Reconstruction of semileptonically decaying beauty hadrons produced in high energy pp collisions

It is well known that in $b$ hadron decays with a single unreconstructible final state particle, the decay kinematics can be solved up to a quadratic ambiguity, without any knowledge of the $b$ hadron momentum. We present a method to infer the momenta of $b$ hadrons produced in hadron collider experiments using information from their reconstructed flight vectors. Our method is strictly agnostic to the decay itself, which implies that it can be validated with control samples of topologically similar decays to fully reconstructible final states. A multivariate regression algorithm based on the flight information provides a $b$ hadron momentum estimate with a resolution of around 60% which is sufficient to select the correct solution to the quadratic equation in around 70% of cases. This will improve the ability of hadron collider experiments to make differential decay rate measurements with semileptonic $b$ hadron decays.Comment: 18 pages, 17 figures. Updated version to be published in JHE

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

On the Mass to Charge Ratio of Neutron Cores and Heavy Nuclei

We determine theoretically the relation between the total number of protons $N_{p}$ and the mass number $A$ (the charge to mass ratio) of nuclei and neutron cores with the model recently proposed by Ruffini et al. (2007) and we compare it with other $N_p$ versus $A$ relations: the empirical one, related to the Periodic Table, and the semi-empirical relation, obtained by minimizing the Weizs\"{a}cker mass formula. We find that there is a very good agreement between all the relations for values of $A$ typical of nuclei, with differences of the order of per cent. Our relation and the semi-empirical one are in agreement up to $A\sim 10^4$; for higher values, we find that the two relations differ. We interprete the different behaviour of our theoretical relation as a result of the penetration of electrons (initially confined in an external shell) inside the core, that becomes more and more important by increasing $A$; these effects are not taken into account in the semi-empirical mass-formula.Comment: Some misprints of the published version corrected (value of nuclear density and eq. 7). Talk given at the 4th Italian-Sino Workshop, July 20-30 (2007), Pescara (Italy

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

Intrinsic dimension estimation for locally undersampled data

Identifying the minimal number of parameters needed to describe a dataset is a challenging problem known in the literature as intrinsic dimension estimation. All the existing intrinsic dimension estimators are not reliable whenever the dataset is locally undersampled, and this is at the core of the so called curse of dimensionality. Here we introduce a new intrinsic dimension estimator that leverages on simple properties of the tangent space of a manifold and extends the usual correlation integral estimator to alleviate the extreme undersampling problem. Based on this insight, we explore a multiscale generalization of the algorithm that is capable of (i) identifying multiple dimensionalities in a dataset, and (ii) providing accurate estimates of the intrinsic dimension of extremely curved manifolds. We test the method on manifolds generated from global transformations of high-contrast images, relevant for invariant object recognition and considered a challenge for state-of-the-art intrinsic dimension estimators

Counting the learnable functions of geometrically structured data

Cover's function counting theorem is a milestone in the theory of artificial neural networks. It provides an answer to the fundamental question of determining how many binary assignments (dichotomies) of p points in n dimensions can be linearly realized. Regrettably, it has proved hard to extend the same approach to more advanced problems than the classification of points. In particular, an emerging necessity is to find methods to deal with geometrically structured data, and specifically with non-point-like patterns. A prominent case is that of invariant recognition, whereby identification of a stimulus is insensitive to irrelevant transformations on the inputs (such as rotations or changes in perspective in an image). An object is thus represented by an extended perceptual manifold, consisting of inputs that are classified similarly. Here, we develop a function counting theory for structured data of this kind, by extending Cover's combinatorial technique, and we derive analytical expressions for the average number of dichotomies of generically correlated sets of patterns. As an application, we obtain a closed formula for the capacity of a binary classifier trained to distinguish general polytopes of any dimension. These results extend our theoretical understanding of the role of data structure in machine learning, and provide useful quantitative tools for the analysis of generalization, feature extraction, and invariant object recognition by neural networks

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