Non-autonomous stochastic evolution equations and applications to stochastic partial differential equations

In this paper we study the following non-autonomous stochastic evolution equation on a UMD Banach space $E$ with type 2, {equation}\label{eq:SEab}\tag{SE} {{aligned} dU(t) & = (A(t)U(t) + F(t,U(t))) dt + B(t,U(t)) dW_H(t), \quad t\in [0,T], U(0) & = u_0. {aligned}. {equation} Here $(A(t))_{t\in [0,T]}$ are unbounded operators with domains $(D(A(t)))_{t\in [0,T]}$ which may be time dependent. We assume that $(A(t))_{t\in [0,T]}$ satisfies the conditions of Acquistapace and Terreni. The functions $F$ and $B$ are nonlinear functions defined on certain interpolation spaces and $u_0\in E$ is the initial value. $W_H$ is a cylindrical Brownian motion on a separable Hilbert space $H$. Under Lipschitz and linear growth conditions we show that there exists a unique mild solution of \eqref{eq:SEab}. Under assumptions on the interpolation spaces we extend the factorization method of Da Prato, Kwapie\'n, and Zabczyk, to obtain space-time regularity results for the solution $U$ of \eqref{eq:SEab}. For Hilbert spaces $E$ we obtain a maximal regularity result. The results improve several previous results from the literature. The theory is applied to a second order stochastic partial differential equation which has been studied by Sanz-Sol\'e and Vuillermot. This leads to several improvements of their result.Comment: Accepted for publication in Journal of Evolution Equation

2019 Italian Society of Cardiology census on telemedicine in cardiovascular disease : a report from the working group on telecardiology and informatics

Background The aim of this study was to assess by a census supported by the Italian Society of Cardiology (Societ\ue0 Italiana di Cardiologia, SIC) the present implementation of telemedicine in the field of cardiovascular disease in Italy. Methods A dedicated questionnaire was sent by email to all the members of the SIC: data on telemedicine providers, service provided, reimbursement, funding and organisational solutions were collected and analysed. Results Reported telemedicine activities were mostly stable and public hospital based, focused on acute cardiovascular disease and prehospital triage of suspected acute myocardial infarction (prehospital ECG, always interpreted by a cardiologist and not automatically reported by computerised algorithms). Private companies delivering telemedicine services in cardiology (ECGs, ambulatory ECG monitoring) were also present. In 16% of cases, ECGs were also delivered through pharmacies or general practitioners. ICD/CRT-D remote control was performed in 42% of cases, heart failure patient remote monitoring in 37% (21% vital parameters monitoring, 32% nurse telephone monitoring). Telemedicine service was public in 74% of cases, paid by the patient in 26%. About half of telemedicine service received no funding, 17% received State and/or European Union funding. Conclusions Several telemedicine activities have been reported for the management of acute and chronic cardiovascular disease in Italy. The whole continuum of cardiovascular disease is covered by telemedicine solutions. A periodic census may be useful to assess the implementation of guidelines recommendations on telemedicine

Regularity of Ornstein-Uhlenbeck processes driven by a L{\'e}vy white noise

The paper is concerned with spatial and time regularity of solutions to linear stochastic evolution equation perturbed by L\'evy white noise "obtained by subordination of a Gaussian white noise". Sufficient conditions for spatial continuity are derived. It is also shown that solutions do not have in general \cadlag modifications. General results are applied to equations with fractional Laplacian. Applications to Burgers stochastic equations are considered as well.Comment: This is an updated version of the same paper. In fact, it has already been publishe

An interpolation theorem for proper holomorphic embeddings

Given a Stein manifold X of dimension n>1, a discrete sequence a_j in X, and a discrete sequence b_j in C^m where m > [3n/2], there exists a proper holomorphic embedding of X into C^m which sends a_j to b_j for every j=1,2,.... This is the interpolation version of the embedding theorem due to Eliashberg, Gromov and Schurmann. The dimension m cannot be lowered in general due to an example of Forster

An Experimentalist's View of Neutrino Oscillations

Neutrinos, and primarily neutrino oscillations, have undoubtedly been one of the most exciting topics in the field of high-energy physics over the past few years. The existence of neutrino oscillations would require an extension of the currently accepted description of sub-nuclear phenomena beyond the Standard Model. Compelling evidence of new physics, which seems to be pointing towards neutrino oscillations, is coming from the solar neutrino deficit and from the atmospheric neutrino anomaly. More controversial effects have been observed with artificially produced neutrinos. The present experimental status of neutrino oscillations is reviewed, as well as the planned future experimental programme, which, it is hoped, will solve most of the outstanding puzzles.Comment: 64 pages, 29 figures, to be published in Intern. J. Mod. Phys. A (2001

