On Gaussian Comparison Inequality and Its Application to Spectral Analysis of Large Random Matrices

Recently, Chernozhukov, Chetverikov, and Kato [Ann. Statist. 42 (2014) 1564--1597] developed a new Gaussian comparison inequality for approximating the suprema of empirical processes. This paper exploits this technique to devise sharp inference on spectra of large random matrices. In particular, we show that two long-standing problems in random matrix theory can be solved: (i) simple bootstrap inference on sample eigenvalues when true eigenvalues are tied; (ii) conducting two-sample Roy's covariance test in high dimensions. To establish the asymptotic results, a generalized $\epsilon$-net argument regarding the matrix rescaled spectral norm and several new empirical process bounds are developed and of independent interest.Comment: to appear in Bernoull

Relaxation Behavior of Residual Stress on Deck-to-Rib Welded Joints by Fatigue Loading in an Orthotropic Bridge Deck

To accurately evaluate the influence of the actual tension and compression state and stress ratio at the deck-to-rib welding seam position on the fatigue life of a bridge deck, this paper establishes a coupled stress analysis model that considers the welding residual stress and vehicle stress. Taking the Jiangyin Bridge as an example, a qualitative analysis of the fatigue life under the vehicle load and residual stress field is carried out using the proposed method. A case analysis showed that when the residual tensile stress in the welding seam position is superimposed on the mainly tensile cyclic vehicle load stress, the longitudinal stress relaxation exceeds the peak vehicle load stress; significant longitudinal stress relaxation occurred, while the transverse stress relaxation is not significant. However, when the residual tensile stress is superimposed on the mainly compressive cyclic vehicle load stress, the relaxations of both the longitudinal and transverse stresses are not obvious. Compared with the stress state of the welding point under the action of only the vehicle stress, when the coupling effect of the residual stress and vehicle stress is considered, i.e., the loading condition, the fatigue stress state of the weld point has undergone an essential change under cyclic compressive stress, that is, the compressive stress state that does not require a fatigue check is changed to the tensile stress state. Although the fatigue state of the tensile stress cycle condition has not changed, the fatigue life is reduced by varying degrees under either the compressive or tensile condition

Methyl 3-(4-methyl­benzyl­idene)carbazate

The title compound, C10H12N2O2, was prepared by the reaction of methyl carbazate and 4-methyl­benzaldehyde. The dihedral angle between the benzene ring and the carbazate fragment is 20.86 (10)°. In the crystal structure, mol­ecules are linked by inter­molecular N—H⋯O hydrogen bonds

Analysis of CKM-Favored Quasi-Two-Body B→D(R→)KπB \to D (R\to) K \pi Decays in PQCD Approach

LHCb Collaboration studied the resonant structure of $B_s\to \overline{D}^0K^-\pi^+$ decays using the Dalitz plot analysis technique, based on a data sample corresponding to an integrated luminosity of $3.0{\rm fb}^{-1}$ of $pp$ collision. The $K^-\pi^+$ components have been analyzed in the amplitude model, where the decay amplitude is modeled to be the resonant contributions with respect to the intermediate resonances $K^*(892)$, $K_0^*(1430)$ and $K_2^*(1430)$. Motivated by the experimental results, we investigate the color-favored quasi-two-body $B \to \overline{D}^0K\pi$ decays in the framework of the perturbative QCD (PQCD) approach. We calculate the the branching fractions by introducing the appropriate wave functions of $K\pi$ pair. Our results are in agreement well the available data, and others can be tested in LHCb and Belle-II experiments. Using the narrow-width-approximation, we also extract the branching fractions of the corresponding two-body $B\to \overline D R$ decays, which agree to the previous theoretical calculations and the experimental data within the errors. There are no $CP$ asymmetries in these decays in the standard model, because these decays are all governed by only the tree operators.Comment: 18 pages, 1 figure

