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The power of DNN has been successfully demonstrated on a wide variety of high-dimensional problems that cannot be solved by conventional control design methods. These successes also uncover some fundamental and pressing challenges in understanding the representability of deep neural networks for complex and high dimensional input–output relations. Towards the goal of understanding these fundamental questions, we applied an algebraic framework developed in our previous work to analyze ReLU neural network approximation of compositional functions. We prove that for Lipschitz continuous functions, ReLU neural networks have an approximation error upper bound that is a polynomial of the network’s complexity and the compositional features. If the compositional features do not increase exponentially with dimension, which is the case in many applications, the complexity of DNN has a polynomial growth. In addition to function approximations, we also establish ReLU network approximation results for the trajectories of control systems, and for a Lyapunov function that characterizes the domain of attraction. 

IceCube alert events are neutrinos with a moderate-to-high probability of having astrophysical origin. In this study, we analyze 11 yr of IceCube data and investigate 122 alert events and a selection of high-energy tracks detected between 2009 and the end of 2021. This high-energy event selection (alert events + high-energy tracks) has an average probability of ≥0.5 of being of astrophysical origin. We search for additional continuous and transient neutrino emission within the high-energy events’ error regions. We find no evidence for significant continuous neutrino emission from any of the alert event directions. The only locally significant neutrino emission is the transient emission associated with the blazar TXS 0506+056, with a local significance of 3σ, which confirms previous IceCube studies. When correcting for 122 test positions, the globalp-value is 0.156 and compatible with the background hypothesis. We constrain the total continuous flux emitted from all 122 test positions at 100 TeV to be below 1.2 × 10⁻¹⁵(TeV cm²s)⁻¹at 90% confidence assuming anE⁻²spectrum. This corresponds to 4.5% of IceCube’s astrophysical diffuse flux. Overall, we find no indication that alert events in general are linked to lower-energetic continuous or transient neutrino emission.

 

Abstract We present a background model for dark matter searches using an array of NaI(Tl) crystals in the COSINE-100 experiment that is located in the Yangyang underground laboratory. The model includes background contributions from both internal and external sources, including cosmogenic radionuclides and surface $$^{210}$$ 210 Pb contamination. To build the model in the low energy region, with a threshold of 1 keV, we used a depth profile of $$^{210}$$ 210 Pb contamination in the surface of the NaI(Tl) crystals determined in a comparison between measured and simulated spectra. We also considered the effect of the energy scale errors propagated from the statistical uncertainties and the nonlinear detector response at low energies. The 1.7 years COSINE-100 data taken between October 21, 2016 and July 18, 2018 were used for this analysis. Our Monte Carlo simulation provides a non-Gaussian peak around 50 keV originating from beta decays of bulk $$^{210}$$ 210 Pb in a good agreement with the measured background. This model estimates that the activities of bulk $$^{210}$$ 210 Pb and $$^{3}$$ 3 H are dominating the background rate that amounts to an average level of $$2.85\pm 0.15$$ 2.85 ± 0.15  counts/day/keV/kg in the energy region of (1–6) keV, using COSINE-100 data with a total exposure of 97.7 kg $$\cdot $$ · years. 

We report the identification of metastable isomeric states of$$^{228}$$${}^{228}$Ac at 6.28 keV, 6.67 keV and 20.19 keV, with lifetimes of an order of 100 ns. These states are produced by the$$\beta $$$\beta$-decay of$$^{228}$$${}^{228}$Ra, a component of the$$^{232}$$${}^{232}$Th decay chain, with$$\beta $$$\beta$Q-values of 39.52 keV, 39.13 keV and 25.61 keV, respectively. Due to the low Q-value of$$^{228}$$${}^{228}$Ra as well as the relative abundance of$$^{232}$$${}^{232}$Th and their progeny in low background experiments, these observations potentially impact the low-energy background modeling of dark matter search experiments.