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1. Distributional stability of the Szarek and Ball inequalities

   https://doi.org/10.1007/s00208-023-02669-9  

   Eskenazis, Alexandros; Nayar, Piotr; Tkocz, Tomasz (June 2024, Mathematische Annalen)

   Abstract We prove an extension of Szarek’s optimal Khinchin inequality (1976) for distributions close to the Rademacher one, when all the weights are uniformly bounded by a$$1/\sqrt{2}$$ $1/\sqrt{2}$fraction of their total$$\ell _2$$ ${\ell }_2$-mass. We also show a similar extension of the probabilistic formulation of Ball’s cube slicing inequality (1986). These results establish the distributional stability of these optimal Khinchin-type inequalities. The underpinning to such estimates is the Fourier-analytic approach going back to Haagerup (1981). 

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2. Einstein–Klein–Gordon system via Cauchy-characteristic evolution: computation of memory and ringdown tail

   https://doi.org/10.1088/1361-6382/adaf6f  

   Ma, Sizheng; Nelli, Kyle C; Moxon, Jordan; Scheel, Mark A; Deppe, Nils; Kidder, Lawrence E; Throwe, William; Vu, Nils L (February 2025, Classical and Quantum Gravity)

   Abstract Cauchy-characteristic evolution (CCE) is a powerful method for accurately extracting gravitational waves at future null infinity. In this work, we extend the previously implemented CCE system within the numerical relativity code SpECTRE by incorporating a scalar field. This allows the system to capture features of beyond-general-relativity theories. We derive scalar contributions to the equations of motion, Weyl scalar computations, Bianchi identities, and balance laws at future null infinity. Our algorithm, tested across various scenarios, accurately reveals memory effects induced by both scalar and tensor fields and captures Price’s power-law tail ( $u^{-l-2}$) in scalar fields at future null infinity, in contrast to the $t^{-2l-3}$tail at future timelike infinity. 

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3. An Efficient ZK Compiler from SIMD Circuits to General Circuits

   https://doi.org/10.1007/s00145-024-09531-4  

   Bui, Dung; Chu, Haotian; Couteau, Geoffroy; Wang, Xiao; Weng, Chenkai; Yang, Kang; Yu, Yu (January 2025, Journal of Cryptology)

   Abstract We propose a generic compiler that can convert any zero-knowledge (ZK) proof for SIMD circuits to general circuits efficiently, and an extension that can preserve the space complexity of the proof systems. Our compiler can immediately produce new results improving upon state of the art.By plugging in our compiler to Antman, an interactive sublinear-communication protocol, we improve the overall communication complexity for general circuits from$$\mathcal {O}(C^{3/4})$$ $O\left(C^{3/4}\right)$to$$\mathcal {O}(C^{1/2})$$ $O\left(C^{1/2}\right)$. Our implementation shows that for a circuit of size$$2^{27}$$ $2^{27}$, it achieves up to$$83.6\times $$ $83.6\times$improvement on communication compared to the state-of-the-art implementation. Its end-to-end running time is at least$$70\%$$ $70\%$faster in a 10Mbps network.Using the recent results on compressed$$\varSigma $$ $\Sigma$-protocol theory, we obtain a discrete-log-based constant-round zero-knowledge argument with$$\mathcal {O}(C^{1/2})$$ $O\left(C^{1/2}\right)$communication and common random string length, improving over the state of the art that has linear-size common random string and requires heavier computation.We improve the communication of a designatedn-verifier zero-knowledge proof from$$\mathcal {O}(nC/B+n^2B^2)$$ $O(nC/B+n^2{B}^2)$to$$\mathcal {O}(nC/B+n^2)$$ $O(nC/B+n^2)$.To demonstrate the scalability of our compilers, we were able to extract a commit-and-prove SIMD ZK from Ligero and cast it in our framework. We also give one instantiation derived from LegoSNARK, demonstrating that the idea of CP-SNARK also fits in our methodology. 

