Horizontal dynamic response of a tubular pile based on the Timoshenko theory

Horizontally vibrating characteristics of a tubular pile in saturated soil layer are studied in this paper. Governing equations of the pile is deduced based on the popular Timoshenko theory. Analytical solutions of the pile response are derived based on the continuous boundary conditions in the pile-soil interface. Accordingly, analytical expressions of the pile impedances are obtained. Based on it, a comparison with the Euler-Bernoulli Model is performed to verify this solution. Parametric analyses are carried out to study horizontal responses of the tubular pile

Currents and current correlations in a topological superconducting nanowire beam splitter

A beam splitter consisting of two normal leads coupled to one end of a topological superconducting nanowire via double quantum dot is investigated. In this geometry, the linear current cross-correlations at zero temperature change signs versus the overlap between the two Majorana bound states hosted by the nanowire. Under symmetric bias voltages the net current flowing through the nanowire is noiseless. These two features highlight the fermionic nature of such exotic Majorana excitations though they are based on the superconductivity. Moreover, there exists a unique local particle-hole symmetry inherited from the self-Hermitian property of Majorana bound states, which is apparently scarce in other systems. We show that such particular symmetry can be revealed through measuring the currents under complementary bias voltages.Comment: 6 pages, 4 figure

Option-implied Betas, Moment Risk Premia and Stock Returns

This thesis examines how stock returns are determined by different ex ante risk factors implied from options; these ex ante risk factors include option-implied betas, the variance, skew and kurtosis risk premia. I first compare different option-implied beta measures in future stock return prediction on the basis of Buss and Vilkov (2012). The option-implied beta proposed by Buss and Vilkov (2012) (BV) is found to outperform other beta approaches included in the research. I also propose the implied downside betas and find that the BV implied downside beta performs best and offers an improvement over the BV implied beta. However, the relationship between option-implied or implied downside betas and stock returns is not robust to firm-level variables such as firm size, book-to-market ratio or option-implied moments. These variables are correlated with option-implied betas and implied downside betas, which may obscure the beta-return relationship. Next, I investigate comprehensively whether the moment risk premia are able to predict the cross-section of stock returns. Cross-sectionally, I find that the variance, skew and kurtosis risk premia are determined differently by firm-level and risk factors. I also find that the moment risk premia have different effects on stock returns. For ex post realised stock returns, there is a negative relationship with both the variance and skew risk premia. However, the kurtosis risk premium has a noisy and insignificant relationship with realised stock returns. The price target expected return (PTER) and the implied cost of capital (ICC) are adopted as proxies for ex ante expected stock returns. I demonstrate that there is a significantly negative relationship between the variance and skew risk premia and expected stock returns, while there is a significantly positive relationship between the kurtosis risk premium and expected stock returns. The results are robust to firm-level and risk factors, sub-periods and different maturities. 3 Finally, I investigate whether the moment risk premia are able to explain future index returns at the aggregate stock market level; they are found to have different impacts on index returns depending on the return measure. Both the variance and skew risk premia are inversely related to subsequent realised S&P 500 index returns; however, the variance risk premium has a stronger relationship than the skew risk premium. The kurtosis risk premium has no effect on realised index returns. For the index price target expected return (PTER), neither the variance risk premium nor the skew risk premium has explanatory power with the PTER, while the kurtosis risk premium has a robust and positive relationship with the PTER. For the index implied cost of capital (ICC), both the variance and skew risk premia are significantly and positively related to the ICC, while the kurtosis risk premium has a significantly negative relationship with the ICC. However, the relationships between the moment risk premia and the ICC are not robust to macroeconomic variables. I also find that both the PTER and the ICC can be explained by macroeconomic factors

Finite sample theory for high-dimensional functional/scalar time series with applications

Statistical analysis of high-dimensional functional times series arises in various applications. Under this scenario, in addition to the intrinsic infinite-dimensionality of functional data, the number of functional variables can grow with the number of serially dependent observations. In this paper, we focus on the theoretical analysis of relevant estimated cross-(auto)covariance terms between two multivariate functional time series or a mixture of multivariate functional and scalar time series beyond the Gaussianity assumption. We introduce a new perspective on dependence by proposing functional cross-spectral stability measure to characterize the effect of dependence on these estimated cross terms, which are essential in the estimates for additive functional linear regressions. With the proposed functional cross-spectral stability measure, we develop useful concentration inequalities for estimated cross-(auto)covariance matrix functions to accommodate more general sub-Gaussian functional linear processes and, furthermore, establish finite sample theory for relevant estimated terms under a commonly adopted functional principal component analysis framework. Using our derived non-asymptotic results, we investigate the convergence properties of the regularized estimates for two additive functional linear regression applications under sparsity assumptions including functional linear lagged regression and partially functional linear regression in the context of high-dimensional functional/scalar time series

Adaptive functional thresholding for sparse covariance function estimation in high dimensions

Covariance function estimation is a fundamental task in multivariate functional data analysis and arises in many applications. In this paper, we consider estimating sparse covariance functions for high-dimensional functional data, where the number of random functions p is comparable to, or even larger than the sample size n. Aided by the Hilbert–Schmidt norm of functions, we introduce a new class of functional thresholding operators that combine functional versions of thresholding and shrinkage, and propose the adaptive functional thresholding estimator by incorporating the variance effects of individual entries of the sample covariance function into functional thresholding. To handle the practical scenario where curves are partially observed with errors, we also develop a nonparametric smoothing approach to obtain the smoothed adaptive functional thresholding estimator and its binned implementation to accelerate the computation. We investigate the theoretical properties of our proposals when p grows exponentially with n under both fully and partially observed functional scenarios. Finally, we demonstrate that the proposed adaptive functional thresholding estimators significantly outperform the competitors through extensive simulations and the functional connectivity analysis of two neuroimaging datasets