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

Structured matrices and unconstrained rational interpolation problems

Biological systems are often treated as time-invariant by computational models that use fixed parameter values In this study, we demonstrate that the behavior of the p53-MDM2 gene network in individual cells can be tracked using adaptive filtering algorithms and the resulting time-variant models can approximate experimental measurements more accurately than time-invariant models Adaptive models with time-variant parameters can help reduce modeling complexity and can more realistically represent biological systems

/pdf/adaptive-models-for-gene-networks-2wgp0x0u3y.pdf

Adaptive models for gene networks.

This paper studies the operation of multi-agent networks engaged in multi-task decision problems under the paradigm of simultaneous learning and adaptation. Two scenarios are considered:one in which a decision must be taken among multiple states of nature that are known but can vary over time and space, and another in which there exists a known “normal” state of nature and the task is to detect unpredictable and unknown deviations from it. In both cases the network learns from the past and adapts to changes in real time in a multi-task scenario with different clusters of agents addressing different decision problems. The system design takes care of challenging situations with clusters of complicated structure, and the performance assessment is conducted by computer simulations. A theoretical analysis is developed to obtain a statistical characterization of the agents’ status at steady-state, under the simplifying assumption that clustering is made without errors. This provides approximate bounds for the steady-state decision performance of the agents. Insights are provided for deriving accurate performance prediction by exploiting the derived theoretical results.

Decision Learning and Adaptation Over Multi-Task Networks

CORDIC-Based MMSE-DFE Coefficient Computation

The steady-state performance of adaptive filters can vary significantly when they are implemented in finite precision arithmetic, which makes it vital to analyse their performance in a quantized environment. Such analyses can become difficult for adaptive algorithms with non-linear update equations. This paper develops a feedback and energy-conservation approach to the steady-state analysis of quantized adaptive algorithms that bypasses some of the difficulties encountered by traditional approaches. Copyright © 2003 John Wiley & Sons, Ltd.

Ali H. Sayed

Papers

Structured matrices and unconstrained rational interpolation problems

Adaptive models for gene networks.

Decision Learning and Adaptation Over Multi-Task Networks

CORDIC-Based MMSE-DFE Coefficient Computation

Fixed‐point steady‐state analysis of adaptive filters