Effects of retirement on cognitive function: A gender and international perspecive

Background: As the global population is ageing, studying cognitive impairments including dementia, one of the leading causes of disability in old age worldwide, is of fundamental importance to public health. As a major transition in older age, a focus on the complex impacts of the duration, timing, and voluntariness of retirement on health is important for policy changes in the future. Longer retirement periods, as well as leaving the workforce early, have been associated with poorer health, including reduced cognitive functioning. These associations are hypothesized to differ based on gender, as well as on pre-retirement educational and occupational experiences, and on post-retirement social factors and health conditions. Methods: A cross-sectional study is conducted to determine the relationship between duration and timing of retirement and cognitive function, using data from the five sites of International Mobility in Aging Study (IMIAS). Cognitive function is assessed using the Leganes Cognitive Test (LCT) scores in 2012. Data are analyzed using multiple linear regressions. Analyses are also done by site/region separately (Canada, Latin America, and Albania). Robustness checks are done with an analysis of cognitive change from 2012 to 2014, the effect of voluntariness of retirement on cognitive function. An instrumental variable (IV) approach is also applied to the cross-sectional and longitudinal analyses as a robustness check to address the potential endogeneity of the retirement variable. Results: Descriptive statistics highlight differences between men and women, as well as between sites. In linear regression analysis, there was no relationship between timing or duration of retirement and cognitive function in 2012, when adjusting for site/region. There was no association between retirement characteristics and cognitive function in site/region/stratified analyses. In IV analysis, longer retirement and on time or late retirement was associated with lower cognitive function among men. In IV analysis, there is no relationship between retirement characteristics and cognitive function among women. Conclusions: While results of the thesis suggest a negative effect of retirement on cognitive function, especially among men, the relationship remains uncertain. A lack of power results in the inability to draw conclusions for site/region-specific analysis and site-adjusted analysis in both linear and IV regressions.

RELIBILITY ANALYSIS OF SIMPLE SLOPES AND SOIL-STRUCTURES WITH LINEAR LIMIT STATES

The first objective of this research was to develop closed-form and numerical probabilistic methods of analysis that can be applied to otherwise conventional methods of unreinforced and geosynthetic reinforced slopes and walls. These probabilistic methods explicitly include random variability of soil and reinforcement, spatial variability of the soil, and cross-correlation between soil input parameters on probability of failure. The quantitative impact of simultaneously considering the influence of random and/or spatial variability in soil properties in combination with cross-correlation in soil properties is investigated for the first time in the research literature. Depending on the magnitude of these statistical descriptors, margins of safety based on conventional notions of safety may be very different from margins of safety expressed in terms of probability of failure (or reliability index). The thesis work also shows that intuitive notions of margin of safety using conventional factor of safety and probability of failure can be brought into alignment when cross-correlation between soil properties is considered in a rigorous manner. The second objective of this thesis work was to develop a general closed-form solution to compute the true probability of failure (or reliability index) of a simple linear limit state function with one load term and one resistance term expressed first in general probabilistic terms and then migrated to a LRFD format for the purpose of LRFD calibration. The formulation considers contributions to probability of failure due to model type, uncertainty in bias values, bias dependencies, uncertainty in estimates of nominal values for correlated and uncorrelated load and resistance terms, and average margin of safety expressed as the operational factor of safety (OFS). Bias is defined as the ratio of measured to predicted value. Parametric analyses were carried out to show that ignoring possible correlations between random variables can lead to conservative (safe) values of resistance factor in some cases and in other cases to non-conservative (unsafe) values. Example LRFD calibrations were carried out using different load and resistance models for the pullout internal stability limit state of steel strip and geosynthetic reinforced soil walls together with matching bias data reported in the literature.

Linear Hyperspectral Unmixing Using L0-norm Approximations and Nonnegative Matrix Factorization

Spectral unmixing (SU) is a technique to characterize mixed pixels of the hyperspectral images measured by remote sensors. Most of the existing spectral unmixing algorithms are developed using the linear mixing models. Since the number of endmembers/materials present at each mixed pixel is normally scanty compared with the number of total endmembers (the dimension of spectral library), the problem becomes sparse. This thesis introduces sparse hyperspectral unmixing methods for the linear mixing model through two different scenarios. In the first scenario, the library of spectral signatures is assumed to be known and the main problem is to find the minimum number of endmembers under a reasonable small approximation error. Mathematically, the corresponding problem is called the $\ell_0$-norm problem which is NP-hard problem. Our main study for the first part of thesis is to find more accurate and reliable approximations of $\ell_0$-norm term and propose sparse unmixing methods via such approximations. The resulting methods are shown considerable improvements to reconstruct the fractional abundances of endmembers in comparison with state-of-the-art methods such as having lower reconstruction errors. In the second part of the thesis, the first scenario (i.e., dictionary-aided semiblind unmixing scheme) will be generalized as the blind unmixing scenario that the library of spectral signatures is also estimated. We apply the nonnegative matrix factorization (NMF) method for proposing new unmixing methods due to its noticeable supports such as considering the nonnegativity constraints of two decomposed matrices. Furthermore, we introduce new cost functions through some statistical and physical features of spectral signatures of materials (SSoM) and hyperspectral pixels such as the collaborative property of hyperspectral pixels and the mathematical representation of the concentrated energy of SSoM for the first few subbands. Finally, we introduce sparse unmixing methods for the blind scenario and evaluate the efficiency of the proposed methods via simulations over synthetic and real hyperspectral data sets. The results illustrate considerable enhancements to estimate the spectral library of materials and their fractional abundances such as smaller values of spectral angle distance (SAD) and abundance angle distance (AAD) as well.