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.

Thank you very much for downloading table of integrals series and products. Maybe you have knowledge that, people have look hundreds times for their chosen books like this table of integrals series and products, but end up in harmful downloads. Rather than reading a good book with a cup of coffee in the afternoon, instead they cope with some harmful virus inside their laptop. table of integrals series and products is available in our book collection an online access to it is set as public so you can get it instantly. Our book servers saves in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Merely said, the table of integrals series and products is universally compatible with any devices to read.

Table Of Integrals Series And Products

The utilization of online stochastic algorithms is popular in large-scale learning settings due to their ability to compute updates on the fly, without the need to store and process data in large batches. When a constant step-size is used, these algorithms also have the ability to adapt to drifts in problem parameters, such as data or model properties, and track the optimal solution with reasonable accuracy. Building on analogies with the study of adaptive filters, we establish a link between steady-state performance derived under stationarity assumptions and the tracking performance of online learners under random walk models. The link allows us to infer the tracking performance from steady-state expressions directly and almost by inspection.

Tracking Performance of Online Stochastic Learners

This paper first investigates a companded differential pulse-coded modulator and. derives an expression for its SNR performance. Analysis and simulations show that, the coder has superior SNR and dynamic range performance over other coders of similar complexity. The companded modulator is then extended to an adaptive differential pulse-coded modulator with high SNR and dynamic range performance, and it is shown to be BIBO stable.

Adaptive differential pulse-coded modulation with exponential tracking

Collective motion is a remarkable phenomenon in biological systems. There have been several models in the literature to regenerate this type of motion, such as averaging consensus strategies where nodes continuously average the velocity vectors of their neighbors. While many models are able to generate forms of collective motion, they nevertheless neglect the important fact that the most informed nodes in a network tend to modulate their information into their speeds. In this work, we show how the speed information can be exploited and incorporated into the design of the combination rules for mobile networks. The analysis leads to a sigmoidal function construction, and the results show that the proposed combination rule leads to more effective information flow over networks of mobile agents.

Effective information flow over mobile adaptive networks

This paper analyzes the implementation of least-mean-squares (LMS)-based, adaptive diffusion algorithms over networks in the frequency-domain (FD). We focus on a scenario of noisy links and include a moving-average step for denoising after self-learning to enhance performance. The mean-square-error convergence behavior of the resulting algorithm is investigated and the theoretical results are illustrated through simulations. In particular, the proposed denoised recursions are shown to perform favorably when compared with partial diffusion LMS (PD-LMS) and diffusion LMS algorithms, in terms of both complexity and performance.

Ali H. Sayed

Papers

Tracking Performance of Online Stochastic Learners

Adaptive differential pulse-coded modulation with exponential tracking

Effective information flow over mobile adaptive networks

Frequency-Domain Diffusion Adaptation Over Networks

Least‐Squares Criterion