Estimating Precision in Functional Images

Abstract

Functional imaging of biologic parameters like in vivo tissue metabolism is made possible by Positron Emission Tomography (PET). Many techniques have been suggested for extracting such images from dynamic time-course sequences of reconstructed PET scans. Quantitating the precision of these estimates is important for drawing inferences on the biologic parameters. Analytic variance formulas are not immediate owing to the nonlinear methods used in extraction. The usual resampling approach is infeasible because each image reconstruction in PET is a computationally demanding solution to a high-dimensional linear inverse problem. We suggest an alternative simulation approach that approximates the distribution of reconstructed PET scans and performs a parametric bootstrap in the imaging domain. Results on a simplified model chosen to match the characteristics of PET reconstruction are very encouraging. Mixture analysis is used to estimate functional images; however, the suggested approach is general enough to extend to other techniques or imaging methods.     

Full rate constant matrix contraction method for obtaining branching ratio of unimolecular decomposition

The branching ratio of unimolecular decomposition can be evaluated by solving the rate equations. Recent advances in automated reaction path search methods have enabled efficient construction of the rate equations based on quantum chemical calculations. However, it is still difficult to solve the rate equations composed of hundreds or more elementary steps. This problem is especially serious when elementary steps that occur in highly different timescales coexist. In this article, we introduce an efficient approach to obtain the branching ratio from a given set of rate equations. It has been derived from a recently proposed rate constant matrix contraction (RCMC) method, and termed full‐RCMC (f‐RCMC). The f‐RCMC gives the branching ratio without solving the rate equations. Its performance was tested numerically for unimolecular decomposition of C₃H₅ and C₄H₅. Branching ratios obtained by the f‐RCMC precisely reproduced the values obtained by numerically solving the rate equations. It took about 95 h to solve the rate equations of C₄H₅ consisting of 234 elementary steps. In contrast, the f‐RCMC gave the branching ratio in less than 1 s. The f‐RCMC would thus be an efficient alternative of the conventional kinetic simulation approach. © 2016 Wiley Periodicals, Inc.     

The convergence on spectrum of sample covariance matrices for information-plus-noise type data

In this paper,we consider the limiting spectral distribution of the information-plusnoise type sample covariance matrices Cn =1/N (Rn + σXn) (Rn + σXn)*,under the assumption that the entries of Xn are ...     

A LabVIEW-based real-time measurement system for polarization detection and calibration

A rapid real-time polarization measurement system was designed and implemented in this paper. The system is centered round a computer running application developed for the purpose. The paper illustrates how to build such an excellent application with National Instruments’ graphical programming language LabVIEW, a synchronized high speed multi-channels data acquisition card and some photoelectric conversion module in detail. With simple and friendly user interface, the experimental result shows that the measurement system has high computational efficiency, high precision calibration matrix, which can be efficiently utilized in experiments relating to the measurement of polarization.     

Impact of APCI ionization source in liquid chromatography tandem mass spectrometry based tissue distribution studies

Measurement of test article concentration in tissue samples has been an important part of pharmacokinetic study and has helped to co‐relate pharmacokinetic/pharmacodynamic relationships since the 1950s. Bioanalysis of tissue samples using LC–MS/MS comes with unique challenges in terms of sample handling and inconsistent analyte response owing to nonvolatile matrix components. Matrix effect is a phenomenon where the target analyte response is either suppressed or enhanced in the presence of matrix components. Based on previous reports electrospray ionization (ESI) mode of ionization is believed to be more affected by matrix components than atmospheric pressure chemical ionization (APCI) or atmospheric pressure photoionization. To explore the impact of ionization source with respect to bioanalysis of tissue samples, five structurally diverse compounds – atenolol, verapamil, diclofenac, propranolol and flufenamic acid – were selected. Quality control standards were spiked into 10 different biological matrices like whole blood, liver, heart, brain, spleen, kidney, skeletal muscle, eye and skin tissue and were quantified against calibration standards prepared in rat plasma. Quantitative bioanalysis was performed utilizing both APCI and ESI mode and results were compared. Quality control standards when analyzed with APCI mode were found to be more consistent in terms of accuracy and precision as compared with ESI mode. Additionally, for some instances, up to 20‐fold broader dynamic linearity range was observed with APCI mode as compared with ESI mode. As phospholid interferences have poor response in APCI mode, protein precipitation extraction technique can be used for multimatrix quantitation, which is more amenable to automation. The approach of multiple biological matrix quantitation against a single calibration curve helps bioanalysts to reduce turnaround time. Copyright © 2016 John Wiley & Sons, Ltd.     

