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1. Rates of convergence for regression with the graph poly-Laplacian

   https://doi.org/10.1007/s43670-023-00075-5  

   Trillos, Nicolás García; Murray, Ryan; Thorpe, Matthew (November 2023, Sampling Theory, Signal Processing, and Data Analysis)

   Abstract In the (special) smoothing spline problem one considers a variational problem with a quadratic data fidelity penalty and Laplacian regularization. Higher order regularity can be obtained via replacing the Laplacian regulariser with a poly-Laplacian regulariser. The methodology is readily adapted to graphs and here we consider graph poly-Laplacian regularization in a fully supervised, non-parametric, noise corrupted, regression problem. In particular, given a dataset$$\{x_i\}_{i=1}^n$$ ${\left\{x_i\right\}}_{i=1}^n$and a set of noisy labels$$\{y_i\}_{i=1}^n\subset \mathbb {R}$$ ${\left\{y_i\right\}}_{i=1}^n\subset R$we let$$u_n{:}\{x_i\}_{i=1}^n\rightarrow \mathbb {R}$$ $u_n:{\left\{x_i\right\}}_{i=1}^n\to R$be the minimizer of an energy which consists of a data fidelity term and an appropriately scaled graph poly-Laplacian term. When$$y_i = g(x_i)+\xi _i$$ $y_i=g\left(x_i\right)+{\xi }_i$, for iid noise$$\xi _i$$ ${\xi }_i$, and using the geometric random graph, we identify (with high probability) the rate of convergence of$$u_n$$ $u_n$togin the large data limit$$n\rightarrow \infty $$ $n\to \infty$. Furthermore, our rate is close to the known rate of convergence in the usual smoothing spline model. 

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2. Measurement of beauty-quark production in pp collisions at $$ \sqrt{s} $$ = 13 TeV via non-prompt D mesons

   https://doi.org/10.1007/JHEP10(2024)110  

   Acharya, S; Adamová, D; Agarwal, A; Aglieri_Rinella, G; Aglietta, L; Agnello, M; Agrawal, N; Ahammed, Z; Ahmad, S; Ahn, S U; et al (October 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> Thep_T-differential production cross sections of non-prompt D⁰, D⁺, and$$ {\textrm{D}}_{\textrm{s}}^{+} $$ $D_s^{+}$mesons originating from beauty-hadron decays are measured in proton–proton collisions at a centre-of-mass energy$$ \sqrt{s} $$ $\sqrt{s}$= 13 TeV. The measurements are performed at midrapidity, |y|<0.5, with the data sample collected by ALICE from 2016 to 2018. The results are in agreement with predictions from several perturbative QCD calculations. The fragmentation fraction of beauty quarks to strange mesons divided by the one to non-strange mesons,f_s/(f_u+f_d), is found to be 0.114 ± 0.016 (stat.) ± 0.006 (syst.) ± 0.003 (BR) ± 0.003 (extrap.). This value is compatible with previous measurements at lower centre-of-mass energies and in different collision systems in agreement with the assumption of universality of fragmentation functions. In addition, the dependence of the non-prompt D meson production on the centre-of-mass energy is investigated by comparing the results obtained at$$ \sqrt{s} $$ $\sqrt{s}$= 5.02 and 13 TeV, showing a hardening of the non-prompt D-mesonp_T-differential production cross section at higher$$ \sqrt{s} $$ $\sqrt{s}$. Finally, the$$ \textrm{b}\overline{\textrm{b}} $$ $b\overline{b}$production cross section per unit of rapidity at midrapidity is calculated from the non-prompt D⁰, D⁺,$$ {\textrm{D}}_{\textrm{s}}^{+} $$ $D_s^{+}$, and$$ {\Lambda}_{\textrm{c}}^{+} $$ ${\Lambda }_c^{+}$hadron measurements, obtaining$$ \textrm{d}\sigma /\textrm{d}y=75.2\pm 3.2\left(\textrm{stat}.\right)\pm 5.2{\left(\textrm{syst}.\right)}_{-3.2}^{+12.3}\left(\textrm{extrap}.\right) $$ $d\sigma /dy=75.2\pm 3.2\left(\text{stat}.\right)\pm 5.2{\left(\text{syst}.\right)}_{-3.2}^{+12.3}\left(\text{extrap}.\right)$μb. 

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3. Spherical convex hull of random points on a wedge

   https://doi.org/10.1007/s00208-023-02704-9  

   Besau, Florian; Gusakova, Anna; Reitzner, Matthias; Schütt, Carsten; Thäle, Christoph; Werner, Elisabeth_M (August 2023, Mathematische Annalen)

   Abstract Consider two half-spaces$$H_1^+$$ $H_1^{+}$and$$H_2^+$$ $H_2^{+}$in$${\mathbb {R}}^{d+1}$$ $R^{d+1}$whose bounding hyperplanes$$H_1$$ $H_1$and$$H_2$$ $H_2$are orthogonal and pass through the origin. The intersection$${\mathbb {S}}_{2,+}^d:={\mathbb {S}}^d\cap H_1^+\cap H_2^+$$ $S_{2,+}^d:=S^d\cap H_1^{+}\cap H_2^{+}$is a spherical convex subset of thed-dimensional unit sphere$${\mathbb {S}}^d$$ $S^d$, which contains a great subsphere of dimension$$d-2$$ $d-2$and is called a spherical wedge. Choosenindependent random points uniformly at random on$${\mathbb {S}}_{2,+}^d$$ $S_{2,+}^d$and consider the expected facet number of the spherical convex hull of these points. It is shown that, up to terms of lower order, this expectation grows like a constant multiple of$$\log n$$ $logn$. A similar behaviour is obtained for the expected facet number of a homogeneous Poisson point process on$${\mathbb {S}}_{2,+}^d$$ $S_{2,+}^d$. The result is compared to the corresponding behaviour of classical Euclidean random polytopes and of spherical random polytopes on a half-sphere. 

