30,246 research outputs found
Calculation of exciton densities in SMMC
We develop a shell-model Monte Carlo (SMMC) method to calculate densities of
states with varying exciton (particle-hole) number. We then apply this method
to the doubly closed-shell nucleus 40Ca in a full 0s-1d-0f-1p shell-model space
and compare our results to those found using approximate analytic expressions
for the partial densities. We find that the effective one-body level density is
reduced by approximately 22% when a residual two-body interaction is included
in the shell model calculation.Comment: 10 pages, 4 figure
Skill set profile clustering: the empty K-means algorithm with automatic specification of starting cluster centers
While studentsā 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
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