Observables for possible QGP signatures in central pp collisions

Proton-proton (pp) data show collective effects, such as long-range azimuthal correlations and strangeness enhancement, which are similar to phenomenology observed in heavy ion collisions. Using simulations with and without explicit existing models of collective effects, we explore new ways to probe pp collisions at high multiplicity, in order to suggest measurements that could help identify the similarities and differences between large- and small-scale collective effects. In particular, we focus on the properties of jets produced in ultra-central pp collisions in association with a Z boson. We consider observables such as jet energy loss and jet shapes, which could point to the possible existence of an underlying quark-gluon plasma, or other new dynamical effects related to the presence of large hadronic densities.Comment: 32 pages, 20 figure

A rescaled method for RBF approximation

In the recent paper [8], a new method to compute stable kernel-based interpolants has been presented. This \textit{rescaled interpolation} method combines the standard kernel interpolation with a properly defined rescaling operation, which smooths the oscillations of the interpolant. Although promising, this procedure lacks a systematic theoretical investigation. Through our analysis, this novel method can be understood as standard kernel interpolation by means of a properly rescaled kernel. This point of view allow us to consider its error and stability properties

A rescaled method for RBF approximation

A new method to compute stable kernel-based interpolants has been presented by the second and third authors. This rescaled interpolation method combines the standard kernel interpolation with a properly defined rescaling operation, which smooths the oscillations of the interpolant. Although promising, this procedure lacks a systematic theoretical investigation. Through our analysis, this novel method can be understood as standard kernel interpolation by means of a properly rescaled kernel. This point of view allow us to consider its error and stability properties. First, we prove that the method is an instance of the Shepard\u2019s method, when certain weight functions are used. In particular, the method can reproduce constant functions. Second, it is possible to define a modified set of cardinal functions strictly related to the ones of the not-rescaled kernel. Through these functions, we define a Lebesgue function for the rescaled interpolation process, and study its maximum - the Lebesgue constant - in different settings. Also, a preliminary theoretical result on the estimation of the interpolation error is presented. As an application, we couple our method with a partition of unity algorithm. This setting seems to be the most promising, and we illustrate its behavior with some experiments

Formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential

For the Schrodinger equation at fixed energy with a potential supported in a bounded domain we give formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential. For the case of zero background potential these results were obtained in [R.G.Novikov, Multidimensional inverse spectral problem for the equation -\Delta\psi+(v(x)-Eu(x))\psi=0, Funkt. Anal. i Ego Prilozhen 22(4), pp.11-22, (1988)]

A convergent algorithm for the hybrid problem of reconstructing conductivity from minimal interior data

We consider the hybrid problem of reconstructing the isotropic electric conductivity of a body $\Omega$ from interior Current Density Imaging data obtainable using MRI measurements. We only require knowledge of the magnitude $|J|$ of one current generated by a given voltage $f$ on the boundary $\partial\Omega$. As previously shown, the corresponding voltage potential u in $\Omega$ is a minimizer of the weighted least gradient problem $$u=\hbox{argmin} \{\int_{\Omega}a(x)|\nabla u|: u \in H^{1}(\Omega), \ \ u|_{\partial \Omega}=f\},$$ with $a(x)= |J(x)|$. In this paper we present an alternating split Bregman algorithm for treating such least gradient problems, for $a\in L^2(\Omega)$ non-negative and $f\in H^{1/2}(\partial \Omega)$. We give a detailed convergence proof by focusing to a large extent on the dual problem. This leads naturally to the alternating split Bregman algorithm. The dual problem also turns out to yield a novel method to recover the full vector field $J$ from knowledge of its magnitude, and of the voltage $f$ on the boundary. We then present several numerical experiments that illustrate the convergence behavior of the proposed algorithm