3,311 research outputs found
The Dirichet-Multinomial model for multivariate randomized response data and small samples
In survey sampling the randomized response (RR) technique can be used to obtain truthful answers to sensitive questions. Although the individual answers are masked due to the RR technique, individual (sensitive) response rates can be estimated when observing multivariate response data. The beta-binomial model for binary RR data will be generalized to handle multivariate categorical RR data. The Dirichlet-multinomial model for categorical RR data is extended with a linear transformation of the masked individual categorical-response rates to correct for the RR design and to retrieve the sensitive categorical-response rates even for small data samples. This specification of the Dirichlet-multinomial model enables a straightforward empirical Bayes estimation of the model parameters. A constrained-Dirichlet prior will be introduced to identify homogeneity restrictions in response rates across persons and/or categories. The performance of the full Bayes parameter estimation method is verified using simulated data. The proposed model will be applied to the college alcohol problem scale study, where students were interviewed directly or interviewed via the randomized response technique about negative consequences from drinking. (Contains 5 tables.
Stacking Order dependent Electric Field tuning of the Band Gap in Graphene Multilayers
The effect of different stacking order of graphene multilayers on the
electric field induced band gap is investigated. We considered a positively
charged top and a negatively charged back gate in order to independently tune
the band gap and the Fermi energy of three and four layer graphene systems. A
tight-binding approach within a self-consistent Hartree approximation is used
to calculate the induced charges on the different graphene layers. We found
that the gap for trilayer graphene with the ABC stacking is much larger than
the corresponding gap for the ABA trilayer. Also we predict that for four
layers of graphene the energy gap strongly depends on the choice of stacking,
and we found that the gap for the different types of stacking is much larger as
compared to the case of Bernal stacking. Trigonal warping changes the size of
the induced electronic gap by approximately 30% for intermediate and large
values of the induced electron density
D- shallow donor near a semiconductor-metal and a semiconductor-dielectric interface
The ground state energy and the extend of the wavefunction of a negatively
charged donor (D-) located near a semiconductor-metal or a
semiconductor-dielectric interface is obtained. We apply the effective mass
approximation and use a variational two-electron wavefunction that takes into
account the influence of all image charges that arise due to the presence of
the interface, as well as the correlation between the two electrons bound to
the donor. For a semiconductor-metal interface, the D- binding energy is
enhanced for donor positions d>1.5a_B (a_B is the effective Bohr radius) due to
the additional attraction of the electrons with their images. When the donor
approaches the interface (i.e. d<1.5a_B) the D- binding energy drops and
eventually it becomes unbound. For a semiconductor-dielectric (or a
semiconductor-vacuum) interface the D- binding energy is reduced for any donor
position as compared to the bulk case and the system becomes rapidly unbound
when the donor approaches the interface.Comment: Submitted to Phys. Rev. B on 19 November 200
Approximations in with convergent Fourier series
For a separable finite diffuse measure space and an orthonormal basis of consisting of bounded functions , we find a measurable subset of arbitrarily small complement , such that every measurable function has an approximant with on and the Fourier series of converges to , and a few further properties. The subset is universal in the sense that it does not depend on the function to be approximated. Further in the paper this result is adapted to the case of being a homogeneous space of an infinite compact second countable Hausdorff group. As a useful illustration the case of -spheres with spherical harmonics is discussed. The construction of the subset and approximant is sketched briefly at the end of the paper
Diagrammatic quantum field formalism for localized electrons
We introduce a diagrammatic quantum field formalism for the evaluation of
normalized expectation values of operators, and suitable for systems with
localized electrons. It is used to develop a convergent series expansion for
the energy in powers of overlap integrals of single-particle orbitals. This
method gives intuitive and practical rules for writing down the expansion to
arbitrary order of overlap, and can be applied to any spin configuration and to
any dimension. Its applicability for systems with well localized electrons has
been illustrated with examples, including the two-dimensional Wigner crystal
and spin-singlets in the low-density electron gas.Comment: 13 pages, 0 figure
Refined Chern-Simons theory
The partition function of refined Chern-Simons theory on 3d sphere for the
exceptional gauge algebras is presented in terms of multiple sine
functions. Gopakumar-Vafa (BPS) approximation is calculated and presented in
the form of some refined topological string partition function.Comment: On the basis of the talk given at the workshop SQS'2
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