Cross Section Measurements of the Higgs Boson in the Diphoton Decay Channel Using Proton-Proton Collision Data Recorded by the ATLAS Detector at Centre-of-Mass Energies of 7 TeV and 8 TeV

In July of 2012, both the ATLAS and CMS experiments announced the discovery of a new particle consistent with the Standard Model (SM) Higgs boson. This has ushered in a new era of precision physics: measuring the Higgs boson's properties. Precisely measuring all the properties of the newly discovered Higgs boson will tell us if this is the particle predicted by the SM or another particle entirely. This thesis focuses on cross section measurements of the Higgs boson in the diphoton decay channel. The analysis is preformed using 4.5 fb-1 and 20.3 fb-1 of proton-proton collision data recorded by the ATLAS detector at CERN's Large Hadron Collider in 2011 and 2012, at centre-of-mass energies of 7 TeV and 8 TeV, respectively. Fiducial cross sections are measured and corrected for experimental effects such as detector acceptance and resolution. The results are compared to the latest state-of-the-art theoretical prediction for SM Higgs boson cross sections.The Higgs boson signal is extracted and the background subtracted by performing a signal plus background fit to the invariant diphoton mass spectrum. The pp -> H -> gamma gamma inclusive fiducial cross section is measured to be 45.3 +/- 16.9 (stat.) +5.3 -5.3 (syst.) +/- 0.8 (lumi.) fb at 7 TeV and 43.2 +/- 9.4 (stat.) +3.2 -2.9 (syst.) +/- 1.2 (lumi.) fb at 8 TeV, for a Higgs boson of mass 125.36 GeV. Using the larger 8 TeV dataset, additional fiducial and differential cross section measurements of the Higgs boson are also reported. This thesis will particularly focus on the following aspects of the Higgs boson cross section measurements: (i) jet calibration and performance, (ii) a data-driven method for obtaining the diphoton background rate estimations required for deriving the background parameterization used in the signal extraction, (iii) extracting the Higgs boson signal by performing a simultaneous s+b likelihood fit to the diphoton invariant mass spectrum, and (iv) deriving the `unfolding' factors used to translate the measurements to a set of detector corrected model-independent observables

Analogues Between Leibniz\u27s Harmonic Triangle and Pascal\u27s Arithmetic Triangle

This paper will discuss the analogues between Leibniz\u27s Harmonic Triangle and Pascal\u27s Arithmetic Triangle by utilizing mathematical proving techniques like partial sums, committees, telescoping, mathematical induction and applying George Polya\u27s perspective. The topics presented in this paper will show that Pascal\u27s triangle and Leibniz\u27s triangle both have hockey stick type patterns, patterns of sums within shapes, and have the natural numbers, triangular numbers, tetrahedral numbers, and pentatope numbers hidden within. In addition, this paper will show how Pascal\u27s Arithmetic Triangle can be used to construct Leibniz\u27s Harmonic Triangle and show how both triangles relate to combinatorics and arithmetic through the coefficients of the binomial expansion. Furthermore, combinatorics plays an increasingly important role in mathematics, starting when students enter high school and continuing on into their college years. Students become familiar with the traditional arguments based on classical arithmetic and algebra, however, methods of combinatorics can vary greatly. In combinatorics, perhaps the most important concept revolves around the coefficients of the binomial expansion, studying and proving their properties, and conveying a greater insight into mathematics

Gold, Blood, and Power: Finance and War Through the Ages

This monograph presents a survey of the crucial link between state (national) power and finance from the ancient era through to the present day. Cicero once said that the true sinew of war was “endless streams of money.” His observation remains as accurate today as it was when Rome first began constructing its Empire. Unfortunately, too many historical works leave this crucial underpinning link out of their narratives. Even those that do discuss economic and financial concerns typically miss the fact that the size of a state’s economy often has little to do with its capacity to wield influence on the global stage. Much more crucial, in this regard, is the possession of an administrative system capable of efficiently mobilizing a state’s resources. It was such an administrative apparatus that allowed Britain to punch far above its weight in the international arena for centuries. As a survey, this work is far from comprehensive, but the author hopes it will provide a stepping stone for a much-needed in-depth examination of the topic.https://press.armywarcollege.edu/monographs/1454/thumbnail.jp

Expanding Sustainable Community Health Centers in New York City

The Community Health Care Association of New York State (CHCANYS) has authored an updated analysis identifying New York City neighborhoods with the greatest need for expanded access to primary care and the ability to support sustainable growth of federally qualified health centers (FQHC).Building on its Plan for Expanding Sustainable Community Health Centers, published in 2013 with support from the NYS Health Foundation, CHCANYS has partnered with the Office of the Mayor of New York City to release the updated report, which ranks the primary care need and sustainability of 42 United Hospital Fund (UHF) New York City neighborhoods using a quantitative analysis of communities' relative need for additional FQHC capacity and the feasibility of such expansions. Authored with financial support from the Office of the Mayor of New York City, Expanding Sustainable Community Health Centers in New York City informed development of the New York City Caring Neighborhoods initiative, a new program that will significantly increase primary care access in underserved areas across the City's five boroughs. New York City-based FQHCs served 972,000 patients in 2014, and it is anticipated that this number will rise to over 1 million patients in 2015. Current state and federal health reform efforts emphasize the critical role of primary care in achieving improved delivery system outcomes, and increasing the capacity of FQHCs to meet these demands is essential.

