Estimation and model selection in generalized additive partial linear models for correlated data with diverging number of covariates

We propose generalized additive partial linear models for complex data which allow one to capture nonlinear patterns of some covariates, in the presence of linear components. The proposed method improves estimation efficiency and increases statistical power for correlated data through incorporating the correlation information. A unique feature of the proposed method is its capability of handling model selection in cases where it is difficult to specify the likelihood function. We derive the quadratic inference function-based estimators for the linear coefficients and the nonparametric functions when the dimension of covariates diverges, and establish asymptotic normality for the linear coefficient estimators and the rates of convergence for the nonparametric functions estimators for both finite and high-dimensional cases. The proposed method and theoretical development are quite challenging since the numbers of linear covariates and nonlinear components both increase as the sample size increases. We also propose a doubly penalized procedure for variable selection which can simultaneously identify nonzero linear and nonparametric components, and which has an asymptotic oracle property. Extensive Monte Carlo studies have been conducted and show that the proposed procedure works effectively even with moderate sample sizes. A pharmacokinetics study on renal cancer data is illustrated using the proposed method.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1194 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Learning user-specific latent influence and susceptibility from information cascades

Predicting cascade dynamics has important implications for understanding information propagation and launching viral marketing. Previous works mainly adopt a pair-wise manner, modeling the propagation probability between pairs of users using n^2 independent parameters for n users. Consequently, these models suffer from severe overfitting problem, specially for pairs of users without direct interactions, limiting their prediction accuracy. Here we propose to model the cascade dynamics by learning two low-dimensional user-specific vectors from observed cascades, capturing their influence and susceptibility respectively. This model requires much less parameters and thus could combat overfitting problem. Moreover, this model could naturally model context-dependent factors like cumulative effect in information propagation. Extensive experiments on synthetic dataset and a large-scale microblogging dataset demonstrate that this model outperforms the existing pair-wise models at predicting cascade dynamics, cascade size, and "who will be retweeted".Comment: from The 29th AAAI Conference on Artificial Intelligence (AAAI-2015

Effect of sodium hyaluronate in treating fungal corneal ulcer

AIM: To retrospectively analyze the effects of sodium hyaluronate in treating fungal corneal ulcer.<p>METHODS: Since June, 2006, there were 178 patients(178 eyes)with fungal corneal ulcer receiving medical treatment in our hospital. Among them, 81 patients(81 eyes)as the control group received the traditional antifungal treatment with the natamycin and fluconazole being the major medicine, from June 2006 to June 2008. While, 97 patients(97 eyes)as the treatment group received sodium hyaluronate treatment based on traditional antifungal treatment during the period of June 2008 to March 2010. Effects of two therapeutic methods were compared and analyzed. <p>RESULTS: Of the 97 cases in the treatment group, the average hospital stay was: 14.15±4.23d, with 90 cases(92.8%)cured, 5 cases(5.2%)improved, 2 cases(2.1%)ineffective, the final visual acuity of 51.6% patients better than 0.3. Of the 81 cases in the control group, average hospital stay was: 17.26±6.23d, with 69 cases(85.2%)cured, 7 cases(8.6%)improved, 5 cases(6.2%)ineffective, the final visual acuity of 39.5% patients better than 0.3. After statistical analysis, the average hospital stay, the cure rate, the effective rate and the final visual acuity in both groups showed statistically significant difference(<i>P</i><0.05). The average hospital stay of the treatment group was shorter than that of the control group, while the cure rate and effective rate and the final visual acuity was better than that of the control group.<p>CONCLUSION: Sodium hyaluronate can promote fungal corneal ulcer healing, improve the cure rate and reduce the formation of corneal scar

On the Upper Bound of Non-Thermal Fusion Reactivity with Fixed Total Energy

Fusion reactivity represents the integration of fusion cross-sections and the velocity distributions of two reactants. In this study, we investigate the upper bound of fusion reactivity for a non-thermal reactant coexisting with a thermal Maxwellian background reactant while maintaining a constant total energy. Our optimization approach involves fine-tuning the velocity distribution of the non-thermal reactant. We employ both Lagrange multiplier and Monte Carlo methods to analyze Deuterium-Tritium (D-T) and Proton-Boron11 (p-B11) fusion scenarios. Our findings demonstrate that, within the relevant range of fusion energy, the maximum fusion reactivity can often surpass that of the conventional Maxwellian-Maxwellian reactants case by a substantial margin, ranging from 50\% to 300\%. These enhancements are accompanied by distinctive distribution functions for the non-thermal reactant, characterized by one or multiple beams. These results not only establish an upper limit for fusion reactivity but also provide valuable insights into augmenting fusion reactivity through non-thermal fusion, which holds particular significance in the realm of fusion energy research.Comment: 10 pages, 9 figure

Optical localization and polarization microscopy with angstrom precision based on position-ultra-sensitive giant Lamb shift

We propose an optical localization and polarization microscopy scheme with sub-nanometer precision for an emitter (atom/molecule/quantum dot) based on its Lamb shift. It is revealed that the position-ultra-sensitive giant Lamb shift with three or more orders of magnitude larger than that in the free space, can be induced by higher-order plasmonic dark modes of a metal nanoparticle. More importantly, this giant Lamb shift can be ultra-sensitively observed from the optical scattering spectrum of the nanoparticle via scanning an emitter by a sub-nanometer step, and the orientation of the Lamb shift image can be utilized to identify the dipole polarization of the emitter. They enable the optical spectrum microscope technology with angstrom precision and polarization identification, which will bring about broad applications in many fields, such as physics, chemistry, medicine, life science and materials science

Giant Lamb shift in photonic crystals

We obtain a general result for the Lamb shift of excited states of multilevel atoms in inhomogeneous electromagnetic structures and apply it to study atomic hydrogen in inverse-opal photonic crystals. We find that the photonic-crystal environment can lead to very large values of the Lamb shift, as compared to the case of vacuum. We also suggest that the position-dependent Lamb shift should extend from a single level to a miniband for an assembly of atoms with random distribution in space, similar to the velocity-dependent Doppler effect in atomic/molecular gases