Skill set profile clustering: the empty K-means algorithm with automatic specification of starting cluster centers

While students’ skill set profiles can be estimated with formal cognitive diagnosis models [8], their computational complexity makes simpler proxy skill estimates attractive [1, 4, 6]. These estimates can be clustered to generate groups of similar students. Often hierarchical agglomerative clustering or k-means clustering is utilized, requiring, for K skills, the specification of 2^K clusters. The number of skill set profiles/clusters can quickly become computationally intractable. Moreover, not all profiles may be present in the population. We present a flexible version of k-means that allows for empty clusters. We also specify a method to determine efficient starting centers based on the Q-matrix. Combining the two substantially improves the clustering results and allows for analysis of data sets previously thought impossible

Skill set profile clustering based on student capability vectors computed from online tutoring data

In educational research, a fundamental goal is identifying which skills students have mastered, which skills they have not, and which skills they are in the process of mastering. As the number of examinees, items, and skills increases, the estimation of even simple cognitive diagnosis models becomes difficult. To address this, we introduce a capability matrix showing for each skill the proportion correct on all items tried by each student involving that skill. We apply variations of common clustering methods to this matrix and discuss conditioning on sparse subspaces. We demonstrate the feasibility and scalability of our method on several simulated datasets and illustrate the difficulties inherent in real data using a subset of online mathematics tutor data. We also comment on the interpretability and application of the results for teachers

Pressure inequalities for nuclear and neutron matter

We prove several inequalities using lowest-order effective field theory for nucleons which give an upper bound on the pressure of asymmetric nuclear matter and neutron matter. We prove two types of inequalities, one based on convexity and another derived from shifting an auxiliary field.Comment: 16 pages, published journal version - includes inequalities for spin polarized system

Renormalization of Drift and Diffusivity in Random Gradient Flows

We investigate the relationship between the effective diffusivity and effective drift of a particle moving in a random medium. The velocity of the particle combines a white noise diffusion process with a local drift term that depends linearly on the gradient of a gaussian random field with homogeneous statistics. The theoretical analysis is confirmed by numerical simulation. For the purely isotropic case the simulation, which measures the effective drift directly in a constant gradient background field, confirms the result previously obtained theoretically, that the effective diffusivity and effective drift are renormalized by the same factor from their local values. For this isotropic case we provide an intuitive explanation, based on a {\it spatial} average of local drift, for the renormalization of the effective drift parameter relative to its local value. We also investigate situations in which the isotropy is broken by the tensorial relationship of the local drift to the gradient of the random field. We find that the numerical simulation confirms a relatively simple renormalization group calculation for the effective diffusivity and drift tensors.Comment: Latex 16 pages, 5 figures ep

Topical Menthol, Ice, Peripheral Blood Flow, and Perceived Discomfort

Context : Injury management commonly includes decreasing arterial blood flow to the affected site in an attempt to reduce microvascular blood flow and edema and limit the induction of inflammation. Applied separately, ice and menthol gel decrease arterial blood flow, but the combined effects of ice and menthol gel on arterial blood flow are unknown. Objectives : To compare radial artery blood flow, arterial diameter, and perceived discomfort before and after the application of 1 of 4 treatment conditions. Design : Experimental crossover design. Setting : Clinical laboratory. Participants or Other Participants : Ten healthy men, 9 healthy women (mean age = 25.68 years, mean height = 1.73 m, mean weight = 76.73 kg). Intervention(s) : Four treatment conditions were randomly applied for 20 minutes to the right forearm of participants on 4 different days separated by at least 24 hours: (1) 3.5 mL menthol gel, (2) 0.5 kg of crushed ice, (3) 3.5 mL of menthol gel and 0.5 kg of crushed ice, or (4) no treatment (control). Main Outcome Measure(s) : Using high-resolution ultrasound, we measured right radial artery diameter (cm) and blood flow (mL/min) every 5 minutes for 20 minutes after the treatment was applied. Discomfort with the treatment was documented using a 1-to-10 intensity scale. Results : Radial artery blood flow decreased (P \u3c .05) from baseline in the ice (−20% to −24%), menthol (−17% to −24%), and ice and menthol (−36% to −39%) treatments but not in the control (3% to 9%) at 5, 10, and 15 minutes. At 20 minutes after baseline, only the ice (−27%) and combined ice and menthol (−38%) treatments exhibited reductions in blood flow (P \u3c .05). Discomfort was less with menthol than with the ice treatment at 5, 10, and 20 minutes after application (P \u3c .05). Arterial diameter and heart rate did not change. Conclusions : The application of 3.5 mL of menthol was similar to the application of 0.5 kg of crushed ice in reducing peripheral blood flood. Combining crushed ice with menthol appeared to have an additive effect on reducing blood flow

