A Provable Smoothing Approach for High Dimensional Generalized Regression with Applications in Genomics

In many applications, linear models fit the data poorly. This article studies an appealing alternative, the generalized regression model. This model only assumes that there exists an unknown monotonically increasing link function connecting the response $Y$ to a single index $X^T\beta^*$ of explanatory variables $X\in\mathbb{R}^d$. The generalized regression model is flexible and covers many widely used statistical models. It fits the data generating mechanisms well in many real problems, which makes it useful in a variety of applications where regression models are regularly employed. In low dimensions, rank-based M-estimators are recommended to deal with the generalized regression model, giving root-$n$ consistent estimators of $\beta^*$. Applications of these estimators to high dimensional data, however, are questionable. This article studies, both theoretically and practically, a simple yet powerful smoothing approach to handle the high dimensional generalized regression model. Theoretically, a family of smoothing functions is provided, and the amount of smoothing necessary for efficient inference is carefully calculated. Practically, our study is motivated by an important and challenging scientific problem: decoding gene regulation by predicting transcription factors that bind to cis-regulatory elements. Applying our proposed method to this problem shows substantial improvement over the state-of-the-art alternative in real data.Comment: 53 page

Large-field CO(1--0) observations toward the Galactic historical supernova remnants: a large cavity around Tycho's supernova remnant

The investigation of the interaction between the supernova remnants (SNRs) and interstellar gas is not only necessary to improve our knowledge of SNRs, but also to understand the nature of the progenitor systems. As a part of the Milky Way Imaging Scroll Painting CO line survey (MWISP), we study the interstellar gas surrounding the Galactic historical SNRs, using the PMO 13.7-meter telescope. In this work, we present large-field (3$^\circ$$\times$2$^\circ$) and high-sensitivity CO(1-0) molecular line observations toward Tycho's SNR. The CO observations reveal, from the outside in, large molecular clouds, stream-like structures, and an inner rim around Tycho's SNR. We derived the basic properties (column density, mass, and kinematics) of these objects based on the CO observations. The large molecular clouds individually show an arc toward the remnant center, outlining a large cavity with radii of $\sim$0.3$^\circ$$\times$0.6$^\circ$ (or 13 pc $\times$27 pc at a distance of 2.5 kpc) around the remnant. The CO line broadenings and asymmetries detected in the surrounding clouds, the observed expansion of the cavity, in concert with enhanced $^{12}$CO(2-1)/(1-0) intensity ratio detected in previous studies, suggest the interaction of the large cavity with a wind in the region. After excluding the scenario of a large bubble produced by bright massive stars, we suggest that the large cavity could be explained by accretion wind from the progenitor system of Tycho's supernova. Nevertheless, the possibility of the random distribution of a large cavity around Tycho's SNR cannot be ruled out thus far. Further observations are needed to confirm the physical association of the large cavity with Tycho's SNR.Comment: 15 pages, 9 figures, updated according to the A&A proo

Accelerating Stochastic Composition Optimization

Consider the stochastic composition optimization problem where the objective is a composition of two expected-value functions. We propose a new stochastic first-order method, namely the accelerated stochastic compositional proximal gradient (ASC-PG) method, which updates based on queries to the sampling oracle using two different timescales. The ASC-PG is the first proximal gradient method for the stochastic composition problem that can deal with nonsmooth regularization penalty. We show that the ASC-PG exhibits faster convergence than the best known algorithms, and that it achieves the optimal sample-error complexity in several important special cases. We further demonstrate the application of ASC-PG to reinforcement learning and conduct numerical experiments

Pseudorandom States, Non-Cloning Theorems and Quantum Money

We propose the concept of pseudorandom states and study their constructions, properties, and applications. Under the assumption that quantum-secure one-way functions exist, we present concrete and efficient constructions of pseudorandom states. The non-cloning theorem plays a central role in our study---it motivates the proper definition and characterizes one of the important properties of pseudorandom quantum states. Namely, there is no efficient quantum algorithm that can create more copies of the state from a given number of pseudorandom states. As the main application, we prove that any family of pseudorandom states naturally gives rise to a private-key quantum money scheme.Comment: 20 page

Study on Fusarium toxins contamination of cereal grains in Jiangsu Province, China.

Doctoral Degree. University of KwaZulu-Natal, Durban.Jiangsu Province is located in the transition zone from subtropical to warm temperate zone, with the characteristics of monsoon climate. The province's natural ecological conditions are suitable for the production of winter wheat and rice. In this region, the warm and humid climate is very suitable for the plant epidemics such as Fusarium head blight (FHB). Fusarium mycotoxins are secondary metabolites produced by Fusarium species; and can cause acute and chronic toxic effects on the body and are a threat to humans and animal health. Therefore, knowledge about the prevalence of FHB-producing Fusarium species, incidence of deoxynivalenol, zearalenone and fumonisins as well as possible influencing factors is imperative for preventing influx of contaminated grains into food supply chain. The present study focuses on the occurrence of Fusarium species coupled with contamination levels of Fusarium mycotoxins from different Jiangsu Province, China for three years, and the influences of rainfall and temperature on accumulation of DON. In addition, Fusarium strains were isolated from rice and assessed for the potential to produce fumonisins and beauvericin. The findings of this study increase the knowledge on important rice fungal pathogens and provide relevant information on the high variability of these pathogens, as well as their implications for the development of further diseases. The ICS test developed in our study has advantages, such as rapid and efficient screening of samples. The data obtained from the ICS test shows good agreement with LC-MS/MS data. These results showed that the ICS test is suitable for on-site monitoring of ZEN

Development of a high strength Al-Mg2Si-Mg-Zn based alloy for high pressure die casting

A high strength Al-Mg2Si-Mg-Zn based alloy has been developed for the application in high pressure die casting to provide improved mechanical properties. The effect of various alloying elements on the microstructure and mechanical properties including yield strength, ultimate tensile strength and elongation of the alloy was investigated under the as-cast and heat-treated conditions. The typical composition of the high strength alloy has been optimised to be Al-8.0wt%Mg2Si-6.0wt%Mg-3.5wt%Zn-0.6wt%Mn (Al-11.0wt%Mg-2.9wt%Si-3.5wt%Zn-0.6wt%Mn) with unavoidable trace impurities. The mechanical properties of the alloy were enhanced by a quick solution treatment followed by ageing treatment. The improved tensile properties were at a level of yield strength over 300MPa, the ultimate tensile strength over 420MPa and the elongation over 3% assessed using international standard tensile samples made by high pressure die casting. The microstructure of the die-cast alloy consisted of the primary α-Al phase, Al-Mg2Si eutectics, AlMgZn intermetallics and α-AlFeMnSi intermetallics under the as-cast condition. The AlMgZn intermetallic compound was dissolved into the Al-matrix during solution treatment and subsequently precipitated during ageing treatment for providing the effective improvement of the mechanical properties.The financial support is gratefully acknowledged for the Engineering and Physical Sciences Research Council (EPSRC) (Project number: EP/I038616/1), Technology Strategy Board (TSB) (Project number: 101172) and Jaguar Land Rover (JLR), United Kingdom