The global well-posedness and Newtonian limit for the relativistic Boltzmann equation in a periodic box

In this paper, we study the Newtonian limit for relativistic Boltzmann equation in a periodic box $\mathbb{T}^3$. We first establish the global-in-time mild solutions of relativistic Boltzmann equation with uniform-in-$\mathfrak{c}$ estimates and time decay rate. Then we rigorously justify the global-in-time Newtonian limits from the relativistic Boltzmann solutions to the solution of Newtonian Boltzmann equation in $L^1_pL^{\infty}_x$. Moreover, if the initial data of Newtonian Boltzmann equation belong to $W^{1,\infty}(\mathbb{T}^3\times\mathbb{R}^3)$, based on a decomposition and $L^2-L^\infty$ argument, the global-in-time Newtonian limit is proved in $L^{\infty}_{x,p}$. The convergence rates of Newtonian limit are obtained both in $L^1_pL^{\infty}_x$ and $L^{\infty}_{x,p}$.Comment: 56 pages, All comments are welcom

Developmental patterns and characteristics of epicardial cell markers Tbx18 and Wt1 in murine embryonic heart

<p>Abstract</p> <p>Background</p> <p>Although recent studies have highlighted the role of epicardial cells during cardiac development and regeneration, their cardiomyogenic potential is still controversial due to the question of lineage tracing of epicardial cells. The present study therefore aimed to examine the the expression of Tbx18 and Wt1 in embryonic heart and to identify whether Tbx18 and Wt1 themselves expressed in the cardiomyocyte.</p> <p>Methods</p> <p>Mouse embryonic hearts were collected at different stages for immunofluorescence costaining with either Tbx18 and the cardiac transcription factor Nkx2.5 or Wilms tumor 1 (Wt1) and Nkx2.5.</p> <p>Results</p> <p>Tbx18 and Wt1, but not Nkx2.5, were expressed in the proepicardium and epicardium. Tbx18 was expressed in cells within the heart from E10.5 to at least E14.5; these Tbx18-expressing cells were Nkx2.5 positive, except for a few cells that were Nkx2.5 negative at E14.5. Wt1 was expressed in cells within the heart from E12.5 to at least E14.5, but these Wt1-expressing cells were Nkx2.5 negative.</p> <p>Conclusion</p> <p>The data obtained in this study demonstrate that Tbx18 is expressed in the cardiomyocytes from E10.5 to at least E14.5, and Wt1 is expressed within the heart from E12.5 to at least E14.5, but not in the cardiomyocyte. These findings may provide new insights on the role of the epicardial cells in cardiac regeneration.</p

Machine Unlearning Method Based On Projection Residual

Machine learning models (mainly neural networks) are used more and more in real life. Users feed their data to the model for training. But these processes are often one-way. Once trained, the model remembers the data. Even when data is removed from the dataset, the effects of these data persist in the model. With more and more laws and regulations around the world protecting data privacy, it becomes even more important to make models forget this data completely through machine unlearning. This paper adopts the projection residual method based on Newton iteration method. The main purpose is to implement machine unlearning tasks in the context of linear regression models and neural network models. This method mainly uses the iterative weighting method to completely forget the data and its corresponding influence, and its computational cost is linear in the feature dimension of the data. This method can improve the current machine learning method. At the same time, it is independent of the size of the training set. Results were evaluated by feature injection testing (FIT). Experiments show that this method is more thorough in deleting data, which is close to model retraining.Comment: This paper is accepted by DSAA2022. The 9th IEEE International Conference on Data Science and Advanced Analytic

A pair of orthologs of a leucine-rich repeat receptor kinase-like disease resistance gene family regulates rice response to raised temperature

