18,290 research outputs found
A unified approach to exact solutions of time-dependent Lie-algebraic quantum systems
By using the Lewis-Riesenfeld theory and the invariant-related unitary
transformation formulation, the exact solutions of the {\it time-dependent}
Schr\"{o}dinger equations which govern the various Lie-algebraic quantum
systems in atomic physics, quantum optics, nuclear physics and laser physics
are obtained. It is shown that the {\it explicit} solutions may also be
obtained by working in a sub-Hilbert-space corresponding to a particular
eigenvalue of the conserved generator ({\it i. e.}, the {\it time-independent}
invariant) for some quantum systems without quasi-algebraic structures. The
global and topological properties of geometric phases and their adiabatic limit
in time-dependent quantum systems/models are briefly discussed.Comment: 11 pages, Latex. accepted by Euro. Phys. J.
A comprehensive study of sparse codes on abnormality detection
Sparse representation has been applied successfully in abnormal event
detection, in which the baseline is to learn a dictionary accompanied by sparse
codes. While much emphasis is put on discriminative dictionary construction,
there are no comparative studies of sparse codes regarding abnormality
detection. We comprehensively study two types of sparse codes solutions -
greedy algorithms and convex L1-norm solutions - and their impact on
abnormality detection performance. We also propose our framework of combining
sparse codes with different detection methods. Our comparative experiments are
carried out from various angles to better understand the applicability of
sparse codes, including computation time, reconstruction error, sparsity,
detection accuracy, and their performance combining various detection methods.
Experiments show that combining OMP codes with maximum coordinate detection
could achieve state-of-the-art performance on the UCSD dataset [14].Comment: 7 page
Link Prediction via Matrix Completion
Inspired by practical importance of social networks, economic networks,
biological networks and so on, studies on large and complex networks have
attracted a surge of attentions in the recent years. Link prediction is a
fundamental issue to understand the mechanisms by which new links are added to
the networks. We introduce the method of robust principal component analysis
(robust PCA) into link prediction, and estimate the missing entries of the
adjacency matrix. On one hand, our algorithm is based on the sparsity and low
rank property of the matrix, on the other hand, it also performs very well when
the network is dense. This is because a relatively dense real network is also
sparse in comparison to the complete graph. According to extensive experiments
on real networks from disparate fields, when the target network is connected
and sufficiently dense, whatever it is weighted or unweighted, our method is
demonstrated to be very effective and with prediction accuracy being
considerably improved comparing with many state-of-the-art algorithms
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