A Note On Obata's Rigidity Theorem I

In this note we present various extensions of Obata's rigidity theorem concerning the Hessian of a function on a Riemannian manifold. They include general rigidity theorems for the generalized Obata equation, and hyperbolic and Euclidean analogs of Obata's theorem. Besides analyzing the full rigidity case we also characterize the geometry and topology of the underlying manifold in more general situations.Comment: Some remarks are added. A few typos are removed. The proof of one lemma is modifie

Rigidity of Schouten Tensor under Conformal Deformation

We obtain some rigidity results for metrics whose Schouten tensor is bounded from below after conformal transformations. Liang Cheng recently proved that a complete, nonflat, locally conformally flat manifold with Ricci pinching condition ($Ric-\epsilon Rg\geq 0$) must be compact. This answers higher dimensional Hamilton's pinching conjecture on locally conformally flat manifolds affirmatively. Since (modified) Schouten tensor being nonnegative is equivalent to a Ricci pinching condition, our main result yields a simple proof of Cheng's theorem

Toward Understanding Generative Data Augmentation

Generative data augmentation, which scales datasets by obtaining fake labeled examples from a trained conditional generative model, boosts classification performance in various learning tasks including (semi-)supervised learning, few-shot learning, and adversarially robust learning. However, little work has theoretically investigated the effect of generative data augmentation. To fill this gap, we establish a general stability bound in this not independently and identically distributed (non-i.i.d.) setting, where the learned distribution is dependent on the original train set and generally not the same as the true distribution. Our theoretical result includes the divergence between the learned distribution and the true distribution. It shows that generative data augmentation can enjoy a faster learning rate when the order of divergence term is $o(\max\left( \log(m)\beta_m, 1 / \sqrt{m})\right)$, where $m$ is the train set size and $\beta_m$ is the corresponding stability constant. We further specify the learning setup to the Gaussian mixture model and generative adversarial nets. We prove that in both cases, though generative data augmentation does not enjoy a faster learning rate, it can improve the learning guarantees at a constant level when the train set is small, which is significant when the awful overfitting occurs. Simulation results on the Gaussian mixture model and empirical results on generative adversarial nets support our theoretical conclusions. Our code is available at https://github.com/ML-GSAI/Understanding-GDA.Comment: 39 page

Numerical Simulation of Q345 Steel Pipe Joint Weld

Q345 steel pipe is a commonly used welding material. Whether it is shipbuilding, boiler pressure vessel or construction engineering, the demand for Q345 steel is very large. In this paper, the numerical simulation of Q345 steel pipe is carried out. It is analyzed whether the temperature field and stress field of the welded joint are similar to the reality under the condition of two-layer weld seam, so as to prove that the welding process can be implemented accordingly

An investigation into the role of information and communication technologies on travel behaviour of working adults and youth

This thesis aims to investigate the diverse roles information and communications technologies (ICT) play in shaping individuals’ mobility behaviour. In doing so, three strands of interrelated research questions are empirically analysed to better understand the use of ICT and its implications for travel among both working adults and millennials. A cross-sectional analysis is firstly performed to examine the variations in the relationships between Internet use and non-mandatory travel patterns according to household working status. By employing data from the 2005/06 Scottish Household Survey (SHS) and the two-part model, the ICT-travel relationships are found to be characterised by individual employment status and intra-household interactions, which impose different constraints on individuals’ non-mandatory mobility patterns. A repeated cross-sectional analysis using the difference-in-differences (DD) estimation and the pooling of cross sections from the 2005/06 SHS data and the 2015 Integrated Multimedia City Data (iMCD) subsequently examines the evolutions in the ICT-travel relationships over time, and how temporal changes differ between the general adult population and the millennial generation. Findings suggest that the changes over time are generally characterised by diminishing complementarity and increasing substitution. Moreover, while the temporal changes for the general population are mostly found among the medium-to-heavy Internet users, for millennials, it is the light or medium-to-light users who see significant temporal changes. Finally, using the longitudinal datasets from the British Household Panel Survey (BHPS) and the Understanding Society Survey, an exploration is undertaken of the direct and indirect effects of prior experience with using ICT (as children) on millennials’ current travel behaviour. The structural equation model is applied to examine the relationships between ICT use, travel choices, and environmental attitude. The longitudinal analysis finds that millennials’ long-term exposure to ICT (since adolescence) may shape their current travel patterns by influencing their environmental attitudes. The findings from these analyses highlight the importance of considering the effects of personal, household, and social characteristics on the ICT-travel interactions. In addition, the research focuses on dynamic interactions and on the indirect or higher-order roles of ICT in affecting travel behaviour as well as on the implications for transport planning practices and policy making

Induction, development and regulation of trimolters: Great progress in the domesticated silkworm (Bombyx mori L.)

As the only truly agricultural and great economic domesticated insect, the silkworm is not only value as a model for genetics and rmolecular biology research, but it also has great value for new silk materials. Induction and regulation of trimolter induced by anti-juvenile hormone have shown vast potential to be significant patterns in silkworm research, especially after the further studies on the regulation mechanism of trimolters. This paper reviews the great progress of the induction technique of trimolter silkworms, particularly focusing on its cocoon quality, cocoon filament and the production of advanced silk materials. This review also presents the control technology of fine filament size and the regulatory mechanism of trimolters during the developmental stages.Key words: Silkworm, trimolter, chemical induction, development, filament control, regulatory mechanism