Issues of partial credit in mathematical assessment by computer

The CALM Project for Computer Aided Learning in Mathematics has operated at Heriot‐Watt University since 1985. From the beginning CALM has featured assessment in its programs (Beevers, Cherry, Foster and McGuire, 1991), and enabled both students and teachers to view progress in formative assessment The computer can play a role in at least four types of assessment: diagnostic, self‐test, continuous and grading assessment. The TLTP project Mathwise employs the computer in three of these roles. In 1994 CALM reported on an educational experiment in which the computer was used for the first time to grade, in part, the learning of a large class of service mathematics students (Beevers, McGuire, Stirling and Wild ,1995), using the Mathwise assessment template. At that time the main issues identified were those of ‘partial credit’ and communication between the student and the computer. These educational points were addressed in the next phase of the CALM Project in which the commercial testing program Interactive PastPapers was developed. The main aim of this paper is to describe how Interactive Past Papers has been able to incorporate some approaches to partial credit which has helped to alleviate student worries on these issues. Background information on other features in Interactive Past Papers is also included to provide context for the discussion

Dynamical Hartree-Fock-Bogoliubov Theory of Vortices in Bose-Einstein Condensates at Finite Temperature

We present a method utilizing the continuity equation for the condensate density to make predictions of the precessional frequency of single off-axis vortices and of vortex arrays in Bose-Einstein condensates at finite temperature. We also present an orthogonalized Hartree-Fock-Bogoliubov (HFB) formalism. We solve the continuity equation for the condensate density self-consistently with the orthogonalized HFB equations, and find stationary solutions in the frame rotating at this frequency. As an example of the utility of this formalism we obtain time-independent solutions for quasi-two-dimensional rotating systems in the co-rotating frame. We compare these results with time-dependent predictions where we simulate stirring of the condensate.Comment: 13 pages, 11 figures, 1 tabl

Clouds, photolysis and regional tropospheric ozone budgets.

We use a three-dimensional chemical transport model to examine the shortwave radiative effects of clouds on the tropospheric ozone budget. In addition to looking at changes in global concentrations as previous studies have done, we examine changes in ozone chemical production and loss caused by clouds and how these vary in different parts of the troposphere. On a global scale, we find that clouds have a modest effect on ozone chemistry, but on a regional scale their role is much more significant, with the size of the response dependent on the region. The largest averaged changes in chemical budgets (±10–14%) are found in the marine troposphere, where cloud optical depths are high. We demonstrate that cloud effects are small on average in the middle troposphere because this is a transition region between reduction and enhancement in photolysis rates. We show that increases in boundary layer ozone due to clouds are driven by large-scale changes in downward ozone transport from higher in the troposphere rather than by decreases in in-situ ozone chemical loss rates. Increases in upper tropospheric ozone are caused by higher production rates due to backscattering of radiation and consequent increases in photolysis rates, mainly J(NO2). The global radiative effect of clouds on isoprene, through decreases of OH in the lower troposphere, is stronger than on ozone. Tropospheric isoprene lifetime increases by 7% when taking clouds into account. We compare the importance of clouds in contributing to uncertainties in the global ozone budget with the role of other radiatively-important factors. The budget is most sensitive to the overhead ozone column, while surface albedo and clouds have smaller effects. However, uncertainty in representing the spatial distribution of clouds may lead to a large sensitivity of the ozone budget components on regional scales

Discriminants, symmetrized graph monomials, and sums of squares

Motivated by the necessities of the invariant theory of binary forms J. J. Sylvester constructed in 1878 for each graph with possible multiple edges but without loops its symmetrized graph monomial which is a polynomial in the vertex labels of the original graph. In the 20-th century this construction was studied by several authors. We pose the question for which graphs this polynomial is a non-negative resp. a sum of squares. This problem is motivated by a recent conjecture of F. Sottile and E. Mukhin on discriminant of the derivative of a univariate polynomial, and an interesting example of P. and A. Lax of a graph with 4 edges whose symmetrized graph monomial is non-negative but not a sum of squares. We present detailed information about symmetrized graph monomials for graphs with four and six edges, obtained by computer calculations

Interannual variability of tropospheric composition:the influence of changes in emissions, meteorology and clouds

We have run a chemistry transport model (CTM) to systematically examine the drivers of interannual variability of tropospheric composition during 1996-2000. This period was characterised by anomalous meteorological conditions associated with the strong El Nino of 1997-1998 and intense wildfires, which produced a large amount of pollution. On a global scale, changing meteorology (winds, temperatures, humidity and clouds) is found to be the most important factor driving interannual variability of NO2 and ozone on the timescales considered. Changes in stratosphere-troposphere exchange, which are largely driven by meteorological variability, are found to play a particularly important role in driving ozone changes. The strong influence of emissions on NO2 and ozone interannual variability is largely confined to areas where intense biomass burning events occur. For CO, interannual variability is almost solely driven by emission changes, while for OH meteorology dominates, with the radiative influence of clouds being a very strong contributor. Through a simple attribution analysis for 1996-2000 we conclude that changing cloudiness drives 25% of the interannual variability of OH over Europe by affecting shortwave radiation. Over Indonesia this figure is as high as 71%. Changes in cloudiness contribute a small but non-negligible amount (up to 6%) to the interannual variability of ozone over Europe and Indonesia. This suggests that future assessments of trends in tropospheric oxidizing capacity should account for interannual variability in cloudiness, a factor neglected in many previous studies