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4. Proton capture on $$^{90}$$Zr revisited

   https://doi.org/10.1140/epja/s10050-025-01521-9  

   Simon, A; Koros, J; Olivas-Gomez, O; Kelmar, R; Churchman, E; Clark, A M; Harris, C; Henderson, S L; Kelly, S E; Millican, P; et al (March 2025, The European Physical Journal A)

   Abstract The$$^{90}$$ $_{}^{90}$Zr(p,$$\gamma $$ $\gamma$)$$^{91}$$ $_{}^{91}$Nb reaction is one of the important reactions in the$$A\approx 90$$ $A\approx 90$mass region and part of the nucleosynthesis path responsible for production of$$^{92}$$ $_{}^{92}$Mo during the$$\gamma $$ $\gamma$-process. Discrepant data in the literature provide a cross section that varies up to 30% within the Gamow window for the$$^{90}$$ $_{}^{90}$Zr(p,$$\gamma $$ $\gamma$)$$^{91}$$ $_{}^{91}$Nb reaction. Thus, the cross section measurements of$$^{90}$$ $_{}^{90}$Zr(p,$$\gamma $$ $\gamma$)$$^{91}$$ $_{}^{91}$Nb reaction were revisited using the$$\gamma $$ $\gamma$-summing technique. The results are consistent with the lower-value cross sections found in the literature. Based on the new data an updated reaction rate for$$^{90}$$ $_{}^{90}$Zr(p,$$\gamma $$ $\gamma$)$$^{91}$$ $_{}^{91}$Nb is provided that is up to 20% higher than that obtained from thenon-smokercode. 

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5. $1/f$ Noise in the Heliosphere: A Target for PUNCH Science

   https://doi.org/10.1007/s11207-024-02401-z  

   Wang, Jiaming; Matthaeus, William H; Chhiber, Rohit; Roy, Sohom; Pradata, Rayta A; Pecora, Francesco; Yang, Yan (December 2024, Solar Physics)

   Abstract We present a broad review of$$1/f$$ $1/f$noise observations in the heliosphere, and discuss and complement the theoretical background of generic$$1/f$$ $1/f$models as relevant to NASA’s Polarimeter to UNify the Corona and Heliosphere (PUNCH) mission. First observed in the voltage fluctuations of vacuum tubes, the scale-invariant$$1/f$$ $1/f$spectrum has since been identified across a wide array of natural and artificial systems, including heart rate fluctuations and loudness patterns in musical compositions. In the solar wind the interplanetary magnetic field trace spectrum exhibits$$1/f$$ $1/f$scaling within the frequency range from around$$\unit[2 \times 10^{-6}]{Hz}$$to around$$\unit[10^{-3}]{{Hz}}$$at 1 au. One compelling mechanism for the generation of$$1/f$$ $1/f$noise is the superposition principle, where a composite$$1/f$$ $1/f$spectrum arises from the superposition of a collection of individual power-law spectra characterized by a scale-invariant distribution of correlation times. In the context of the solar wind, such a superposition could originate from scale-invariant reconnection processes in the corona. Further observations have detected$$1/f$$ $1/f$signatures in the photosphere and corona at frequency ranges compatible with those observed at 1 au, suggesting an even lower altitude origin of$$1/f$$ $1/f$spectrum in the solar dynamo itself. This hypothesis is bolstered by dynamo experiments and simulations that indicate inverse cascade activities, which can be linked to successive flux tube reconnections beneath the corona, and are known to generate$$1/f$$ $1/f$noise possibly through nonlocal interactions at the largest scales. Conversely, models positing in situ generation of$$1/f$$ $1/f$signals face causality issues in explaining the low-frequency portion of the$$1/f$$ $1/f$spectrum. Understanding$$1/f$$ $1/f$noise in the solar wind may inform central problems in heliospheric physics, such as the solar dynamo, coronal heating, the origin of the solar wind, and the nature of interplanetary turbulence. 

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