Optimal Jackknife for Discrete Time and Continuous Time Unit Root Models

Maximum likelihood estimation of the persistence parameter in the discrete time unit root model is known for suffering from a downward bias. The bias is more pronounced in the continuous time unit root model. Recently Chambers and Kyriacou (2010) introduced a new jackknife method to remove the fi…rst order bias in the estimator of the persistence parameter in a discrete time unit root model. This paper proposes an improved jackknife estimator of the persistence parameter that works for both the discrete time unit root model and the continuous time unit root model. The proposed jackknife estimator is optimal in the sense that it minimizes the variance. Simulations highlight the performance of the proposed method in both contexts. They show that our optimal jackknife reduces the variance of the jackknife method of Chambers and Kyriacou by at least 10% in both cases.Bias reduction, Variance reduction, Vasicek model, Long-span Asymptotics, Autoregression

Density Functional Theory Studies of Magnetically Confined Fermi Gas

A theory is developed for magnetically confined Fermi gas at low temperature based on the density functional theory. The theory is illustrated by numerical calculation of density distributions of Fermi atoms $^{40}$K with parameters according to DeMarco and Jin's experiment[Science, 285(1999)1703]. Our results are in good agreement with the experiment. To check the theory, we also performed calculations using our theory at high temperature and compared very well to the result of classical limit.Comment: 6 page

Fault Location in Power Distribution Systems via Deep Graph Convolutional Networks

This paper develops a novel graph convolutional network (GCN) framework for fault location in power distribution networks. The proposed approach integrates multiple measurements at different buses while taking system topology into account. The effectiveness of the GCN model is corroborated by the IEEE 123 bus benchmark system. Simulation results show that the GCN model significantly outperforms other widely-used machine learning schemes with very high fault location accuracy. In addition, the proposed approach is robust to measurement noise and data loss errors. Data visualization results of two competing neural networks are presented to explore the mechanism of GCN's superior performance. A data augmentation procedure is proposed to increase the robustness of the model under various levels of noise and data loss errors. Further experiments show that the model can adapt to topology changes of distribution networks and perform well with a limited number of measured buses.Comment: Accepcted by IEEE Journal on Selected Areas in Communicatio

Effect of size, shape, and surface modification on cytotoxicity of gold nanoparticles to human Hep-2 and canine MDCK cells

There have been increasing interests in applying gold nanoparticles in biological research, drug delivery, and therapy. As the interaction of gold nanoparticles with cells relies on properties of nanoparticles, the cytotoxicity is complex and still under debating. In this work, we investigate the cytotoxicity of gold nanoparticles of different encapsulations, surface charge states, sizes and shapes to both human HEp-2 and canine MDCK cells. We found that cetyltrimethylammonium-bromide- (CTAB-) encapsulated gold nanorods (GNRs) were relatively higher cytotoxic than GNRs undergone further polymer coating and citrate stabilized gold nanospheres (GNSs). The toxicity of CTAB-encapsulated GNRs was mainly caused by CTAB on GNRs’ surface but not free CTAB in the solution. No obvious difference was found among GNRs of different aspect ratios. Time-lapse study revealed that cell death caused by GNRs occurred predominately within one hour through apoptosis, whereas cell death by free CTAB was in a time- and dose-dependent manner. Both positively and negatively surface-charged polymer-coated GNRs (PSS-GNRs and PAH-PSS-GNRs) showed similar levels of cytotoxic, suggesting the significance of surface functionality rather than surface charge in this case

Effect of size, shape, and surface modification on cytotoxicity of gold nanoparticles to human Hep-2 and canine MDCK cells

There have been increasing interests in applying gold nanoparticles in biological research, drug delivery, and therapy. As the interaction of gold nanoparticles with cells relies on properties of nanoparticles, the cytotoxicity is complex and still under debating. In this work, we investigate the cytotoxicity of gold nanoparticles of different encapsulations, surface charge states, sizes and shapes to both human HEp-2 and canine MDCK cells. We found that cetyltrimethylammonium-bromide- (CTAB-) encapsulated gold nanorods (GNRs) were relatively higher cytotoxic than GNRs undergone further polymer coating and citrate stabilized gold nanospheres (GNSs). The toxicity of CTAB-encapsulated GNRs was mainly caused by CTAB on GNRs’ surface but not free CTAB in the solution. No obvious difference was found among GNRs of different aspect ratios. Time-lapse study revealed that cell death caused by GNRs occurred predominately within one hour through apoptosis, whereas cell death by free CTAB was in a time- and dose-dependent manner. Both positively and negatively surface-charged polymer-coated GNRs (PSS-GNRs and PAH-PSS-GNRs) showed similar levels of cytotoxic, suggesting the significance of surface functionality rather than surface charge in this case

Effect of size, shape, and surface modification on cytotoxicity of gold nanoparticles to human Hep-2 and canine MDCK cells

There have been increasing interests in applying gold nanoparticles in biological research, drug delivery, and therapy. As the interaction of gold nanoparticles with cells relies on properties of nanoparticles, the cytotoxicity is complex and still under debating. In this work, we investigate the cytotoxicity of gold nanoparticles of different encapsulations, surface charge states, sizes and shapes to both human HEp-2 and canine MDCK cells. We found that cetyltrimethylammonium-bromide- (CTAB-) encapsulated gold nanorods (GNRs) were relatively higher cytotoxic than GNRs undergone further polymer coating and citrate stabilized gold nanospheres (GNSs). The toxicity of CTAB-encapsulated GNRs was mainly caused by CTAB on GNRs’ surface but not free CTAB in the solution. No obvious difference was found among GNRs of different aspect ratios. Time-lapse study revealed that cell death caused by GNRs occurred predominately within one hour through apoptosis, whereas cell death by free CTAB was in a time- and dose-dependent manner. Both positively and negatively surface-charged polymer-coated GNRs (PSS-GNRs and PAH-PSS-GNRs) showed similar levels of cytotoxic, suggesting the significance of surface functionality rather than surface charge in this case