9,235 research outputs found
The Emergent Use of Online Learning in Secondary Education: A Preliminary Review of the Literature
While the preponderance of online learning is geared toward adult learners, its use in the United States for secondary education students has been around for over a decade and has a growing literature. As online learning for adolescents gains popularity, questions are being raised about the quality, strategies, and effectiveness of the programs being offered. There are several delivery methods of online learning from the full-time virtual school to the ‘blended’ model. This review of the literature will provide an understanding of current theory and practice online learning for secondary students, recommendations for implementation, and where it may lead
Index statistical properties of sparse random graphs
Using the replica method, we develop an analytical approach to compute the
characteristic function for the probability that a
large adjacency matrix of sparse random graphs has eigenvalues
below a threshold . The method allows to determine, in principle, all
moments of , from which the typical sample to sample
fluctuations can be fully characterized. For random graph models with localized
eigenvectors, we show that the index variance scales linearly with
for , with a model-dependent prefactor that can be exactly
calculated. Explicit results are discussed for Erd\"os-R\'enyi and regular
random graphs, both exhibiting a prefactor with a non-monotonic behavior as a
function of . These results contrast with rotationally invariant
random matrices, where the index variance scales only as , with an
universal prefactor that is independent of . Numerical diagonalization
results confirm the exactness of our approach and, in addition, strongly
support the Gaussian nature of the index fluctuations.Comment: 10 pages, 5 figure
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