23,093 research outputs found
Confidence sets for split points in decision trees
We investigate the problem of finding confidence sets for split points in
decision trees (CART). Our main results establish the asymptotic distribution
of the least squares estimators and some associated residual sum of squares
statistics in a binary decision tree approximation to a smooth regression
curve. Cube-root asymptotics with nonnormal limit distributions are involved.
We study various confidence sets for the split point, one calibrated using the
subsampling bootstrap, and others calibrated using plug-in estimates of some
nuisance parameters. The performance of the confidence sets is assessed in a
simulation study. A motivation for developing such confidence sets comes from
the problem of phosphorus pollution in the Everglades. Ecologists have
suggested that split points provide a phosphorus threshold at which biological
imbalance occurs, and the lower endpoint of the confidence set may be
interpreted as a level that is protective of the ecosystem. This is illustrated
using data from a Duke University Wetlands Center phosphorus dosing study in
the Everglades.Comment: Published at http://dx.doi.org/10.1214/009053606000001415 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Connecting anomaly and tunneling methods for Hawking effect through chirality
The role of chirality is discussed in unifying the anomaly and the tunneling
formalisms for deriving the Hawking effect. Using the chirality condition and
starting from the familiar form of the trace anomaly, the chiral
(gravitational) anomaly, manifested as a nonconservation of the stress tensor,
near the horizon of a black hole, is derived. Solution of this equation yields
the stress tensor whose asymptotic infinity limit gives the Hawking flux.
Finally, use of the same chirality condition in the tunneling formalism gives
the Hawking temperature that is compatible with the flux obtained by anomaly
method.Comment: LaTex, 8 pages, no figures, reformulation of tunneling mechanism, to
appear in Phys. Rev.
Non-Abelian Proca model based on the improved BFT formalism
We present the newly improved Batalin-Fradkin-Tyutin (BFT) Hamiltonian
formalism and the generalization to the Lagrangian formulation, which provide
the much more simple and transparent insight to the usual BFT method, with
application to the non-Abelian Proca model which has been an difficult problem
in the usual BFT method. The infinite terms of the effectively first class
constraints can be made to be the regular power series forms by ingenious
choice of and -matrices. In this new
method, the first class Hamiltonian, which also needs infinite correction terms
is obtained simply by replacing the original variables in the original
Hamiltonian with the BFT physical variables. Remarkably all the infinite
correction terms can be expressed in the compact exponential form. We also show
that in our model the Poisson brackets of the BFT physical variables in the
extended phase space are the same structure as the Dirac brackets of the
original phase space variables. With the help of both our newly developed
Lagrangian formulation and Hamilton's equations of motion, we obtain the
desired classical Lagrangian corresponding to the first class Hamiltonian which
can be reduced to the generalized St\"uckelberg Lagrangian which is non-trivial
conjecture in our infinitely many terms involved in Hamiltonian and Lagrangian.Comment: Notable improvements in Sec. I
Certainty Equivalent Farm Returns from Bt and Non-Bt Cotton
Replaced with revised version of paper 02/14/06.Bt cotton, certainty equivalent, insecticide, refuge, returns, risk, simulated yield, spray, Farm Management,
Spin injection and perpendicular spin transport in graphite nanostructures
Organic and carbon-based materials are attractive for spintronics because
their small spin-orbit coupling and low hyperfine interaction is expected to
give rise to large spin-relaxation times. However, the corresponding
spin-relaxation length is not necessarily large when transport is via weakly
interacting molecular orbitals. Here we use graphite as a model system and
study spin transport in the direction perpendicular to the weakly bonded
graphene sheets. We achieve injection of highly (75%) spin-polarized electrons
into graphite nanostructures of 300-500 nm across and up to 17 nm thick, and
observe transport without any measurable loss of spin information. Direct
visualization of local spin transport in graphite-based spin-valve sandwiches
also shows spatially uniform and near-unity transmission for electrons at 1.8
eV above the Fermi level
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