Unloaded shape identification of human cornea by variational shape optimization

Abstract

The present study proposes a computational method to identify the unloaded corneal shape based on the prescribed surface profile of the cornea acquired from in vivo measurements. Variational shape optimization of the unloaded corneal shape was formulated to satisfy that the corneal shape at the mechanical equilibrium state in the physiological situation corresponded to the prescribed surface profile. The shape variation was calculated using the Lagrange multiplier method with a finite element solution. Numerical solution showed that the optimized corneal shape was in excellent agreement with the prescribed surface profile of the cornea without μm-scale surface irregularities.     

Fast acquisition of NMR spectra using Fourier transform of non-equispaced data

Rapid acquisition of high-resolution 2D and 3D NMR spectra is essential for studying biological macromolecules. In order to minimize the experimental time, a non-linear sampling scheme is proposed for the indirect dimensions of multidimensional experiments. These data can be processed using the algorithm proposed by Dutt and Rokhlin (Appl. Comp. Harm. Anal. 1995, 2, 85–100) for fast Fourier transforms of non equispaced data. Examples of ¹H−¹⁵N HSQC spectra are shown, where crowded correlation peaks can be resolved using non-linear acquisition. Simulated data have been used to analyze the artefacts produced by the Lagrange interpolation. As compared to non-linear processing methods, this algorithm is simple and highly robust since no parameters need to be adjusted by the user.     

A Lagrange-based generalised formulation for the equations of motion of simple walking models

Simple 2D models of walking often approximate the human body to multi-link dynamic systems, where body segments are represented by rigid links connected by frictionless hinge joints. Performing forward dynamics on the equations of motion (EOM) of these systems can be used to simulate their movement. However, deriving these equations can be time consuming. Using Lagrangian mechanics, a generalised formulation for the EOM of n-link open-loop chains is derived. This can be used for single support walking models. This has an advantage over Newton–Euler mechanics in that it is independent of coordinate system and prior knowledge of the ground reaction force (GRF) is not required. Alternative strategies, such as optimisation algorithms, can be used to estimate joint activation and simulate motion. The application of Lagrange multipliers, to enforce motion constraints, is used to adapt this general formulation for application to closed-loop chains. This can be used for double support walking models. Finally, inverse dynamics are used to calculate the GRF for these general n-link chains. The necessary constraint forces to maintain a closed-loop chain, calculated from the Lagrange multipliers, are one solution to the indeterminate problem of GRF distribution in double support models. An example of this method’s application is given, whereby an optimiser estimates the joint moments by tracking kinematic data.     

On the Role of Baseline Measurements for Crossover Designs under the Self and Mixed Carryover Effects Model

Summary .  It is well known that optimal designs are strongly model dependent. In this article, we apply the Lagrange multiplier approach to the optimal design problem, using a recently proposed model for carryover effects. Generally, crossover designs are not recommended when carryover effects are present and when the primary goal is to obtain an unbiased estimate of the treatment effect. In some cases, baseline measurements are believed to improve design efficiency. This article examines the impact of baselines on optimal designs using two different assumptions about carryover effects during baseline periods and employing a nontraditional crossover design model. As anticipated, baseline observations improve design efficiency considerably for two-period designs, which use the data in the first period only to obtain unbiased estimates of treatment effects, while the improvement is rather modest for three- or four-period designs. Further, we find little additional benefits for measuring baselines at each treatment period as compared to measuring baselines only in the first period. Although our study of baselines did not change the results on optimal designs that are reported in the literature, the problem of strong model dependency problem is generally recognized. The advantage of using multiperiod designs is rather evident, as we found that extending two-period designs to three- or four-period designs significantly reduced variability in estimating the direct treatment effect contrast.     

Unconditional global exponential stability in Lagrange sense of genetic regulatory networks with SUM regulatory logic

In this paper, the global exponential stability in Lagrange sense for genetic regulatory networks (GRNs) with SUM regulatory logic is firstly studied. By constructing appropriate Lyapunov-like functions, several criteria are presented for the boundedness, ultimate boundedness and global exponential attractivity of GRNs. It can be obtained that GRNs with SUM regulatory logic are unconditionally globally exponentially stable in Lagrange sense. These results can be applied to analyze monostable as well as multistable networks. Furthermore, to analyze the stability for GRNs more comprehensively, the existence of equilibrium point of GRNs is proved, and some sufficient conditions of the global exponential stability in Lyapunov sense for GRNs are derived. Finally two numerical examples are given to illustrate the application of the obtained results.     

On Mendelian randomization analysis of case-control study

Mendelian randomization (MR) analysis uses genotypes as instruments to estimate the causal effect of an exposure in the presence of unobserved confounders. The existing MR methods focus on the data generated from prospective cohort studies. We develop a procedure for studying binary outcomes under a case-control design. The proposed procedure is built upon two working models commonly used for MR analyses and adopts a quasi-empirical likelihood framework to address the ascertainment bias from case-control sampling. We derive various approaches for estimating the causal effect and hypothesis testing under the empirical likelihood framework. We conduct extensive simulation studies to evaluate the proposed methods. We find that the proposed empirical likelihood estimate is less biased than the existing estimates. Among all the approaches considered, the Lagrange multiplier (LM) test has the highest power, and the confidence intervals derived from the LM test have the most accurate coverage. We illustrate the use of our method in MR analysis of prostate cancer case-control data with vitamin D level as exposure and three single nucleotide polymorphisms as instruments.     

多观测序列HMM2的Baum-Welch算法

介绍了在观测噪声和马尔可夫链不相互独立的条件下二阶隐马尔可夫模型（second-orderHMM：HMM2）的结构．研究了在多观测序列不相互独立的情况下HMM2的学习算法,并由此导出了该模型的参数重估公式．