In this thesis, we study the topology and geometry of homogeneous spaces of the form $G/T^k$, where $G$ is a compact semisimple Lie group, $T^k$ is an embedded torus in $G$. We say that a principal $Spin(n)$-bundle $P\rightarrow M$ admits a string structure if the structure group lifts to $String(n)$. In particular, a spin manifold is string if the principal $Spin(n)$-bundle associated to the tangent bundle has a string structure. It's known that $G/T^k$ are string manifolds and we prove the uniqueness of string structures on $G/T^k$ when $G$ is simply connected . There is a canonical metric on $G/T^k$, which has positive Ricci curvature. We deform this metric to a 1-parameter family of invariant metrics on $G/T^k$. We prove that the first Pontrjagin forms associated to the Levi-Civita connection of these metrics do not vanish. This verifies a conjecture by Redden-Stolz on the TMF-Witten genus of Ricci positive string manifolds.

This study examines whether analysts efficiently impound information about innovation into their short-term (quarterly and annual) and long-term forecasts. I use patents to measure technological innovation outputs, and trademarks to measure non-technological product and marketing innovation outputs. Analysts appear to understand that patents increase only long-term earnings growth whereas trademarks increase both short-term earnings and long-term earnings growth. However, their forecasts contain systematic errors. Analysts underreact to the short-term earnings implications of trademarks, and overreact to the long-term earnings implications of both patents and trademarks. In addition, analysts’ short-term forecast errors predicted from trademarks partially explain investor mispricing of trademarks. Collectively, my findings improve our knowledge of whether analysts understand innovation and how analysts’ inefficient use of information about innovation affects the stock market valuation of innovation.

Research in reading comprehension traditionally relied on the experimental setting of word-by-word presentation which eventually revealed many neural biomarkers as well as establishing the basis of modern reading research. Since the development of brain-computer techniques and computational methods in the past decades, it has become possible to study reading comprehension in natural settings. This study used a variety of advanced technologies to analyze a dataset collected by the ZuCo group regarding reading comprehension. With natural language processing tools, we extracted the words essential for understanding sentences, and identified eye-tracking patterns that relate to these words. Using the EEG time series and frequency series, we also looked at neural patterns associated with those words and tried to build up a statistical model and neural network model that predicted the linguistic patterns. Consequently, the study is likely to provide new insights into future cognitive linguistics and brain-computer interaction research, which may help advance reading-aid technologies.

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