discrete-time state-delayed system with uncertainties and the proposed algorithm achieves better SIR performance than a conventional power control scheme. keywords: Robust estimation, congestion control, power control, rate control, wireless network, convex optimization.

Ali H. Sayed

Papers

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Frequency domain compensation of spurious sidebands in A/D circuits

Reducing spurious PLL tones in spectrum sensing architectures

A power and rate control algorithm for wireless networks with state-delayed dynamics

Fast stable solvers for structured linear systems