THE REGULARITY AND UNIQUENESS OF A GLOBAL SOLUTION TO THE ISENTROPIC NAVIER-STOKES EQUATION WITH ROUGH INITIAL DATA

A global weak solution to the isentropic Navier-Stokes equation with initial data around a constant state in the L^(1)∩BV class was constructed in[1].In the current paper,we will continue to study the uniqueness and regularity of the constructed solution.The key ingredients are the Holder continuity estimates of the heat kernel in both spatial and time variables.With these finer estimates,we obtain higher order regularity of the constructed solution to Navier-Stokes equation,so that all of the derivatives in the equation of conservative form are in the strong sense.Moreover,this regularity also allows us to identify a function space such that the stability of the solutions can be established there,which eventually implies the uniqueness.

含过渡层TiAlN和CrAlN硬质膜的制备及其抗氧化性能研究

采用磁控溅射技术制备TiAlN、CrAlN及含Ti、Cr过渡层的TiAlN、CrAlN四种薄膜,并对其进行850℃大气热处理实验,通过激光共聚焦显微镜、纳米压痕仪对热处理后的试样进行测试。表征结果显示:热处理后的TiAlN薄膜及含有Ti过渡层的TiAlN薄膜硬度及弹性模量都大幅降低,前者比后者的表面粗糙度小、抗氧化性能更优;热处理后CrAlN薄膜的硬度和弹性模量大幅下降,而含Cr过渡层的CrAlN薄膜热处理后的硬度、模量相对较高,表面粗糙度也相对较小。

Reachability analysis of switched linear discrete singular systems

This paper studies the reachability problem of the switched linear discrete singular （SLDS） systems. Under the condition that all subsystems are regular, the reachability of the SLDS systems is characterized based on a peculiar repeatedly introduced switching sequence. The necessary and sufficient conditions are obtained for the reachability of the SLDS systems.

A Linear Frequency Principle Model to Understand the Absence of Overfitting in Neural Networks

Why heavily parameterized neural networks(NNs) do not overfit the data is an important long standing open question. We propose a phenomenological model of the NN training to explain this non-overfitting puzzle. Our linear frequency principle(LFP) model accounts for a key dynamical feature of NNs: they learn low frequencies first, irrespective of microscopic details. Theory based on our LFP model shows that low frequency dominance of target functions is the key condition for the non-overfitting of NNs and is verified by experiments. Furthermore,through an ideal two-layer NN, we unravel how detailed microscopic NN training dynamics statistically gives rise to an LFP model with quantitative prediction power.

多响应的分组Hotelling’s T^2检验（英文）

两样本的多响应比较在实际中应用非常广泛.当样本不服从正态分布时,Hotelling’s T^2检验(HT)的功效普遍不高.为了解决这一问题,本文提出了分组Hotelling’s T^2检验(GHT),即对数据进行逆正态变换后,在每一组中进行HT,然后基于每组的p值构造统计量并取最大值.大量模拟表明,GHT比HT和其他已有检验更加稳健.最后,应用于血浆肾素活性和大脑衰老数据进一步验证GHT的有效性.

WEAK SOLUTION TO THE INCOMPRESSIBLE VISCOUS FLUID AND A THERMOELASTIC PLATE INTERACTION PROBLEM IN 3D

In this paper we deal with a nonlinear interaction problem between an incompressible viscous fluid and a nonlinear thermoelastic plate.The nonlinearity in the plate equation corresponds to nonlinear elastic force in various physically relevant semilinear and quasilinear plate models.We prove the existence of a weak solution for this problem by constructing a hybrid approximation scheme that,via operator splitting,decouples the system into two sub-problems,one piece-wise stationary for the fluid and one time-continuous and in a finite basis for the structure.To prove the convergence of the approximate quasilinear elastic force,we develop a compensated compactness method that relies on the maximal monotonicity property of this nonlinear function.

