Heat kernel estimates and their stabilities for symmetric jump processes with general mixed polynomial growths on metric measure spaces

In this paper, we consider a symmetric pure jump Markov process $X$ on a general metric measure space that satisfies volume doubling conditions. We study estimates of the transition density $p(t,x,y)$ of $X$ and their stabilities when the jumping kernel for $X$ has general mixed polynomial growths. Unlike [24], in our setting, the rate function which gives growth of jumps of $X$ may not be comparable to the scale function which provides the borderline for $p(t,x,y)$ to have either near-diagonal estimates or off-diagonal estimates. Under the assumption that the lower scaling index of scale function is strictly bigger than $1$, we establish stabilities of heat kernel estimates. If underlying metric measure space admits a conservative diffusion process which has a transition density satisfying a general sub-Gaussian bounds, we obtain heat kernel estimates which generalize [2, Theorems 1.2 and 1.4]. In this case, scale function is explicitly given by the rate function and the function $F$ related to walk dimension of underlying space. As an application, we proved that the finite moment condition in terms of $F$ on such symmetric Markov process is equivalent to a generalized version of Khintchine-type law of iterated logarithm at the infinity

CO2 and Er:YAG laser interaction with grass tissues

Plant leaves are multi-component optical materials consisting of water, pigments, and dry matter, among which water is the predominant constituent. In this article, we investigate laser interaction with grass using CO2 and Er:YAG lasers theoretically and experimentally, especially targeting water in grass tissues. We have first studied the optical properties of light absorbing constituents of grass theoretically, and then have identified interaction regimes and constructed interaction maps through a systematic experiment. Using the interaction maps, we have studied how interaction regimes change as process parameters are varied. This study reveals some interesting findings concerning carbonization and ablation mechanisms, the effect of laser beam diameter, and the ablation efficiency and quality of CO2 and Er: YAG lasers.open0

Laser Interaction with Grass Tissues

Mechanical EngineeringThis thesis has three chapters as first chapter: UV, Visible and IR light interaction with grass-tissues, second chapter: IR light with different water absorption coefficient interaction with grass-tissues and third chapter: laser lawn mowing system. Fist chapter, we investigated how UV, Visible and IR light affectgrass tissues. Grass tissues are composed mainly of pigments and water. Chlorophyll plays the role of the photosynthesis and it is not only the green pigment but it also absorbs visible light(blue and red) well. The water content of grass tissues helps the photosynthesis with carbondioxide and it can react well with absorbed IR light. UV light canbreak the chemical bonding of materials more easily than longerwavelengths (i.e. Visible and IR regimes), since the shorter wavelengths have higher electrical potential than longer wavelengths. 355nm (UV), 532nm (Visible) and 1064nm (NIR) wavelengths generated by a picosecond pulsed laser were used in the experiment. Thus, we made a process map of each wavelength and we analyzed the difference between the three wavelength regimes by using a scanning electron microscope and an optical microscope.From a process map of each wavelength, we found that the 355nm is most effective energy transfer to grass-tissues than 532nm and 1064nm wavelength and 1064nm (IR) light can reduce the damage of grass-tissues because of water absorption coefficient dominant. Therefore, we believed that chlorophyll dominant case and water dominant case have difference interaction mechanism. The chlorophyll dominant case makes directly energy of light transfer to grass-tissues then grass-tissues ablated directly. However, the water dominant case makes responses (carbonization, through-cut, partial-cut and decoloration) by heat of around absorbed area from water evaporation in grass-tissue or on surface of grass. In chapter II,Er:YAG (2.94??m) and CO2 (10.6??m) laser interaction with grass tissues had investigated. 2.94??m and 10.6??m light, Infrared (IR) regimes, laser have high water absorption coefficient as 12000 and 860 respectively. The sample thickness (grass thickness) is around 110??m. Since we can believe that the water content can reduce damage to grass-tissues from results previous Chapter I, the effect of water content in grass tissues had investigated in this chapter as how differently affect grass tissues as different water absorption coefficient at 2.94??m and 10.6??m wavelength cases. Plus, we investigated beam size effect and how seasonally affect grass-tissues (water concentration). Therefore, some results were found. Even though same intensity and interaction time, response is different as large beam size makes only carbonization response. 2.94??m with high water absorption coefficient light made faster response change than 10.6??mlight at using same beam size (1mm). Chapter III, Typical lawn mower is cut the lawn by contact method such as rotate blade and its equipment used foil fuel engine. From these reason, typical lawn mower can make noise seriously and dangerous and some pollution. However, laser lawn mower is using non-contact method and electrical power. Thus, it can be more quite, safety and little pollution. Furthermore, from previous results Chapter I and II, developed process maps of each laser can be used to manufacturing laser lawn mowing system. In this chapter, we will introduce concept of laser lawn mowing system and suggest optical-setups to cut-well and advantage and disadvantage of each wavelengths.ope

