Critical temperature of pair condensation in a dilute Bose gas with spin-orbit coupling

We study the Bardeen-Cooper-Shrieffer (BCS) pairing state of a two-component Bose gas with a symmetric spin-orbit coupling. In the dilute limit at low temperatures, this system is essentially a dilute gas of diatomic molecules. We compute the effective mass of the molecule and find that it is anisotropic in momentum space. The critical temperature of the pairing state is about eight times smaller than the Bose-Einstein condensation (BEC) transition temperature of an ideal Bose gas with the same density.Comment: 7 pages, 1 figur

Kinetics of Singlet Oxygen Release from Endoperoxides of 2-Pyridone Derivatives

Singlet oxygen can decompose toxic substances by oxidation, but its direct generation from atmospheric oxygen by a photosensitizer requires a light source. In this project, six derivatives of 2-pyridone that can reversibly trap singlet oxygen under irradiation and release it in the dark were studied. The rates of thermolysis of their endoperoxides were measured by UV-Vis spectroscopy. Theoretical modeling was also carried out with Gaussian 09. Overall, N-isoamyl-2-pyridone has the best release performance. This study also evaluates the effects of sterics and electronics on this trend, and discusses the possibility of theoretical modeling to evaluate N-substituted 2-pyridones. Pyridone samples investigated in this study were provided by Ventana Research Corporation

Renewable Estimation and Incremental Inference with Streaming Health Datasets

The overarching objective of my dissertation is to develop a new methodology that allows to sequentially update parameter estimates and their standard errors along with data streams. The key technical novelty pertains to the fact that the proposed estimation method, termed as renewable estimation in my dissertation, uses current data and summary statistics of historical data, but no use of any historical subject-level data. To implement renewable estimation, I utilize the powerful Lambda architecture in Apache Spark to design a new paradigm that includes an inference layer in addition to the existing speed layer. This expanded architecture is named as the Rho architecture, which accommodates inference-related statistics and to facilitate sequential updating of quantities involved in estimation and inference. The first project focuses on the renewable estimation in the setting of generalized linear models (RenewGLM) in which I develop a new sequential updating algorithm to calculate numerical solutions of parameter estimates and related inferential quantities. The proposed procedure aggregates both score functions and information matrices over streaming data batches through some summary statistics. I show that the resulting estimation is asymptotically equivalent to the maximum likelihood estimation (MLE) obtained with the entire data once. I demonstrate this new methodology on the analysis of the National Automotive Sampling System-Crashworthiness Data System (NASS CDS) to evaluate the effectiveness of graduated driver licensing (GDL) in the USA. The second project focuses on a substantial extension of the first project to analyze streaming datasets with correlated outcomes, such as clustered data and longitudinal data. I establish the theoretical guarantees for the proposed renewable quadratic inference function (RenewQIF) for dependent outcomes and implement it within the Rho architecture. Furthermore, I relax the homogeneous assumption in the first project and consider regime-switching regression models with a structural change-point. I propose a real-time hypothesis testing procedure based on a goodness-of-fit test statistic that is shown to achieve both proper type I error control and desirable change-point detection power. The third project concerns data streams that involve both inter-data batch correlation and dynamic heterogeneity, arising typically from various types of electronic health records (EHR) and mobile health data. This project is built in the framework of state space models in which the observed data stream is driven by a latent state process that may incorporate trend, seasonal, or time-varying covariate effects. In this setting, calculating the online MLE is challenge due to the involvement of high-dimensional integrals and complex covariance structures. In this project, I develop a Kalman filter to facilitate a multivariate online regression analysis (MORA) in the context of linear state space mixed models. MORA enables to renew both point estimates and standard errors of the fixed effects. We also apply the MORA method to analyze an EHR data example, adjusting for some heterogeneous batch-specific effects.PHDBiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163085/1/luolsph_1.pd

Socio-spatial inequalities in late-stage cancer diagnosis in Illinois: spatiotemporal trends and methodological challenges

