Triad representation of the Chern-Simons state in quantum gravity

We investigate a triad representation of the Chern-Simons state of quantum gravity with a non-vanishing cosmological constant. It is shown that the Chern-Simons state, which is a well-known exact wavefunctional within the Ashtekar theory, can be transformed to the real triad representation by means of a suitably generalized Fourier transformation, yielding a complex integral representation for the corresponding state in the triad variables. It is found that topologically inequivalent choices for the complex integration contour give rise to linearly independent wavefunctionals in the triad representation, which all arise from the one Chern-Simons state in the Ashtekar variables. For a suitable choice of the normalization factor, these states turn out to be gauge-invariant under arbitrary, even topologically non-trivial gauge-transformations. Explicit analytical expressions for the wavefunctionals in the triad representation can be obtained in several interesting asymptotic parameter regimes, and the associated semiclassical 4-geometries are discussed. In restriction to Bianchi-type homogeneous 3-metrics, we compare our results with earlier discussions of homogeneous cosmological models. Moreover, we define an inner product on the Hilbert space of quantum gravity, and choose a natural gauge-condition fixing the time-gauge. With respect to this particular inner product, the Chern-Simons state of quantum gravity turns out to be a non-normalizable wavefunctional.Comment: Latex, 30 pages, 1 figure, to appear in Phys. Rev.

Validation of a 40-Gene Expression Profile Test to Predict Metastatic Risk in Localized High-Risk Cutaneous Squamous Cell Carcinoma

Background: Current staging systems for cutaneous squamous cell carcinoma (cSCC) have limited positive predictive value (PPV) for identifying patients who will experience metastasis. Objective: To develop and validate a gene expression profile (GEP) test for predicting risk for metastasis in localized, high-risk cSCC with the goal of improving risk-directed patient management. Methods: Archival formalin-fixed paraffin-embedded primary cSCC tissue and clinicopathologic data (n=586) were collected from 23 independent centers in a prospectively designed study. A GEP signature was developed using a discovery cohort (n=202) and validated in a separate, non-overlaping, independent cohort (n=324). Results: A prognostic, 40-gene expression profile (40-GEP) test was developed and validated, stratifying high-risk cSCC patients into classes based on metastasis risk: Class 1 (low-risk), Class 2A (high-risk), and Class 2B (highest-risk). For the validation cohort, 3-year metastasis-free survival (MFS) rates were 91.4%, 80.6%, and 44.0%, respectively. A PPV of 60% was achieved for the highest-risk group (Class 2B), an improvement over staging systems; while negative predictive value, sensitivity, and specificity were comparable to staging systems. Limitations: Potential understaging of cases could affect metastasis rate accuracy.Conclusion: The 40-GEP test is an independent predictor of metastatic risk that can complement current staging systems for patients with high-risk cSCC

Coronal Heating as Determined by the Solar Flare Frequency Distribution Obtained by Aggregating Case Studies

Flare frequency distributions represent a key approach to addressing one of the largest problems in solar and stellar physics: determining the mechanism that counter-intuitively heats coronae to temperatures that are orders of magnitude hotter than the corresponding photospheres. It is widely accepted that the magnetic field is responsible for the heating, but there are two competing mechanisms that could explain it: nanoflares or Alfv\'en waves. To date, neither can be directly observed. Nanoflares are, by definition, extremely small, but their aggregate energy release could represent a substantial heating mechanism, presuming they are sufficiently abundant. One way to test this presumption is via the flare frequency distribution, which describes how often flares of various energies occur. If the slope of the power law fitting the flare frequency distribution is above a critical threshold, $\alpha=2$ as established in prior literature, then there should be a sufficient abundance of nanoflares to explain coronal heating. We performed $>$600 case studies of solar flares, made possible by an unprecedented number of data analysts via three semesters of an undergraduate physics laboratory course. This allowed us to include two crucial, but nontrivial, analysis methods: pre-flare baseline subtraction and computation of the flare energy, which requires determining flare start and stop times. We aggregated the results of these analyses into a statistical study to determine that $\alpha = 1.63 \pm 0.03$. This is below the critical threshold, suggesting that Alfv\'en waves are an important driver of coronal heating.Comment: 1,002 authors, 14 pages, 4 figures, 3 tables, published by The Astrophysical Journal on 2023-05-09, volume 948, page 7