Stochastic Gravitational Wave Background originating from Halo Mergers

The stochastic gravitational wave background (GWB) from halo mergers is investigated by a quasi-analytic method. The method we employ consists of two steps. The first step is to construct a merger tree by using the Extended Press-Schechter formalism or the Sheth & Tormen formalism, with Monte-Carlo realizations. This merger tree provides evolution of halo masses. From $N$-body simulation of two-halo mergers, we can estimate the amount of gravitational wave emission induced by the individual merger process. Therefore the second step is to combine this gravitaional wave emission to the merger tree and obtain the amplitude of GWB. We find $\Omega_{GW}\sim 10^{-19}$ for $f\sim 10^{-17}-10^{-16}$ Hz, where $\Omega_{GW}$ is the energy density of the GWB. It turns out that most of the contribution on the GWB comes from halos with masses below $10^{15} M_\odot$ and mergers at low redshift, i.e., $0<z<0.8$.Comment: 5 pages, 8 figures. Accepted for publication in Physical Review

The Degrees of Freedom of Partial Least Squares Regression

The derivation of statistical properties for Partial Least Squares regression can be a challenging task. The reason is that the construction of latent components from the predictor variables also depends on the response variable. While this typically leads to good performance and interpretable models in practice, it makes the statistical analysis more involved. In this work, we study the intrinsic complexity of Partial Least Squares Regression. Our contribution is an unbiased estimate of its Degrees of Freedom. It is defined as the trace of the first derivative of the fitted values, seen as a function of the response. We establish two equivalent representations that rely on the close connection of Partial Least Squares to matrix decompositions and Krylov subspace techniques. We show that the Degrees of Freedom depend on the collinearity of the predictor variables: The lower the collinearity is, the higher the Degrees of Freedom are. In particular, they are typically higher than the naive approach that defines the Degrees of Freedom as the number of components. Further, we illustrate how the Degrees of Freedom approach can be used for the comparison of different regression methods. In the experimental section, we show that our Degrees of Freedom estimate in combination with information criteria is useful for model selection.Comment: to appear in the Journal of the American Statistical Associatio

Tumor Biology and Racial Disparities in Reconstruction After Mastectomy: A SEER Database Analysis

Introduction: Significant disparities in immediate breast reconstruction after mastectomy have persisted, and may even be increasing, despite large-scale efforts to minimize them, such as the Women’s Health and Cancer Rights Act of 1998. Immediate breast reconstruction has been shown to lead to higher rates of surgical satisfaction, minimize delay in post-operative cancer treatment, and improve the quality of life and overall well-being of mastectomy patients. However only 25-40% of eligible women in the United States receive reconstruction. The rate of reconstruction is even lower in African American and Hispanic women compared to White women. To better understand this disparity, this study uses national population-based data to examine how demographic factors, socioeconomic factors, and disease characteristics interact and affect the rate of immediate breast reconstruction (IBR) after mastectomy. Methods: Women with AJCC7 Stage 0-III breast cancer who underwent mastectomy from 2010 to 2012 were identified in the Surveillance, Epidemiology and End Results Program (SEER) database. Race, Hispanic ethnicity, age, marital status, insurance status, tumor grade, AJCC7 stage and hormone receptor/ Her2Neu profile were compared between women undergoing mastectomy with IBR and mastectomy alone using univariate and multivariate analysis. Results: We identified 51,115 women who underwent mastectomy for Stage 0-III breast cancer from 2010-2012, of whom 15,389 (30.1%) received IBR. On multivariate analysis, age (p Conclusion: The decision to undergo reconstruction after mastectomy is influenced by many factors. Our results show that even after adjusting for tumor characteristics, socioeconomic factors are independently associated with receiving IBR after mastectomy. Further research is needed to elucidate the factors that influence the decision to undergo IBR in order to eliminate these persistent disparities

Volumetric formulation of lattice Boltzmann models with energy conservation

We analyze a volumetric formulation of lattice Boltzmann for compressible thermal fluid flows. The velocity set is chosen with the desired accuracy, based on the Gauss-Hermite quadrature procedure, and tested against controlled problems in bounded and unbounded fluids. The method allows the simulation of thermohydrodyamical problems without the need to preserve the exact space-filling nature of the velocity set, but still ensuring the exact conservation laws for density, momentum and energy. Issues related to boundary condition problems and improvements based on grid refinement are also investigated.Comment: 8 figure

