Verification of Monte-Carlo Simulation for STAR EEMC

Spin experiments using the STAR detector at Brookhaven National Laboratory seek to measure the gluon contribution to the proton’s spin. The Endcap Electromagnetic Calorimeter (EEMC), a portion of the STAR detector, is used to enhance the clarity and quality of the measurements from proton-proton collisions. These measurements require the EEMC to be well–modeled in the STAR simulation package. This analysis will confront simulations and data from proton-proton collision runs taken in 2006. Comparisons of qualities, such as cluster energy, opening angle, particle invariant masses, and hit distributions will be shown. When validated, the Monte-Carlo simulation will serve STAR physicists as an important tool to help identify and quantify the presence of particles produced in proton-proton collisions, thus aiding the extraction of the gluon contribution to the proton’s spin

Most Subsets are Balanced in Finite Groups

The sumset is one of the most basic and central objects in additive number theory. Many of the most important problems (such as Goldbach's conjecture and Fermat's Last theorem) can be formulated in terms of the sumset $S + S = \{x+y : x,y\in S\}$ of a set of integers $S$. A finite set of integers $A$ is sum-dominated if $|A+A| > |A-A|$. Though it was believed that the percentage of subsets of $\{0,...,n\}$ that are sum-dominated tends to zero, in 2006 Martin and O'Bryant proved a very small positive percentage are sum-dominated if the sets are chosen uniformly at random (through work of Zhao we know this percentage is approximately $4.5 \cdot 10^{-4}$). While most sets are difference-dominated in the integer case, this is not the case when we take subsets of many finite groups. We show that if we take subsets of larger and larger finite groups uniformly at random, then not only does the probability of a set being sum-dominated tend to zero but the probability that $|A+A|=|A-A|$ tends to one, and hence a typical set is balanced in this case. The cause of this marked difference in behavior is that subsets of $\{0,..., n\}$ have a fringe, whereas finite groups do not. We end with a detailed analysis of dihedral groups, where the results are in striking contrast to what occurs for subsets of integers.Comment: Version 2.0, 11 pages, 2 figure

The Pythagorean Won-Loss Formula and Hockey: A Statistical Justification for Using the Classic Baseball Formula as an Evaluative Tool in Hockey

Originally devised for baseball, the Pythagorean Won-Loss formula estimates the percentage of games a team should have won at a particular point in a season. For decades, this formula had no mathematical justification. In 2006, Steven Miller provided a statistical derivation by making some heuristic assumptions about the distributions of runs scored and allowed by baseball teams. We make a similar set of assumptions about hockey teams and show that the formula is just as applicable to hockey as it is to baseball. We hope that this work spurs research in the use of the Pythagorean Won-Loss formula as an evaluative tool for sports outside baseball.Comment: 21 pages, 4 figures; Forthcoming in The Hockey Research Journal: A Publication of the Society for International Hockey Research, 2012/1

An Early Holiday Surprise: Cholecystitis Wrapped in Takotsubo Cardiomyopathy

This is a novel case report of a 44-year-old woman who presented to the emergency department with epigastric pain wrapping around to her back. She had no risk factors for cardiac disease, but her initial electrocardiogram (ECG) showed a Wellens syndrome pattern and she was taken urgently to the catheterization lab. After a negative catheterization, she underwent cardiac magnetic resonance imaging, which was positive for Takotsubo cardiomyopathy (TC). Ultimately, abdominal computed tomography revealed that she had cholecystitis, which likely was the cause of her TC and ECG changes

Suprachoroidal hemorrhage during femtosecond laser assisted cataract surgery.

Purpose:To describe a case of suprachoroidal hemorrhage that occurred during femtosecond laser assisted cataract surgery (FLACS). Observations:A 67-year-old woman with high myopia underwent FLACS. Following two unsuccessful attempts at docking due to interface air bubbles, the third attempt was successful. Laser treatment and cataract surgery proceeded uneventfully until intraocular lens (IOL) implantation. While positioning the IOL within the capsular bag, the anterior chamber began to shallow, intraocular pressure became high by palpation, and the optic of the IOL prolapsed partially out of the bag. A segmental suprachoroidal hemorrhage was identified in the superior peripheral retina by intraoperative indirect ophthalmoscopy. Following an hour of waiting in the recovery room, the anterior chamber deepened and the intraocular pressure was low enough to position the IOL centrally within the bag. Her subsequent postoperative course was uneventful. Conclusions and Importance:To our knowledge, this is the first report of suprachoroidal hemorrhage during FLACS. We speculate that repeated sudden drops in intraocular pressure associated with multiple undockings triggered the suprachoroidal hemorrhage in this case

The Simple Truth About the Gender Pay Gap, Spring 2017 Edition

This guide provides key facts about the gender pay gap in the United States, along with explanations and resources. Information is organized around five common questions:1. What is the pay gap?2. How does the pay gap affect women of different demographics?3. What causes the pay gap?4. How can I make a difference?5. What should I do if I experience sex discrimination at work

In-Situ Colloidal MnO2 Deposition and Ozonation of 2,4-Dinitrotoluene

Laboratory experiments are presented that demonstrate a novel in situ semipassive reactive barrier for the degradation of 2,4 dinitrotoluene created by coating aquifer surfaces by deposition of colloidal MnO2, which catalyzes ozone degradation and enhances contaminant oxidation. Ozone is added to the reactive barrier and is transported through the zone with the contaminants by existing hydraulic gradients. The communication presents the preliminary laboratory investigation demonstrating the viability of this method. Studies were conducted by coating Ottawa sand with colloidal MnO2. Results show that concentrations of MnO2 in the range of 0.2 mg/g can be deposited with no measurable change in hydraulic conductivity, that there is significant coverage of the sand material by MnO2, and the deposition was not reversible under a wide range of chemical conditions. Ozonation of 2,4-dinitrotoluene in the presence of MnO2- coated sand was demonstrated to result in pseudo-first-order degradation kinetics with respect to DNT with half-lives ranging from 28 to 22 min (at pH 6 and 7, respectively), approximately 25% faster than experiments performed in the absence of MnO2

Several Habits of Highly Successful Breakeruppers

In lieu of an abstract, below is the essay\u27s first paragraph. She takes in a deep breath, and subsequently sucks the remaining air right out of the room; like a toy soldier, her wind up key has already been turned, and she proceeds to recount one of those monotonous stories that makes a man wish he were temporarily deaf. After a long day at work, with his eyes glazing over faster than a doughnut, the man wonders why his girlfriend can not be quiet for at least five minutes

Verification of Monte-Carlo Simulation for STAR Endcap ElectroMagnetic Calorimeter

The STAR experiment at Brookhaven National Laboratory seeks to measure the source of the protons spin, a fundamental property of matter. To accomplish this measurement, a simulation method called Monte-Carlo will be used to model the true detector responses to proton-proton collisions. My work is to confirm the accuracy of the Monte-Carlo simulation for the Endcap Electromagnetic Calorimeter (EEMC). By comparing histograms of fundamental parameters from the Monte-Carlo simulated data and true data from 2006 experimentation, we will be able to test the simulations accuracy. When validated, the Monte-Carlo simulation will be used to achieve a greater understanding of the physics occurring during the proton-proton collisions. In particular, Monte-Carlo will help in extracting the gluon contribution to protons spin