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1. On the Phase Transition of Wilk’s Phenomenon

   https://doi.org/10.1093/biomet/asaa078  

   He, Yinqiu; Meng, Bo; Zeng, Zhenghao; Xu, Gongjun (September 2020, Biometrika)

   null (Ed.)

   Abstract Wilk’s theorem, which offers universal chi-squared approximations for likelihood ratio tests, is widely used in many scientific hypothesis testing problems. For modern datasets with increasing dimension, researchers have found that the conventional Wilk’s phenomenon of the likelihood ratio test statistic often fails. Although new approximations have been proposed in high dimensional settings, there still lacks a clear statistical guideline regarding how to choose between the conventional and newly proposed approximations, especially for moderate-dimensional data. To address this issue, we develop the necessary and sufficient phase transition conditions for Wilk’s phenomenon under popular tests on multivariate mean and covariance structures. Moreover, we provide an in-depth analysis of the accuracy of chi-squared approximations by deriving their asymptotic biases. These results may provide helpful insights into the use of chi-squared approximations in scientific practices. 

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2. Effect of Aerosol Size on Glass Transition Temperature

   https://doi.org/10.1021/acs.jpclett.4c01415  

   Mahant, Sunandan; Snider, Jefferson_R; Petters, Sarah_S; Petters, Markus_D (July 2024, The Journal of Physical Chemistry Letters)
3. Impacts of Extratropical Transition on Tropical Cyclone Tornadoes

   https://doi.org/10.1175/MWR-D-25-0006.1  

   Wheeler, Kayla; Schenkel, Benjamin A; Brown, Matthew C; Edwards, Roger; Dickinson, Ty (November 2025, Monthly Weather Review)

   The impact of extratropical transition (ET) on tropical cyclone (TC) tornadoes is not fully understood with no prior tornado climatologies for ET cases. Hence, this study investigates how ET impacts tornadoes and convective-scale environments within TCs using multidecadal tornado and radiosonde data from North Atlantic TCs. This research divides ET into three phases: tropical (i.e., pre-ET), transition (i.e., during ET), and extratropical (i.e., post-ET). These results show that the largest portion of tornadoes occurs before and during ET, with the greatest frequencies during ET. As TCs progress through ET, tornado location shifts north and east in the United States but farther south or more strongly downshear right relative to the TC center. Tornadoes also tend to occur later in the day and are more likely to be associated with greater damage. Evaluation of radiosondes shows that the downshear-right quadrant of the TC is frequently the most favorable for tornado production, with sufficient entrainment CAPE (ECAPE) and strong storm-relative helicity (SRH). Specifically, the downshear-right quadrant shows slower decreases in ECAPE (associated with synoptic-scale cooling and drying) and increased SRH and associated lower-tropospheric vertical wind shear through ET, relative to the other quadrants relative to the deep-tropospheric (i.e., 850–200-hPa) vertical wind shear vector. These results inform the physical model and prediction of ET-related TC structure, both in terms of their convective-scale environments and subsequent hazard production. 

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4. On the black hole/string transition

   https://doi.org/10.1007/JHEP01(2023)103  

   Chen, Yiming; Maldacena, Juan; Witten, Edward (January 2023, Journal of High Energy Physics)

   A bstract We discuss aspects of the possible transition between small black holes and highly excited fundamental strings. We focus on the connection between black holes and the self gravitating string solution of Horowitz and Polchinski. This solution is interesting because it has non-zero entropy at the classical level and it is natural to suspect that it might be continuously connected to the black hole. Surprisingly, we find a different behavior for heterotic and type II cases. For the type II case we find an obstruction to the idea that the two are connected as classical solutions of string theory, while no such obstruction exists for the heterotic case. We further provide a linear sigma model analysis that suggests a continuous connection for the heterotic case. We also describe a solution generating transformation that produces a charged version of the self gravitating string. This provides a fuzzball-like construction of near extremal configurations carrying fundamental string momentum and winding charges. We provide formulas which are exact in α ′ relating the thermodynamic properties of the charged and the uncharged solutions. 

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5. Bounds on the superconducting transition temperature

   https://doi.org/10.1142/S0217984924300047  

   Randeria, Mohit (December 2024, Modern Physics Letters B)

   I summarize recent progress on obtaining rigorous upper bounds on superconducting transition temperature [Formula: see text] in two dimensions independent of pairing mechanism or interaction strength. These results are derived by finding a general upper bound for the superfluid stiffness for a multi-band system with arbitrary interactions, with the only assumption that the external vector potential couples to the kinetic energy and not to the interactions. This bound is then combined with the universal relation between the superfluid stiffness and the Berezinskii–Kosterlitz–Thouless [Formula: see text] in 2D. For parabolic dispersion, one obtains the simple result that [Formula: see text], which has been tested in recent experiments. More generally, the bounds are expressed in terms of the optical spectral weight and lead to stringent constraints for the [Formula: see text] of low-density, strongly correlated superconductors. Results for [Formula: see text] bounds for models of flat-band superconductors, where the kinetic energy vanishes and the vector potential must couple to interactions, are briefly summarized. Upper bounds on [Formula: see text] in 3D remains an open problem, and I describe how questions of universality underlie the challenges in 3D. 

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