General Law of iterated logarithm for Markov processes

In this paper, we discuss general criteria and forms of both liminf and limsup laws of iterated logarithm (LIL) for continuous-time Markov processes. We consider minimal assumptions for both LILs to hold at zero (at infinity, respectively) in general metric measure spaces. We establish LILs under local assumptions near zero (near infinity, respectively) on uniform bounds of the first exit time from balls in terms of a function $\phi$ and uniform bounds on the tails of the jumping measure in terms of a function $\psi$. One of the main results is that a simple ratio test in terms of the functions $\phi$ and $\psi$ completely determines whether there exists a positive nondecreasing function $\Psi$ such that $\limsup |X_t|/\Psi(t)$ is positive and finite a.s., or not. We also provide a general formulation of liminf LIL, which covers jump processes whose jumping measures have logarithmic tails. Our results cover a large class of subordinated diffusions, jump processes with mixed polynomial local growths, jump processes with singular jumping kernels and random conductance models with long range jumps.Comment: 59 pages, 1 figure, Unbridged versio

Generative Autoregressive Networks for 3D Dancing Move Synthesis from Music

This paper proposes a framework which is able to generate a sequence of three-dimensional human dance poses for a given music. The proposed framework consists of three components: a music feature encoder, a pose generator, and a music genre classifier. We focus on integrating these components for generating a realistic 3D human dancing move from music, which can be applied to artificial agents and humanoid robots. The trained dance pose generator, which is a generative autoregressive model, is able to synthesize a dance sequence longer than 5,000 pose frames. Experimental results of generated dance sequences from various songs show how the proposed method generates human-like dancing move to a given music. In addition, a generated 3D dance sequence is applied to a humanoid robot, showing that the proposed framework can make a robot to dance just by listening to music.Comment: 8 pages, 10 figure

