The self-consistent general relativistic solution for a system of degenerate neutrons, protons and electrons in beta-equilibrium

We present the self-consistent treatment of the simplest, nontrivial, self-gravitating system of degenerate neutrons, protons and electrons in $\beta$-equilibrium within relativistic quantum statistics and the Einstein-Maxwell equations. The impossibility of imposing the condition of local charge neutrality on such systems is proved, consequently overcoming the traditional Tolman-Oppenheimer-Volkoff treatment. We emphasize the crucial role of imposing the constancy of the generalized Fermi energies. A new approach based on the coupled system of the general relativistic Thomas-Fermi-Einstein-Maxwell equations is presented and solved. We obtain an explicit solution fulfilling global and not local charge neutrality by solving a sophisticated eigenvalue problem of the general relativistic Thomas-Fermi equation. The value of the Coulomb potential at the center of the configuration is $eV(0)\simeq m_\pi c^2$ and the system is intrinsically stable against Coulomb repulsion in the proton component. This approach is necessary, but not sufficient, when strong interactions are introduced.Comment: Letter in press, Physics Letters B (2011

A nearly zero-energy microgrid testbed laboratory: Centralized control strategy based on SCADA system

Currently, despite the use of renewable energy sources (RESs), distribution networks are facing problems, such as complexity and low productivity. Emerging microgrids (MGs) with RESs based on supervisory control and data acquisition (SCADA) are an effective solution to control, manage, and finally deal with these challenges. The development and success of MGs is highly dependent on the use of power electronic interfaces. The use of these interfaces is directly related to the progress of SCADA systems and communication infrastructures. The use of SCADA systems for the control and operation of MGs and active distribution networks promotes productivity and efficiency. This paper presents a real MG case study called the LAMBDA MG testbed laboratory, which has been implemented in the electrical department of the Sapienza University of Rome with a centralized energy management system (CEMS). The real-time results of the SCADA system show that a CEMS can create proper energy balance in a LAMBDA MG testbed and, consequently, minimize the exchange power of the LAMBDA MG and main grid

Strong electric fields induced on a sharp stellar boundary

Due to a first order phase transition, a compact star may have a discontinuous distribution of baryon as well as electric charge densities, as e.g. at the surface of a strange quark star. The induced separation of positive and negative charges may lead to generation of supercritical electric fields in the vicinity of such a discontinuity. We study this effect within a relativistic Thomas-Fermi approximation and demonstrate that the strength of the electric field depends strongly on the degree of sharpness of the surface. The influence of strong electric fields on the stability of compact stars is discussed. It is demonstrated that stable configurations appear only when the counter-pressure of degenerate fermions is taken into consideration.Comment: 13 pages, 2 figure

The relativistic Thomas-Fermi treatment for compressed atoms at finite temperatures

The degenerate relativistic Feynman, Metropolis and Teller treatment of compressed atoms is extended to finite temperatures. We present numerical calculations of the equation of state for dense matter as well as profiles of the electron density as a function of distance from the atomic nucleus for selected values of the total matter density and temperature. Marked differences appear especially in the low-density regimes

Universal mean-field upper bound for the generalization gap of deep neural networks

Modern deep neural networks (DNNs) represent a formidable challenge for theorists: according to the commonly accepted probabilistic framework that describes their performance, these architectures should overfit due to the huge number of parameters to train, but in practice they do not. Here we employ results from replica mean field theory to compute the generalization gap of machine learning models with quenched features, in the teacher-student scenario and for regression problems with quadratic loss function. Notably, this framework includes the case of DNNs where the last layer is optimized given a specific realization of the remaining weights. We show how these results-combined with ideas from statistical learning theory-provide a stringent asymptotic upper bound on the generalization gap of fully trained DNN as a function of the size of the dataset P. In particular, in the limit of large P and N-out (where N-out is the size of the last layer) and N-out << P, the generalization gap approaches zero faster than 2N(out)/P, for any choice of both architecture and teacher function. Notably, this result greatly improves existing bounds from statistical learning theory. We test our predictions on a broad range of architectures, from toy fully connected neural networks with few hidden layers to state-of-the-art deep convolutional neural networks