This dissertation examines the effects of social and spatial inequalities on late-stage diagnosis of colorectal and breast cancer, and it addresses several methodological challenges surrounding the use of ZIP codes as a study unit in analyzing late-stage cancer at diagnosis. Given that my dissertation follows the ???three-paper??? format, the abstract section is divided into three parts to describe each paper respectively. The first paper entitled ???Spatial Distribution of Late-Stage Colorectal Cancer in Illinois from 1988 to 2002: Associations with Social-Spatial Covariates???, examines spatial patterns of late-stage colorectal cancer diagnosis over time in Illinois during a period of increasing screening, and it analyzes the varying associations between social, demographic and spatial risk factors and late-stage colorectal cancer diagnosis within the same period. The Bernoulli-based spatial scan statistic was used to detect clusters of late-to-early stage cancer ratios at the ZIP code level in Illinois during two periods: 1988 to 1992, and 1998 to 2002. Then the whole state was divided into three study region: Chicago city, Chicago suburbs, and other areas. For each region in each time period, hierarchical logistic regression models were estimated to assess the associations between demographic, social and spatial factors and late-stage colorectal cancer risk. ZIP code level risk factors include three indicators of socio-economic status and the shortest travel time to the nearest colonoscopy facility and individual-level factors including age, race, and gender. The socio-economic indicators were created using factor analysis. The results show some changes over time in the spatial distribution of late-stage colorectal cancer and the impacts of risk factors at the ZIP code and individual levels. Specifically, results of the Bernoulli-based spatial scan statistic find statistically significant clusters of late-stage colorectal cancer in the Chicago metropolitan area and rural region in southern Illinois in the period of 1988 to 1992. In the later time period, the cluster outcomes were no longer statistically significant. The change indicates that late-stage risk of colorectal cancer has become more evenly distributed in Illinois over time. In terms of the hierarchical logistic regression results, both individual-level demographic factors and zip-code level covariates present variously important impacts on the risk of the late-stage colorectal cancer diagnosis in different study regions in the two time periods. The risk of late-stage diagnosis is higher among younger colorectal cancer patients. Gender has contradictory impacts on risk in Chicago city and its suburb. The shortest travel time to the nearest cancer screening providers is positively associated with late-stage diagnosis risk outside the Chicago region, suggesting that spatial access to screening services may be an important barrier to early detection in rural areas of the state. One socio-economic status indicator, Minority Disparities, demonstrated a significantly positive relationship with late-stage diagnosis risk outside the Chicago region. Similar to the effects of gender, Factor 3 (Cultural-Language Barriers) also had contradictory effects in Chicago city and suburbs. Overall, the results showed no clear trends over time in the effects of various factors on late-stage risk, and few strong and statistically significant results. The inconsistent findings suggest the need for more detailed and localized information. The second paper is titled ???Analyzing Spatial Aggregation Error in Statistical Models of Late-Stage Cancer Risk: A Monte Carlo Simulation Approach???. This paper examines the effect of spatial aggregation error on statistical estimates of the association between spatial access to health care and late-stage cancer. Monte Carlo simulation was used to disaggregate breast cancer cases for two Illinois counties from ZIP codes to census blocks in proportion to the age-race composition of the block population. After the disaggregation, a hierarchical logistic model was estimated examining the relationship between late-stage breast cancer and risk factors including travel distance to mammography, at both the ZIP code and census block levels. Model coefficients were compared between the two levels to assess the impact of spatial aggregation error. Spatial aggregation error is found to influence the coefficients of regression-type models at the ZIP code level, and this impact is highly dependent on the study area. In one study area (Kane County), block-level coefficients were very similar to those estimated on the basis of ZIP code data; whereas in the other study area (Peoria County), the two sets of coefficients differed substantially raising the possibility of drawing inaccurate inferences about the association between distance to mammography and late-stage cancer risk. The paper reveals that spatial aggregation error can significantly affect the coefficient values in statistical models of the association between cancer outcomes and spatial and non-spatial variables and thus affect inferences drawn from these models. Relying on data at the ZIP code level may lead to inaccurate findings on health risk factors, and the effects are likely to vary from one study area to another. The third paper, titled ???The Impact of Spatial Aggregation Error on Spatial Scan Analysis: A Case Study of Colorectal Cancer,??? aims to examine the effect of spatial aggregation error on results of the spatial scan statistic by geographically and statistically comparing results at the ZIP code level and three reference (census tract, census block group and census block) levels. Data on colorectal cancer cases in Cook County, IL for a 5-year interval (1998-2002) were used. The Monte Carlo simulation approach from the second paper was applied to disaggregate the cancer data from the ZIP code level to each reference level. The Bernoulli-based spatial scan statistic was implemented in SaTScan to detect primary clusters based on cancer data at the four levels. An interactive procedure involving SAS and Java programming, was designed to automatically run SaTScan hundreds of times. Characteristics of clusters at each reference level were compared to those of the ZIP code level cluster to observe differences related to spatial aggregation. The comparison reveals that the ZIP code level spatial scan statistic can generate reliable clusters at the global level in areas with a large number of cases. Nonetheless, the ZIP code analysis sometimes fails to detect clusters in areas with a lower density of cases. Spatial aggregation error is minimized in areas with sizeable numbers of cases. In the absence of cancer data at a lower level, the ZIP code level data can be used effectively to implement the spatial scan statistic and identify large and dominant clusters. However, smaller clusters located in areas with a relatively low density of cases may be missed. Given that this study focused on a highly urbanized and populated area, future research should assess the influence of spatial aggregation error on spatial scan analysis in suburban and rural regions

Using Micro-Credentials to Promote Effective Teacher Professional Development: A Case Study from Xi’an Jiaotong-Liverpool University

This study illuminates the characteristics of micro-credentials, which can effectively meet the needs of working professionals in higher education for teacher professional development and career competence-building