基于转移概率分布的组合信用转移风险参数估计与压力测试

近年来,压力测试因其衡量金融危机等极端环境下风险的特性在现代银行风险管理中发挥着越来越重要的作用.准确衡量组合风险受系统性因素的驱动作用,是有效控制金融风险,防范金融危机的关键.本文研究了组合信用风险参数估计与压力测试问题,建立了包含系统性因子和多级相关性系数的Vasicek信用转移模型,分析了相关性系数对各评级间信用转移概率的影响,给出了使得评级单调一致的相关性系数条件,保证了信用评级转移概率的单调一致性;构造了基于降级概率分布的参数估计方法,利用转移概率矩阵推导出市场均衡状态下的评级寿命分布,进而给出了相关性系数和系统性因子的估计算法.与已有算法相比,本文提出的方法减弱了系统性因子固定偏差的影响,克服了算法对系统性因子分布的依赖,在降低计算代价的同时提高了估计的精确度.仿真实验结果表明,本文提出的方法有效提高了计算速度,对系统性因子、相关系数及组合损失的估计效果都显著优于已有方法;利用该方法估计的极端损失可以更充分地覆盖样本外组合损失,使得在压力测试中能够更好地预判和防范金融风险,维护金融市场稳定.

Dielectric polymer grafted electrodes enhanced aqueous supercapacitors

Supercapacitors(SCs)have become increasingly important in electrical energy storage and delivery owing to their high power densities and long lifetimes.Aqueous SCs are promising for large-scale engineering applications because of their low cost and safety.However,the low operating voltage and low energy density of aqueous SCs severely limit their practical applications.In this study,a nanoscale dielectric layer is grafted onto a graphene electrode to achieve both a high operating voltage and enhanced capacitance.Compared with an SC without dielectric grafting,a dielectric-enhanced SC(DESC)shows a higher capacitance by 2200%.The mechanism of the capacitance enhancement can be attributed to three factors:the dielectric polarization,the ions desolvation by the dielectric,and the enhanced quantum capacitance from charge transfer and ion adsorption in the polymer molecules.In addition,a 2.5 V pouch DESC with a 1 M KCl electrolyte is confirmed to cycle up to 50,000 times with a capacitance retention of 87.5%.The DESC presents the optimal electrochemical properties after it is grafted with a 5 nm dielectric layer.This study provides new insights into the design of high-voltage and high-energy-density aqueous SCs.

On Hierarchical Compensation Based Active Disturbance Rejection Control for ACMM Problem of Spacecraft

The attitude control and momentum management(ACMM)problem is quite fundamental for many spacecrafts including space stations,sky laboratories and etc.Instead of single attitude control problem,ACMM problem has to take account of both disturbance rejection and energy optimization.This paper studies the ACMM problem for general spacecraft.A practical active disturbance rejection control architecture is proposed with hierarchical compensation to different kinds of uncertain dynamics or disturbances.In particular,by integrating RLS into ESO,the constant and sinusoidal disturbance terms to be compensated are reconstructed.Also,the LQR law is implemented to achieve the desired performance of control systems after disturbance compensation.Furthermore,quantitative performances of the generalized ESO,the RLS algorithm and the closed-loop tracking system are rigorously analyzed.Finally,the results under 9-DOF semi-physical test environment show the effectiveness of our control method.

Distance-Based Regression Analysis for Measuring Associations

Distance-based regression model,as a nonparametric multivariate method,has been widely used to detect the association between variations in a distance or dissimilarity matrix for outcomes and predictor variables of interest in genetic association studies,genomic analyses,and many other research areas.Based on it,a pseudo-F statistic which partitions the variation in distance matrices is often constructed to achieve the aim.To the best of our knowledge,the statistical properties of the pseudo-F statistic has not yet been well established in the literature.To fill this gap,the authors study the asymptotic null distribution of the pseudo-F statistic and show that it is asymptotically equivalent to a mixture of chi-squared random variables.Given that the pseudo-F test statistic has unsatisfactory power when the correlations of the response variables are large,the authors propose a square-root F-type test statistic which replaces the similarity matrix with its square root.The asymptotic null distribution of the new test statistic and power of both tests are also investigated.Simulation studies are conducted to validate the asymptotic distributions of the tests and demonstrate that the proposed test has more robust power than the pseudo-F test.Both test statistics are exemplified with a gene expression dataset for a prostate cancer pathway.