Wigner crystals in two-dimensional transition-metal dichalcogenides: Spin physics and readout

Wigner crystals are prime candidates for the realization of regular electron lattices under minimal requirements on external control and electronics. However, several technical challenges have prevented their detailed experimental investigation and applications to date. We propose an implementation of two-dimensional electron lattices for quantum simulation of Ising spin systems based on self-assembled Wigner crystals in transition-metal dichalcogenides. We show that these semiconductors allow for minimally invasive all-optical detection schemes of charge ordering and total spin. For incident light with optimally chosen beam parameters and polarization, we predict a strong dependence of the transmitted and reflected signals on the underlying lattice periodicity, thus revealing the charge order inherent in Wigner crystals. At the same time, the selection rules in transition-metal dichalcogenides provide direct access to the spin degree of freedom via Faraday rotation measurements.Comment: 15 pages, 12 figure

Association between cartilage degeneration and subchondral bone remodeling in patients with knee osteoarthritis comparing MRI and 99mTc-DPD-SPECT/CT

SummaryObjectiveThe purpose of this retrospective cross-sectional study was to investigate the association between cartilage lesions assessed with 3T-MRI and remodeling of the subchondral bone detected by 99mTc-DPD-SPECT/CT.Design99mTc-DPD-SPECT/CT and MRI of 27 knees of 25 patients with chronic knee pain and risk factors for osteoarthritis (OA) were evaluated by one nuclear physician and one radiologist. Six regions of the knee (in total 162 regions in 27 knees) were assessed according to structural joint lesions graded with a modified Whole Organ MR imaging score (WORMS) and according to subchondral 99mTc-DPD-SPECT uptake. Relationships between regional WORMS scores and uptake were quantified using general estimating equations. In a secondary analysis the uptake sum with the WORMS sum per joint was compared using Spearman correlations.ResultsElevated subchondral uptake was significantly associated with the grade of cartilage lesions (P < 0.0001). Mean uptake was significantly higher subjacent to full thickness cartilage lesions compared to partial thickness lesions (P < 0.0001). A similar association was observed between bone marrow edema pattern (BMEP) and cartilage lesions. The sum of uptakes per joint was positively correlated to the WORMS sum (rs = 0.42) and to the sum of cartilage lesions per joint (rs = 0.50).ConclusionBoth functional and structural changes of the subchondral bone in terms of scintigraphic osseous activity and the presence and degree of BMEP were significantly associated with cartilage lesions in patients with OA of the knee. This association was pronounced with full thickness lesions, indicating a possible protective effect of the cartilage layer for the subjacent bone

Non-locality of non-Abelian anyons

Topological systems, such as fractional quantum Hall liquids, promise to successfully combat environmental decoherence while performing quantum computation. These highly correlated systems can support non-Abelian anyonic quasiparticles that can encode exotic entangled states. To reveal the non-local character of these encoded states we demonstrate the violation of suitable Bell inequalities. We provide an explicit recipe for the preparation, manipulation and measurement of the desired correlations for a large class of topological models. This proposal gives an operational measure of non-locality for anyonic states and it opens up the possibility to violate the Bell inequalities in quantum Hall liquids or spin lattices.Comment: 7 pages, 3 figure

Far Infrared and Submillimeter Emission from Galactic and Extragalactic Photo-Dissociation Regions

Photodissociation Region (PDR) models are computed over a wide range of physical conditions, from those appropriate to giant molecular clouds illuminated by the interstellar radiation field to the conditions experienced by circumstellar disks very close to hot massive stars. These models use the most up-to-date values of atomic and molecular data, the most current chemical rate coefficients, and the newest grain photoelectric heating rates which include treatments of small grains and large molecules. In addition, we examine the effects of metallicity and cloud extinction on the predicted line intensities. Results are presented for PDR models with densities over the range n=10^1-10^7 cm^-3 and for incident far-ultraviolet radiation fields over the range G_0=10^-0.5-10^6.5, for metallicities Z=1 and 0.1 times the local Galactic value, and for a range of PDR cloud sizes. We present line strength and/or line ratio plots for a variety of useful PDR diagnostics: [C II] 158 micron, [O I] 63 and 145 micron, [C I] 370 and 609 micron, CO J=1-0, J=2-1, J=3-2, J=6-5 and J=15-14, as well as the strength of the far-infrared continuum. These plots will be useful for the interpretation of Galactic and extragalactic far infrared and submillimeter spectra observable with ISO, SOFIA, SWAS, FIRST and other orbital and suborbital platforms. As examples, we apply our results to ISO and ground based observations of M82, NGC 278, and the Large Magellenic Cloud.Comment: 54 pages, 20 figures, accepted for publication in The Astrophysical Journa