Predictions of the causal entropic principle for environmental conditions of the universe

The causal entropic principle has been proposed as a superior alternative to the anthropic principle for understanding the magnitude of the cosmological constant. In this approach, the probability to create observers is assumed to be proportional to the entropy production \Delta S in a maximal causally connected region -- the causal diamond. We improve on the original treatment by better quantifying the entropy production due to stars, using an analytic model for the star formation history which accurately accounts for changes in cosmological parameters. We calculate the dependence of \Delta S on the density contrast Q=\delta\rho/\rho, and find that our universe is much closer to the most probable value of Q than in the usual anthropic approach and that probabilities are relatively weakly dependent on this amplitude. In addition, we make first estimates of the dependence of \Delta S on the baryon fraction and overall matter abundance. Finally, we also explore the possibility that decays of dark matter, suggested by various observed gamma ray excesses, might produce a comparable amount of entropy to stars.Comment: RevTeX4, 13pp, 10 figures; v2. clarified introduction, added ref

Concentrations of Dark Halos from their Assembly Histories

(abridged) We study the relation between the density profiles of dark matter halos and their mass assembly histories, using a statistical sample of halos in a high-resolution N-body simulation of the LCDM cosmology. For each halo at z=0, we identify its merger-history tree, and determine concentration parameters c_vir for all progenitors, thus providing a structural merger tree for each halo. We fit the mass accretion histories by a universal function with one parameter, the formation epoch a_c, defined when the log mass accretion rate dlogM/dloga falls below a critical value S. We find that late forming galaxies tend to be less concentrated, such that c_vir ``observed'' at any epoch a_o is strongly correlated with a_c via c_vir=c_1*a_o/a_c. Scatter about this relation is mostly due to measurement errors in c_v and a_c, implying that the actual spread in c_vir for halos of a given mass can be mostly attributed to scatter in a_c. We demonstrate that this relation can also be used to predict the mass and redshift dependence of c_v, and the scatter about the median c_vir(M,z), using accretion histories derived from the Extended Press-Schechter (EPS) formalism, after adjusting for a constant offset between the formation times as predicted by EPS and as measured in the simulations;this new ingredient can thus be easily incorporated into semi-analytic models of galaxy formation. The correlation found between halo concentration and mass accretion rate suggests a physical interpretation: for high mass infall rates the central density is related to the background density; when the mass infall rate slows, the central density stays approximately constant and the halo concentration just grows as R_vir. The tight correlation demonstrated here provides an essential new ingredient for galaxy formation modeling.Comment: 19 pages, 18 figures, uses emulateapj5.tex. ApJ, in press; revised to match accepted versio

Connecting Cluster Substructure in Galaxy Cluster Cores at z=0.2 With Cluster Assembly Histories

We use semi-analytic models of structure formation to interpret gravitational lensing measurements of substructure in galaxy cluster cores (R<=250kpc/h) at z=0.2. The dynamic range of the lensing-based substructure fraction measurements is well matched to the theoretical predictions, both spanning f_sub~0.05-0.65. The structure formation model predicts that f_sub is correlated with cluster assembly history. We use simple fitting formulae to parameterize the predicted correlations: Delta_90 = tau_90 + alpha_90 * log(f_sub) and Delta_50 = tau_50 + alpha_50 * log(f_sub), where Delta_90 and Delta_50 are the predicted lookback times from z=0.2 to when each theoretical cluster had acquired 90% and 50% respectively of the mass it had at z=0.2. The best-fit parameter values are: alpha_90 = (-1.34+/-0.79)Gyr, tau_90 = (0.31+/-0.56)Gyr and alpha_50 = (-2.77+/-1.66)Gyr, tau_50 = (0.99+/-1.18)Gyr. Therefore (i) observed clusters with f_sub<~0.1 (e.g. A383, A1835) are interpreted, on average, to have formed at z>~0.8 and to have suffered <=10% mass growth since z~0.4, (ii) observed clusters with f_sub>~0.4 (e.g. A68, A773) are interpreted as, on average, forming since z~0.4 and suffering >10% mass growth in the ~500Myr preceding z=0.2, i.e. since z=0.25. In summary, observational measurements of f_sub can be combined with structure formation models to estimate the age and assembly history of observed clusters. The ability to ``age-date'' approximately clusters in this way has numerous applications to the large clusters samples that are becoming available.Comment: Accepted by ApJL, 4 pages, 2 figure