Abstract:
Clouds play a central role in many aspects of the climate system and their forms and shapes are remarkably diverse. Appropriate representation of clouds in climate models is a major challenge because cloud processes span at least eight orders of magnitude in spatial scales. Here we show that there exists order in cloud size distribution of low-level clouds, and that it follows a power-law distribution with exponent γ close to 2. γ is insensitive to yearly variations in environmental conditions, but has regional variations and land-ocean contrasts. More importantly, we demonstrate this self-organizing behavior of clouds emerges naturally from a complex network model with simple, physical organizing principles: random clumping and merging. We also demonstrate symmetry between clear and cloudy skies in terms of macroscopic organization because of similar fundamental underlying organizing principles. The order in the apparently complex cloud-clear field thus has its root in random local interactions. Studying cloud organization with complex network models is an attractive new approach that has wide applications in climate science. We also propose a concept of cloud statistic mechanics approach. This approach is fully complementary to deterministic models, and the two approaches provide a powerful framework to meet the challenge of representing clouds in our climate models when working in tandem.

Abstract:
Direct $J/\psi$ and $\psi'$ production rates at Tevatron are calculated in the $k_t$-factorization approach within the color-singlet model. In this approach, the production rates are enhanced by a factor of 20 compared to the naive collinear parton model. However, the theoretical predictions are still below the experimental data by at least one order of magnitude. This means that to explain charmonium productions at Tevatron, we still need to call for the contributions from color-octet channels or other production mechanisms.

Abstract:
We perform a calculation on the polarization of J/psi production in deep inelastic scattering in the HERA energy range. For the inclusive production distributions, we find that the color-singlet contributions are consistent with the experimental data in the major region of z (z>0.4). Only in low z regions, there are some hints of the need of the color-octet contributions to describe the experimental data. For the polarization of J/psi in DIS processes, we find the parameter alpha changes with Q^2. Especially, at higher Q^2, difference on alpha between color-singlet and color-octet contributions become more distinctive. In the two regions of lower and larger z, the polarization parameter alpha have different features. These properties can provide important information on the polarization mechanism for J/psi production.

Abstract:
Discussion of "A significance test for the lasso" by Richard Lockhart, Jonathan Taylor, Ryan J. Tibshirani, Robert Tibshirani [arXiv:1301.7161].

Abstract:
We study in this paper a smoothness regularization method for functional linear regression and provide a unified treatment for both the prediction and estimation problems. By developing a tool on simultaneous diagonalization of two positive definite kernels, we obtain shaper results on the minimax rates of convergence and show that smoothness regularized estimators achieve the optimal rates of convergence for both prediction and estimation under conditions weaker than those for the functional principal components based methods developed in the literature. Despite the generality of the method of regularization, we show that the procedure is easily implementable. Numerical results are obtained to illustrate the merits of the method and to demonstrate the theoretical developments.

Abstract:
Estimation of large covariance matrices has drawn considerable recent attention, and the theoretical focus so far has mainly been on developing a minimax theory over a fixed parameter space. In this paper, we consider adaptive covariance matrix estimation where the goal is to construct a single procedure which is minimax rate optimal simultaneously over each parameter space in a large collection. A fully data-driven block thresholding estimator is proposed. The estimator is constructed by carefully dividing the sample covariance matrix into blocks and then simultaneously estimating the entries in a block by thresholding. The estimator is shown to be optimally rate adaptive over a wide range of bandable covariance matrices. A simulation study is carried out and shows that the block thresholding estimator performs well numerically. Some of the technical tools developed in this paper can also be of independent interest.

Abstract:
The problem of estimating the mean of random functions based on discretely sampled data arises naturally in functional data analysis. In this paper, we study optimal estimation of the mean function under both common and independent designs. Minimax rates of convergence are established and easily implementable rate-optimal estimators are introduced. The analysis reveals interesting and different phase transition phenomena in the two cases. Under the common design, the sampling frequency solely determines the optimal rate of convergence when it is relatively small and the sampling frequency has no effect on the optimal rate when it is large. On the other hand, under the independent design, the optimal rate of convergence is determined jointly by the sampling frequency and the number of curves when the sampling frequency is relatively small. When it is large, the sampling frequency has no effect on the optimal rate. Another interesting contrast between the two settings is that smoothing is necessary under the independent design, while, somewhat surprisingly, it is not essential under the common design.

Abstract:
Motivated by a range of applications in engineering and genomics, we consider in this paper detection of very short signal segments in three settings: signals with known shape, arbitrary signals, and smooth signals. Optimal rates of detection are established for the three cases and rate-optimal detectors are constructed. The detectors are easily implementable and are based on scanning with linear and quadratic statistics. Our analysis reveals both similarities and differences in the strategy and fundamental difficulty of detection among these three settings.

Abstract:
We present the rest-frame optical spectrum of a strongly lensed galaxy at redshift z =1.7 behind the cluster Abell 1689. We detect the temperature sensitive auroral line [O III] 4363, which allows the first direct metallicity measurement for galaxies at z > 1. Our high signal-to-noise spectrum indicates that the target is an extremely low metallicity star-forming galaxy.We estimate an intrinsic absolute B band magnitude of M_{B}=-18.3 \pm 0.1$, with a stellar mass of 4.4$\pm1.2\times10^{8}$ M$_{\odot}$. This galaxy extends the luminosity-metallicity relation of star-forming galaxies at z > 2 by more than an order of magnitude. Given the double-nuclei like morphology and velocity profile of \ha, we tentatively suggest that it could be a merger or a proto-rotating disk galaxy.

We give a study result to analyze a rather different, semi-analytical numerical
algorithms based on splitting-step methods with their applications to mathematical
finance. As certain subsistent numerical schemes may fail due to producing
negative values for financial variables which require non-negativity preserving.
These algorithms which we are analyzing preserve not only the
non-negativity, but also the character of boundaries (natural, reflecting, absorbing,
etc.). The derivatives of the CIR process and the Heston model are
being extensively studied. Beyond plain vanilla European options, we creatively
apply our splitting-step methods to a path-dependent option valuation.
We compare our algorithms to a class of numerical schemes based on Euler
discretization which are prevalent currently. The comparisons are given with
respect to both accuracy and computational time for the European call option
under the CIR model whereas with respect to convergence rate for the
path-dependent option under the CIR model and the European call option
under the Heston model.