The Ohio Grain Marketing Legislation of 1982 and 1983

PDF pages: 6

Evaluation of SLAR and thematic mapper MSS data for forest cover mapping using computer-aided analysis techniques

Separate holograms of horizontally (HH) and vertically (HV) polarized responses obtained by the APQ-102 side-looking radar were processed through an optical correlator and the resulting image was recorded on positive film from which black and white negative and positive prints were made. Visual comparison of the HH and HV images reveals a distinct dark band in the imagery which covers about 30% of the radar strip. Preliminary evaluaton of the flight line 1 date indicates that various features on the HH and HV images seem to have different response levels. The amount of sidelap due to the look angle between flight lines 1 and 2 is negligible. NASA mission #425 to obtain flightlines of NS-001 MSS data and supporting aerial photography was successfully flown. Flight line 3 data are of very good quality and virtually cloud-free. Results of data analysis for selection of test fields and for evaluation of waveband combination and spatial resolution are presented

Perturbation theory for the effective diffusion constant in a medium of random scatterer

We develop perturbation theory and physically motivated resummations of the perturbation theory for the problem of a tracer particle diffusing in a random media. The random media contains point scatterers of density $\rho$ uniformly distributed through out the material. The tracer is a Langevin particle subjected to the quenched random force generated by the scatterers. Via our perturbative analysis we determine when the random potential can be approximated by a Gaussian random potential. We also develop a self-similar renormalisation group approach based on thinning out the scatterers, this scheme is similar to that used with success for diffusion in Gaussian random potentials and agrees with known exact results. To assess the accuracy of this approximation scheme its predictions are confronted with results obtained by numerical simulation.Comment: 22 pages, 6 figures, IOP (J. Phys. A. style

Evaluation of SLAR and thematic mapper MSS data for forest cover mapping using computer-aided analysis techniques

A set of training statistics for the 30 meter resolution simulated thematic mapper MSS data was generated based on land use/land cover classes. In addition to this supervised data set, a nonsupervised multicluster block of training statistics is being defined in order to compare the classification results and evaluate the effect of the different training selection methods on classification performance. Two test data sets, defined using a stratified sampling procedure incorporating a grid system with dimensions of 50 lines by 50 columns, and another set based on an analyst supervised set of test fields were used to evaluate the classifications of the TMS data. The supervised training data set generated training statistics, and a per point Gaussian maximum likelihood classification of the 1979 TMS data was obtained. The August 1980 MSS data was radiometrically adjusted. The SAR data was redigitized and the SAR imagery was qualitatively analyzed

Solution of large scale nuclear structure problems by wave function factorization

Low-lying shell model states may be approximated accurately by a sum over products of proton and neutron states. The optimal factors are determined by a variational principle and result from the solution of rather low-dimensional eigenvalue problems. Application of this method to sd-shell nuclei, pf-shell nuclei, and to no-core shell model problems shows that very accurate approximations to the exact solutions may be obtained. Their energies, quantum numbers and overlaps with exact eigenstates converge exponentially fast as the number of retained factors is increased.Comment: 12 pages, 12 figures (from 15 eps files) include