Dirichlet-Neumann inverse spectral problem for a star graph of Stieltjes strings

We solve two inverse spectral problems for star graphs of Stieltjes strings with Dirichlet and Neumann boundary conditions, respectively, at a selected vertex called root. The root is either the central vertex or, in the more challenging problem, a pendant vertex of the star graph. At all other pendant vertices Dirichlet conditions are imposed; at the central vertex, at which a mass may be placed, continuity and Kirchhoff conditions are assumed. We derive conditions on two sets of real numbers to be the spectra of the above Dirichlet and Neumann problems. Our solution for the inverse problems is constructive: we establish algorithms to recover the mass distribution on the star graph (i.e. the point masses and lengths of subintervals between them) from these two spectra and from the lengths of the separate strings. If the root is a pendant vertex, the two spectra uniquely determine the parameters on the main string (i.e. the string incident to the root) if the length of the main string is known. The mass distribution on the other edges need not be unique; the reason for this is the non-uniqueness caused by the non-strict interlacing of the given data in the case when the root is the central vertex. Finally, we relate of our results to tree-patterned matrix inverse problems.

Standalone vertex finding in the ATLAS muon spectrometer

A dedicated reconstruction algorithm to find decay vertices in the ATLAS muon spectrometer is presented. The algorithm searches the region just upstream of or inside the muon spectrometer volume for multi-particle vertices that originate from the decay of particles with long decay paths. The performance of the algorithm is evaluated using both a sample of simulated Higgs boson events, in which the Higgs boson decays to long-lived neutral particles that in turn decay to b final states, and pp collision data at √s = 7 TeV collected with the ATLAS detector at the LHC during 2011.

Measurement of the flavour composition of dijet events in pp collisions at sqrts=7 TeV with the AT detector

This paper describes a measurement of the flavour composition of dijet events produced in pp collisions at root s = 7 TeV using the ATLAS detector. The measurement uses the full 2010 data sample, corresponding to an integrated luminosity of 39 pb(-1). Six possible combinations of light, charm and bottom jets are identified in the dijet events, where the jet flavour is defined by the presence of bottom, charm or solely light flavour hadrons in the jet. Kinematic variables, based on the properties of displaced decay vertices and optimised for jet flavour identification, are used in a multidimensional template fit to measure the fractions of these dijet flavour states as functions of the leading jet transverse momentum in the range 40 GeV to 500 GeV and jet rapidity vertical bar y vertical bar < 2.1. The fit results agree with the predictions of leading-and next-to-leading-order calculations, with the exception of the dijet fraction composed of bottom and light flavour jets, which is underestimated by all models at large transverse jet momenta. The ability to identify jets containing two b-hadrons, originating from e. g. gluon splitting, is demonstrated. The difference between bottom jet production rates in leading and subleading jets is consistent with the next-to-leading-order predictions.

gems: An R Package for Simulating from Disease Progression Models

Mathematical models of disease progression predict disease outcomes and are useful epidemiological tools for planners and evaluators of health interventions. The R package gems is a tool that simulates disease progression in patients and predicts the effect of different interventions on patient outcome. Disease progression is represented by a series of events (e.g., diagnosis, treatment and death), displayed in a directed acyclic graph. The vertices correspond to disease states and the directed edges represent events. The package gems allows simulations based on a generalized multistate model that can be described by a directed acyclic graph with continuous transition-specific hazard functions. The user can specify an arbitrary hazard function and its parameters. The model includes parameter uncertainty, does not need to be a Markov model, and may take the history of previous events into account. Applications are not limited to the medical field and extend to other areas where multistate simulation is of interest. We provide a technical explanation of the multistate models used by gems, explain the functions of gems and their arguments, and show a sample application.

Measuring the gravitational free-fall of antihydrogen

Antihydrogen holds the promise to test, for the first time, the universality of freefall with a system composed entirely of antiparticles. The AEgIS experiment at CERN’s antiproton decelerator aims to measure the gravitational interaction between matter and antimatter by measuring the deflection of a beam of antihydrogen in the Earths gravitational field (g). The principle of the experiment is as follows: cold antihydrogen atoms are synthesized in a Penning-Malberg trap and are Stark accelerated towards a moir´e deflectometer, the classical counterpart of an atom interferometer, and annihilate on a position sensitive detector. Crucial to the success of the experiment is the spatial precision of the position sensitive detector.We propose a novel free-fall detector based on a hybrid of two technologies: emulsion detectors, which have an intrinsic spatial resolution of 50 nm but no temporal information, and a silicon strip / scintillating fiber tracker to provide timing and positional information. In 2012 we tested emulsion films in vacuum with antiprotons from CERN’s antiproton decelerator. The annihilation vertices could be observed directly on the emulsion surface using the microscope facility available at the University of Bern. The annihilation vertices were successfully reconstructed with a resolution of 1–2 μmon the impact parameter. If such a precision can be realized in the final detector, Monte Carlo simulations suggest of order 500 antihydrogen annihilations will be sufficient to determine gwith a 1 % accuracy. This paper presents current research towards the development of this technology for use in the AEgIS apparatus and prospects for the realization of the final detector.

Measurement of the neutrino-oxygen neutral-current interaction cross section by observing nuclear deexcitation γ rays

We report the first measurement of the neutrino-oxygen neutral-current quasielastic (NCQE) cross section. It is obtained by observing nuclear deexcitation γ rays which follow neutrino-oxygen interactions at the Super-Kamiokande water Cherenkov detector. We use T2K data corresponding to 3.01 × 1020 protons on target. By selecting only events during the T2K beam window and with well-reconstructed vertices in the fiducial volume, the large background rate from natural radioactivity is dramatically reduced. We observe 43 events in the 4–30 MeV reconstructed energy window, compared with an expectation of 51.0, which includes an estimated 16.2 background events. The background is primarily nonquasielastic neutral-current interactions and has only 1.2 events from natural radioactivity. The flux-averaged NCQE cross section we measure is 1.55 × 10−38 cm2 with a 68% confidence interval of ð1.22; 2.20Þ × 10−38 cm2 at a median neutrino energy of 630 MeV, compared with the theoretical prediction of 2.01 × 10−38 cm2.

A double-edged sword: How perceived variety and perceived choice difficulty jointly determine consumers’ satisfaction with a customized product

High variety assortments are a double-edged sword. On one hand perceiving large variety is attractive, on the other hand choosing from it can cause perceived choice difficulty. Using mass-customizations tools our two studies show how both antipodal processes jointly determine consumers’ satisfaction with the customized product.

Non-self-adjoint graphs

On finite metric graphs we consider Laplace operators, subject to various classes of non-self-adjoint boundary conditions imposed at graph vertices. We investigate spectral properties, existence of a Riesz basis of projectors and similarity transforms to self-adjoint Laplacians. Among other things, we describe a simple way to relate the similarity transforms between Laplacians on certain graphs with elementary similarity transforms between matrices defining the boundary conditions.