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1. Measurement of the CP properties of Higgs boson interactions with $$\tau $$-leptons with the ATLAS detector

   https://doi.org/10.1140/epjc/s10052-023-11583-y  

   Aad, G.; Abbott, B.; Abbott, D. C.; Abeling, K.; Abidi, S. H.; Aboulhorma, A.; Abramowicz, H.; Abreu, H.; Abulaiti, Y.; Hoffman, A. C.; et al (July 2023, The European Physical Journal C)

   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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2. Performance of a machine learning model for real-time prediction of health status of lactating cows

   Aguero, S; Perez, M M; Reyes_Fajardo, O D; Messi, O; An, S H; Giordano, JO (June 2025, American Dairy Science Association J. Dairy Sci. 108 (E-Suppl. 1):370. (Abstr))

   The objective of this study was to evaluate the performance of an XGBoost model trained with behavioral, physiological, performance, environmental, and cow feature data for classifying cow health status (HS). The model predicted HS based on physical activity, resting, reticulo-rumen temperature, rumination and eating behavior, milk yield, conductivity and components, temperature and humidity index, parity, calving features, and stocking density. Daily at 5 a.m., the model generated a HS prediction [0 = no health disorder (HD); 1 = health disorder]. At 7 a.m., technicians blind to the prediction conducted clinical exams on cows from 3 to 11 DIM to classify cows (n = 625) as affected (HD = 1) or not (HD = 0) by metritis, mastitis, ketosis, indigestion, displaced abomasum, and pneumonia. Using each day a cow presented clinical signs of HD as a positive case (i.e., HD = 1), metrics of performance (%; 95% CI) were: sensitivity (Se) = 57 [52, 62], specificity = 81 [80, 82]; positive predictive value (PPV) = 20 [18, 22], negative predictive value = 96 [95, 96], accuracy = 79 [78, 80], balanced accuracy = 69 [66, 72], F-1 Score = 29 [26, 32]. Sensitivity was also evaluated using fixed time intervals around clinical diagnosis of disease as a positive case (Table 1). Our findings suggest that the ability of an XGBoost algorithm trained on diverse sensor and nonsensor data to identify cows with HD was moderate when only days when cows presented clinical signs of disease were considered a positive case. Sensitivity and PPV can be improved substantially when all days within fixed intervals before and after clinical diagnosis are used as positive cases. Table 1 (Abstr. 2614). Sensitivity and PPV for an XGBoost algorithm trained to predict cow health status using fixed intervals before and after clinical diagnosis as positive cases Day relative to CD Se (%) 95% CI PPV (%) 95% CI −5 to 0 58 49, 67 21 16, 25 −3 to 0 55 46, 64 19 15, 24 −5 to 1 69 61, 78 24 20, 29 −5 to 3 81 73, 88 28 23, 33 −5 to 5 86 80, 92 30 25, 34 −3 to 1 67 58, 75 23 18, 27 −3 to 3 78 70, 86 27 22, 31 −3 to 5 83 76, 90 28 24, 33 0 to 3 75 68, 83 24 20, 29 0 to 5 81 73, 88 26 21, 31 −1 to 0 54 44, 63 18 14, 22 0 to 1 63 54, 72 20 16, 25 −1 to 1 66 57, 75 21 17, 26 

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3. Far beyond the planar limit in strongly-coupled $$ \mathcal{N} $$ = 4 SYM

   https://doi.org/10.1007/JHEP01(2021)103  

   Chester, Shai M.; Pufu, Silviu S. (January 2021, Journal of High Energy Physics)

   A bstract When the SU( N ) $$ \mathcal{N} $$ N = 4 super-Yang-Mills (SYM) theory with complexified gauge coupling τ is placed on a round four-sphere and deformed by an $$ \mathcal{N} $$ N = 2-preserving mass parameter m , its free energy F ( m, τ, $$ \overline{\tau} $$ τ ¯ ) can be computed exactly using supersymmetric localization. In this work, we derive a new exact relation between the fourth derivative $$ {\partial}_m^4F\left(m,\tau, \overline{\tau}\right)\left|{{}_m}_{=0}\right. $$ ∂ m 4 F m τ τ ¯ m = 0 of the sphere free energy and the integrated stress-tensor multiplet four-point function in the $$ \mathcal{N} $$ N = 4 SYM theory. We then apply this exact relation, along with various other constraints derived in previous work (coming from analytic bootstrap, the mixed derivative $$ {\partial}_{\tau }{\partial}_{\overline{\tau}}{\partial}_m^2F\left(m,\tau, \overline{\tau}\right)\left|{{}_m}_{=0}\right. $$ ∂ τ ∂ τ ¯ ∂ m 2 F m τ τ ¯ m = 0 , and type IIB superstring theory scattering amplitudes) to determine various perturbative terms in the large N and large ’t Hooft coupling λ expansion of the $$ \mathcal{N} $$ N = 4 SYM correlator at separated points. In particular, we determine the leading large- λ term in the $$ \mathcal{N} $$ N = 4 SYM correlation function at order 1 /N 8 . This is three orders beyond the planar limit. 