LASER WELDING OF ZINC-COATED AND UNCOATED STEEL SHEETS AT ATMOSPHERIC AND SUBATMOSPHERIC PRESSURES

Department of Mechanical EngineeringIn the automotive industry, zinc-coated steel is widely used because of its high corrosion resistance. Many automotive industry companies have tried to employ laser welding because of its many benefits, such as low heat input, high-intensity heat source, minimal distortion in heat affected zones, and high productivity. In lap joint laser welding of zinc-coated steel sheets, a proper gap needs to be maintained to avoid weld defects in weldment because the zinc vaporization temperature (1180 K) is lower than the steel melting temperature (1809 K). However, in this case, additional processes are required for application to actual industrial production lines, and it is difficult to precisely control the gap. Furthermore, although many researchers have investigated ways to mitigate the influence of high zinc vaporization pressure, it remains an issue because of erratic and unstable keyhole motion and melt pool behavior. Therefore, the purpose of this dissertation is to investigate the keyhole behavior and weldability of zero-gap laser welding of zinc-coated and uncoated steel sheets at atmospheric and subatmospheric pressures according to process parameters to develop the gap insensitive lap joint laser welding of zinc-coated steel. In this dissertation, firstly, a scaling law for predicting penetration depth was proposed, because the determination of penetration depth is the first consideration before the welding process. Moreover, then precisely observation method and analysis method were developed to observe clearly keyhole behavior, and effect of relative configuration of the laser beam and keyhole geometry on weldability for zero-gap lap laser welding of zinc-coated steel sheets. Also, the influence of ambient pressure on keyhole behavior and weldability were investigated to find solutions and possibilities for obtaining good welds for zero-gap lap laser welding of zinc-coated steel sheets by adjusting processing parameters (i.e. laser intensity and welding speed and ambient pressures).These studies can be summarized as follows. Firstly, a scaling law for predicting penetration depth was proposed that can be applied to both conduction mode and keyhole mode laser welding. The proposed scaling law was formulated based on a simple one-dimensional heat conduction model, and the effect of multiple reflections was accounted for. Because the scaling law was obtained from a laser heating problem, its physical meaning and why it needs to be formulated that way can be clearly explained. Experiments were conducted, and the obtained results were found to be in good agreement with the proposed scaling law. Secondly, in order to observe the keyhole behavior and reconstruct the keyhole geometry, a coaxial observation method was developed using a high-speed camera. A coaxial observation is a more useful and precise method to observe keyhole behavior than other lateral observation methods, and it was possible to study how the keyhole shape changes as the process parameters are varied. This chapter investigated the overall differences in the keyhole geometry between the zinc-coated and uncoated steels over a large process parameter space. Thirdly, using the obtained keyhole geometry data, the effect of keyhole geometry and dynamics on weldability was investigated by defining several key factors. It was found that the relative configuration of the keyhole and the laser beam is the most influential factor for obtaining good welds. For the zinc-coated steel, good welds were obtained at low welding speeds even zero-gap lap joint laser welding of zinc-coated steel sheets. Finally, based on the observation and analysis method from previous chapters, we investigated the laser welding of zinc-coated steel at subatmospheric pressures in order to compare between laser welding at atmospheric pressure and subatmospheric pressure. The purpose of this work is because the pressures inside the keyhole play a major role in weldability during zero-gap lap joint laser welding of the zinc-coated steel sheets. In this chapter, the main focus was to reconstruct time-averaged 3-D keyhole shapes and studying the influence of ambient pressures on keyhole behavior and weldability.ope

Hepatitis B Virus X Protein Impairs Hepatic Insulin Signaling Through Degradation of IRS1 and Induction of SOCS3

Hepatitis B virus (HBV) is a major cause of chronic liver diseases, and frequently results in hepatitis, cirrhosis, and ultimately hepatocellular carcinoma. The role of HCV in associations with insulin signaling has been elucidated. However, the pathogenesis of HBV-associated insulin signaling remains to be clearly characterized. Therefore, we have attempted to determine the mechanisms underlying the HBV-associated impairment of insulin signaling.The expressions of insulin signaling components were investigated in HBx-transgenic mice, HBx-constitutive expressing cells, and transiently HBx-transfected cells. Protein and gene expression was examined by Western blot, immunohistochemistry, RT-PCR, and promoter assay. Protein-protein interaction was detected by coimmunoprecipitation.HBx induced a reduction in the expression of IRS1, and a potent proteasomal inhibitor blocked the downregulation of IRS1. Additionally, HBx enhanced the expression of SOCS3 and induced IRS1 ubiquitination. Also, C/EBPalpha and STAT3 were involved in the HBx-induced expression of SOCS3. HBx interfered with insulin signaling activation and recovered the insulin-mediated downregulation of gluconeogenic genes.These results provide direct experimental evidences for the contribution of HBx in the impairment of insulin signaling

Probabilistic Imputation for Time-series Classification with Missing Data

Multivariate time series data for real-world applications typically contain a significant amount of missing values. The dominant approach for classification with such missing values is to impute them heuristically with specific values (zero, mean, values of adjacent time-steps) or learnable parameters. However, these simple strategies do not take the data generative process into account, and more importantly, do not effectively capture the uncertainty in prediction due to the multiple possibilities for the missing values. In this paper, we propose a novel probabilistic framework for classification with multivariate time series data with missing values. Our model consists of two parts; a deep generative model for missing value imputation and a classifier. Extending the existing deep generative models to better capture structures of time-series data, our deep generative model part is trained to impute the missing values in multiple plausible ways, effectively modeling the uncertainty of the imputation. The classifier part takes the time series data along with the imputed missing values and classifies signals, and is trained to capture the predictive uncertainty due to the multiple possibilities of imputations. Importantly, we show that na\"ively combining the generative model and the classifier could result in trivial solutions where the generative model does not produce meaningful imputations. To resolve this, we present a novel regularization technique that can promote the model to produce useful imputation values that help classification. Through extensive experiments on real-world time series data with missing values, we demonstrate the effectiveness of our method