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1. P–P Coupling with and without Terminal Metal–Phosphorus Intermediates

   https://doi.org/10.1021/jacs.4c16833  

   Thompson, Richard R; Figgins, Matthew T; Wannipurage, Duleeka C; Renteria-Gomez, Angel; Gogoi, Achyut Ranjan; Telser, Joshua; Tierney, David L; Neben, Marc C; Demeshko, Serhiy; Gutierrez, Osvaldo; et al (February 2025, Journal of the American Chemical Society)
2. Are p -values under attack? Contribution to the discussion of ‘A critical evaluation of the current “ p -value controversy” ’: Are p -value under attack?

   https://doi.org/10.1002/bimj.201700031  

   Piegorsch, Walter W. (September 2017, Biometrical Journal)
3. IWASAWA THEORY FOR p -TORSION CLASS GROUP SCHEMES IN CHARACTERISTIC p

   https://doi.org/10.1017/nmj.2022.30  

   BOOHER, JEREMY; CAIS, BRYDEN (June 2023, Nagoya Mathematical Journal)

   Abstract We investigate a novel geometric Iwasawa theory for$${\mathbf Z}_p$$-extensions of function fields over a perfect fieldkof characteristic$$p>0$$by replacing the usual study ofp-torsion in class groups with the study ofp-torsion class groupschemes. That is, if$$\cdots \to X_2 \to X_1 \to X_0$$is the tower of curves overkassociated with a$${\mathbf Z}_p$$-extension of function fields totally ramified over a finite nonempty set of places, we investigate the growth of thep-torsion group scheme in the Jacobian of$$X_n$$as$$n\rightarrow \infty $$. By Dieudonné theory, this amounts to studying the first de Rham cohomology groups of$$X_n$$equipped with natural actions of Frobenius and of the Cartier operatorV. We formulate and test a number of conjectures which predict striking regularity in the$$k[V]$$-module structure of the space$$M_n:=H^0(X_n, \Omega ^1_{X_n/k})$$of global regular differential forms as$$n\rightarrow \infty .$$For example, for each tower in a basic class of$${\mathbf Z}_p$$-towers, we conjecture that the dimension of the kernel of$$V^r$$on$$M_n$$is given by$$a_r p^{2n} + \lambda _r n + c_r(n)$$for allnsufficiently large, where$$a_r, \lambda _r$$are rational constants and$$c_r : {\mathbf Z}/m_r {\mathbf Z} \to {\mathbf Q}$$is a periodic function, depending onrand the tower. To provide evidence for these conjectures, we collect extensive experimental data based on new and more efficient algorithms for working with differentials on$${\mathbf Z}_p$$-towers of curves, and we prove our conjectures in the case$$p=2$$and$$r=1$$. 

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4. Combining exchangeable P -values

   https://doi.org/10.1073/pnas.2410849122  

   Gasparin, Matteo; Wang, Ruodu; Ramdas, Aaditya (March 2025, Proceedings of the National Academy of Sciences)

   The problem of combiningP-values is an old and fundamental one, and the classic assumption of independence is often violated or unverifiable in many applications. There are many well-known rules that can combine a set of arbitrarily dependentP-values (for the same hypothesis) into a singleP-value. We show that essentially all these existing rules can be strictly improved when theP-values are exchangeable, or when external randomization is allowed (or both). For example, we derive randomized and/or exchangeable improvements of well-known rules like “twice the median” and “twice the average,” as well as geometric and harmonic means. ExchangeableP-values are often produced one at a time (for example, under repeated tests involving data splitting), and our rules can combine them sequentially as they are produced, stopping when the combinedP-values stabilize. Our work also improves rules for combining arbitrarily dependentP-values, since the latter becomes exchangeable if they are presented to the analyst in a random order. The main technical advance is to show that all existing combination rules can be obtained by calibrating theP-values to e-values (using an $\alpha$-dependent calibrator), averaging those e-values, converting to a level- $\alpha$test using Markov’s inequality, and finally obtainingP-values by combining this family of tests; the improvements are delivered via recent randomized and exchangeable variants of Markov’s inequality. 

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5. The correlation-bound anion of p -chloroaniline

   https://doi.org/10.1063/1.5096986  

   Ciborowski, Sandra M.; Harris, Rachel M.; Liu, Gaoxiang; Martinez-Martinez, Chalynette J.; Skurski, Piotr; Bowen, Jr., Kit H. (April 2019, The Journal of Chemical Physics)