Transition probabilities of Lévy‐type processes: Parametrix construction

We present an existence result for Lévy‐type processes which requires only weak regularity assumptions on the symbol with respect to the space variable x. Applications range from existence and uniqueness results for Lévy‐driven SDEs with Hölder continuous coefficients to existence results for stable‐like processes and Lévy‐type processes with symbols of variable order. Moreover, we obtain heat kernel estimates for a class of Lévy and Lévy‐type processes. The paper includes an extensive list of Lévy(‐type) processes satisfying the assumptions of our results.     

Continuum versus discrete networks,graph Laplacians,and reproducing kernel Hilbert spaces

Motivated by applications to machine learning, we construct a reversible and irreducible Markov chain whose state space is a certain collection of measurable sets of a chosen l.c.h. space $\mathfrak{X}$. We study the resulting network (connected undirected graph), including transience, Royden and Riesz decompositions, and kernel factorization. We describe a construction for Hilbert spaces of signed measures which comes equipped with a new notion of reproducing kernels and there is a unique solution to a regularized optimization problem involving the approximation of $L^2$ functions by functions of finite energy. The latter has applications to machine learning (for Markov random fields, for example).     

桃仁与红花配伍对药材成分溶出的影响

对桃仁与红花配伍对药材成分溶出的影响进行研究.采用单因素试验和正交试验,以羟基红花黄色素A提取转移率与干膏率的综合评分为指标,优选红花最佳提取工艺,以苦杏仁苷提取转移率与干膏率的综合评分为指标,优选桃仁最佳提取工艺.在最佳提取工艺下,将桃仁与红花配伍,采用高效液相色谱法测定红花中羟基红花黄色素A提取转移率,并进行统计分析.实验结果显示,红花最佳提取工艺为提取2次,每次提取1.5 h,液料比为50∶1,桃仁最佳提取工艺为提取3次,每次提取3.5 h,液料比为8∶1.实验结果表明,桃仁对红花中羟基红花黄色素A提取转移率无显著性影响.     

Uniform limit laws of the logarithm for nonparametric estimators of the regression function in presence of censored data

In this paper, we establish uniform-in-bandwidth limit laws of the logarithm for nonparametric Inverse Probability of Censoring Weighted (I.P.C.W.) estimators of the multivariate regression function under random censorship. A similar result is deduced for estimators of the conditional distribution function. The uniform-in-bandwidth consistency for estimators of the conditional density and the conditional hazard rate functions are also derived from our main result. Moreover, the logarithm laws we establish are shown to yield almost sure simultaneous asymptotic confidence bands for the functions we consider. Examples of confidence bands obtained from simulated data are displayed.      

Infinitely many singular interactions on noncompact manifolds

We show that the ground state energy is bounded from below when there are infinitely many attractive delta function potentials placed in arbitrary locations, while all being separated at least by a minimum distance, on two dimensional non-compact manifold. To facilitate the reading of the paper, we first present the arguments in the setting of Cartan–Hadamard manifolds and then subsequently discuss the general case. For this purpose, we employ the heat kernel techniques as well as some comparison theorems of Riemannian geometry, thus generalizing the arguments in the flat case following the approach presented in Albeverio et al. (2004).     

Explicit–implicit mapping approach to nonlinear blind separation of sparse nonnegative dependent sources from a single mixture: pure component extraction from nonlinear mixture mass spectra

The nonlinear, nonnegative single‐mixture blind source separation problem consists of decomposing observed nonlinearly mixed multicomponent signal into nonnegative dependent component (source) signals. The problem is difficult and is a special case of the underdetermined blind source separation problem. However, it is practically relevant for the contemporary metabolic profiling of biological samples when only one sample is available for acquiring mass spectra; afterwards, the pure components are extracted. Herein, we present a method for the blind separation of nonnegative dependent sources from a single, nonlinear mixture. First, an explicit feature map is used to map a single mixture into a pseudo multi‐mixture. Second, an empirical kernel map is used for implicit mapping of a pseudo multi‐mixture into a high‐dimensional reproducible kernel Hilbert space. Under sparse probabilistic conditions that were previously imposed on sources, the single‐mixture nonlinear problem is converted into an equivalent linear, multiple‐mixture problem that consists of the original sources and their higher‐order monomials. These monomials are suppressed by robust principal component analysis and hard, soft, and trimmed thresholding. Sparseness‐constrained nonnegative matrix factorizations in reproducible kernel Hilbert space yield sets of separated components. Afterwards, separated components are annotated with the pure components from the library using the maximal correlation criterion. The proposed method is depicted with a numerical example that is related to the extraction of eight dependent components from one nonlinear mixture. The method is further demonstrated on three nonlinear chemical reactions of peptide synthesis in which 25, 19, and 28 dependent analytes are extracted from one nonlinear mixture mass spectra. The goal application of the proposed method is, in combination with other separation techniques, mass spectrometry‐based non‐targeted metabolic profiling, such as biomarker identification studies. Copyright © 2015 John Wiley & Sons, Ltd.     

