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1. Instantaneous everywhere-blowup of parabolic SPDEs

   https://doi.org/10.1007/s00440-024-01263-7  

   Foondun, Mohammud; Khoshnevisan, Davar; Nualart, Eulalia (October 2024, Probability Theory and Related Fields)

   Abstract We consider the following stochastic heat equation$$\begin{aligned} \partial _t u(t,x) = \tfrac{1}{2} \partial ^2_x u(t,x) + b(u(t,x)) + \sigma (u(t,x)) {\dot{W}}(t,x), \end{aligned}$$ $\begin{array}{c}{\partial }_{t}u(t,x)=\frac{1}{2}{\partial }_x^{2}u(t,x)+b\left(u(t,x)\right)+\sigma \left(u(t,x)\right)\dot{W}(t,x),\end{array}$defined for$$(t,x)\in (0,\infty )\times {\mathbb {R}}$$ $(t,x)\in (0,\infty )\times R$, where$${\dot{W}}$$ $\dot{W}$denotes space-time white noise. The function$$\sigma $$ $\sigma$is assumed to be positive, bounded, globally Lipschitz, and bounded uniformly away from the origin, and the functionbis assumed to be positive, locally Lipschitz and nondecreasing. We prove that the Osgood condition$$\begin{aligned} \int _1^\infty \frac{\textrm{d}y}{b(y)}<\infty \end{aligned}$$ $\begin{array}{c}{\int }_1^{\infty }\frac{\text{d}y}{b\left(y\right)}<\infty \end{array}$implies that the solution almost surely blows up everywhere and instantaneously, In other words, the Osgood condition ensures that$$\textrm{P}\{ u(t,x)=\infty \quad \hbox { for all } t>0 \hbox { and } x\in {\mathbb {R}}\}=1.$$ $\text{P}\left\{u\right(t,x)=\infty \text{for all}t>0\text{and}x\in R\}=1.$The main ingredients of the proof involve a hitting-time bound for a class of differential inequalities (Remark 3.3), and the study of the spatial growth of stochastic convolutions using techniques from the Malliavin calculus and the Poincaré inequalities that were developed in Chen et al. (Electron J Probab 26:1–37, 2021, J Funct Anal 282(2):109290, 2022). 

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2. VC-Dimension of Hyperplanes Over Finite Fields

   https://doi.org/10.1007/s00373-025-02909-6  

   Ascoli, Ruben; Betti, Livia; Cheigh, Justin; Iosevich, Alex; Jeong, Ryan; Liu, Xuyan; McDonald, Brian; Milgrim, Wyatt; Miller, Steven_J; Romero_Acosta, Francisco; et al (March 2025, Graphs and Combinatorics)

   Abstract Let$$\mathbb {F}_q^d$$ $F_q^d$be thed-dimensional vector space over the finite field withqelements. For a subset$$E\subseteq \mathbb {F}_q^d$$ $E\subseteq F_q^d$and a fixed nonzero$$t\in \mathbb {F}_q$$ $t\in F_q$, let$$\mathcal {H}_t(E)=\{h_y: y\in E\}$$ $H_t\left(E\right)=\{h_y:y\in E\}$, where$$h_y:E\rightarrow \{0,1\}$$ $h_y:E\to \{0,1\}$is the indicator function of the set$$\{x\in E: x\cdot y=t\}$$ $\{x\in E:x·y=t\}$. Two of the authors, with Maxwell Sun, showed in the case$$d=3$$ $d=3$that if$$|E|\ge Cq^{\frac{11}{4}}$$ $\left|E\right|\ge C{q}^{\frac{11}{4}}$andqis sufficiently large, then the VC-dimension of$$\mathcal {H}_t(E)$$ $H_t\left(E\right)$is 3. In this paper, we generalize the result to arbitrary dimension by showing that the VC-dimension of$$\mathcal {H}_t(E)$$ $H_t\left(E\right)$isdwhenever$$E\subseteq \mathbb {F}_q^d$$ $E\subseteq F_q^d$with$$|E|\ge C_d q^{d-\frac{1}{d-1}}$$ $\left|E\right|\ge C_d{q}^{d-\frac{1}{d-1}}$. 

