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  1. In some applications, it is reasonable to assume that geodesics (rays) have a consistent orientation so that a time-harmonic elastic wave equation may be viewed as an evolution equation in one of the spatial directions. With such applications in mind, motivated by our recent work [Hadamard- Babich ansatz for point-source elastic wave equations in variable media at high frequencies, Multiscale Model Simul. 19/1 (2021) 46–86], we propose a new truncated Hadamard-Babich ansatz based globally valid asymptotic method, dubbed the fast Huygens sweeping method, for computing Green’s functions of frequency-domain point-source elastic wave equations in inhomogeneous media in the high-frequency asymptotic regime and in the presence of caustics. The first novelty of the fast Huygens sweeping method is that the Huygens-Kirchhoff secondary-source principle is used to integrate many locally valid asymptotic solutions to yield a globally valid asymptotic solution so that caustics can be treated automatically. This yields uniformly accurate solutions both near the source and away from it. The second novelty is that a butterfly algorithm is adapted to accelerate matrix-vector products induced by the Huygens-Kirchhoff integral. The new method enjoys the following desired features: (1) it treats caustics automatically; (2) precomputed asymptotic ingredients can be used to construct Green’s functions of elastic wave equations for many different point sources and for arbitrary frequencies; (3) given a specified number of points per wavelength, it constructs Green’s functions in nearly optimal complexity O(N logN) in terms of the total number of mesh points N, where the prefactor of the complexity depends only on the specified accuracy and is independent of the frequency parameter. Three-dimensional numerical examples are presented to demonstrate the performance and accuracy of the new method. 
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    Free, publicly-accessible full text available March 1, 2024
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  3. Belkin, M. ; Kpotufe, S. (Ed.)
    We study the problem of robust learning under clean-label data-poisoning attacks, where the at-tacker injects (an arbitrary set of) correctly-labeled examples to the training set to fool the algorithm into making mistakes on specific test instances at test time. The learning goal is to minimize the attackable rate (the probability mass of attackable test instances), which is more difficult than optimal PAC learning. As we show, any robust algorithm with diminishing attackable rate can achieve the optimal dependence on ε in its PAC sample complexity, i.e., O(1/ε). On the other hand, the attackable rate might be large even for some optimal PAC learners, e.g., SVM for linear classifiers. Furthermore, we show that the class of linear hypotheses is not robustly learnable when the data distribution has zero margin and is robustly learnable in the case of positive margin but requires sample complexity exponential in the dimension. For a general hypothesis class with bounded VC dimension, if the attacker is limited to add at most t >0 poison examples, the optimal robust learning sample complexity grows almost linearly with t. 
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  7. Abstract A study of the charge conjugation and parity ( $$\textit{CP}$$ CP ) properties of the interaction between the Higgs boson and $$\tau $$ τ -leptons is presented. The study is based on a measurement of $$\textit{CP}$$ CP -sensitive angular observables defined by the visible decay products of $$\tau $$ τ -leptons produced in Higgs boson decays. The analysis uses 139 fb $$^{-1}$$ - 1 of proton–proton collision data recorded at a centre-of-mass energy of $$\sqrt{s}= 13$$ s = 13  TeV with the ATLAS detector at the Large Hadron Collider. Contributions from $$\textit{CP}$$ CP -violating interactions between the Higgs boson and $$\tau $$ τ -leptons are described by a single mixing angle parameter $$\phi _{\tau }$$ ϕ τ in the generalised Yukawa interaction. Without constraining the $$H\rightarrow \tau \tau $$ H → τ τ signal strength to its expected value under the Standard Model hypothesis, the mixing angle $$\phi _{\tau }$$ ϕ τ is measured to be $$9^{\circ } \pm 16^{\circ }$$ 9 ∘ ± 16 ∘ , with an expected value of $$0^{\circ } \pm 28^{\circ }$$ 0 ∘ ± 28 ∘ at the 68% confidence level. The pure $$\textit{CP}$$ CP -odd hypothesis is disfavoured at a level of 3.4 standard deviations. The results are compatible with the predictions for the Higgs boson in the Standard Model. 
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    Free, publicly-accessible full text available July 1, 2024