An Analysis of the Relationship between Principal Employment Interview Scores and the Achievement Scores of Students with Specific Learning Disabilities

The primary purpose of this study was to examine the relationship between five of ISSLC's 2008 leadership standards as measured by a standardized employment interview (ICIS Principal) and the achievement of students with specific learning disabilities in core areas of instruction. Findings did not support the rejection of the null hypothesis. That is, a statistically significant relationship between these leadership measures and achievement levels of students with specific learning disabilities was not demonstrated. The analysis, however, did indicate that the relationship varied for students with specific learning disabilities in comparison to their grade-level peers. This latter evaluation encourages further investigation of methodological and conceptual issues that influence the relationship between principals and student achievement

Real Time Simulations of Quantum Spin Chains: Density-of-States and Reweighting approaches

We put the Density-of-States (DoS) approach to Monte-Carlo (MC) simulations under a stress test by applying it to a physical problem with the worst possible sign problem: the real time evolution of a non-integrable quantum spin chain. Benchmarks against numerical exact diagonalisation and stochastic reweighting are presented. Both MC methods, the DoS approach and reweighting, allow for simulations of spin chains as long as $L=40$, far beyond exact diagonalisability, though only for short evolution times $t\lesssim 1$. We identify discontinuities of the density of states as one of the key problems in the MC simulations and propose to calculate some of the dominant contributions analytically, increasing the precision of our simulations by several orders of magnitude. Even after these improvements the density of states is found highly non-smooth and therefore the DoS approach cannot outperform reweighting. We prove this implication theoretically and provide numerical evidence, concluding that the DoS approach is not well suited for quantum real time simulations with discrete degrees of freedom.Comment: 16 + 4 pages, 7 figures; code and data available (DOI: 10.5281/zenodo.7164902

Beer Mats make bad Frisbees

In this article we show why flying and rotating beer mats, CDs, or other flat disks will eventually flip in the air and end up flying with backspin, thus, making them unusable as frisbees. The crucial effect responsible for the flipping is found to be the lift attacking not in the center of mass but slightly offset to the forward edge. This induces a torque leading to a precession towards backspin orientation. An effective theory is developed providing an approximate solution for the disk's trajectory with a minimal set of parameters. Our theoretical results are confronted with experimental results obtained using a beer mat shooting apparatus and a high speed camera. Very good agreement is found.Comment: 4 videos in ancillary file

Real-time simulations of quantum spin chains: Density of states and reweighting approaches

We put the density of states (DoS) approach to Monte Carlo (MC) simulations under a stress test by applying it to a physical problem with the worst possible sign problem: the real-time evolution of a nonintegrable quantum spin chain. Benchmarks against numerical exact diagonalization and stochastic reweighting are presented. Both MC methods, the DoS approach and reweighting, allow for simulations of spin chains as long as L=40, far beyond exact diagonalizability, though only for short evolution times t≲1. We identify discontinuities of the DoS as one of the key problems in the MC simulations and propose calculating some of the dominant contributions analytically, increasing the precision of our simulations by several orders of magnitude. Even after these improvements, the DoS is found highly nonsmooth, and therefore, the DoS approach cannot outperform reweighting. We prove this implication theoretically and provide numerical evidence, concluding that the DoS approach is not well suited for quantum real-time simulations with discrete degrees of freedom

Accelerating Hybrid Monte Carlo simulations of the Hubbard model on the hexagonal lattice

We present different methods to increase the performance of Hybrid Monte Carlo simulations of the Hubbard model in two-dimensions. Our simulations concentrate on a hexagonal lattice, though can be easily generalized to other lattices. It is found that best results can be achieved using a flexible GMRES solver for matrix inversions and the second order Omelyan integrator with Hasenbusch acceleration on different time scales for molecular dynamics. We demonstrate how an arbitrary number of Hasenbusch mass terms can be included into this geometry and find that the optimal speed depends weakly on the choice of the number of Hasenbusch masses and their values. As such, the tuning of these masses is amenable to automization and we present an algorithm for this tuning that is based on the knowledge of the dependence of solver time and forces on the Hasenbusch masses. We benchmark our algorithms to systems where direct numerical diagonalization is feasible and find excellent agreement. We also simulate systems with hexagonal lattice dimensions up to $102\times 102$ and $N_t=64$. We find that the Hasenbusch algorithm leads to a speed up of more than an order of magnitude.Comment: Corrected Proof in Press in Computer Physics Communication