N=2 Supersymmetric Sigma Models and D-branes

We study D-branes of N=2 supersymmetric sigma models. Supersymmetric nonlinear sigma models with 2-dimensional target space have D0,D1,D2-branes, which are realized as A-,B-type supersymmetric boundary conditions on the worldsheet. When we embed the models in the string theory, the Kahler potential is restricted and leads to a 2-dim black hole metric with a dilaton background. The D-branes in this model are susy cycles and consistent with the analysis of conjugacy classes. The generalized metrics with U(n) isometry is proposed and dynamics on them are realized by linear sigma models. We investigate D-branes of the linear sigma models and compare the results with those in the nonlinear sigma models.Comment: 23 pages, 5 figure

Re-entrant hidden order at a metamagnetic quantum critical end point

Magnetization measurements of URu2Si2 in pulsed magnetic fields of 44 T reveal that the hidden order phase is destroyed before appearing in the form of a re-entrant phase between ~ 36 and 39 T. Evidence for conventional itinerant electron metamagnetism at higher temperatures suggests that the re-entrant phase is created in the vicinity of a quantum critical end point.Comment: 8 pages, including 3 figures (Physical Review Letters, in press) a systematic error in the field calibration has been fixed since the original submission of this manuscrip

A common behavior of thermoelectric layered cobaltites: incommensurate spin density wave states in [Ca2_2Co4/3_{4/3}Cu2/3_{2/3}O4_4]0.62_{0.62}[CoO2_2] and [Ca2_2CoO3_3]0.62_{0.62}[CoO2_2]

Magnetism of a misfit layered cobaltite [Ca$_2$Co$_{4/3}$Cu$_{2/3}$O$_4$]$_x^{\rm RS}$[CoO$_2$] ($x \sim$ 0.62, RS denotes a rocksalt-type block) was investigated by a positive muon spin rotation and relaxation ($\mu^+$SR) experiment. A transition to an incommensurate ({\sf IC}) spin density wave ({\sf SDW}) state was found below 180 K (= $T_{\rm C}^{\rm on}$); and a clear oscillation due to a static internal magnetic field was observed below 140 K (= $T_{\rm C}$). Furthermore, an anisotropic behavior of the zero-field $\mu^+$SR experiment indicated that the {\sf IC-SDW} propagates in the $a$-$b$ plane, with oscillating moments directed along the c axis. These results were quite similar to those for the related compound [Ca$_2$CoO$_3$]$_{0.62}^{\rm RS}$[CoO$_2$], {\sl i.e.}, Ca$_3$Co$_4$O$_9$. Since the {\sf IC-SDW} field in [Ca$_2$Co$_{4/3}$Cu$_{2/3}$O$_4$]$_{0.62}^{\rm RS}$[CoO$_2$] was approximately same to those in pure and doped [Ca$_2$CoO$_3$]$_{0.62}^{\rm RS}$[CoO$_2$], it was concluded that the {\sf IC-SDW} exist in the [CoO$_2$] planes.Comment: 15 pages, 6 figures. accepted for publication in J. Phys.: Condens. Matte

Magnetic nanostructures by adaptive twinning in strained epitaxial films

We exploit the intrinsic structural instability of the Fe70Pd30 magnetic shape memory alloy to obtain functional epitaxial films exhibiting a self-organized nanostructure. We demonstrate that coherent epitaxial straining by 54% is possible. The combination of thin film experiments and large-scale first-principles calculations enables us to establish a lattice relaxation mechanism, which is not expected for stable materials. We identify a low twin boundary energy compared to a high elastic energy as key prerequisite for the adaptive nanotwinning. Our approach is versatile as it allows to control both, nanostructure and intrinsic properties for ferromagnetic, ferroelastic and ferroelectric materials.Comment: Final version. Supplementary information available on request or at the publisher's websit

Effect of nonnegativity on estimation errors in one-qubit state tomography with finite data

We analyze the behavior of estimation errors evaluated by two loss functions, the Hilbert-Schmidt distance and infidelity, in one-qubit state tomography with finite data. We show numerically that there can be a large gap between the estimation errors and those predicted by an asymptotic analysis. The origin of this discrepancy is the existence of the boundary in the state space imposed by the requirement that density matrices be nonnegative (positive semidefinite). We derive an explicit form of a function reproducing the behavior of the estimation errors with high accuracy by introducing two approximations: a Gaussian approximation of the multinomial distributions of outcomes, and linearizing the boundary. This function gives us an intuition for the behavior of the expected losses for finite data sets. We show that this function can be used to determine the amount of data necessary for the estimation to be treated reliably with the asymptotic theory. We give an explicit expression for this amount, which exhibits strong sensitivity to the true quantum state as well as the choice of measurement.Comment: 9 pages, 4 figures, One figure (FIG. 1) is added to the previous version, and some typos are correcte