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4. Maps from Feigin and Odesskii's elliptic algebras to twisted homogeneous coordinate rings

   https://doi.org/10.1017/fms.2020.60  

   Chirvasitu, Alex; Kanda, Ryo; Smith, S. Paul (January 2021, Forum of Mathematics, Sigma)

   null (Ed.)

   Abstract The elliptic algebras in the title are connected graded $$\mathbb {C}$$ -algebras, denoted $$Q_{n,k}(E,\tau )$$ , depending on a pair of relatively prime integers $$n>k\ge 1$$ , an elliptic curve E and a point $$\tau \in E$$ . This paper examines a canonical homomorphism from $$Q_{n,k}(E,\tau )$$ to the twisted homogeneous coordinate ring $$B(X_{n/k},\sigma ',\mathcal {L}^{\prime }_{n/k})$$ on the characteristic variety $$X_{n/k}$$ for $$Q_{n,k}(E,\tau )$$ . When $$X_{n/k}$$ is isomorphic to $E^g$ or the symmetric power $S^gE$ , we show that the homomorphism $$Q_{n,k}(E,\tau ) \to B(X_{n/k},\sigma ',\mathcal {L}^{\prime }_{n/k})$$ is surjective, the relations for $$B(X_{n/k},\sigma ',\mathcal {L}^{\prime }_{n/k})$$ are generated in degrees $$\le 3$$ and the noncommutative scheme $$\mathrm {Proj}_{nc}(Q_{n,k}(E,\tau ))$$ has a closed subvariety that is isomorphic to $E^g$ or $S^gE$ , respectively. When $$X_{n/k}=E^g$$ and $$\tau =0$$ , the results about $$B(X_{n/k},\sigma ',\mathcal {L}^{\prime }_{n/k})$$ show that the morphism $$\Phi _{|\mathcal {L}_{n/k}|}:E^g \to \mathbb {P}^{n-1}$$ embeds $E^g$ as a projectively normal subvariety that is a scheme-theoretic intersection of quadric and cubic hypersurfaces. 

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5. A Duality Principle for Groups II: Multi-frames Meet Super-Frames

   https://doi.org/10.1007/s00041-020-09792-0  

   Balan, R.; Dutkay, D.; Han, D.; Larson, D.; Luef, F. (December 2020, Journal of Fourier Analysis and Applications)

   null (Ed.)

   Abstract The duality principle for group representations developed in Dutkay et al. (J Funct Anal 257:1133–1143, 2009), Han and Larson (Bull Lond Math Soc 40:685–695, 2008) exhibits a fact that the well-known duality principle in Gabor analysis is not an isolated incident but a more general phenomenon residing in the context of group representation theory. There are two other well-known fundamental properties in Gabor analysis: the biorthogonality and the fundamental identity of Gabor analysis. The main purpose of this this paper is to show that these two fundamental properties remain to be true for general projective unitary group representations. Moreover, we also present a general duality theorem which shows that that muti-frame generators meet super-frame generators through a dual commutant pair of group representations. Applying it to the Gabor representations, we obtain that $$\{\pi _{\Lambda }(m, n)g_{1} \oplus \cdots \oplus \pi _{\Lambda }(m, n)g_{k}\}_{m, n \in {\mathbb {Z}}^{d}}$$ { π Λ ( m , n ) g 1 ⊕ ⋯ ⊕ π Λ ( m , n ) g k } m , n ∈ Z d is a frame for $$L^{2}({\mathbb {R}}\,^{d})\oplus \cdots \oplus L^{2}({\mathbb {R}}\,^{d})$$ L 2 ( R d ) ⊕ ⋯ ⊕ L 2 ( R d ) if and only if $$\cup _{i=1}^{k}\{\pi _{\Lambda ^{o}}(m, n)g_{i}\}_{m, n\in {\mathbb {Z}}^{d}}$$ ∪ i = 1 k { π Λ o ( m , n ) g i } m , n ∈ Z d is a Riesz sequence, and $$\cup _{i=1}^{k} \{\pi _{\Lambda }(m, n)g_{i}\}_{m, n\in {\mathbb {Z}}^{d}}$$ ∪ i = 1 k { π Λ ( m , n ) g i } m , n ∈ Z d is a frame for $$L^{2}({\mathbb {R}}\,^{d})$$ L 2 ( R d ) if and only if $$\{\pi _{\Lambda ^{o}}(m, n)g_{1} \oplus \cdots \oplus \pi _{\Lambda ^{o}}(m, n)g_{k}\}_{m, n \in {\mathbb {Z}}^{d}}$$ { π Λ o ( m , n ) g 1 ⊕ ⋯ ⊕ π Λ o ( m , n ) g k } m , n ∈ Z d is a Riesz sequence, where $$\pi _{\Lambda }$$ π Λ and $$\pi _{\Lambda ^{o}}$$ π Λ o is a pair of Gabor representations restricted to a time–frequency lattice $$\Lambda $$ Λ and its adjoint lattice $$\Lambda ^{o}$$ Λ o in $${\mathbb {R}}\,^{d}\times {\mathbb {R}}\,^{d}$$ R d × R d . 

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