Numerical discretization-based kernel type estimation methods for ordinary differential equation models

We consider the problem of parameter estimation in both linear and nonlinear ordinary differential equation(ODE) models. Nonlinear ODE models are widely used in applications. But their analytic solutions are usually not available. Thus regular methods usually depend on repetitive use of numerical solutions which bring huge computational cost. We proposed a new two-stage approach which includes a smoothing method(kernel smoothing or local polynomial fitting) in the first stage, and a numerical discretization method(Eulers discretization method, the trapezoidal discretization method,or the Runge–Kutta discretization method) in the second stage. Through numerical simulations, we find the proposed method gains a proper balance between estimation accuracy and computational cost.Asymptotic properties are also presented, which show the consistency and asymptotic normality of estimators under some mild conditions. The proposed method is compared to existing methods in term of accuracy and computational cost. The simulation results show that the estimators with local linear smoothing in the first stage and trapezoidal discretization in the second stage have the lowest average relative errors. We apply the proposed method to HIV dynamics data to illustrate the practicability of the estimator.     

Identification,Characterization and Antihypertensive Effect In Vivo of a Novel ACE-Inhibitory Heptapeptide from Defatted Areca Nut Kernel Globulin Hydrolysates

The areca (Areca catechu L.) nut kernel (ANK) is a good potential protein source for its high protein content of 9.89–14.62 g/100 g and a high yield of around 300,000 tons per year in China. However, utilization of the areca nut kernel is limited. To expand the usage of ANK in pharmaceutical or foods industries, areca nut kernel globulin was extracted and angiotensin-I converting enzyme (ACE) inhibition peptides were prepared and identified using gel chromatography, reversed phase HPLC separation, UPLC-ESI-MS/MS analysis and in silico screening. Finally, a novel ACE-inhibitory heptapeptide (Ala–Pro–Lys–Ile–Glu–Glu–Val) was identified and chemically synthesized. The combination pattern between APKIEEV and ACE, and the inhibition kinetics, antihypertensive effect and endothlein-1 inhibition activity of APKIEEV were studied. The results of the molecular docking demonstrated that APKIEEV could bind to four active sites (not the key active sites) of ACE via short hydrogen bonds and demonstrated high ACE-inhibitory activity (IC₅₀: 550.41 μmol/L). Moreover, APKIEEV exhibited a significantly lowering effect on both the systolic blood pressure and diastolic blood pressure of spontaneously hypertensive rats, and had considerable suppression ability on intracellular endothelin-1. These results highlight the potential usage of APKIEEV as ingredients of antihypertensive drugs or functional foods.     

A macroscopic model for an intermediate state between type‐I and type‐II superconductivity

A vectorial nonlocal and nonlinear parabolic problem on a bounded domain for an intermediate state between type‐I and type‐II superconductivity is proposed. The domain is for instance a multiband superconductor that combines the characteristics of both types. The nonlocal term is represented by a (space) convolution with a singular kernel arising in Eringen's model. The nonlinearity is coming from the power law relation by Rhyner. The well‐posedness of the problem is discussed under low regularity assumptions and the error estimate for a semi‐implicit time‐discrete scheme based on backward Euler approximation is established. In the proofs, the monotonicity methods and the Minty–Browder argument are used. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1551–1567, 2015     

Numerical solution of one‐dimensional Burgers' equation

In this article, an iterative method for the approximate solution of a class of Burgers' equation is obtained in reproducing kernel space . It is proved the approximation converges uniformly to the exact solution u(x, t) for any initial function under trivial conditions, the derivatives of are also convergent to the derivatives of u(x, t), and the approximate solution is the best approximation under the system © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1251–1264, 2015