Association Testing for High-Dimensional Multiple Response Regression

Multiple response regression model is commonly employed to investigate the relationship between multiple outcomes and a set of potential predictors,where single-response analysis and multivariate analysis of variance(MANOVA)are two frequently used methods for association analysis.However,both methods have their own limitations.The basis of the former method is independence of multiple responses and the latter one assumes that multiple responses are normally distributed.In this work,the authors propose a test statistic for multiple response association analysis in high-dimensional situations based on F statistic.It is free of normal distribution assumption and the asymptotic normal distribution is obtained under some regular conditions.Extensive computer simulations and four real data applications show its superiority over single-response analysis and MANOVA methods.

Nested Group Testing Procedure

We investigated the false-negative,true-negative,false-positive,and true-positive predictive values from a general group testing procedure for a heterogeneous population.We show that its false(true)-negative predictive value of a specimen is larger(smaller),and the false(true)-positive predictive value is smaller(larger)than that from individual testing procedure,where the former is in aversion.Then we propose a nested group testing procedure,and show that it can keep the sterling characteristics and also improve the false-negative predictive values for a specimen,not larger than that from individual testing.These characteristics are studied from both theoretical and numerical points of view.The nested group testing procedure is better than individual testing on both false-positive and false-negative predictive values,while retains the efficiency as a basic characteristic of a group testing procedure.Applications to Dorfman’s,Halving and Sterrett procedures are discussed.Results from extensive simulation studies and an application to malaria infection in microscopy-negative Malawian women exemplify the findings.

基于局部波动率模型的上证50ETF期权定价研究

局部波动率模型被广泛运用于风险管理、期权定价等领域,该模型不仅可以描述波动率微笑、期限结构等实际现象,同时能保证市场的完备性.研究局部波动率模型的核心目标是对隐含波动率进行建模.本文分别通过参数法和非参数法对隐含波动率建模,不仅保证了波动率曲面的无套利性,同时给出了非参数法求解局部波动率的显式表达式,从而消除了近似误差,得到较为光滑的波动率曲面.此外,本文基于局部波动率模型对我国上证50ETF指数期权的定价进行了实证研究,分别从样本内定价误差、样本外定价误差、套期保值效果三个方面分析比较了该模型的定价效果.实证结果显示:对样本内数据,非参数法拟合的定价结果优于参数方法;对样本外数据以及套期保值效果来说,参数法取得的效果较好.特别地,隐含波动率建模方法无论是对期权定价还是套期保值,效果均优于直接根据市场数据建模的结果,样本内定价误差可减少一半以上,均方误差可降低1~2个数量级.

Retinoic acid inducible gene-I,more than a virus sensor

Retinoic acid inducible gene-I(RIG-I)is a caspase recruitment domain(CARD)containing protein that acts as an intracellular RNA receptor and senses virus infection.After binding to double stranded RNA(dsRNA)or 5′-triphosphate single stranded RNA(ssRNA),RIG-I transforms into an open conformation,translocates onto mitochondria,and interacts with the downstream adaptor mitochondrial antiviral signaling(MAVS)to induce the production of type Ⅰ interferon and inflammatory factors via IRF3/7 and NF-κB pathways,respectively.Recently,accumulating evidence suggests that RIG-I could function in non-viral systems and participate in a series of biological events,such as inflammation and inflammation related diseases,cell proliferation,apoptosis and even senescence.Here we review recent advances in antiviral study of RIG-I as well as the functions of RIG-I in other fields.

Identifying topologies and system parameters of uncertaintime-varying delayed complex networks

Node dynamics and network topologies play vital roles in determining the network features and network dynamical behaviors.Thus it is of great theoretical significance and practical value to recover the topology structures and system parameters of uncertain complex networks with available information. This paper presents an adaptive anticipatory synchronization-based approach to identify the unknown system parameters and network topological structures of uncertain time-varying delayed complex networks in the presence of noise. Moreover, during the identification process, our proposed scheme guarantees anticipatory synchronization between the uncertain drive and constructed auxiliary response network simultaneously. Particularly, our method can be extended to several special cases. Furthermore, numerical simulations are provided to verify the effectiveness and applicability of our method for reconstructing network topologies and node parameters. We hope our method can provide basic insight into future research on addressing reconstruction issues of uncertain realistic and large-scale complex networks.