Calibration of the complex matrix effects on the sampling of polycyclic aromatic hydrocarbons in milk samples using solid phase microextraction

Solid phase microextraction (SPME), a simple, fast and promising sampling technique, has been widely used for complex sample analysis. However, complex matrices could modify the absorption property of coatings as well as the uptake kinetics of analytes, eventually biasing the quantification results. In the current study, we demonstrated the feasibility of a developed calibration method for the analysis of polycyclic aromatic hydrocarbons (PAHs) in complex milk samples. Effects of the complex matrices on the SPME sampling process and the sampling conditions were investigated. Results showed that short exposure time (pre-equilibrium SPME, PE-SPME) could increase the lifetime of coatings, and the complex matrices in milk samples could significantly influence the sampling kinetics of SPME. In addition, the optimized sampling time, temperature and dilution factor for PAHs were 10 min, 85 °C and 20, respectively. The obtained LODs and LOQs of all the PAHs were 0.1–0.8 ng/mL and 1.4–4.7 ng/mL, respectively. Furthermore, the accuracy of the proposed PE-SPME method for milk sampling was validated by the recoveries of the studied compounds in two concentration levels, which ranged from 75% to 110% for all the compounds. Finally, the proposed method was applied to the screening of PAHs in milk samples.     

关于全国大学生数学竞赛决赛试题的解析与思考

本文对二道全国大学生数学竞赛决赛试题(数学类)给予了诠释与解析.     

基于现场可编程门阵列单探测器复合轴控制技术

为了解决空间激光通信系统中单探测器复合轴结构的粗精解耦难题,通过分析二维关联控制矩阵,得出粗精跟踪解耦的必要条件,提出了一种单探测器复合轴结构的工作方式.在跟踪过程中,相机直接配合子轴执行器完成精跟踪工作,而主轴的跟踪信息由子轴的角度偏转器来提供,同时所有的图像处理算法、位置检测算法、以及粗精伺服控制算法都在现场可编程门阵列中实现,完成了系统的轻小型化设计.实验搭建了测试系统,并对现场可编程门阵列硬件和系统跟踪性能进行测试,结果表明单探测器复合控制系统可以实现跟踪准确度优于3μrad,为工程化奠定了良好的基础.     

Calibration Curve with Improved Limit of Detection for Cadmium in Soil: An Approach to Minimize the Matrix Effect in Laser-Induced Breakdown Spectroscopic Analysis

The present article describes a working or combined calibration curve in laser-induced breakdown spectroscopic analysis, which is the cumulative result of the calibration curves obtained from neutral and singly ionized atomic emission spectral lines. This working calibration curve reduces the effect of change in matrix between different zone soils and certified soil samples because it includes both the species' (neutral and singly ionized) concentration of the element of interest. The limit of detection using a working calibration curve is found better as compared to its constituent calibration curves (i.e., individual calibration curves). The quantitative results obtained using the working calibration curve is in better agreement with the result of inductively coupled plasma–atomic emission spectroscopy as compared to the result obtained using its constituent calibration curves.     

Orthonormal bases generated by Cuntz algebras

We show how some orthonormal bases can be generated by representations of the Cuntz algebra; these include Fourier bases on fractal measures, generalized Walsh bases on the unit interval and piecewise exponential bases on the middle third Cantor set.