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Latency in the control loop of Adaptive Optics (AO) systems can severely limit its performance. Theories describing the temporal evolution of the atmospheric turbulence, such as the frozen flow hypothesis, justify the feasibility of predicting the turbulence (or equivalently its measurements) to compensate for the resultant temporal error in the system. This will mostly benefit AO assisted High Contrast Imaging (HCI) instruments for enhanced contrast, or wide-field AO systems for improved sky coverage. In this thesis, we explore the potential of an Artificial Neural Network (ANN) as a nonlinear tool for open-loop wavefront prediction. The ANN predictor composes mainly Long Short-Term Memory (LSTM) cells, an ANN type specialised in sequence modelling and prediction. We demonstrate the efficiency and robustness of an ANN predictor both with simulated and on-sky 7 × 7 Shack-Hartmann Wavefront Sensor (SHWFS) CANARY data measured at 150 Hz, an AO demonstrator on the 4.2 m William Herschel Telescope (WHT), La Palma. We provide evidence that in addition to accurately predicting the wavefronts, an ANN predictor is also filtering high temporal frequencies such as Wavefront Sensor (WFS) noise. We show that an ANN predictor is adaptive to time-variant turbulence on sub-second level without user tuning. Specifically, we show that an ANN predictor is capable of predicting both frozen flow and non-frozen flow such as dome seeing, and that the ANN prediction can be based on a per-subaperture basis. As a pioneer, this thesis examines in great detail the characteristics of an ANN wavefront predictor and provides implications towards an on-sky implementation.

Essay 1: Stage Financing and Syndication in Venture Capital Investment: The combined use of stage financing and syndication is one of the most remarkable characteristics of venture capital financing. In particular, the majority of later-stage venture capital investments rather than early-stage are syndicated. The paper presents a theoretical rationale for this financial arrangement. The model shows that tight control (i.e. efficient refinancing or continuation/liquidation decision) of the venture capitalist by stage financing can achieve ex-post efficiency but may disincentivize the entrepreneur's effort provision ex-ante. Hence, the project value is not maximized. I show that the combined use of later-stage syndication with stage financing is a mechanism that can realize the optimal tradeoff between high effort ex ante and efficient continuation ex post thus maximizing project value. The model offers testable empirical predictions. Essay 2: The Capital Structure of Private Equity-backed Firms: In this paper I study one fundamental tension between venture capitalist and management in private equity-backed firms and show capital structure (of private equity-back firms) is a mechanism to resolve the tension. The paper gives rationale for several financial arrangements in private equity investment. (1) Private equity deals are typically partially outside financed even though the private equity fund may not be financially constrained at the deal level. (2) The optimal security for outside financing is debt. (3) The maturity of outside security is long-term. The insight of the paper has applications outside of private equity. Essay 3: Market Transparency and the Accounting Regime: We model the interaction of financial market transparency and different accounting regimes. This paper provides a theoretical rationale for the recently proposed shift in accounting standards from historic cost accounting to marking to market. The paper shows that marking to market can provide investors with an early warning mechanism while historical cost gives management a "veil" under which they can potentially mask a firm's true economic performance. The model provides new explanations for several empirical findings and has some novel implications. We show that greater opacity in financial markets leads to more frequent and more severe crashes in asset prices (under a historic-cost-accounting regime). Moreover, our model indicates that historic cost accounting can make the financial market more rather than less volatile, which runs counter to conventional wisdom. The mechanism shown in the model also sheds light on the cause of many financial scandals in recent years.