Adaptive discretization for signal detection in statistical inverse problems

We discuss statistical tests in inverse problems when the original equation is replaced by a discretized one, i.e. a linear system of equations. Previous studies revealed that using the discretization level as regularizing procedure is possible, but its application is limited unless discretization is restricted to the singular value decomposition, see C. Marteau and P. Mathé, General regularization schemes for signal detection in inverse problems, 2013. General linear regularization may circumvent this, and we propose a regularization of the discretized equations. The discretization level may be chosen adaptively, which may save computational budget. This results in tests which are known to yield the optimal separation rate up to some constant in many cases.     

Accelerated Landweber iteration with convex penalty for linear inverse problems in Banach spaces

In recent years, Landweber iteration has been extended to solve linear inverse problems in Banach spaces by incorporating non-smooth convex penalty functionals to capture features of solutions. This method is known to be slowly convergent. However, because it is simple to implement, it still receives a lot of attention. By making use of the subspace optimization technique, we propose an accelerated version of Landweber iteration with non-smooth convex penalty which significantly speeds up the method. Numerical simulations are given to test the efficiency.     

Automatic kinetic model generation and selection based on concentration versus time curves

The goal of the paper is to automatize the construction and parameterization of kinetic reaction mechanisms that can describe a set of experimentally measured concentration versus time curves. Using the framework and theorems of formal reaction kinetics, first, we build a set of possible mechanisms with a given number of measured and unmeasured (real or fictitious) species and reaction steps that fulfill some chemically reasonable requirements. Then we fit all the corresponding mass-action kinetic models and offer the best one to the chemist to help explain the underlying chemical phenomenon or to use it for predictions. We demonstrate the use of the method via two simple examples: on an artificial, simulated set of data and on a small real-life data set. The method can also be used to do a kind of lumping to generate a model that can reproduce the simulation results of a detailed mechanism with less species and thereby can largely accelerate spatially inhomogeneous simulations.     

Estimation of coefficient of variation in a weighted inverse Gaussian model

The coefficient of variation is an important parameter in many physical, biological and medical sciences. In this paper we study the estimation of the square of the coefficient of variation in a weighted inverse Gaussian model which is a mixture of the inverse Gaussian and the length biased inverse Gaussian distribution. This represents a rich family of distributions for different values of the mixing parameter and can be used for modelling various life testing situations. The maximum likelihood as well as the Bayes estimates of the parameters are obtained. These estimates are used to derive the estimates of the square of the coefficient of variation of the model under study. Several important data sets are analysed to illustrate the results. © 1996 John Wiley & Sons, Ltd.     

一个二进小波变换像空间的再生核函数

1 引言 小波分析是结合泛函分析、应用数学、逼近论、调和分析、广义函数论等数学知识的结晶,具有深刻的理论意义和广泛的应用范围,被称为”数学显微镜”.基于其多分辨分析的特点以及在时、频两域都具有表征信号局部特征的功能,应用它可以解决许多Fourier变换不能解决的难题,为工程应用提供了一种新的、更有效的分析工具[1],由...     

逆极限空间上渐近伪轨跟踪性质

The connection between APOTP （asymptotic pseudo orbit tracing property） for a continuous map on a compact metric space and that for the shift map on the inverse limit space is investigated. As an application, it is showed that the shift map on Henderson pseudoarc has APOTP.     

Lamb波频域逆散射全聚焦成像方法研究

Lamb波因其传播距离远、衰减小常被用于板状结构的无损检测中,在基于Lamb波损伤检测的诸多成像技术中,全聚焦方法(Total Focus Method,TFM)方法因其成像分辨率高、信噪比高而受青睐.然而Lamb波的频散效应导致时域延时量不能被准确计算,进而影响传统TFM方法对损伤定位及成像的精度;此外,既有的TFM...     

Approximation Theorems of Moore-Penrose Inverse by Outer Inverses

1 Introduction and preliminaries Let X and Y be two Hilbert spaces and T a bounded linear operator from X into Y . We use D(T ), N(T ) and R(T ), respectively, to denote the domain, null space and range of T . Recall that a linear operator T # : Y → X is…     

锥形透镜光纤聚焦特性研究

锥形透镜光纤(TLF)是实现光纤与平面光波光路(PLC)芯片高效耦合的核心元件。了解和掌握其聚焦特性是指导平面光波光路尾纤封装技术的关键。给出了表征锥形透镜光纤聚焦特性的两个参量出射光斑直径和远场发散角的理论分析模型,其误差小于1.14%;采用光束传播法数值模拟了锥形透镜光纤中的光波传输和模斑的演化,确定了锥形透镜光纤端面出射光斑的大小;优化锥形透镜光纤结构参量为:拉锥长度300μm,锥角0.733°,透镜曲率半径13.485μm;建立了基于数字摄像机的锥形透镜光纤出射光场测试系统,提出了物理光学反向推演法,计算出锥形透镜光纤聚焦光斑尺寸和远场发散角。理论与实验结果有着良好的一致:对于相同结构参量的锥形透镜光纤,实验反推法得到的出射光斑尺寸与理论值相比误差为3.15%,远场发散角误差为3.67%。     

Tumor Hypoxia Heterogeneity Affects Radiotherapy: Inverse-Percolation Shell-Model Monte Carlo Simulations

Tumor hypoxia was discovered a century ago, and the interference of hypoxia with all radiotherapies is well known. Here, we demonstrate the potentially extreme effects of hypoxia heterogeneity on radiotherapy and combination radiochemotherapy. We observe that there is a decrease in hypoxia from tumor periphery to tumor center, due to oxygen diffusion, resulting in a gradient of radiative cell-kill probability, mathematically expressed as a probability gradient of occupied space removal. The radiotherapy-induced break-up of the tumor/TME network is modeled by the physics model of inverse percolation in a shell-like medium, using Monte Carlo simulations. The different shells now have different probabilities of space removal, spanning from higher probability in the periphery to lower probability in the center of the tumor. Mathematical results regarding the variability of the critical percolation concentration show an increase in the critical threshold with the applied increase in the probability of space removal. Such an observation will have an important medical implication: a much larger than expected radiation dose is needed for a tumor breakup enabling successful follow-up chemotherapy. Information on the TME’s hypoxia heterogeneity, as shown here with the numerical percolation model, may enable personalized precision radiation oncology therapy.