Minimizing Rational Functions by Exact Jacobian SDP Relaxation Applicable to Finite Singularities

This paper considers the optimization problem of minimizing a rational function. We reformulate this problem as polynomial optimization by the technique of homogenization. These two problems are shown to be equivalent under some generic conditions. The exact Jacobian SDP relaxation method proposed by Nie is used to solve the resulting polynomial optimization. We also prove that the assumption of nonsingularity in Nie's method can be weakened as the finiteness of singularities. Some numerical examples are given to illustrate the efficiency of our method.Comment: 23 page

A Deterministic Equivalent for the Analysis of Non-Gaussian Correlated MIMO Multiple Access Channels

Large dimensional random matrix theory (RMT) has provided an efficient analytical tool to understand multiple-input multiple-output (MIMO) channels and to aid the design of MIMO wireless communication systems. However, previous studies based on large dimensional RMT rely on the assumption that the transmit correlation matrix is diagonal or the propagation channel matrix is Gaussian. There is an increasing interest in the channels where the transmit correlation matrices are generally nonnegative definite and the channel entries are non-Gaussian. This class of channel models appears in several applications in MIMO multiple access systems, such as small cell networks (SCNs). To address these problems, we use the generalized Lindeberg principle to show that the Stieltjes transforms of this class of random matrices with Gaussian or non-Gaussian independent entries coincide in the large dimensional regime. This result permits to derive the deterministic equivalents (e.g., the Stieltjes transform and the ergodic mutual information) for non-Gaussian MIMO channels from the known results developed for Gaussian MIMO channels, and is of great importance in characterizing the spectral efficiency of SCNs.Comment: This paper is the revision of the original manuscript titled "A Deterministic Equivalent for the Analysis of Small Cell Networks". We have revised the original manuscript and reworked on the organization to improve the presentation as well as readabilit

FEDRR: Fast, Exhaustive Detection of Redundant Hierarchical Relations for Quality Improvement of Large Biomedical Ontologies

Background: Redundant hierarchical relations refer to such patterns as two paths from one concept to another, one with length one (direct) and the other with length greater than one (indirect). Each redundant relation represents a possibly unintended defect that needs to be corrected in the ontology quality assurance process. Detecting and eliminating redundant relations would help improve the results of all methods relying on the relevant ontological systems as knowledge source, such as the computation of semantic distance between concepts and for ontology matching and alignment. Results: This paper introduces a novel and scalable approach, called FEDRR – Fast, Exhaustive Detection of Redundant Relations – for quality assurance work during ontological evolution. FEDRR combines the algorithm ideas of Dynamic Programming with Topological Sort, for exhaustive mining of all redundant hierarchical relations in ontological hierarchies, in O(c·|V|+|E|) time, where |V| is the number of concepts, |E| is the number of the relations, and c is a constant in practice. Using FEDRR, we performed exhaustive search of all redundant is-a relations in two of the largest ontological systems in biomedicine: SNOMED CT and Gene Ontology (GO). 372 and 1609 redundant is-a relations were found in the 2015-09-01 version of SNOMED CT and 2015-05-01 version of GO, respectively. We have also performed FEDRR on over 190 source vocabularies in the UMLS - a large integrated repository of biomedical ontologies, and identified six sources containing redundant is-a relations. Randomly generated ontologies have also been used to further validate the efficiency of FEDRR. Conclusions: FEDRR provides a generally applicable, effective tool for systematic detecting redundant relations in large ontological systems for quality improvement

Motion Predicting of Autonomous Tracked Vehicles with Online Slip Model Identification

Precise understanding of the mobility is essential for high performance autonomous tracked vehicles in challenging circumstances, though the complex track/terrain interaction is difficult to model. A slip model based on the instantaneous centers of rotation (ICRs) of treads is presented and identified to predict the motion of the vehicle in a short term. Unlike many research studies estimating current ICRs locations using velocity measurements for feedback controllers, we focus on predicting the forward trajectories by estimating ICRs locations using position measurements. ICRs locations are parameterized over both tracks rolling speeds and the kinematic parameters are estimated in real time using an extended Kalman filter (EKF) without requiring prior knowledge of terrain parameters. Simulation results verify that the proposed algorithm performs better than the traditional method when the pose measuring frequencies are low. Experiments are conducted on a tracked vehicle with a weight of 13.6 tons. Results demonstrate that the predicted position and heading errors are reduced by about 75% and the reduction of pose errors is over 24% in the absence of the real-time kinematic global positioning system (RTK GPS)

High Performance Metasurface Antennas

Recently, metasurfaces (MSs) have received tremendous attention because their electromagnetic properties can be controlled at will. Generally, metasurface with hyperbolic phase distributions, namely, focusing metasurface, can be used to design high-gain antennas. Besides, metasurface has the ability of controlling the polarization state of electromagnetic wave. In this chapter, we first propose a new ultrathin broadband reflected MS and take it into application for high-gain planar antenna. Then, we propose multilayer multifunctional transmitted MSs to simultaneously enhance the gain and transform the linear polarization to circular polarization of the patch antenna. This kind of high-gain antenna eliminates the feed-block effect of the reflected ones