On Bounding and Approximating Functions of Multiple Expectations using Quasi-Monte Carlo

Monte Carlo and Quasi-Monte Carlo methods present a convenient approach for approximating the expected value of a random variable. Algorithms exist to adaptively sample the random variable until a user defined absolute error tolerance is satisfied with high probability. This work describes an extension of such methods which supports adaptive sampling to satisfy general error criteria for functions of a common array of expectations. Although several functions involving multiple expectations are being evaluated, only one random sequence is required, albeit sometimes of larger dimension than the underlying randomness. These enhanced Monte Carlo and Quasi-Monte Carlo algorithms are implemented in the QMCPy Python package with support for economic and parallel function evaluation. We exemplify these capabilities on problems from machine learning and global sensitivity analysis

Challenges in Developing Great Quasi-Monte Carlo Software

Quasi-Monte Carlo (QMC) methods have developed over several decades. With the explosion in computational science, there is a need for great software that implements QMC algorithms. We summarize the QMC software that has been developed to date, propose some criteria for developing great QMC software, and suggest some steps toward achieving great software. We illustrate these criteria and steps with the Quasi-Monte Carlo Python library (QMCPy), an open-source community software framework, extensible by design with common programming interfaces to an increasing number of existing or emerging QMC libraries developed by the greater community of QMC researchers

Simultaneous determination of moxifloxacin and cefixime by first and ratio first derivative ultraviolet spectrophotometry

<p>Abstract</p> <p>Background</p> <p>The new combination of moxifloxacin HCl and cefixime trihydrate is approved for the treatment of lower respiratory tract infections in adults. At initial formulation development and screening stage a fast and reliable method for the dissolution and release testing of moxifloxacin and cefixime were highly desirable. The zero order overlaid UV spectra of moxifloxacin and cefixime showed >90% overlapping. Hence, simple, accurate precise and validated two derivative spectrophotometric methods have been developed for the determination of moxifloxacin and cefixime.</p> <p>Methods</p> <p>In the first derivative spectrophotometric method varying concentration of moxifloxacin and cefixime were prepared and scanned in the range of 200 to 400 nm and first derivative spectra were calculated (n = 1). The zero crossing wavelengths 287 nm and 317.9 nm were selected for determination of moxifloxacin and cefixime, respectively. In the second method the first derivative of ratio spectra was calculated and used for the determination of moxifloxacin and cefixime by measuring the peak intensity at 359.3 nm and 269.6 nm respectively.</p> <p>Results</p> <p>Calibration graphs were established in the range of 1–16 μg /mL and 1–15 μg /mL for both the drugs by first and ratio first derivative spectroscopic methods respectively with good correlation coefficients. Average accuracy of assay of moxifloxacin and cefixime were found to be 100.68% and 98 93%, respectively. Relative standard deviations of both inter and intraday assays were less than 1.8%. Moreover, recovery of moxifloxacin and cefixime was more than 98.7% and 99.1%, respectively.</p> <p>Conclusions</p> <p>The described derivative spectrophotometric methods are simple, rapid, accurate, precise and excellent alternative to sophisticated chromatographic techniques. Hence, the proposed methods can be used for the quality control of the cited drugs and can be extended for routine analysis of the drugs in formulations.</p