Asymptotic normality of the deconvolution kernel density estimator under the vanishing error variance

Let $X_1,...,X_n$ be i.i.d. observations, where $X_i=Y_i+\sigma_n Z_i$ and the $Y$'s and $Z$'s are independent. Assume that the $Y$'s are unobservable and that they have the density $f$ and also that the $Z$'s have a known density $k.$ Furthermore, let $\sigma_n$ depend on $n$ and let $\sigma_n\to 0$ as $n\to\infty.$ We consider the deconvolution problem, i.e. the problem of estimation of the density $f$ based on the sample $X_1,...,X_n.$ A popular estimator of $f$ in this setting is the deconvolution kernel density estimator. We derive its asymptotic normality under two different assumptions on the relation between the sequence $\sigma_n$ and the sequence of bandwidths $h_n.$ 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 $\sigma_n\to 0$ have to be preferred to the models with fixed $\sigma.$Comment: 22 pages, 8 figure

Giant spin-orbit splitting of point defect states in monolayer WS2_2

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 $\mu_{B}$ 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 $L_1$-penalty. It is completely data-adaptive and does not require prior knowledge of the error distribution. The weighted $L_1$-penalty is used both to ensure the convexity of the penalty term and to ameliorate the bias caused by the $L_1$-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 $M_{ap}$ to describe the cosmic shear. We divide the foreground galaxy redshift $z_f<z_s$ into several bins, where $z_s$ is the redshift of the source galaxies, and calculate the quantity $^2/$ for each redshift bin. Then the ratio of the summation of $^2/< N_g^2(z_f)>$ over the bins to $$ gives a measure of the nonlinear/stochastic bias. Here $N_g(z_f)$ is the projected surface number density fluctuation of foreground galaxies at redshift $z_f$, and $M_{ap}$ is the aperture mass from the cosmic-shear analysis. We estimate that for a moderately deep weak-lensing survey with $z_s=1$, source galaxy surface number density $n_b=30 \hbox {gal}/\hbox {arcmin}^2$ and a survey area of $25 \hbox {deg}^2$, the effective $r$-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 $z_s=0.5$, $n_b=5 \hbox {gal}/\hbox {arcmin}^2$, and a survey area of $10^4 \hbox {deg}^2$, a 10% detection of $r$ is possible over the angular range $1'-100'$.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