A Mode-Sum Prescription for Vacuum Polarization in Even Dimensions

We present a mode-sum regularization prescription for computing the vacuum polarization of a scalar field in static spherically-symmetric black hole spacetimes in even dimensions. This is the first general and systematic approach to regularized vacuum polarization in higher even dimensions, building upon a previous scheme we developed for odd dimensions. Things are more complicated here since the even-dimensional propagator possesses logarithmic singularities which must be regularized. However, in spite of this complication, the regularization parameters can be computed in closed form in arbitrary even dimensions and for arbitrary metric function $f(r)$. As an explicit example of our method, we show plots for vacuum polarization of a massless scalar field in the Schwarzschild-Tangherlini spacetime for even $d=4,...,10$. However, the method presented applies straightforwardly to massive fields or to nonvacuum spacetimes.Comment: arXiv admin note: text overlap with arXiv:1609.0816

Extended Wiener-Khinchin theorem for quantum spectral analysis

The classical Wiener-Khinchin theorem (WKT), which can extract spectral information by classical interferometers through Fourier transform, is a fundamental theorem used in many disciplines. However, there is still need for a quantum version of WKT, which could connect correlated biphoton spectral information by quantum interferometers. Here, we extend the classical WKT to its quantum counterpart, i.e., extended WKT (e-WKT), which is based on two-photon quantum interferometry. According to the e-WKT, the difference-frequency distribution of the biphoton wavefunctions can be extracted by applying a Fourier transform on the time-domain Hong-Ou-Mandel interference (HOMI) patterns, while the sum-frequency distribution can be extracted by applying a Fourier transform on the time-domain NOON state interference (NOONI) patterns. We also experimentally verified the WKT and e-WKT in a Mach-Zehnder interference (MZI), a HOMI and a NOONI. This theorem can be directly applied to quantum spectroscopy, where the spectral correlation information of biphotons can be obtained from time-domain quantum interferences by Fourier transform. This may open a new pathway for the study of light-matter interaction at the single photon level.Comment: 13 pages, 5 figure

Additional file 1: Table S1. of FOXA1 inhibits hepatocellular carcinoma progression by suppressing PIK3R1 expression in male patients

siRNA used in this study. Table S2 Primers used in qPCR. Table S3 Primers used in ChIP analysis. Table S4 Correlation between clinical pathological factors and expression of FOXA1, PI3Kp85 in HCC Table S5 Specimens exhibit low or high FOXA1 expression in relation to PI3Kp85 expression. (DOCX 25 kb

Developed equations for predicting total body skeletal muscle mass.

<p>Values are means ± SD.</p><p><b>Abbreviations</b>: ALST, appendicular lean soft tissue; IMAT, intermuscular adipose tissue; SM, total body skeletal muscle.</p

Comparison of SM measured by MRI and predicted by Kim’s equation [10].

<p>Values are means ± SD.</p><p><b>Abbreviation:</b> SM, total body skeletal muscle.</p

Difference of total body skeletal muscle (SM) by MRI and by Kim <i>et al</i>. on the ordinate versus SM by MRI on the abscissa in men (•, n = 52) and women (○, n = 14).

<p>The correlation between the difference of SM by MRI and by Kim <i>et al.</i> and SM by MRI was 0.57 (SEE = 1.03 kg, <i>P</i><0.001) in men and 0.67 (SEE = 0.62 kg, <i>P</i><0.001) in women. The reference line (y = 0) is shown.</p

Intermuscular adipose tissue free total body skeletal muscle (IMAT-free SM) measured by MRI on the ordinate versus appendicular lean soft tissue (ALST) measured by DXA on the abscissa.

<p>The correlation between IMAT-free SM and ALST in men (•, n = 52) and women (○, n = 14) are <i>r</i> = 0.94 and <i>r</i> = 0.98, respectively. IMAT-free SM = 1.20×ALST−1.13; <i>R²</i> = 0.94, SEE<i> = </i>1.11 <i>kg,</i> n = 66.</p

Segmentation of the original T1- weighted magnetic resonance image of legs.

<p>Subcutaneous adipose tissue (SAT), intermuscular adipose tissue (IMAT), skeletal muscle, bone and bone with marrow are shown.</p

Ratio of IMAT-free SM to ALST (IMAT-free SM/ALST) on the ordinate versus age on the abscissa in men (•) and women (○).

<p>Men : IMAT-free SM = −.0.001× age +1.22 <i>r</i> = −0.31, <i>P = </i>0.02; n = 52. Women : IMAT-free SM = −.0.004×age +1.14 <i>r</i> = −0.09, <i>P = </i>0.77; n = 14.</p

Prediction equations from the current study and Kim <i>et al.</i>

<p>IMAT-free SM values in Kim <i>et al</i>. were transformed using base 10 logarithms to explore the contributions of gender and race to the model.</p><p>Gender, male = 1 and female = 0.</p