Physical properties of noncentrosymmetric superconductor Ru7_7B3_3

Transition metal boride Ru$_7$B$_3$ was found to be a noncentrosymmetric superconductor with $T_{C}$ equal to 3.3 K. Superconducting and normal state properties of Ru$_7$B$_3$ were determined by a self-consistent analysis through resistivity($\rho_{xx}$ and $\rho_{xy}$), specific heat, lower critical field measurement and electronic band structure calculation. It is found that Ru$_7$B$_3$ belongs to an s-wave dominated single band superconductor with energy gap 0.5 meV and could be categorized into type II superconductor with weak electron-phonon coupling. Unusual 'kink' feature is clearly observed in field-broadening resistivity curves, suggesting the possible mixture of spin triplet induced by the lattice without inversion symmetry.Comment: 11 pages, 16 figures. submitted to Phys. Rev.

Cardiovascular End Points and Mortality Are Not Closer Associated With Central Than Peripheral Pulsatile Blood Pressure Components

Pulsatile blood pressure (BP) confers cardiovascular risk. Whether associations of cardiovascular end points are tighter for central systolic BP (cSBP) than peripheral systolic BP (pSBP) or central pulse pressure (cPP) than peripheral pulse pressure (pPP) is uncertain. Among 5608 participants (54.1% women; mean age, 54.2 years) enrolled in nine studies, median follow-up was 4.1 years. cSBP and cPP, estimated tonometrically from the radial waveform, averaged 123.7 and 42.5 mm Hg, and pSBP and pPP 134.1 and 53.9 mm Hg. The primary composite cardiovascular end point occurred in 255 participants (4.5%). Across fourths of the cPP distribution, rates increased exponentially (4.1, 5.0, 7.3, and 22.0 per 1000 person-years) with comparable estimates for cSBP, pSBP, and pPP. The multivariable-adjusted hazard ratios, expressing the risk per 1-SD increment in BP, were 1.50 (95% CI, 1.33–1.70) for cSBP, 1.36 (95% CI, 1.19–1.54) for cPP, 1.49 (95% CI, 1.33–1.67) for pSBP, and 1.34 (95% CI, 1.19–1.51) for pPP (P\u3c0.001). Further adjustment of cSBP and cPP, respectively, for pSBP and pPP, and vice versa, removed the significance of all hazard ratios. Adding cSBP, cPP, pSBP, pPP to a base model including covariables increased the model fit (P\u3c0.001) with generalized R2 increments ranging from 0.37% to 0.74% but adding a second BP to a model including already one did not. Analyses of the secondary end points, including total mortality (204 deaths), coronary end points (109) and strokes (89), and various sensitivity analyses produced consistent results. In conclusion, associations of the primary and secondary end points with SBP and pulse pressure were not stronger if BP was measured centrally compared with peripherally

Mutations in the PKM2 exon-10 region are associated with reduced allostery and increased nuclear translocation.

PKM2 is a key metabolic enzyme central to glucose metabolism and energy expenditure. Multiple stimuli regulate PKM2's activity through allosteric modulation and post-translational modifications. Furthermore, PKM2 can partner with KDM8, an oncogenic demethylase and enter the nucleus to serve as a HIF1α co-activator. Yet, the mechanistic basis of the exon-10 region in allosteric regulation and nuclear translocation remains unclear. Here, we determined the crystal structures and kinetic coupling constants of exon-10 tumor-related mutants (H391Y and R399E), showing altered structural plasticity and reduced allostery. Immunoprecipitation analysis revealed increased interaction with KDM8 for H391Y, R399E, and G415R. We also found a higher degree of HIF1α-mediated transactivation activity, particularly in the presence of KDM8. Furthermore, overexpression of PKM2 mutants significantly elevated cell growth and migration. Together, PKM2 exon-10 mutations lead to structure-allostery alterations and increased nuclear functions mediated by KDM8 in breast cancer cells. Targeting the PKM2-KDM8 complex may provide a potential therapeutic intervention