JOYCE: Jülich Observatory for cloud evolution

The Jülich Observatory for Cloud Evolution (JOYCE), located at Forschungszentrum Jülich in the most western part of Germany, is a recently established platform for cloud research. The main objective of JOYCE is to provide observations, which improve our understanding of the cloudy boundary layer in a midlatitude environment. Continuous and temporally highly resolved measurements that are specifically suited to characterize the diurnal cycle of water vapor, stability, and turbulence in the lower troposphere are performed with a special focus on atmosphere–surface interaction. In addition, instruments are set up to measure the micro- and macrophysical properties of clouds in detail and how they interact with different boundary layer processes and the large-scale synoptic situation. For this, JOYCE is equipped with an array of state-of-the-art active and passive remote sensing and in situ instruments, which are briefly described in this scientific overview. As an example, a 24-h time series of the evolution of a typical cumulus cloud-topped boundary layer is analyzed with respect to stability, turbulence, and cloud properties. Additionally, we present longer-term statistics, which can be used to elucidate the diurnal cycle of water vapor, drizzle formation through autoconversion, and warm versus cold rain precipitation formation. Both case studies and long-term observations are important for improving the representation of clouds in climate and numerical weather prediction models

Lorentzian and Euclidean Quantum Gravity - Analytical and Numerical Results

We review some recent attempts to extract information about the nature of quantum gravity, with and without matter, by quantum field theoretical methods. More specifically, we work within a covariant lattice approach where the individual space-time geometries are constructed from fundamental simplicial building blocks, and the path integral over geometries is approximated by summing over a class of piece-wise linear geometries. This method of ``dynamical triangulations'' is very powerful in 2d, where the regularized theory can be solved explicitly, and gives us more insights into the quantum nature of 2d space-time than continuum methods are presently able to provide. It also allows us to establish an explicit relation between the Lorentzian- and Euclidean-signature quantum theories. Analogous regularized gravitational models can be set up in higher dimensions. Some analytic tools exist to study their state sums, but, unlike in 2d, no complete analytic solutions have yet been constructed. However, a great advantage of our approach is the fact that it is well-suited for numerical simulations. In the second part of this review we describe the relevant Monte Carlo techniques, as well as some of the physical results that have been obtained from the simulations of Euclidean gravity. We also explain why the Lorentzian version of dynamical triangulations is a promising candidate for a non-perturbative theory of quantum gravity.Comment: 69 pages, 16 figures, references adde

Muon and Cosmogenic Neutron Detection in Borexino

Borexino, a liquid scintillator detector at LNGS, is designed for the detection of neutrinos and antineutrinos from the Sun, supernovae, nuclear reactors, and the Earth. The feeble nature of these signals requires a strong suppression of backgrounds below a few MeV. Very low intrinsic radiogenic contamination of all detector components needs to be accompanied by the efficient identification of muons and of muon-induced backgrounds. Muons produce unstable nuclei by spallation processes along their trajectory through the detector whose decays can mimic the expected signals; for isotopes with half-lives longer than a few seconds, the dead time induced by a muon-related veto becomes unacceptably long, unless its application can be restricted to a sub-volume along the muon track. Consequently, not only the identification of muons with very high efficiency but also a precise reconstruction of their tracks is of primary importance for the physics program of the experiment. The Borexino inner detector is surrounded by an outer water-Cherenkov detector that plays a fundamental role in accomplishing this task. The detector design principles and their implementation are described. The strategies adopted to identify muons are reviewed and their efficiency is evaluated. The overall muon veto efficiency is found to be 99.992% or better. Ad-hoc track reconstruction algorithms developed are presented. Their performance is tested against muon events of known direction such as those from the CNGS neutrino beam, test tracks available from a dedicated External Muon Tracker and cosmic muons whose angular distribution reflects the local overburden profile. The achieved angular resolution is 3-5 deg and the lateral resolution is 35-50 cm, depending on the impact parameter of the crossing muon. The methods implemented to efficiently tag cosmogenic neutrons are also presented.Comment: 42 pages. 32 figures on 37 files. Uses JINST.cls. 1 auxiliary file (defines.tex) with TEX macros. submitted to Journal of Instrumentatio

Electron/pion separation with an Emulsion Cloud Chamber by using a Neural Network

We have studied the performance of a new algorithm for electron/pion separation in an Emulsion Cloud Chamber (ECC) made of lead and nuclear emulsion films. The software for separation consists of two parts: a shower reconstruction algorithm and a Neural Network that assigns to each reconstructed shower the probability to be an electron or a pion. The performance has been studied for the ECC of the OPERA experiment [1]. The $e/\pi$ separation algorithm has been optimized by using a detailed Monte Carlo simulation of the ECC and tested on real data taken at CERN (pion beams) and at DESY (electron beams). The algorithm allows to achieve a 90% electron identification efficiency with a pion misidentification smaller than 1% for energies higher than 2 GeV