The shifted classical circulant and skew circulant splitting iterative methods for Toeplitz matrices

It is known that every Toeplitz matrix T enjoys a circulant and skew circulant splitting (denoted by CSCS), i.e., T=C-S with C a circulant matrix and S a skew circulant matrix. Based on the variant of such a splitting (also referred to as CSCS), we first develop classical CSCS iterative methods and then introduce shifted CSCS iterative methods for solving hermitian positive definite Toeplitz systems in this paper. The convergence of each method is analyzed. Numerical experiments show that the classical CSCS iterative methods work slightly better than the Gauss-Seidel (GS) iterative methods if the CSCS is convergent and that there is always a constant $\alpha$ such that the shifted CSCS iteration converges much faster than the Gauss-Seidel iteration, no matter whether the CSCS itself is convergent or not.National Natural Science Foundation of China No. 11371075The authors would like to thank the supports of the National Natural Science Foundation of China under Grant No. 11371075, the research innovation program of Hunan province for postgraduate students under Grant No. CX2015B374, the Portuguese Funds through FCT–Fundac˜ao para a Ciˆencia, within the Project UID/MAT/00013/2013.info:eu-repo/semantics/publishedVersio

Trigonometric transform splitting methods for real symmetric Toeplitz systems

In this paper, we study efficient iterative methods for real symmetric Toeplitz systems based on the trigonometric transformation splitting (TTS) of the real symmetric Toeplitz matrix A. Theoretical analyses show that if the generating function f of the n × n Toeplitz matrix A is a real positive even function, then the TTS iterative methods converge to the unique solution of the linear system of equations for sufficient large n. Moreover, we derive an upper bound of the contraction factor of the TTS iteration which is dependent solely on the spectra of the two TTS matrices involved. Different from the CSCS iterative method in Ng (2003) in which all operations counts concern complex operations when the DFTs are employed, even if the Toeplitz matrix A is real and symmetric, our method only involves real arithmetics when the DCTs and DSTs are used. The numerical experiments show that our method works better than CSCS iterative method and much better than the positive definite and skew-symmetric splitting (PSS) iterative method in Bai et al. (2005) and the symmetric Gauss–Seidel (SGS) iterative method.National Natural Science Foundation of China under Grant No. 11371075info:eu-repo/semantics/publishedVersio

Semiconducting transport in Pb10−x_{10-x}Cux_x(PO4_4)6_6O sintered from Pb2_2SO5_5 and Cu3_3P

The very recent claim on the discovery of ambient-pressure room-temperature superconductivity in modified lead-apatite has immediately excited sensational attention in the entire society, which is fabricated by sintering lanarkite (Pb2SO5) and copper(I) phosphide (Cu$_3$P). To verify this exciting claim, we have successfully synthesized Pb$_2$SO$_5$, Cu$_3$P, and finally the modified lead-apatite Pb$_{10-x}$Cu$_x$(PO$_4$)$_6$O. Detailed electrical transport and magnetic properties of these compounds were systematically analyzed. It turns out that Pb$_2$SO$_5$ is a highly insulating diamagnet with a room-temperature resistivity of ~7.18x10$^9$ Ohm.cm and Cu$_3$P is a paramagnetic metal with a room-temperature resistivity of ~5.22x10$^{-4}$ Ohm.cm. In contrast to the claimed superconductivity, the resulting Pb$_{10-x}$Cu$_x$(PO$_4$)$_6$O compound sintered from Pb$_2$SO$_5$ and Cu$_3$P exhibits semiconductor-like transport behavior with a large room-temperature resistivity of ~1.94x10$^4$ Ohm.cm although our compound shows greatly consistent x-ray diffraction spectrum with the previously reported structure data. In addition, when a pressed Pb$_{10-x}$Cu$_x$(PO$_4$)$_6$O pellet is located on top of a commercial Nd$_2$Fe$_{14}$B magnet at room temperature, no repulsion could be felt and no magnetic levitation was observed either. These results imply that the claim of a room-temperature superconductor in modified lead-apatite may need more careful re-examination, especially for the electrical transport properties.Comment: 12 pages, 13 figure

