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

Under appropriate cooperation protocols and parameter choices, fully decentralized solutions for stochastic optimization have been shown to match the performance of centralized solutions and result in linear speedup (in the number of agents) relative to non-cooperative approaches in the strongly-convex setting. More recently, these results have been extended to the pursuit of first-order stationary points in non-convex environments. In this work, we examine in detail the dependence of second-order convergence guarantees on the spectral properties of the combination policy for non-convex multi agent optimization. We establish linear speedup in saddle-point escape time in the number of agents for symmetric combination policies and study the potential for further improvement by employing asymmetric combination weights. The results imply that a linear speedup can be expected in the pursuit of second-order stationary points, which exclude local maxima as well as strict saddle-points and correspond to local or even global minima in many important learning settings.

Linear Speedup in Saddle-Point Escape for Decentralized Non-Convex Optimization

In this paper we study the problem of social learning under multiple true hypotheses and self-interested agents. In this setup, each agent receives data that might be generated from a different hypothesis (or state) than the data other agents receive. In contrast to the related literature on social learning, which focuses on showing that the network achieves consensus, here we study the case where every agent is self-interested and wants to find the hypothesis that generates its own observations. To this end, we propose a scheme with adaptive combination weights and study the consistency of the agents' learning process. We analyze the asymptotic behavior of agents' beliefs under the proposed social learning algorithm and provide sufficient conditions that enable all agents to correctly identify their true hypotheses. The theoretical analysis is corroborated by numerical simulations.

Social Learning with Disparate Hypotheses

It is my distinct joy and privilege to present our second 2022 issue of Ergonomics in Design, which proves exemplary in terms of its content quality. In particular, I’d like to bring to your attention the fact that, for each of the three investigations presented in this issue, human factors design principles were exceptionally applied at every stage of their work. Use errors, previously known as human error or user error in the human factors literature, emphasize minimizing the user’s blame while using a medical device. In the first manuscript, Smith and Gray present a smart infusion pump design that incorporates usability engineering principles and potential use error safety mitigation strategies. The innovative pump design incorporates guidelines from the Association for the Advancement of Medical Instrumentation and the International Electrotechnical Commission to reduce the risk of inadvertently harming the patient during infusion therapy. After testing the infusion pump for usability among both näıve and trained licensed health care professionals, the authors completed a use-related risk analysis on both software and hardware user interfaces. This analysis involved identifying hazards and harms, use scenario testing, task analysis, and potential use errors. The authors also explored and implemented risk control strategies. The final step of human factors validation testing demonstrated that the smart pump could be used safely without adverse use errors for infusion therapy under the expected use conditions. It is no surprise that this manuscript took first place in the Human Factors and Ergonomics Society 2019 Stanley Caplan User-Centered Design Competition. The utility of exoskeletons across various industries is well documented in the current ergonomics literature. However, these wearable devices’ user experience and usability in the healthcare industry are not extensively studied. The second manuscript examines Finnish nurses’ experience with exoskeletons during geriatric care. The authors, Turja et al. conducted two studies. One study involved a controlled environment in which two nurses transferred a geriatric patient from a hospital bed into a wheelchair under three experimental conditions: no nurses wearing exoskeletons; one nurse wearing an exoskeleton; and both nurses wearing an exoskeleton. Another study was conducted in a home care environment where two nurses wore the exoskeleton while transferring a patient in and out of a wheelchair and while assisting the patient during eating and toileting. For analyzing the user experience, the authors employed the unified theory of the acceptance and use of technology model and collected data on: perceived usefulness, ease of use, trust toward the device, user satisfaction, and anxiety about exoskeleton use. The study showed the significance of addressing technology acceptance by the end-user (e.g., comfort, fit, and ease of donning and doffing). Interestingly, the authors also reported on the importance of evaluating trust between caregivers and patients while working with exoskeleton technology. The third manuscript reveals the importance of developing locally and culturally relevant pictograms for easy understanding in low-resources settings. Kisaalita and Sempiira conducted their research in Uganda, where farmer illiteracy can be a considerable communications hurdle. They established a five-step pictogram development process in which local artists drew the intended messages to be conveyed, tested them with a sample of target farmers, reengaged a subset to fine-tune the right pictograms, and then retested the revised pictograms with a new subgroup of cohorts. From ideation to iteration to execution, the processes presented in this manuscript are simple, thoughtful, and powerful. It was also most impressive that the authors incorporated best practice guidelines from the International Standards and the American National Standards Institute. While clearly diverse in topic and scope, all three manuscripts in this issue of EID provide excellent examples of how human factors principles should be embedded in every step of a product design. For that, I commend the authors, Smith and Gray, Turja et al., Kisaalita and Sempiira, and all who contributed to these exemplary studies.

https://journals.sagepub.com/doi/pdf/10.1177/10648046221085697

Message from the Editor-in-Chief

The paper develops a dynamic antenna scheduling strategy for downlink MIMO communications, where the transmitted signal for each user is beamformed towards a selected subset of receive antennas at this user. The proposed method removes the condition on the number of transmit-receive antennas in comparison to traditional zero-forcing and time-scheduling strategies. By characterizing the probability distribution of the so-called signal-to-leakage-plus-noise (SLNR) ratio, we show that there is an optimal set of receive antennas that maximizes the system performance for each channel realization. This fact is used to propose an antenna scheduling scheme that leads to improvements in terms of SINR outage probabilities.

A dynamic antenna scheduling strategy for multi-user MIMO communications

Studies the relation between the solutions of two minimization problems with indefinite quadratic forms. The authors show that a complete link between both solutions can be established by invoking a fundamental set of inertia conditions. While these inertia conditions are automatically satisfied in a standard Hilbert space setting, they nevertheless turn out to mark the differences between the two optimization problems in indefinite metric spaces. They also include, as special cases, the well-known conditions for the existence of H/sup /spl infin//-filters and controllers.

Ali H. Sayed

Papers

Linear Speedup in Saddle-Point Escape for Decentralized Non-Convex Optimization

Social Learning with Disparate Hypotheses

Message from the Editor-in-Chief

A dynamic antenna scheduling strategy for multi-user MIMO communications

Fundamental inertia conditions for the solution of H/sup /spl infin//-problems