Assessing schematic knowledge of introductory probability theory

[Abstract]: The ability to identify schematic knowledge is an important goal for both assessment and instruction. In the current paper, schematic knowledge of statistical probability theory is explored from the declarative-procedural framework using multiple methods of assessment. A sample of 90 undergraduate introductory statistics students was required to classify 10 pairs of probability problems as similar or different; to identify whether 15 problems contained sufficient, irrelevant, or missing information (text-edit); and to solve 10 additional problems. The complexity of the schema on which the problems were based was also manipulated. Detailed analyses compared text-editing and solution accuracy as a function of text-editing category and schema complexity. Results showed that text-editing tends to be easier than solution and differentially sensitive to schema complexity. While text-editing and classification were correlated with solution, only text-editing problems with missing information uniquely predicted success. In light of previous research these results suggest that text-editing is suitable for supplementing the assessment of schematic knowledge in development

An eccentrically perturbed Tonks-Girardeau gas

We investigate the static and dynamic properties of a Tonks-Girardeau gas in a harmonic trap with an eccentric $\delta$-perturbation of variable strength. For this we first find the analytic eigensolution of the single particle problem and use this solution to calculate the spatial density and energy profiles of the many particle gas as a function of the strength and position of the perturbation. We find that the crystal nature of the Tonks state is reflected in both the lowest occupation number and momentum distribution of the gas. As a novel application of our model, we study the time evolution of the the spatial density after a sudden removal of the perturbation. The dynamics exhibits collapses and revivals of the original density distribution which occur in units of the trap frequency. This is reminiscent of the Talbot effect from classical optics.Comment: Comments and suggestions are welcom

Evaluating the merits of using brief measures of PTSD or general mental health measures in two-stage PTSD screening

Psychological screening of large numbers of personnel returning from deployments should be as brief as possible without sacrificing the ability to detect individuals who are experiencing serious psychological difficulties. This study focused on screening for posttraumatic stress disorder (PTSD) symptomatology in 421 deployed male members of the Australian Army while they were on deployment and again 3 to 6 months after they returned home. The first aim was to evaluate the performance of the Primary Care—Posttraumatic Stress Disorder Screen (PC-PTSD) and a 4-item version of the 17-item Posttraumatic Stress Disorder Checklist (PCL). A second aim was to evaluate the role of the Kessler-10 (K10) in psychological screening. The results indicated that the short form of the PCL was a better substitute for the full PCL than the PC-PTSD. Other results suggested that a more efficient screening process can be achieved using an initial K10 screening followed by more intensive PTSD screening for people identified as high risk. An additional advantage of an initial K10 filter is that other forms of mental illness could also be targeted in the second stage screening

Complex diffuse radio emission in the merging PLANCK ESZ cluster Abell 3411

We present VLA radio and Chandra X-ray observations of the merging galaxy cluster Abell 3411. For the cluster, we find an overall temperature of 6.4 keV and an X-ray luminosity of 2.8 x 10^{44} erg s^{-1} between 0.5 and 2.0 keV. The Chandra observation reveals the cluster to be undergoing a merger event. The VLA observations show the presence of large-scale diffuse emission in the central region of the cluster, which we classify as a 0.9 Mpc size radio halo. In addition, a complex region of diffuse, polarized emission is found in the southeastern outskirts of the cluster, along the projected merger axis of the system. We classify this region of diffuse emission as a radio relic. The total extent of this radio relic is 1.9 Mpc. For the combined emission in the cluster region, we find a radio spectral index of -1.0 \pm 0.1 between 74 MHz and 1.4 GHz. The morphology of the radio relic is peculiar, as the relic is broken up into five fragments. This suggests that the shock responsible for the relic has been broken up due to interaction with a large-scale galaxy filament connected to the cluster or other substructures in the ICM. Alternatively, the complex morphology reflects the presence of electrons in fossil radio bubbles that are re-accelerated by a shock.Comment: Accepted for publication in ApJ, 8 pages, 5 figure

US GLOBEC: Program Goals, Approaches, and Advances

This special issue summarizes the major achievements of the US Global Ocean Ecosystem Dynamics (GLOBEC) program and celebrates its accomplishments. The articles grew out of a final symposium held in October 2009 under the auspices of the National Academy of Sciences Ocean Studies Board (http://usglobec.org/Symposium). This special issue updates the US GLOBEC "mid-life" Oceanography issue (Vol. 15, No. 2, 2002, http://tos.org/oceanography/archive/15-2.html), which put forward many of the goals and activities of the program, but was published while field work was still being conducted and results had yet to be synthesized across regional programs. The present special issue highlights the advances in understanding achieved through the synthesis of regional studies and pan-regional comparisons

On the generalized Davenport constant and the Noether number

Known results on the generalized Davenport constant related to zero-sum sequences over a finite abelian group are extended to the generalized Noether number related to the rings of polynomial invariants of an arbitrary finite group. An improved general upper bound is given on the degrees of polynomial invariants of a non-cyclic finite group which cut out the zero vector.Comment: 14 page

A controlled migration genetic algorithm operator for hardware-in-the-loop experimentation

In this paper, we describe the development of an extended migration operator, which combats the negative effects of noise on the effective search capabilities of genetic algorithms. The research is motivated by the need to minimize the num- ber of evaluations during hardware-in-the-loop experimentation, which can carry a significant cost penalty in terms of time or financial expense. The authors build on previous research, where convergence for search methods such as Simulated Annealing and Variable Neighbourhood search was accelerated by the implementation of an adaptive decision support operator. This methodology was found to be effective in searching noisy data surfaces. Providing that noise is not too significant, Genetic Al- gorithms can prove even more effective guiding experimentation. It will be shown that with the introduction of a Controlled Migration operator into the GA heuristic, data, which repre- sents a significant signal-to-noise ratio, can be searched with significant beneficial effects on the efficiency of hardware-in-the- loop experimentation, without a priori parameter tuning. The method is tested on an engine-in-the-loop experimental example, and shown to bring significant performance benefits

The Tate conjecture for K3 surfaces over finite fields

Artin's conjecture states that supersingular K3 surfaces over finite fields have Picard number 22. In this paper, we prove Artin's conjecture over fields of characteristic p>3. This implies Tate's conjecture for K3 surfaces over finite fields of characteristic p>3. Our results also yield the Tate conjecture for divisors on certain holomorphic symplectic varieties over finite fields, with some restrictions on the characteristic. As a consequence, we prove the Tate conjecture for cycles of codimension 2 on cubic fourfolds over finite fields of characteristic p>3.Comment: 20 pages, minor changes. Theorem 4 is stated in greater generality, but proofs don't change. Comments still welcom