5,878 research outputs found
Marginal empirical likelihood and sure independence feature screening
We study a marginal empirical likelihood approach in scenarios when the
number of variables grows exponentially with the sample size. The marginal
empirical likelihood ratios as functions of the parameters of interest are
systematically examined, and we find that the marginal empirical likelihood
ratio evaluated at zero can be used to differentiate whether an explanatory
variable is contributing to a response variable or not. Based on this finding,
we propose a unified feature screening procedure for linear models and the
generalized linear models. Different from most existing feature screening
approaches that rely on the magnitudes of some marginal estimators to identify
true signals, the proposed screening approach is capable of further
incorporating the level of uncertainties of such estimators. Such a merit
inherits the self-studentization property of the empirical likelihood approach,
and extends the insights of existing feature screening methods. Moreover, we
show that our screening approach is less restrictive to distributional
assumptions, and can be conveniently adapted to be applied in a broad range of
scenarios such as models specified using general moment conditions. Our
theoretical results and extensive numerical examples by simulations and data
analysis demonstrate the merits of the marginal empirical likelihood approach.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1139 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Principles and Practices Report on Online Enrichment and Extension for the Gifted and Talented
Based on analysis of the individual characteristics and needs of gifted and talented students, this report gives a brief discussion of the attributes of online enrichment and extension to support quick learners. A conceptual framework for the structure and processes of good online enrichment and extension will also be explained. Key words: attributes; online enrichment and extension; the gifted and talented Résumé: Basé sur les analyses des caractères individuels et des besoins des étudiants doués et talentueux, ce rapport nous donne une discussion brève sur les attributs de l’enrichissement et de l’extension en ligne en tant qu’un support pour les débutants rapides. Le cadre conceptuel pour la structure et les processus de l’enrichissement et de l’extension en lighe sera également expliqué dans cet article . Mots-Clés: attributs; enrishissement et extension en ligne; les doués et les talentueu
A General Theorem Relating the Bulk Topological Number to Edge States in Two-dimensional Insulators
We prove a general theorem on the relation between the bulk topological
quantum number and the edge states in two dimensional insulators. It is shown
that whenever there is a topological order in bulk, characterized by a
non-vanishing Chern number, even if it is defined for a non-conserved quantity
such as spin in the case of the spin Hall effect, one can always infer the
existence of gapless edge states under certain twisted boundary conditions that
allow tunneling between edges. This relation is robust against disorder and
interactions, and it provides a unified topological classification of both the
quantum (charge) Hall effect and the quantum spin Hall effect. In addition, it
reconciles the apparent conflict between the stability of bulk topological
order and the instability of gapless edge states in systems with open
boundaries (as known happening in the spin Hall case). The consequences of time
reversal invariance for bulk topological order and edge state dynamics are
further studied in the present framework.Comment: A mistake corrected in reference
Negative entanglement measure for bipartite separable mixed states
We define a negative entanglement measure for separable states which shows
that how much entanglement one should compensate the unentangled state at least
for changing it into an entangled state. For two-qubit systems and some special
classes of states in higher-dimensional systems, the explicit formula and the
lower bounds for the negative entanglement measure have been presented, and it
always vanishes for bipartite separable pure states. The negative entanglement
measure can be used as a useful quantity to describe the entanglement dynamics
and the quantum phase transition. In the transverse Ising model, the first
derivatives of negative entanglement measure diverge on approaching the
critical value of the quantum phase transition, although these two-site reduced
density matrices have no entanglement at all. In the 1D Bose-Hubbard model, the
NEM as a function of changes from zero to negative on approaching the
critical point of quantum phase transition.Comment: 6 pages, 3 figure
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