The purpose of this study is to explore the performance in Chess and in Mathematics of the college players in Cabanatuan City, Philippines. Specif-ically, it aimed to determine the respondents’ mathematics and chess per-formances, their playing styles and their beliefs regarding chess players and mathematicians. The descriptive correlational research design was utilized in this study and the data gathered by the researcher were tallied and tabulated using frequency, percentage, mean and Pearson’s r. Furthermore, open-ended questions were used to solicit remarks/comments from the respondents regarding the role of chess in enhancing their thinking skills. It was found out that the general weighted average (GWA) in Mathematics of the respondents was above average. Most of them are barangay/school level champions. Males are tactician type of players while females are positional players. A respondent who performed better in higher chess competition also performed better or obtained higher GWA in Mathematics. Furthermore, the respondents believed that a chess player can be a good mathematician especially if they start playing early in life and if chess was a part of the school curriculum since playing chess continuously has helped them in developing and improving their problem solving and critical thinking skills.

This collective case study examines
secondary science teachers’ responses to a professional development program
designed to assist in the transformation of inquiry belief structures and
inquiry instructional practices. These teachers were participants in a
year-long professional development institute that focused on increasing the
quantity and quality of inquiry in secondary science classrooms. This
multi-case design examines multiple data sources in order to answer the
following research question: How do the beliefs and practices of teachers
regarding inquiry-based instruction evolve over the year of intervention? Participants
were selected using the data from an inquiry observational protocol to
represent a variety of abilities and beliefs regarding inquiry instructional
practice. The results provide insights into teachers’ belief structures and
classroom structure related to inquiry instruction. Further, we detail the role
of the professional development experience in facilitating transformation of
classroom practice. Implications for how professional development programs are
developed and led are provided.

Abstract:
Dark Matter detectors with directional sensitivity have the potential of yielding an unambiguous positive observation of WIMPs as well as discriminating between galactic Dark Matter halo models. In this article, we introduce the motivation for directional detectors, discuss the experimental techniques that make directional detection possible, and review the status of the experimental effort in this field.

Abstract:
We use a sample of z~3 Lyman Break Galaxies (LBGs) to examine close pair clustering statistics in comparison to LCDM-based models of structure formation. Samples are selected by matching the LBG number density and by matching the observed LBG 3-D correlation function of LBGs over the two-halo term region. We show that UV-luminosity abundance matching cannot reproduce the observed data, but if subhalos are chosen to reproduce the observed clustering of LBGs we are able to reproduce the observed LBG pair fraction, (Nc), defined as the average number of companions per galaxy. This model suggests an over abundance of LBGs by a factor of ~5 over those observed, suggesting that only 1 in 5 halos above a fixed mass hosts a galaxy with LBG-like UV luminosity detectable via LBG selection techniques. We find a total observable close pair fraction of 23 \pm 0.6% (17.7 \pm 0.5%) using a prototypical cylinder radius in our overdense fiducial model and 8.3 \pm 0.5% (5.6 \pm 0.2%) in an abundance matched model (impurity corrected). For the matched spectroscopic slit analysis, we find Ncs = 5.1\pm0.2% (1.68\pm0.02%), the average number of companions observed serendipitously in our for fiducial slits (abundance matched), whereas the observed fraction of serendipitous spectroscopic close pairs is 4.7\pm1.5 per cent using the full LBG sample and 7.1\pm2.3% for a subsample with higher signal-to-noise ratio. We show that the standard method of halo assignment fails to reproduce the break in the LBG close pair behavior at small scale. To reconcile these discrepancies we suggest that a plausible fraction of LBGs in close pairs with lower mass than our sample experience interaction-induced enhanced star formation that boosts their luminosity sufficiently to be detected in observational sample but are not included in the abundance matched simulation sample.

Abstract:
We use symmetry considerations to investigate how damped modes affect pattern selection in multi-frequency forced Faraday waves. We classify and tabulate the most important damped modes and determine how the corresponding resonant triad interactions depend on the forcing parameters. The relative phase of the forcing terms may be used to enhance or suppress the nonlinear interactions. We compare our predictions with numerical results and discuss their implications for recent experiments. Our results suggest how to design multi-frequency forcing functions that favor chosen patterns in the lab.

Abstract:
We consider the distribution of the complex phase of the fermion determinant in QCD at nonzero chemical potential and examine the physical conditions under which the distribution takes a Gaussian form. We then calculate the baryon number as a function of the complex phase of the fermion determinant and show 1) that the exponential cancellations produced by the sign problem take the form of total derivatives 2) that the full baryon number is orthogonal to this noise. These insights allow us to define a self-consistency requirement for measurements of the baryon number in lattice simulations.

Abstract:
It has been suggested that the density of states approach to performing lattice simulations in QCD with nonzero chemical potential can be modified to improve the signal to noise ratio by performing a cumulant expansion of the complex phase of the fermion determinant, and then simplified by truncating the expansion after the first non-zero cumulant. This truncation corresponds to approximating the distribution of the complex phase of the fermion determinant by a Gaussian form. The crucial question is: how large are the other cumulants? We calculate the distribution of the complex phase from the hadron resonance gas model and from a combined lattice strong coupling and hopping expansion. In the case of the hadron resonance gas model the distribution takes a Gaussian form, but from the strong coupling and hopping expansion there are corrections. We discuss the implications to lattice simulations.

Abstract:
It has been suggested that for QCD at finite baryon density the distribution of the phase angle, i.e. the angle defined as the imaginary part of the logarithm of the fermion determinant, has a simple Gaussian form. This distribution provides the density in the density of states approach to the sign problem. We calculate this phase angle distribution using i) the hadron resonance gas model; and ii) a combined strong coupling and hopping parameter expansion in lattice gauge theory. While the former model leads only to a Gaussian distribution, in the latter expansion we discover terms which cause the phase angle distribution to deviate, by relative amounts proportional to powers of the inverse lattice volume, from a simple Gaussian form. We show that despite the tiny inverse-volume deviation of the phase angle distribution from a simple Gaussian form, such non-Gaussian terms can have a substantial impact on observables computed in the density of states/reweighting approach to the sign problem.

Abstract:
Calibration parameters in deterministic computer experiments are those attributes that cannot be measured or available in physical experiments. Kennedy and O'Hagan \cite{kennedy2001bayesian} suggested an approach to estimate them by using data from physical experiments and computer simulations. A theoretical framework is given which allows us to study the issues of parameter identifiability and estimation. We define the $L_2$-consistency for calibration as a justification for calibration methods. It is shown that a simplified version of the original KO method leads to asymptotically $L_2$-inconsistent calibration. This $L_2$-inconsistency can be remedied by modifying the original estimation procedure. A novel calibration method, called the $L_2$ calibration, is proposed and proven to be $L_2$-consistent and enjoys optimal convergence rate. A numerical example and some mathematical analysis are used to illustrate the source of the $L_2$-inconsistency problem.