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

Adaptive channel estimation for space-time block coded MIMO-OFDM communications

The authors develop a self-contained theory for linear estimation in Krein spaces. The derivation is based on simple concepts such as projections and matrix factorizations and leads to an interesting connection between Krein space projection and the recursive computation of the stationary points of certain second-order (or quadratic) forms. The authors use the innovations process to obtain a general recursive linear estimation algorithm. When specialized to a state-space structure, the algorithm yields a Krein space generalization of the celebrated Kalman filter with applications in several areas such as Hw- filtering and control, game problems, risk sensitive control, and adaptive filtering.

Linear Estimation in ein Spaces- eory

Multipath propagation is one of the most difficult error sources to compensate in global navigation satellite systems due to its environment-specific nature. In order to gain a better understanding of its impact on the received signal, the establishment of a theoretical performance limit can be of great assistance. In this paper, we derive the Cramer Rao lower bounds (CRLBs), where in one case, the unknown parameter vector corresponds to any of the three multipath signal parameters of carrier phase, code delay, and amplitude, and in the second case, all possible combinations of joint parameter estimation are considered. Furthermore, we study how various channel parameters affect the computed CRLBs, and we use these bounds to compare the performance of three deconvolution methods: least squares, minimum mean square error, and projection onto convex space. In all our simulations, we employ CBOC modulation, which is the one selected for future Galileo E1 signals.

https://downloads.hindawi.com/archive/2011/356975.pdf

Performance of Deconvolution Methods in Estimating CBOC-Modulated Signals

Most available studies on distributed GAN architectures focus on implementations with a fusion center. In this work, we propose a fully decentralized scheme by employing a diffusion strategy to train a network of GANs. We interpret the training procedure as a team competition problem and use the paradigm of competing adaptive networks to solve it. We explain that the local discriminators and generators will cluster around their respective centroids. We present simulation results to illustrate that the proposed strategy allows local agents to match the performance of the centralized GAN. More importantly, we also illustrate that local GANs are able to generate different types of images from a dataset, even when they are locally trained with a subset that does not contain all image types.

Decentralized GAN Training Through Diffusion Learning

This work examines a stochastic formulation of the generalized Nash equilibrium problem (GNEP) where agents are subject to randomness in the environment of unknown statistical distribution. Three stochastic gradient strategies are developed by relying on a penalty-based approach where the constrained GNEP formulation is replaced by a penalized unconstrained formulation. It is shown that this penalty solution is able to approach the Nash equilibrium in a stable manner within O(p), for small step-size values p. The operation of the algorithms is illustrated by considering the Cournot competition problem.

Ali H. Sayed

Papers

Adaptive channel estimation for space-time block coded MIMO-OFDM communications

Linear Estimation in ein Spaces- eory

Performance of Deconvolution Methods in Estimating CBOC-Modulated Signals

Decentralized GAN Training Through Diffusion Learning

Adaptive learning for stochastic generalized Nash equilibrium problems