Search for: All records

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. 

Abstract The recent IceCube detection of TeV neutrino emission from the nearby active galaxy NGC 1068 suggests that active galactic nuclei (AGNs) could make a sizable contribution to the diffuse flux of astrophysical neutrinos. The absence of TeVγ-rays from NGC 1068 indicates neutrino production in the vicinity of the supermassive black hole, where the high radiation density leads toγ-ray attenuation. Therefore, any potential neutrino emission from similar sources is not expected to correlate with high-energyγ-rays. Disk-corona models predict neutrino emission from Seyfert galaxies to correlate with keV X-rays because they are tracers of coronal activity. Using through-going track events from the Northern Sky recorded by IceCube between 2011 and 2021, we report results from a search for individual and aggregated neutrino signals from 27 additional Seyfert galaxies that are contained in the Swift's Burst Alert Telescope AGN Spectroscopic Survey. Besides the generic single power law, we evaluate the spectra predicted by the disk-corona model assuming stochastic acceleration parameters that match the measured flux from NGC 1068. Assuming all sources to be intrinsically similar to NGC 1068, our findings constrain the collective neutrino emission from X-ray bright Seyfert galaxies in the northern sky, but, at the same time, show excesses of neutrinos that could be associated with the objects NGC 4151 and CGCG 420-015. These excesses result in a 2.7σsignificance with respect to background expectations. 

We report a study of the inelasticity distribution in the scattering of neutrinos of energy 80–560 GeV off nucleons. Using atmospheric muon neutrinos detected in IceCube’s sub-array DeepCore during 2012–2021, we fit the observed inelasticity in the data to a parameterized expectation and extract the values that describe it best. Finally, we compare the results to predictions from various combinations of perturbative QCD calculations and atmospheric neutrino flux models. Published by the American Physical Society2025