The Star of David Rule

In this note, a new concept called {\em $SDR$-matrix} is proposed, which is an infinite lower triangular matrix obeying the generalized rule of David star. Some basic properties of $SDR$-matrices are discussed and two conjectures on $SDR$-matrices are presented, one of which states that if a matrix is a $SDR$-matrix, then so is its matrix inverse (if exists).Comment: 7 pages, 1 figur

Montana Business Quarterly, Spring 1985

This is an academic publication produced by the Bureau of Business and Economic Research (BBER) at the University of Montana’s College of Business. This is volume 23, number 1.https://scholarworks.umt.edu/mtbusinessquarterly/1102/thumbnail.jp

Optimization of secure wireless communications for IoT networks in the presence of eavesdroppers

The problem motivates this paper is that securing the critical data of 5G based wireless IoT network is of significant importance. Wireless 5G IoT systems consist of a large number of devices (low-cost legitimate users), which are of low complexity and under strict energy constraints. Physical layer security (PLS) schemes, along with energy harvesting, have emerged as a potential candidate that provides an effective solution to address this issue. During the data collection process of IoT, PHY security techniques can exploit the characteristics of the wireless channel to ensure secure communication. This paper focuses on optimizing the secrecy rate for simultaneous wireless information and power transfer (SWIPT) IoT system, considering that the malicious eavesdroppers can intercept the data. In particular, the main aim is to optimize the secrecy rate of the system under signal to interference noise ratio (SINR), energy harvesting (EH), and total transmits power constraints. We model our design as an optimization problem that advocates the use of additional noise to ensure secure communication and guarantees efficient wireless energy transfer. The primary problem is non-convex due to complex objective functions in terms of transmit beamforming matrix and power splitting ratios. We have considered both the perfect channel state information (CSI) and the imperfect CSI scenarios. To circumvent the non-convexity of the primary problem in perfect CSI case, we proposed a solution based on the concave-convex procedure (CCCP) iterative algorithm, which results in a maximum local solution for the secrecy rate. In the imperfect CSI scenario, we facilitate the use of S-procedure and present a solution based on the iterative successive convex approximation (SCA) approach. Simulation results present the validations of the proposed algorithms. The results provide an insightful view that the proposed iterative method based on the CCCP algorithm achieves higher secrecy rates and lower computational complexity in comparison to the other algorithms

Scheduling Dimension Reduction of LPV Models -- A Deep Neural Network Approach

In this paper, the existing Scheduling Dimension Reduction (SDR) methods for Linear Parameter-Varying (LPV) models are reviewed and a Deep Neural Network (DNN) approach is developed that achieves higher model accuracy under scheduling dimension reduction. The proposed DNN method and existing SDR methods are compared on a two-link robotic manipulator, both in terms of model accuracy and performance of controllers synthesized with the reduced models. The methods compared include SDR for state-space models using Principal Component Analysis (PCA), Kernel PCA (KPCA) and Autoencoders (AE). On the robotic manipulator example, the DNN method achieves improved representation of the matrix variations of the original LPV model in terms of the Frobenius norm compared to the current methods. Moreover, when the resulting model is used to accommodate synthesis, improved closed-loop performance is obtained compared to the current methods.Comment: Accepted to American Control Conference (ACC) 2020, Denve