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

2. Linear Estimation in Krein Spaces

A new amortized variance-reduced gradient (AVRG) algorithm was developed in \cite{ying2017convergence}, which has constant storage requirement in comparison to SAGA and balanced gradient computations in comparison to SVRG. One key advantage of the AVRG strategy is its amenability to decentralized implementations. In this work, we show how AVRG can be extended to the network case where multiple learning agents are assumed to be connected by a graph topology. In this scenario, each agent observes data that is spatially distributed and all agents are only allowed to communicate with direct neighbors. Moreover, the amount of data observed by the individual agents may differ drastically. For such situations, the balanced gradient computation property of AVRG becomes a real advantage in reducing idle time caused by unbalanced local data storage requirements, which is characteristic of other reduced-variance gradient algorithms. The resulting diffusion-AVRG algorithm is shown to have linear convergence to the exact solution, and is much more memory efficient than other alternative algorithms. In addition, we propose a mini-batch strategy to balance the communication and computation efficiency for diffusion-AVRG. When a proper batch size is employed, it is observed in simulations that diffusion-AVRG is more computationally efficient than exact diffusion or EXTRA while maintaining almost the same communication efficiency.

Variance-Reduced Stochastic Learning by Networked Agents under Random Reshuffling

The emergence of wireless sensor networks has imposed many challenges on network design such as severe energy constraints, limited bandwidth and computing capabilities. This kind of networks necessitates network protocol architectures that are robust, energy-efficient, scalable, and easy for deployment. This paper proposes a robust energy-aware clustering architecture (REACA) for large-scale wireless sensor networks. We analyze the performance of the REACA network in terms of quality-of-service, asymptotic throughput capacity, and power consumption. In particular, we study how the throughput capacity scales with the number of nodes and the number of clusters. We show that by exploiting traffic locality, clustering can achieve performance improvement both in capacity and in power consumption over general-purpose ad hoc networks. We also explore the fundamental trade-off between throughput capacity and power consumption for single-hop and multi-hop routing schemes in cluster-based networks. The protocol architecture and performance analysis developed in this paper provide useful insights for practical design and deployment of large-scale wireless sensor network.

/pdf/reaca-an-efficient-protocol-architecture-for-large-scale-4xigsk8mrt.pdf

REACA: An Efficient Protocol Architecture for Large Scale Sensor Networks

Among the challenging issues that affect the performance of wireless location techniques is the temporal and spatial variations of the channel, and the distribution of the scatterers, which introduce non-line-of sight errors at the base station. This paper develops a technique for addressing this problem by exploiting the topology of the cellular network.

A non-line-of-sight equalization scheme for wireless cellular location

This chapter contains sections titled: Introduction Motivation Incremental Adaptive Solutions Diffusion Adaptive Solutions Concluding Remarks Acknowledgments References

Ali H. Sayed

Papers

2. Linear Estimation in Krein Spaces

Variance-Reduced Stochastic Learning by Networked Agents under Random Reshuffling

REACA: An Efficient Protocol Architecture for Large Scale Sensor Networks

A non-line-of-sight equalization scheme for wireless cellular location

Distributed Adaptive Learning Mechanisms