On the fast convergence of random perturbations of the gradient flow

We consider in this work small random perturbations (of multiplicative noise type) of the gradient flow. We prove that under mild conditions, when the potential function is a Morse function with additional strong saddle condition, the perturbed gradient flow converges to the neighborhood of local minimizers in $O(\ln (\varepsilon^{-1}))$ time on the average, where $\varepsilon$ is the scale of the random perturbation. Under a change of time scale, this indicates that for the diffusion process that approximates the stochastic gradient method, it takes (up to logarithmic factor) only a linear time of inverse stepsize to evade from all saddle points. This can be regarded as a manifestation of fast convergence of the discrete-time stochastic gradient method, the latter being used heavily in modern statistical machine learning.Comment: Revise and Resubmit at Asymptotic Analysi

Arsenic Biotransformations in Microbes and Humans, and Catalytic Properties of Human AS3MT Variants

Arsenic is the most pervasive environmental toxic substance. As a consequence of its ubiquity, nearly every organism has genes for resistance to inorganic arsenic. In one project I examined the role of glutaredoxin 2 (Grx2) in reduction of arsenate to arsenite. I demonstrated that Grx2 has both glutaredoxin thiol transfer activity and glutathione S-transferase (GST) activity. In a second project investigated arsenic resistance in a microbiome organism. I discovered that the human gut microflora B. vulgatus has eight continuous genes in its genome and these genes form an arsenical-inducible transcriptional unit. In two other projects I investigated the properties of two As(III) S-adenosylmethionine (SAM) methyltransferase (ArsM in microbes and AS3MT in animals). In this project we demonstrate that most fungal species have ArsM orthologs with only three conserved cysteine residues, and AfArsM from Aspergillus fumigatus methylates only MAs(III) and not As(III). For human, arsenic methylation process is thought to be protective from acute high-level arsenic exposure. However, with long term low-level exposure, hAS3MT is thought to produce intracellular methylarsenite (MAs(III)) and dimethylarsenite (DMAs(III)), which are considerably more toxic than inorganic As(III) and may contribute to arsenic-related diseases. Several single nucleotide polymorphisms (SNPs) in putative regulatory elements of the hAS3MT gene have been shown to be protective. In contrast, three previously identified exonic SNPs (R173W, M287T and T306I) may be deleterious. I identified five additional intragenic variants in hAS3MT (H51R, C61W, I136T, W203C and R251H). I purified the eight polymorphic hAS3MT proteins and characterized their enzymatic properties. Each enzyme had low methylation activity through decreased affinity for substrate, lower overall rates of catalysis and/or lower stability. I propose that amino acid substitutions in hAS3MT with decreased catalytic activity lead to detrimental responses to environmental arsenic and may increase the risk of arsenic-related diseases

Aerodynamic simulation of wind turbine blade airfoil with different turbulence models

The different turbulence models have significant impacts on the aerodynamic performance of wind turbine blade airfoil. A kind of wind turbine blade airfoil was applied as the research object, in order to analyze the impacts of three different turbulence models which are S-A, k-εRNG, k-ωSST on the aerodynamic performance of wind turbine airfoil under different attack angles. By comparing the aerodynamic simulation results with the theoretical values of the lift coefficients, drag coefficients and the ratio of lift coefficient to drag coefficient for the forecast of best angle of attack, the effects of these three turbulence models on the blade airfoil aerodynamic performance were estimated in detail. The simulation of lift coefficient of wind turbine blade airfoil was verified with the flow field simulation of blade airfoil. A combined turbulence model, using different turbulence model for different angle of attack, was put forward. The simulation results demonstrate that, for the selected blade airfoil, using S-A turbulence model before the best attack angle and k-εRNG turbulence model after the best attack angle respectively, can make the simulation of blade airfoil aerodynamic performance much more accurate than the aerodynamic performance simulation using one single turbulence model, with the acceptable iterative time and the acceptable ratio of lift coefficient to drag coefficient. Therefore, the combined turbulence model can overcome the shortcomings when using only a traditional single turbulence model to simulate the aerodynamic performance of wind turbine blade airfoil, which will have a development and application value in the future

Shape-Constraint Recurrent Flow for 6D Object Pose Estimation

Most recent 6D object pose methods use 2D optical flow to refine their results. However, the general optical flow methods typically do not consider the target's 3D shape information during matching, making them less effective in 6D object pose estimation. In this work, we propose a shape-constraint recurrent matching framework for 6D object pose estimation. We first compute a pose-induced flow based on the displacement of 2D reprojection between the initial pose and the currently estimated pose, which embeds the target's 3D shape implicitly. Then we use this pose-induced flow to construct the correlation map for the following matching iterations, which reduces the matching space significantly and is much easier to learn. Furthermore, we use networks to learn the object pose based on the current estimated flow, which facilitates the computation of the pose-induced flow for the next iteration and yields an end-to-end system for object pose. Finally, we optimize the optical flow and object pose simultaneously in a recurrent manner. We evaluate our method on three challenging 6D object pose datasets and show that it outperforms the state of the art significantly in both accuracy and efficiency.Comment: CVPR 202

The aeroelastic analysis of two different wind turbine blades

The aeroelasticity of the wind turbine blade has been emphasized by the related fields as the size of blade increased dramatically. The eigenvalue approach and the time domain method are applied to analyze the aeroelastic responses of wind turbine blade to determine the flutter region respectively. In order to clarify the difference of the flutter analysis for different blade, two different airfoils are used. The flutter region will be obtained directly by judging the sign of the real part of the eigenvalue of the blade system using the eigenvalue approach. Then the time domain analysis of flutter of wind turbine blade will be carried out through the use of the four-order Runge-Kutta numerical method, so the flutter region will be acquired in another way. The time domain analysis can give the changing tread of the aeroelastic responses in great detail than that of the eigenvalue method. For the two different airfoils, the flutter region given by the eigenvalue approach coincides with that of the time domain analysis method accurately. There are two critical tip speed ratios for the two airfoils, the lower tip speed ratio and the higher tip speed ratio. The flap displacement of these two different airfoils will change from convergence to divergence, and change from divergence to convergence. But the extent of flutter differs with the different blade airfoil. The flutter of airfoil NACA63-418 diverges much more dramatically than that of the airfoil FX77-W-153. So the latter is better for the wind turbine blade. The eigenvalue approach combined with the time domain method can be applied to choose the blade airfoil and to determine the flutter region in order to avoid the flutter of wind turbine blade