Exponential ReLU Neural Network Approximation Rates for Point and Edge Singularities

We prove exponential expressivity with stable ReLU Neural Networks (ReLU NNs) in $H^1(\Omega)$ for weighted analytic function classes in certain polytopal domains $\Omega$, in space dimension $d=2,3$. Functions in these classes are locally analytic on open subdomains $D\subset \Omega$, but may exhibit isolated point singularities in the interior of $\Omega$ or corner and edge singularities at the boundary $\partial \Omega$. The exponential expression rate bounds proved here imply uniform exponential expressivity by ReLU NNs of solution families for several elliptic boundary and eigenvalue problems with analytic data. The exponential approximation rates are shown to hold in space dimension $d = 2$ on Lipschitz polygons with straight sides, and in space dimension $d=3$ on Fichera-type polyhedral domains with plane faces. The constructive proofs indicate in particular that NN depth and size increase poly-logarithmically with respect to the target NN approximation accuracy $\varepsilon>0$ in $H^1(\Omega)$. The results cover in particular solution sets of linear, second order elliptic PDEs with analytic data and certain nonlinear elliptic eigenvalue problems with analytic nonlinearities and singular, weighted analytic potentials as arise in electron structure models. In the latter case, the functions correspond to electron densities that exhibit isolated point singularities at the positions of the nuclei. Our findings provide in particular mathematical foundation of recently reported, successful uses of deep neural networks in variational electron structure algorithms.Comment: Found Comput Math (2022

Prevalence of foodborne pathogens in rural pigs and in derived cold pork meats - preliminary report

The rural breeding of one or two pigs and their domestic slaughtering is a significance reality in the Veneto Region, as a consequence of an ancient tradition still surviving in this countryside. In the eastern part of the Venice Province, about 2,500 rural pigs are bred and slaughtered ever year in the period between November and February. Many data are available on mdustnal breeding and processing, whereas very little is known about the prevalence of foodborne pathogens both in live ammals and in denved food, mainly sausage, salami and cold pork meats

Plant height and hydraulic vulnerability to drought and cold

Understanding how plants survive drought and cold is increasingly important as plants worldwide experience dieback with drought in moist places and grow taller with warming in cold ones. Crucial in plant climate adaptation are the diameters of water-transporting conduits. Sampling 537 species across climate zones dominated by angiosperms, we find that plant size is unambiguously the main driver of conduit diameter variation. And because taller plants have wider conduits, and wider conduits within species are more vulnerable to conduction-blocking embolisms, taller conspecifics should be more vulnerable than shorter ones, a prediction we confirm with a plantation experiment. As a result, maximum plant size should be short under drought and cold, which cause embolism, or increase if these pressures relax. That conduit diameter and embolism vulnerability are inseparably related to plant size helps explain why factors that interact with conduit diameter, such as drought or warming, are altering plant heights worldwide

EVALUATION OF THE SHELF LIFE AND MICROBIOLOGICAL PARAMETERS IN A CHILLED READY TO EAT MEAT PRODUCT: THE "VITEL TONNÈ"

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Managerial coordination challenges in the alignment of capabilities and new subsidiary charters in MNEs

Subsidiary-level change requires the alignment of subsidiary charters and capabilities. Yet, the mechanisms through which the alignment of charters and capabilities unfolds are not yet well understood. In this paper, we investigate alignment from the perspective of managerial coordination. Drawing on a longitudinal study of a global IT firm, we identify three coordination mechanisms (charter-, experience-, and interaction-based coordination). By tracing the shifts in these coordination mechanisms over time and by specifying the implications of each mechanism for capability level change, we explain how managerial coordination influences alignment via subsidiary level capability change as well as alignment via the potential renegotiation of charters. This also allows us to provide new insights into situations of misalignment by explaining that particular mechanisms of coordination may become a source of decoupling between subsidiary actions and HQ mandates and may also result in capability level inertia. Moreover, while prior research has already acknowledged the role of interaction-based coordination for capability level change we show how and why such a mechanism of coordination emerges. ABSTRACT FROM AUTHO

On the Finite Energy Weak Solutions to a System in Quantum Fluid Dynamics

In this paper we consider the global existence of weak solutions to a class of Quantum Hydrodynamics (QHD) systems with initial data, arbitrarily large in the energy norm. These type of models, initially proposed by Madelung, have been extensively used in Physics to investigate Supefluidity and Superconductivity phenomena and more recently in the modeling of semiconductor devices . Our approach is based on various tools, namely the wave functions polar decomposition, the construction of approximate solution via a fractional steps method, which iterates a Schr\"odinger Madelung picture with a suitable wave function updating mechanism. Therefore several \emph{a priori} bounds of energy, dispersive and local smoothing type allow us to prove the compactness of the approximating sequences. No uniqueness result is provided