4,406 research outputs found
Selective Population of Edge States in a 2D Topological Band System
We consider a system of interacting spin-one atoms in a hexagonal lattice
under the presence of a synthetic gauge field. Quenching the quadratic Zeeman
field is shown to lead to a dynamical instability of the edge modes. This, in
turn, leads to a spin current along the boundary of the system which grows
exponentially fast in time following the quench. Tuning the magnitude of the
quench can be used to selectively populate edge modes of different momenta.
Implications of the intrinsic symmetries of Hamiltonian on the dynamics are
discussed. The results hold for atoms with both antiferromagnetic and
ferromagnetic interactions.Comment: 7 pages (expanded Supplemental Material
Dirichlet heat kernel for unimodal L\'evy processes
We estimate the heat kernel of the smooth open set for the isotropic unimodal
pure-jump L\'evy process with infinite L\'evy measure and weakly scaling
L\'evy-Kchintchine exponent.Comment: 38 page
A comparison of the Benjamini-Hochberg procedure with some Bayesian rules for multiple testing
In the spirit of modeling inference for microarrays as multiple testing for
sparse mixtures, we present a similar approach to a simplified version of
quantitative trait loci (QTL) mapping. Unlike in case of microarrays, where the
number of tests usually reaches tens of thousands, the number of tests
performed in scans for QTL usually does not exceed several hundreds. However,
in typical cases, the sparsity of significant alternatives for QTL mapping
is in the same range as for microarrays. For methodological interest, as well
as some related applications, we also consider non-sparse mixtures. Using
simulations as well as theoretical observations we study false discovery rate
(FDR), power and misclassification probability for the Benjamini-Hochberg (BH)
procedure and its modifications, as well as for various parametric and
nonparametric Bayes and Parametric Empirical Bayes procedures. Our results
confirm the observation of Genovese and Wasserman (2002) that for small p the
misclassification error of BH is close to optimal in the sense of attaining the
Bayes oracle. This property is shared by some of the considered Bayes testing
rules, which in general perform better than BH for large or moderate 's.Comment: Published in at http://dx.doi.org/10.1214/193940307000000158 the IMS
Collections (http://www.imstat.org/publications/imscollections.htm) by the
Institute of Mathematical Statistics (http://www.imstat.org
One-dimensional quasi-relativistic particle in the box
Two-term Weyl-type asymptotic law for the eigenvalues of one-dimensional
quasi-relativistic Hamiltonian (-h^2 c^2 d^2/dx^2 + m^2 c^4)^(1/2) + V_well(x)
(the Klein-Gordon square-root operator with electrostatic potential) with the
infinite square well potential V_well(x) is given: the n-th eigenvalue is equal
to (n pi/2 - pi/8) h c/a + O(1/n), where 2a is the width of the potential well.
Simplicity of eigenvalues is proved. Some L^2 and L^infinity properties of
eigenfunctions are also studied. Eigenvalues represent energies of a `massive
particle in the box' quasi-relativistic model.Comment: 40 pages, 4 figures; minor correction
Asymptotic Bayes-optimality under sparsity of some multiple testing procedures
Within a Bayesian decision theoretic framework we investigate some asymptotic
optimality properties of a large class of multiple testing rules. A parametric
setup is considered, in which observations come from a normal scale mixture
model and the total loss is assumed to be the sum of losses for individual
tests. Our model can be used for testing point null hypotheses, as well as to
distinguish large signals from a multitude of very small effects. A rule is
defined to be asymptotically Bayes optimal under sparsity (ABOS), if within our
chosen asymptotic framework the ratio of its Bayes risk and that of the Bayes
oracle (a rule which minimizes the Bayes risk) converges to one. Our main
interest is in the asymptotic scheme where the proportion p of "true"
alternatives converges to zero. We fully characterize the class of fixed
threshold multiple testing rules which are ABOS, and hence derive conditions
for the asymptotic optimality of rules controlling the Bayesian False Discovery
Rate (BFDR). We finally provide conditions under which the popular
Benjamini-Hochberg (BH) and Bonferroni procedures are ABOS and show that for a
wide class of sparsity levels, the threshold of the former can be approximated
by a nonrandom threshold.Comment: Published in at http://dx.doi.org/10.1214/10-AOS869 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Lieb-Thirring Bound for Schr\"odinger Operators with Bernstein Functions of the Laplacian
A Lieb-Thirring bound for Schr\"odinger operators with Bernstein functions of
the Laplacian is shown by functional integration techniques. Several specific
cases are discussed in detail.Comment: We revised the first versio
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