Endocrine disrupting chemical Bisphenol A and its association with cancer mortality: a prospective cohort study of NHANES

IntroductionThere is evidence suggesting that Bisphenol A (BPA) is associated with increased all-cause mortality in adults. However, the specific nature of the relationship between BPA exposure and cancer mortality remains relatively unexplored.MethodsThe National Health and Nutrition Examination Survey (NHANES) dataset was used to recruit participants. Urinary BPA was assessed using liquid chromatography-mass spectrum (LC–MS). Through the use of multivariable Cox proportional hazard regressions and constrained cubic splines, the relationships between urine BPA and death from all causes and cancer were investigated.ResultsThis study has a total of 8,035 participants, and 137 died from cancers after a 7.5-year follow-up. The median level of BPA was 2.0 g/mL. Urinary BPA levels were not independently associated with all-cause mortality. For cancer mortality, the second quartile’s multivariable-adjusted hazard ratio was 0.51 (95% confidence interval: 0.30 to 0.86; p = 0.011) compared to the lowest quartile. The restricted cubic splines showed that the association was nonlinear (p for nonlinearity = 0.028) and the inflection point was 1.99 ng/mL.ConclusionUrinary BPA exposure was U-shaped associated with the risk of cancer mortality, and a lower level of BPA less than 1.99 ng/mL was associated with a higher risk of cancer mortality

Observation of the Anomalous Hall Effect in a Collinear Antiferromagnet

Time-reversal symmetry breaking is the basic physics concept underpinning many magnetic topological phenomena such as the anomalous Hall effect (AHE) and its quantized variant. The AHE has been primarily accompanied by a ferromagnetic dipole moment, which hinders the topological quantum states and limits data density in memory devices, or by a delicate noncollinear magnetic order with strong spin decoherence, both limiting their applicability. A potential breakthrough is the recent theoretical prediction of the AHE arising from collinear antiferromagnetism in an anisotropic crystal environment. This new mechanism does not require magnetic dipolar or noncollinear fields. However, it has not been experimentally observed to date. Here we demonstrate this unconventional mechanism by measuring the AHE in an epilayer of a rutile collinear antiferromagnet RuO$_2$. The observed anomalous Hall conductivity is large, exceeding 300 S/cm, and is in agreement with the Berry phase topological transport contribution. Our results open a new unexplored chapter of time-reversal symmetry breaking phenomena in the abundant class of collinear antiferromagnetic materials.Comment: 33 pages, 14 figures, 2 table

GWASdb: a database for human genetic variants identified by genome-wide association studies

Recent advances in genome-wide association studies (GWAS) have enabled us to identify thousands of genetic variants (GVs) that are associated with human diseases. As next-generation sequencing technologies become less expensive, more GVs will be discovered in the near future. Existing databases, such as NHGRI GWAS Catalog, collect GVs with only genome-wide level significance. However, many true disease susceptibility loci have relatively moderate P values and are not included in these databases. We have developed GWASdb that contains 20 times more data than the GWAS Catalog and includes less significant GVs (P < 1.0 × 10−3) manually curated from the literature. In addition, GWASdb provides comprehensive functional annotations for each GV, including genomic mapping information, regulatory effects (transcription factor binding sites, microRNA target sites and splicing sites), amino acid substitutions, evolution, gene expression and disease associations. Furthermore, GWASdb classifies these GVs according to diseases using Disease-Ontology Lite and Human Phenotype Ontology. It can conduct pathway enrichment and PPI network association analysis for these diseases. GWASdb provides an intuitive, multifunctional database for biologists and clinicians to explore GVs and their functional inferences. It is freely available at http://jjwanglab.org/gwasdb and will be updated frequently