37,798 research outputs found
Asymptotic normality of the deconvolution kernel density estimator under the vanishing error variance
Let be i.i.d. observations, where and
the 's and 's are independent. Assume that the 's are unobservable and
that they have the density and also that the 's have a known density
Furthermore, let depend on and let as
We consider the deconvolution problem, i.e. the problem of
estimation of the density based on the sample A popular
estimator of in this setting is the deconvolution kernel density estimator.
We derive its asymptotic normality under two different assumptions on the
relation between the sequence and the sequence of bandwidths
We also consider several simulation examples which illustrate different types
of asymptotics corresponding to the derived theoretical results and which show
that there exist situations where models with have to be
preferred to the models with fixed Comment: 22 pages, 8 figure
Giant spin-orbit splitting of point defect states in monolayer WS
The spin-orbit coupling (SOC) effect has been known to be profound in
monolayer pristine transition metal dichalcogenides (TMDs). Here we show that
point defects, which are omnipresent in the TMD membranes, exhibit even
stronger SOC effects and change the physics of the host materials drastically.
In this Article we chose the representative monolayer WS\sub{2} slabs from the
TMD family together with seven typical types of point defects including
monovacancies, interstitials, and antisites. We calculated the formation
energies of these defects, and studied the effect of spin-orbit coupling (SOC)
on the corresponding defect states. We found that the S monovacancy (V\sub{S} )
and S interstitial (adatom) have the lowest formation energies. In the case of
V\sub{S} and both of the W\sub{S and W\sub{S2} antisites, the defect states
exhibit giant splitting up to 296 meV when SOC is considered. Depending on the
relative position of the defect state with respect to the conduction band
minimum (CBM), the hybrid functional HSE will either increase the splitting by
up to 60 meV (far from CBM), or decrease the splitting by up to 57 meV (close
to CBM). Furthermore, we found that both the W\sub{S} and W\sub{S2} antisites
possess a magnetic moment of 2 localized at the antisite W atom and
the neighboring W atoms. All these findings provide new insights in the defect
behavior under SOC point to new possibilities for spintronics applications for
TMDs.Comment: 8 pages, 6 figure
Penalized Composite Quasi-Likelihood for Ultrahigh-Dimensional Variable Selection
In high-dimensional model selection problems, penalized simple least-square
approaches have been extensively used. This paper addresses the question of
both robustness and efficiency of penalized model selection methods, and
proposes a data-driven weighted linear combination of convex loss functions,
together with weighted -penalty. It is completely data-adaptive and does
not require prior knowledge of the error distribution. The weighted
-penalty is used both to ensure the convexity of the penalty term and to
ameliorate the bias caused by the -penalty. In the setting with
dimensionality much larger than the sample size, we establish a strong oracle
property of the proposed method that possesses both the model selection
consistency and estimation efficiency for the true non-zero coefficients. As
specific examples, we introduce a robust method of composite L1-L2, and optimal
composite quantile method and evaluate their performance in both simulated and
real data examples
Measuring the Deviation from the Linear and Deterministic Bias through Cosmic Gravitational Lensing Effects
Since gravitational lensing effects directly probe inhomogeneities of dark
matter, lensing-galaxy cross-correlations can provide us important information
on the relation between dark matter and galaxy distributions, i.e., the bias.
In this paper, we propose a method to measure the stochasticity/nonlinearity of
the galaxy bias through correlation studies of the cosmic shear and galaxy
number fluctuations. Specifically, we employ the aperture mass statistics
to describe the cosmic shear. We divide the foreground galaxy redshift
into several bins, where is the redshift of the source
galaxies, and calculate the quantity for
each redshift bin. Then the ratio of the summation of over the bins to gives a measure of the
nonlinear/stochastic bias. Here is the projected surface number
density fluctuation of foreground galaxies at redshift , and is
the aperture mass from the cosmic-shear analysis. We estimate that for a
moderately deep weak-lensing survey with , source galaxy surface number
density and a survey area of , the effective -parameter that represents the deviation from the
linear and deterministic bias is detectable in the angular range of 1'-10' if
|r-1|\gsim 10%. For shallow, wide surveys such as the Sloan Digital Sky
Survey with , , and a survey area
of , a 10% detection of is possible over the angular
range .Comment: ApJ in pres
A note on asymptotic normality of kernel deconvolution density estimator with logarithmic Chi-square noise: with application in volatility density estimation
This paper studies the asymptotic normality for kernel deconvolution estimator when the noise distribution is logarithmic Chi-square, both identical and independently distributed observations and strong mixing observations are considered. The dependent case of the result is applied to obtaining the pointwise asymptotic distribution of the deconvolution volatility density estimator in a discrete-time stochastic volatility models
Dynamic Coupling of Convective Flows and Magnetic Field during Flux Emergence
We simulate the buoyant rise of a magnetic flux rope from the solar
convection zone into the corona to better understand the energetic coupling of
the solar interior to the corona. The magnetohydrodynamic model addresses the
physics of radiative cooling, coronal heating and ionization, which allow us to
produce a more realistic model of the solar atmosphere. The simulation
illustrates the process by which magnetic flux emerges at the photosphere and
coalesces to form two large concentrations of opposite polarities. We find that
the large-scale convective motion in the convection zone is critical to form
and maintain sunspots, while the horizontal converging flows in the near
surface layer prevent the concentrated polarities from separating. The foot
points of the sunspots in the convection zone exhibit a coherent rotation
motion, resulting in the increasing helicity of the coronal field. Here, the
local configuration of the convection causes the convergence of opposite
polarities of magnetic flux with a shearing flow along the polarity inversion
line. During the rising of the flux rope, the magnetic energy is first injected
through the photosphere by the emergence, followed by energy transport by
horizontal flows, after which the energy is subducted back to the convection
zone by the submerging flows
Predicting rare events in chemical reactions: application to skin cell proliferation
In a well-stirred system undergoing chemical reactions, fluctuations in the
reaction propensities are approximately captured by the corresponding chemical
Langevin equation. Within this context, we discuss in this work how the Kramers
escape theory can be used to predict rare events in chemical reactions. As an
example, we apply our approach to a recently proposed model on cell
proliferation with relevance to skin cancer [P.B. Warren, Phys. Rev. E {\bf
80}, 030903 (2009)]. In particular, we provide an analytical explanation for
the form of the exponential exponent observed in the onset rate of uncontrolled
cell proliferation.Comment: New materials and references added. To appear in Physical Review
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