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3. Spin density matrix elements in exclusive $$\rho ^0$$ meson muoproduction

   https://doi.org/10.1140/epjc/s10052-023-11359-4  

   Alexeev, G D; Alexeev, M G; Alice, C; Amoroso, A; Andrieux, V; Anosov, V; Augsten, K; Augustyniak, W; Azevedo, C_D R; Badelek, B; et al (October 2023, The European Physical Journal C)

   Abstract We report on a measurement of Spin Density Matrix Elements (SDMEs) in hard exclusive$$\rho ^0$$ ${\rho }^0$meson muoproduction at COMPASS using 160 GeV/cpolarised$$ \mu ^{+}$$ ${\mu }^{+}$and$$ \mu ^{-}$$ ${\mu }^{-}$beams impinging on a liquid hydrogen target. The measurement covers the kinematic range 5.0 GeV/$$c^2$$ $c^2$$$< W<$$ $<W<$17.0 GeV/$$c^2$$ $c^2$, 1.0 (GeV/c)$$^2$$ ${}^2$$$< Q^2<$$ $<Q^2<$10.0 (GeV/c)$$^2$$ ${}^2$and 0.01 (GeV/c)$$^2$$ ${}^2$$$< p_{\textrm{T}}^2<$$ $<p_{\text{T}}^2<$0.5 (GeV/c)$$^2$$ ${}^2$. Here,Wdenotes the mass of the final hadronic system,$$Q^2$$ $Q^2$the virtuality of the exchanged photon, and$$p_{\textrm{T}}$$ $p_{\text{T}}$the transverse momentum of the$$\rho ^0$$ ${\rho }^0$meson with respect to the virtual-photon direction. The measured non-zero SDMEs for the transitions of transversely polarised virtual photons to longitudinally polarised vector mesons ($$\gamma ^*_T \rightarrow V^{ }_L$$ ${\gamma }_T^{\ast }\to V_L^{}$) indicate a violation ofs-channel helicity conservation. Additionally, we observe a dominant contribution of natural-parity-exchange transitions and a very small contribution of unnatural-parity-exchange transitions, which is compatible with zero within experimental uncertainties. The results provide important input for modelling Generalised Parton Distributions (GPDs). In particular, they may allow one to evaluate in a model-dependent way the role of parton helicity-flip GPDs in exclusive$$\rho ^0$$ ${\rho }^0$production. 

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4. 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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5. Search for supersymmetry in final states with missing transverse momentum and three or more b-jets in 139 fb$$^{-1}$$ of proton–proton collisions at $$\sqrt{s} = 13$$ TeV with the ATLAS detector

   https://doi.org/10.1140/epjc/s10052-023-11543-6  

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

   Abstract A search for supersymmetry involving the pair production of gluinos decaying via off-shell third-generation squarks into the lightest neutralino$$(\tilde{\chi }^0_1)$$ $\left({\tilde{\chi }}_1^0\right)$is reported. It exploits LHC proton–proton collision data at a centre-of-mass energy$$\sqrt{s} = 13$$ $\sqrt{s}=13$TeV with an integrated luminosity of 139 fb$$^{-1}$$ ${}^{-1}$collected with the ATLAS detector from 2015 to 2018. The search uses events containing large missing transverse momentum, up to one electron or muon, and several energetic jets, at least three of which must be identified as containingb-hadrons. Both a simple kinematic event selection and an event selection based upon a deep neural-network are used. No significant excess above the predicted background is found. In simplified models involving the pair production of gluinos that decay via off-shell top (bottom) squarks, gluino masses less than 2.44 TeV (2.35 TeV) are excluded at 95% CL for a massless$$\tilde{\chi }^0_1.$$ ${\tilde{\chi }}_1^0.$Limits are also set on the gluino mass in models with variable branching ratios for gluino decays to$$b\bar{b}\tilde{\chi }^0_1,$$ $b\overline{b}{\tilde{\chi }}_1^0,$$$t\bar{t}\tilde{\chi }^0_1$$ $t\overline{t}{\tilde{\chi }}_1^0$and$$t\bar{b}\tilde{\chi }^-_1/\bar{t}b\tilde{\chi }^+_1.$$ $t\overline{b}{\tilde{\chi }}_1^{-}/\overline{t}b{\tilde{\chi }}_1^{+}.$ 

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