<p>Abstract</p> <p>Background</p> <p>Rice <it>Xa3/Xa26 </it>disease-resistance gene encodes a leucine-rich repeat (LRR) receptor kinase-type protein against <it>Xanthomonas oryzae </it>pv. <it>oryzae </it>(<it>Xoo</it>) and belongs to a multigene family. However, the functions of most genes in this family are unknown.</p> <p>Results</p> <p>Here we report that two orthologs of this family, the <it>NRKe </it>from rice variety Nipponbare and <it>9RKe </it>from variety 93-11 at the <it>RKe </it>locus, have similar functions although they encode different proteins. This pair of orthologs could not mediate resistance to <it>Xoo</it>, but they were transcriptionally induced by raised temperature. Transcriptional activation of <it>NRKe </it>or <it>9RKe </it>resulted in the formation of temperature-sensitive lesion mimics, which were spots of dead cells associated with accumulation of superoxides, in different organs of the transgenic plants. These plants were more sensitive to high temperature shock than wild-type controls. Transgenic plants carrying a chimeric protein consisting of the LRR domain of NRKe and the kinase domain of Xa3/Xa26 developed the same lesion mimics as the <it>NRKe</it>-transgenic plants, whereas transgenic plants carrying another chimeric protein consisting of the LRR domain of Xa3/Xa26 and the kinase domain of NRKe were free of lesion mimic. All the transgenic plants carrying a chimeric protein were susceptible to <it>Xoo</it>.</p> <p>Conclusion</p> <p>These results suggest that the <it>RKe </it>locus is involved in rice response to raised temperature. The LRR domain of RKe protein appears to be important to sense increased temperature. The RKe-involved temperature-related pathway and Xa3/Xa26-mediated disease-resistance pathway may partially overlap.</p

Chaos-assisted two-octave-spanning microcombs

Since its invention, optical frequency comb has revolutionized a broad range of subjects from metrology to spectroscopy. The recent development of microresonator-based frequency combs (microcombs) provides a unique pathway to create frequency comb systems on a chip. Indeed, microcomb-based spectroscopy, ranging, optical synthesizer, telecommunications and astronomical calibrations have been reported recently. Critical to many of the integrated comb systems is the broad coverage of comb spectra. Here, microcombs of more than two-octave span (450 nm to 2,008 nm) is demonstrated through χ^((2)) and χ^((3)) nonlinearities in a deformed silica microcavity. The deformation lifts the circular symmetry and creates chaotic tunneling channels that enable broadband collection of intracavity emission with a single waveguide. Our demonstration introduces a new degree of freedom, cavity deformation, to the microcomb studies, and our microcomb spectral range is useful for applications in optical clock, astronomical calibration and biological imaging

THE LONG -TERM VARIATION OF ORGANIC CHARACTERISTICS IN DONGGANG RIVER USING EXCITATION EMISSION FLUORESCENT MATRIX (EEFM) INTEGRATED WITH PARALLEL FACTOR ANALYSIS (PARAFAC)

In this study, Excitation Emission Fluorescent matrix (EEFM) integrated with Parallel factor analysis (PARAFAC) was applied to investigate the variation of organic property in Donggang River located in Southern Taiwan between Oct. 2010 and Oct. 2015. It reveals that both values of BOD5and COD had a closer proximity at twice samplings; however, the four main components in both samplings showed a different location of excitation and emission wavelengths. On Oct., 2010, EX/EM (percentage of area) of four components were respectively 320/410 nm (46 %), 370/460 nm (27 %), 290/350 nm (14 %) and 280/450 nm (13 %) mainly belonging to humic-like substance. Regrading to the result on Oct, 2015, 320/420 nm (29 %), 228,278/358 nm (29 %), 240/420(29 %) nm and 228/310 nm (14 %) were found attributed in amino organic substance with low excitation wavelength. On Oct.2015, the intensities of four main components in Cinsheda Bridge higher than those in other locations may be attributed with of heavily polluted source like piggery wastewater. For the partition of N-organic and C-organic, there had a significant change on both samplings

Optical loss compensation in a bulk left-handed metamaterial by the gain in quantum dots

A bulk left-handed metamaterial with fishnet structure is investigated to show the optical loss compensation via surface plasmon amplification, with the assistance of a Gaussian gain in PbS quantum dots. The optical resonance enhancement around 200 THz is confirmed by the retrieval method. By exploring the dependence of propagation loss on the gain coefficient and metamaterial thickness, we verify numerically that the left-handed response can endure a large propagation thickness with ultralow and stable loss under a certain gain coefficient.Comment: 6 pages with 4 figure