We study expressive power of shallow and deep neural networks with piece-wise linear activation functions. We establish new rigorous upper and lower bounds for the network complexity in the setting of approximations in Sobolev spaces. In particular, we prove that deep ReLU networks more efficiently approximate smooth functions than shallow networks. In the case of approximations of 1D Lipschitz...

Coral reefs worldwide are facing increasing stress due to drastic changes in their environment. Mesophotic coral ecosystems (MCEs) have been considered as a potential refuge from several major stressors, such as warm-water bleaching events. However, their role as a subsequent source of larvae remains unclear for many species, particularly as genetic differentiation of corals over depth has freq...

Background Cochlear implant surgery is an invasive procedure for patients with bilateral Sensorineural hearing loss and may cause some risks such as cochlear damage. We aimed to evaluate the effectiveness of cochlear measures obtained by computed tomography (CT) scan in predicting depth of cochlear implant insertion. Materials and Methods This study was conducted in a retrospective and cross-se...

Coral bleaching caused by rising sea temperature is a primary cause of coral reef degradation. However, bleaching patterns often show significant spatial variability, therefore identifying locations where local conditions may provide thermal refuges is a high conservation priority. Coral bleaching mortality often diminishes with increasing depth, but clear depth zonation of coral communities an...

Footprints are the most direct source of evidence about locomotor biomechanics in extinct vertebrates. One of the principal suppositions underpinning biomechanical inferences is that footprint geometry correlates with dynamic foot pressure, which, in turn, is linked with overall limb motion of the trackmaker. In this study, we perform the first quantitative test of this long-standing assumption...

Earthquake swarms observed before the 2006 and 2011 Nyamuragira eruptions were analysed. The activitiesand hypocenter distributions of these earthquake swarms were mainly examined.The former swarm was characterised by a higher seismic activity than the later. Although the two swarmsaccompanied eruptions, most of the swarms observed in 2006 and 2011 were not followed by any eruptions...

Coral bleaching caused by rising sea temperature is a primary cause of coral reef degradation. However, bleaching patterns often show significant spatial variability, therefore identifying locations where local conditions may provide thermal refuges is a high conservation priority. Coral bleaching mortality often diminishes with increasing depth, but clear depth zonation of coral communities an...

TWODEE-2 is a FORTRAN 90 code based on previous code (TWODEE). It is designed to solve the shallow water equations for fluid depth, depth-averaged horizontal velocities and depth-averaged fluid density. The shallow layer approach used by TWODEE-2 is a compromise between the complexity of CFD models and the simpler integral models. It can be used for forecasting gas dispersion near the ground an...