Some combinatorial theorems with an application to a problem in number theory

The main object of this thesis is to study the following extremal problem in number theory: Let n and k be integers satisfying n ≥ k ≥ 3. Denote by f(n,k) the largest positive integer for which there exists a set S of f(n,k) integers satisfying -- (i) S ⊑ { 1,2...,n } and -- (ii) no k numbers in S have pairwise the same greatest common divisor. -- We investigate the behaviour of f(n,k) in the case where k → ∞ with n. In particular we obtain estimates for f(n, [logαn]) for fixed α > 0 and f(n,[nα]) for fixed α, 0 < α < 1. -- In the course of our investigations we make use of certain intersection theorems for systems of finite sets. We also include a number of new results concerning these theorems

Model Convolution: A Computational Approach to Digital Image Interpretation

Digital fluorescence microscopy is commonly used to track individual proteins and their dynamics in living cells. However, extracting molecule-specific information from fluorescence images is often limited by the noise and blur intrinsic to the cell and the imaging system. Here we discuss a method called “model-convolution,” which uses experimentally measured noise and blur to simulate the process of imaging fluorescent proteins whose spatial distribution cannot be resolved. We then compare model-convolution to the more standard approach of experimental deconvolution. In some circumstances, standard experimental deconvolution approaches fail to yield the correct underlying fluorophore distribution. In these situations, model-convolution removes the uncertainty associated with deconvolution and therefore allows direct statistical comparison of experimental and theoretical data. Thus, if there are structural constraints on molecular organization, the model-convolution method better utilizes information gathered via fluorescence microscopy, and naturally integrates experiment and theory

Human Resources and the Resource Based View of the Firm

The resource-based view (RBV) of the firm has influenced the field of strategic human resource management (SHRM) in a number of ways. This paper explores the impact of the RBV on the theoretical and empirical development of SHRM. It explores how the fields of strategy and SHRM are beginning to converge around a number of issues, and proposes a number of implications of this convergence

The Milky Way Bulge: Observed properties and a comparison to external galaxies

The Milky Way bulge offers a unique opportunity to investigate in detail the role that different processes such as dynamical instabilities, hierarchical merging, and dissipational collapse may have played in the history of the Galaxy formation and evolution based on its resolved stellar population properties. Large observation programmes and surveys of the bulge are providing for the first time a look into the global view of the Milky Way bulge that can be compared with the bulges of other galaxies, and be used as a template for detailed comparison with models. The Milky Way has been shown to have a box/peanut (B/P) bulge and recent evidence seems to suggest the presence of an additional spheroidal component. In this review we summarise the global chemical abundances, kinematics and structural properties that allow us to disentangle these multiple components and provide constraints to understand their origin. The investigation of both detailed and global properties of the bulge now provide us with the opportunity to characterise the bulge as observed in models, and to place the mixed component bulge scenario in the general context of external galaxies. When writing this review, we considered the perspectives of researchers working with the Milky Way and researchers working with external galaxies. It is an attempt to approach both communities for a fruitful exchange of ideas.Comment: Review article to appear in "Galactic Bulges", Editors: Laurikainen E., Peletier R., Gadotti D., Springer Publishing. 36 pages, 10 figure

Expected Performance of the ATLAS Experiment - Detector, Trigger and Physics

A detailed study is presented of the expected performance of the ATLAS detector. The reconstruction of tracks, leptons, photons, missing energy and jets is investigated, together with the performance of b-tagging and the trigger. The physics potential for a variety of interesting physics processes, within the Standard Model and beyond, is examined. The study comprises a series of notes based on simulations of the detector and physics processes, with particular emphasis given to the data expected from the first years of operation of the LHC at CERN

Single hadron response measurement and calorimeter jet energy scale uncertainty with the ATLAS detector at the LHC

The uncertainty on the calorimeter energy response to jets of particles is derived for the ATLAS experiment at the Large Hadron Collider (LHC). First, the calorimeter response to single isolated charged hadrons is measured and compared to the Monte Carlo simulation using proton-proton collisions at centre-of-mass energies of sqrt(s) = 900 GeV and 7 TeV collected during 2009 and 2010. Then, using the decay of K_s and Lambda particles, the calorimeter response to specific types of particles (positively and negatively charged pions, protons, and anti-protons) is measured and compared to the Monte Carlo predictions. Finally, the jet energy scale uncertainty is determined by propagating the response uncertainty for single charged and neutral particles to jets. The response uncertainty is 2-5% for central isolated hadrons and 1-3% for the final calorimeter jet energy scale.Comment: 24 pages plus author list (36 pages total), 23 figures, 1 table, submitted to European Physical Journal

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 bbar b final states, and pp collision data at √s = 7 TeV collected with the ATLAS detector at the LHC during 2011

Measurements of Higgs boson production and couplings in diboson final states with the ATLAS detector at the LHC

Measurements are presented of production properties and couplings of the recently discovered Higgs boson using the decays into boson pairs, H →γ γ, H → Z Z∗ →4l and H →W W∗ →lνlν. The results are based on the complete pp collision data sample recorded by the ATLAS experiment at the CERN Large Hadron Collider at centre-of-mass energies of √s = 7 TeV and √s = 8 TeV, corresponding to an integrated luminosity of about 25 fb−1. Evidence for Higgs boson production through vector-boson fusion is reported. Results of combined fits probing Higgs boson couplings to fermions and bosons, as well as anomalous contributions to loop-induced production and decay modes, are presented. All measurements are consistent with expectations for the Standard Model Higgs boson

Measurement of the flavour composition of dijet events in pp collisions at root s=7 TeV with the ATLAS detector

This paper describes a measurement of the flavour composition of dijet events produced in pp collisions at &#8730;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 |y|&#60;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

Measurement of χ c1 and χ c2 production with s√ = 7 TeV pp collisions at ATLAS

The prompt and non-prompt production cross-sections for the χ c1 and χ c2 charmonium states are measured in pp collisions at s√ = 7 TeV with the ATLAS detector at the LHC using 4.5 fb−1 of integrated luminosity. The χ c states are reconstructed through the radiative decay χ c → J/ψγ (with J/ψ → μ + μ −) where photons are reconstructed from γ → e + e − conversions. The production rate of the χ c2 state relative to the χ c1 state is measured for prompt and non-prompt χ c as a function of J/ψ transverse momentum. The prompt χ c cross-sections are combined with existing measurements of prompt J/ψ production to derive the fraction of prompt J/ψ produced in feed-down from χ c decays. The fractions of χ c1 and χ c2 produced in b-hadron decays are also measured