Peer-Assisted Learning in Calculus II: Examining Gender Differences

Mathematics is a topic in which undergraduate students find challenging, particularly for females. By providing a peer-assisted workshop during the semester, undergraduates are offered academic support throughout the course. New York City College of Technology, though a Department of Education Minority Science and Engineering Improvement Program (DOE MSEIP) grant, has adopted the Peer-Led Team Learning (PLTL) instructional model in a few Calculus II sections. Peer Leaders engage the students one-hour a week in working on selected problems sets in a collaborative setting. This project examines if there are gender differences in Calculus II class in 1) PLTL workshop attendance, 2) departmental final grade, and 3) Calculus II course grade. Results showed that there were no statistically significant gender differences in all three areas. Hence, the PLTL workshops may be an intervention that may help females succeed in higher-level mathematics courses if they persist in the course

Electronic and Structural Properties of C36_{36} Molecule

The extended SSH model and Bogoliubov-de Gennes(BdeG) formalism are applied to investigate the electronic properties and stable lattice configurations of C$_{36}$. We focus the problem on the molecule's unusual $D_{6h}$ symmetry. The electronic part of the Hamiltonian without Coulomb interaction is solved analytically. We find that the gap between HOMO and LUMO is small due to the long distance hopping between the 2nd and 5th layers. The charge densities of HOMO and LUMO are mainly distributed in the two layers, that causes a large splitting between the spin triplet and singlet excitons. The differences of bond lengths, angles and charge densities among the molecule and polarons are discussed.Comment: 15 pages, 4 figures, 4 Table

Improving Simulation Efficiency of MCMC for Inverse Modeling of Hydrologic Systems with a Kalman-Inspired Proposal Distribution

Bayesian analysis is widely used in science and engineering for real-time forecasting, decision making, and to help unravel the processes that explain the observed data. These data are some deterministic and/or stochastic transformations of the underlying parameters. A key task is then to summarize the posterior distribution of these parameters. When models become too difficult to analyze analytically, Monte Carlo methods can be used to approximate the target distribution. Of these, Markov chain Monte Carlo (MCMC) methods are particularly powerful. Such methods generate a random walk through the parameter space and, under strict conditions of reversibility and ergodicity, will successively visit solutions with frequency proportional to the underlying target density. This requires a proposal distribution that generates candidate solutions starting from an arbitrary initial state. The speed of the sampled chains converging to the target distribution deteriorates rapidly, however, with increasing parameter dimensionality. In this paper, we introduce a new proposal distribution that enhances significantly the efficiency of MCMC simulation for highly parameterized models. This proposal distribution exploits the cross-covariance of model parameters, measurements and model outputs, and generates candidate states much alike the analysis step in the Kalman filter. We embed the Kalman-inspired proposal distribution in the DREAM algorithm during burn-in, and present several numerical experiments with complex, high-dimensional or multi-modal target distributions. Results demonstrate that this new proposal distribution can greatly improve simulation efficiency of MCMC. Specifically, we observe a speed-up on the order of 10-30 times for groundwater models with more than one-hundred parameters

Investigating Water Usage Patterns tied to California State Water Project

California (USA) is the largest agricultural producer and one of the populous states in the United State. As the population and agriculture grows, water consumption patterns become crucial to keep track of especially surface water. In this research project, we studied possible changes in water consumption patterns in different counties and water rights holders who obtain surface water supply from the State Water Project (SWP) in California. We conducted a time series analysis on the California Monthly Diverted Surface Water dataset through two different time series forecasting models. Our analysis indicates that the total diverted surface water presents a periodic fluctuation, and the ARIMA model can better describes the fluctuation of diverted surface water