The Anisotropic Convexity of Domains and the Boundary Estimate for Two Monge-Amp\`ere Equations

We study the exact effect of the anisotropic convexity of domains on the boundary estimate for two Monge-Amp\`ere Equations: one is singular which is from the proper affine hyperspheres with constant mean curvature; the other is degenerate which is from the Monge-Amp\`ere eigenvalue problem. As a result, we obtain the sharp boundary boundary estimates and the optimal global H\"older regularity for the two equations

Three-phase optimal power flow for networked microgrids based on semidefinite programming convex relaxation

Many autonomous microgrids have extensive penetration of distributed generation (DG). Optimal power flow (OPF) is necessary for the optimal dispatch of networked microgrids (NMGs). Existing convex relaxation methods for three-phase OPF are limited to radial networks. In light of this, we develop a semidefinite programming (SDP) convex relaxation model which can cope with meshed networks and also includes a model of three-phase DG and under-load voltage regulators with different connection types. The SDP model solves the OPF problem of multi-phase meshed network effectively, with satisfactory accuracy, as validated by real 6-bus, 9-bus, and 30-bus NMGs, and the IEEE 123-bus test cases. In the SDP model, the convex symmetric component of the three-phase DG model is demonstrated to be more accurate than a three-phase DG modelled as three single-phase DG units in three-phase unbalanced OPF. The proposed method also has higher accuracy than the existing convex relaxation methods. The resultant optimal control variables obtained from the convex relaxation optimization can be used for both final optimal dispatch strategy and initial value of the non-convex OPF to obtain the globally optimal solution efficiently

Gene expression analysis of induced pluripotent stem cells from aneuploid chromosomal syndromes

BACKGROUND: Human aneuploidy is the leading cause of early pregnancy loss, mental retardation, and multiple congenital anomalies. Due to the high mortality associated with aneuploidy, the pathophysiological mechanisms of aneuploidy syndrome remain largely unknown. Previous studies focused mostly on whether dosage compensation occurs, and the next generation transcriptomics sequencing technology RNA-seq is expected to eventually uncover the mechanisms of gene expression regulation and the related pathological phenotypes in human aneuploidy. RESULTS: Using next generation transcriptomics sequencing technology RNA-seq, we profiled the transcriptomes of four human aneuploid induced pluripotent stem cell (iPSC) lines generated from monosomy × (Turner syndrome), trisomy 8 (Warkany syndrome 2), trisomy 13 (Patau syndrome), and partial trisomy 11:22 (Emanuel syndrome) as well as two umbilical cord matrix iPSC lines as euploid controls to examine how phenotypic abnormalities develop with aberrant karyotype. A total of 466 M (50-bp) reads were obtained from the six iPSC lines, and over 13,000 mRNAs were identified by gene annotation. Global analysis of gene expression profiles and functional analysis of differentially expressed (DE) genes were implemented. Over 5000 DE genes are determined between aneuploidy and euploid iPSCs respectively while 9 KEGG pathways are overlapped enriched in four aneuploidy samples. CONCLUSIONS: Our results demonstrate that the extra or missing chromosome has extensive effects on the whole transcriptome. Functional analysis of differentially expressed genes reveals that the genes most affected in aneuploid individuals are related to central nervous system development and tumorigenesis

Non-Destructive Techniques Based on Eddy Current Testing

Non-destructive techniques are used widely in the metal industry in order to control the quality of materials. Eddy current testing is one of the most extensively used non-destructive techniques for inspecting electrically conductive materials at very high speeds that does not require any contact between the test piece and the sensor. This paper includes an overview of the fundamentals and main variables of eddy current testing. It also describes the state-of-the-art sensors and modern techniques such as multi-frequency and pulsed systems. Recent advances in complex models towards solving crack-sensor interaction, developments in instrumentation due to advances in electronic devices, and the evolution of data processing suggest that eddy current testing systems will be increasingly used in the future