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   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. Influence of elastic deformations on the supersolid transition

   https://doi.org/10.1103/PhysRevB.84.174304  

   Arpornthip, T. ; Balatsky, A. V. ; Graf, M. J. ; Nussinov, Z. ( November 2011 , Physical Review B)
3. 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)
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. On the liquid–liquid phase transition of dense hydrogen

   https://doi.org/10.1038/s41586-021-04078-x  

   Karasiev, Valentin V. ; Hinz, Joshua ; Hu, S. X. ; Trickey, S. B. ( December 2021 , Nature)