System calibration method for Fourier ptychographic microscopy

Fourier ptychographic microscopy (FPM) is a recently proposed quantitative phase imaging technique with high resolution and wide field-of-view (FOV). In current FPM imaging platforms, systematic error sources come from the aberrations, LED intensity fluctuation, parameter imperfections and noise, which will severely corrupt the reconstruction results with artifacts. Although these problems have been researched and some special methods have been proposed respectively, there is no method to solve all of them. However, the systematic error is a mixture of various sources in the real situation. It is difficult to distinguish a kind of error source from another due to the similar artifacts. To this end, we report a system calibration procedure, termed SC-FPM, based on the simulated annealing (SA) algorithm, LED intensity correction and adaptive step-size strategy, which involves the evaluation of an error matric at each iteration step, followed by the re-estimation of accurate parameters. The great performance has been achieved both in simulation and experiments. The reported system calibration scheme improves the robustness of FPM and relaxes the experiment conditions, which makes the FPM more pragmatic.Comment: 18 pages, 9 figure

Convergence on Gauss-Seidel iterative methods for linear systems with general H-matrices

It is well known that as a famous type of iterative methods in numerical linear algebra, Gauss-Seidel iterative methods are convergent for linear systems with strictly or irreducibly diagonally dominant matrices, invertible $H-$matrices (generalized strictly diagonally dominant matrices) and Hermitian positive definite matrices. But, the same is not necessarily true for linear systems with nonstrictly diagonally dominant matrices and general $H-$matrices. This paper firstly proposes some necessary and sufficient conditions for convergence on Gauss-Seidel iterative methods to establish several new theoretical results on linear systems with nonstrictly diagonally dominant matrices and general $H-$matrices. Then, the convergence results on preconditioned Gauss-Seidel (PGS) iterative methods for general $H-$matrices are presented. Finally, some numerical examples are given to demonstrate the results obtained in this paper

Precise Request Tracing and Performance Debugging for Multi-tier Services of Black Boxes

As more and more multi-tier services are developed from commercial components or heterogeneous middleware without the source code available, both developers and administrators need a precise request tracing tool to help understand and debug performance problems of large concurrent services of black boxes. Previous work fails to resolve this issue in several ways: they either accept the imprecision of probabilistic correlation methods, or rely on knowledge of protocols to isolate requests in pursuit of tracing accuracy. This paper introduces a tool named PreciseTracer to help debug performance problems of multi-tier services of black boxes. Our contributions are two-fold: first, we propose a precise request tracing algorithm for multi-tier services of black boxes, which only uses application-independent knowledge; secondly, we present a component activity graph abstraction to represent causal paths of requests and facilitate end-to-end performance debugging. The low overhead and tolerance of noise make PreciseTracer a promising tracing tool for using on production systems

The coupled hirota equation with a 3*3 lax pair: painleve-type asymptotics in transition zone

We consider the Painleve asymptotics for a solution of integrable coupled Hirota equationwith a 3*3 Lax pair whose initial data decay rapidly at infinity. Using Riemann-Hilbert techniques and Deift-Zhou nonlinear steepest descent arguments, in a transition zone defined by /x/t-1/(12a)/t^2/3<=C, where C>0 is a constant, it turns out that the leading-order term to the solution can be expressed in terms of the solution of a coupled Painleve II equation associated with a 3*3 matrix Riemann-Hilbert problem

Three-dimensional kinematics of the human metatarsophalangeal joint during level walking

The objective of this study is to investigate the three-dimensional (3D) kinematics of the functional rotation axis of the human metatarsophanlangeal (MP) joint during level walking at different speeds. A twelve camera motion analysis system was used to capture the 3D motion of the foot segments and a six force plate array was employed to record the simultaneous ground reaction forces and moments. The 3D orientation and position of the functional axis (FA) of the MP joint were determined based on the relative motion data between the tarsometatarsi (hindfoot) and phalanges (forefoot) segments. From the results of a series of statistical analyses, it was found that the FA remains anterior to the anatomical axis (AA), defined as a line connecting the 1st and 5th metatarsal heads, with an average distance about 16% of the foot length across all walking speeds, and is also superior to the AA with an average distance about 2% of the foot length during normal and fast walking. Whereas, the FA shows a higher obliquity than the AA with an anteriorly more medial and superior orientation. This suggests that using the AA to represent the MP joint may result in overestimated MP joint moment and power and also underestimated muscle moment arms for MP extensor muscles. It was also found that walking speed has statistically significant effect on the position of the FA though the FA orientation remains unchanged with varying speed. The FA moves forwards and upwards towards a more anterior and more superior position with increased speed. This axis shift may help to increase the effective mechanical advantage (EMA) of MP extensor muscles, maximise the locomotor efficiency and also reduce the risk of injury. Those results may further our understanding of the contribution of the intrinsic foot structure to the propulsive function of the foot during locomotion at different speeds