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4. Lifetimes of excited states in $$^{16}$$C as a benchmark for ab initio developments

   https://doi.org/10.1140/epja/s10050-024-01396-2  

   Mathy, M; Petri, M; Roth, R; Wagner, L; Heil, S; Ayangeakaa, A D; Bottoni, S; Carpenter, M P; Crawford, H L; Fallon, P; et al (September 2024, The European Physical Journal A)

   Abstract Lifetimes of higher-lying states ($$2_2^+$$ $2_2^{+}$and$$4_1^+$$ $4_1^{+}$) in$$^{16}$$ $_{}^{16}$C have been measured, employing the Gammasphere and Microball detector arrays, as key observables to test and refine ab initio calculations based on interactions developed within chiral Effective Field Theory. The presented experimental constraints to these lifetimes of$$\tau ({2_2^+}) = [\,244, 446]\,~\textrm{fs}$$ $\tau \left(2_2^{+}\right)=[244,446]\text{fs}$and$$\tau ({4_1^+}) = [\,1.8, 4]\,~\textrm{ps}$$ $\tau \left(4_1^{+}\right)=[1.8,4]\text{ps}$, combined with previous results on the lifetime of the$$2_1^+$$ $2_1^{+}$state of$$^{16}$$ $_{}^{16}$C, provide a rather complete set of key observables to benchmark the theoretical developments. We present No-Core Shell-Model calculations using state-of-the-art chiral 2- (NN) and 3-nucleon (3N) interactions at next-to-next-to-next-to-leading order for both the NN and the 3N contributions and a generalized natural-orbital basis (instead of the conventional harmonic-oscillator single-particle basis) which reproduce, for the first time, the experimental findings remarkably well. The level of agreement of the new calculations as compared to the CD-Bonn meson-exchange NN interaction is notable and presents a critical benchmark for theory. 

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5. Differential cross-section measurements of Higgs boson production in the H → τ+τ− decay channel in pp collisions at $$ \sqrt{s} $$ = 13 TeV with the ATLAS detector

   https://doi.org/10.1007/JHEP03(2025)010  

   Aad, G; Aakvaag, E; Abbott, B; Abdelhameed, S; Abeling, K; Abicht, N J; Abidi, S H; Aboelela, M; Aboulhorma, A; Abramowicz, H; et al (March 2025, Journal of High Energy Physics)

   A<sc>bstract</sc> Differential measurements of Higgs boson production in theτ-lepton-pair decay channel are presented in the gluon fusion, vector-boson fusion (VBF),VHand$$ t\overline{t}H $$ $t\overline{t}H$associated production modes, with particular focus on the VBF production mode. The data used to perform the measurements correspond to 140 fb⁻¹of proton-proton collisions collected by the ATLAS experiment at the LHC. Two methods are used to perform the measurements: theSimplified Template Cross-Section(STXS) approach and anUnfolded Fiducial Differentialmeasurement considering only the VBF phase space. For the STXS measurement, events are categorized by their production mode and kinematic properties such as the Higgs boson’s transverse momentum ($$ {p}_{\textrm{T}}^{\textrm{H}} $$ $p_T^H$), the number of jets produced in association with the Higgs boson, or the invariant mass of the two leading jets (m_jj). For the VBF production mode, the ratio of the measured cross-section to the Standard Model prediction form_jj> 1.5 TeV and$$ {p}_{\textrm{T}}^{\textrm{H}} $$ $p_T^H$> 200 GeV ($$ {p}_{\textrm{T}}^{\textrm{H}} $$ $p_T^H$< 200 GeV) is$$ {1.29}_{-0.34}^{+0.39} $$ ${1.29}_{-0.34}^{+0.39}$($$ {0.12}_{-0.33}^{+0.34} $$ ${0.12}_{-0.33}^{+0.34}$). This is the first VBF measurement for the higher-$$ {p}_{\textrm{T}}^{\textrm{H}} $$ $p_T^H$criteria, and the most precise for the lower-$$ {p}_{\textrm{T}}^{\textrm{H}} $$ $p_T^H$criteria. Thefiducialcross-section measurements, which only consider the kinematic properties of the event, are performed as functions of variables characterizing the VBF topology, such as the signed ∆ϕ_jjbetween the two leading jets. The measurements have a precision of 30%–50% and agree well with the Standard Model predictions. These results are interpreted in the SMEFT framework, and place the strongest constraints to date on the CP-odd Wilson coefficient$$ {c}_{H\overset{\sim }{W}} $$ $c_{H\tilde{W}}$. 

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