Uncoupled PID Control of Coupled Multi-Agent Nonlinear Uncertain Systems

In this paper, PID（proportional-integral-derivative） controllers will be designed to solve the tracking problem for a class of coupled multi-agent systems, where each agent is described by a second-order high-dimensional nonlinear uncertain dynamical system, which only has access to its own tracking error information and does not need to communicate with others. This paper will show that a 3-dimensional manifold can be constructed based on the information about the Lipschitz constants of the system nonlinear dynamics, such that whenever the three parameters of each PID controller are chosen from the manifold, the whole multi-agent system can be stabilized globally and the tracking error of each agent approaches to zero asymptotically. For a class of coupled first-order multi-agent nonlinear uncertain systems, a PI controller will be designed to stabilize the whole system.

A theoretic study of a distance-based regression model

The distance-based regression model has many applications in analysis of multivariate response regression in various ?elds, such as ecology, genomics, genetics, human microbiomics, and neuroimaging. It yields a pseudo F test statistic that assesses the relation between the distance(dissimilarity) of the subjects and the predictors of interest. Despite its popularity in recent decades, the statistical properties of the pseudo F test statistic have not been revealed to our knowledge. This study derives the asymptotic properties of the pseudo F test statistic using spectral decomposition under the matrix normal assumption, when the utilized dissimilarity measure is the Euclidean or Mahalanobis distance. The pseudo F test statistic with the Euclidean distance has the same distribution as the quotient of two Chi-squared-type mixtures. The denominator and numerator of the quotient are approximated using a random variable of the form ξχ_d^2+ η, and the approximate error bound is given. The pseudo F test statistic with the Mahalanobis distance follows an F distribution.In simulation studies, the approximated distribution well matched the "exact" distribution obtained by the permutation procedure. The obtained distribution was further validated on H1N1 in?uenza data, aging human brain data, and embryonic imprint data.

计算神经科学

计算神经科学是近三十年来出现的一个新兴交叉学科,它强调采用数学定量的方法,如数学建模、理论分析和数值模拟等来研究和解决神经科学中的重要科学问题,一方面神经科学实验现象为发展新的数学模型、理论和算法提供了基础,另一方面通过数学定量,能反过来揭示神经科学实验现象背后的数理机制,发现新的科学规律.随着欧盟、美国、日本和我国脑计划的陆续推出,对大脑的探索已成为重要的前沿科学领域,同时随着数据科学、机器学习等领域的兴起,研究如何借鉴大脑的工作原理来实现类脑计算以及人工智能也成为了世界大国科技竞争的战略制高点.鉴于此,计算神经科学作为连接大脑神经科学与类脑人工智能两大研究领域的桥梁,在前沿科学领域和国家战略需求中的地位变得越来越重要.计算神经科学研究领域的发展,对于推动神经科学与数学、物理、统计、计算机、人工智能等其他自然科学学科及工程应用学科之间的共进发展,以及综合利用不同学科的优势互补来取得从零到一的重要科学突破有着重大意义.

三维颗粒物质的能量最小化模拟方法

颗粒物质是大量宏观颗粒的集合,广泛存在于自然界,日常生活和工业生产中.颗粒物质的运动表现出非常复杂的现象,如堵塞(jamming)等.颗粒物质体系的定量研究仍是一个巨大的挑战.本文采用能量最小化方法对颗粒物质进行准静态模拟.对一些典型的非线性优化方法,如共轭梯度法,拟牛顿法等,通过预条件来提高这些方法的效率.这些预条件方法基于颗粒体系的几何结构和能量函数来构建.通过对一些典型的准静态过程,如压缩和剪切试验的数值模拟,观察到对三维颗粒体系,预条件方法可以有40%左右的效率提升.