Ant colony method to control variance reduction techniques in the Monte Carlo simulation of clinical electron linear accelerators of use in cancer therapy

The Monte Carlo simulation of clinical electron linear accelerators requires large computation times to achieve the level of uncertainty required for radiotherapy. In this context, variance reduction techniques play a fundamental role in the reduction of this computational time. Here we describe the use of the ant colony method to control the application of two variance reduction techniques: Splitting and Russian roulette. The approach can be applied to any accelerator in a straightforward way and permits the increasing of the efficiency of the simulation by a factor larger than 50.     

Components of Variance Analysis: A Useful Statistical Technique For Analytical Chemistry

Abstract

A statistical technique, components of variance analysis, was used to quantify three potential sources of variation in the determination of fluoride by ion chromatography (IC). The variance components due to sampling (2.09%) and oxygen bombings (1.47%) were found to be significant while the variance component due to IC repeats was only 0.272%. From these variance components the expected precision of various sampling and testing protocols was estimated. Graphical procedures were also used to visually analyze the experimental data.     

Note on the Error Analysis of the Generalized Rankannihilation Method

ABSTRACT

The generalized rank annihilation method (GRAM) is a method for curveresolution and quantitation that uses two data matrices simultaneously, i.e., onefor the unknown and one for the calibration sample. Requirements have beenderived that ensure the unique resolution of the analyte of interest in thepresence of unknown interferences if the data matrices are free fromexperimental error. In this paper, it is shown that the same requirements allowfor correct determination of bias and variance in the quantitative results obtainedby GRAM if the data matrices are not free from experimental error.     

Achieving the full performance of highly efficient columns by optimizing conventional benchmark high-performance liquid chromatography instruments

A series of experiments and measurements demonstrate the importance of minimizing the extra-column band broadening contribution of the instrument used. The combination of several measures allowed the achievement of the full potential efficiency of three Kinetex-C₁₈ columns, using a conventional liquid chromatograph. The first measure consists in minimizing the extra-column volume of the instrument, without increasing much its back pressure contribution, by changing the needle seat volume, the inner diameter and length of the capillary connectors, and the volume of the detector cell of a standard instrument (Agilent 1100). The second measure consists in injecting a volume of weak eluent (less than half the elution strength of the mobile phase) right after the sample, before the sample had time to reach the column. Experimental results show that these changes could provide most of the resolution expected from the true column performance. After the changes were made, the resolutions of the 2.1 mm ×$\times$ 50 mm, 4.6 mm ×$\times$ 50 mm, and 4.6 mm ×$\times$ 100 mm Kinetex-C₁₈ columns for compounds having retention factors close to 1 were increased by about 180, 35, and 30%, respectively. The resolutions obtained are then similar to those measured with advanced instruments like the Agilent 1200, the Agilent 1290 Infinity HPLC, and the Acquity chromatographs.     

Effects of the A-site cation number on the properties of Ln5/8M3/8MnO3 manganites

The properties of manganites can be tuned by changing the doping level x in Ln_1−xM_xMnO₃. A second mechanism allows tuning of magnetic and electronic properties, for fixed x values, by varying the average A-cation radius, 〈r_A〉. Moreover, for fixed x and 〈r_A〉 values, the changes in the A-cation size variance, σ², also modify the ferromagnetic and metal-insulator transition temperatures. Here, we investigate the influence of the number of A-site cations on Ln_5/8M_3/8MnO₃ manganites, where x, 〈r_A〉 and σ² values are kept constant, and in the absence of phase separation phenomena. We have found that the number of cation species at the A site (N_A) has a strong influence on the width of the ferromagnetic and metal-insulator transitions, and a small influence on the average transition temperature. This behavior is opposite to that observed for increasing values of the variance σ² in manganites, with the same x and 〈r_A〉 values, where average transition temperatures are strongly reduced.     

Fast orthogonal transforms and generation of Brownian paths

We present a number of fast constructions of discrete Brownian paths that can be used as alternatives to principal component analysis and Brownian bridge for stratified Monte Carlo and quasi-Monte Carlo. By fast we mean that a path of length n$n$ can be generated in O(nlog(n))$O(nlog\left(n\right))$ floating point operations. We highlight some of the connections between the different constructions and we provide some numerical examples.     

Monte Carlo construction of hedging strategies against multi-asset European claims

For evaluating a hedging strategy we have to know at every moment the solution of the Cauchy problem for a corresponding parabolic equation (the value of the hedging portfolio) and its derivatives (the deltas). We suggest to find these quantities by Monte Carlo simulation of the corresponding system of stochastic differential equations using weak solution schemes. It turns out that with one and the same control function a variance reduction can be achieved simultaneously for the claim value as well as for the deltas. As illustrations we consider a Markovian multi-asset model with an instantaneously riskless saving bond and also some applications to the LIBOR rate model of Brace, Gatarck, Musiela and Jamshidian.     

Moving least squares based sensitivity analysis for models with dependent variables

For models with dependent input variables, sensitivity analysis is often a troublesome work and only a few methods are available. Mara and Tarantola in their paper (“Variance-based sensitivity indices for models with dependent inputs”) defined a set of variance-based sensitivity indices for models with dependent inputs. We in this paper propose a method based on moving least squares approximation to calculate these sensitivity indices. The new proposed method is adaptable to both linear and nonlinear models since the moving least squares approximation can capture severe change in scattered data. Both linear and nonlinear numerical examples are employed in this paper to demonstrate the ability of the proposed method. Then the new sensitivity analysis method is applied to a cantilever beam structure and from the results the most efficient method that can decrease the variance of model output can be determined, and the efficiency is demonstrated by exploring the dependence of output variance on the variation coefficients of input variables. At last, we apply the new method to a headless rivet model and the sensitivity indices of all inputs are calculated, and some significant conclusions are obtained from the results.     

误差方差的非齐次估计的可容许的充要条件

研究误差方差的非齐次二次估计的可容许性．在平方损失下,给出了一个非齐次二次估计在非齐次二次估计类中是误差方差的容许估计的充要条件．     

Dedollarization in Turkey after decades of dollarization: A myth or reality?

The paper analyzes dollarization in the Turkish economy given the evidence on dedollarization signals. On conducting a Vector Autoregression (VAR) model, the empirical evidence suggests that dollarization has mostly been shaped by macroeconomic imbalances as measured by exchange rate depreciation volatility, inflation volatility and expectations. Furthermore, the generalized impulse response function (IRF) analysis, in addition to the analysis of variance decomposition (VDC) gives support to the notion that dollarization seems to sustain its persistent nature, thus hysteresis still prevails. Hence, unfavorable macroeconomic conditions apparently contribute to dollarization while dollarization itself contains inertia. Furthermore, dedollarization that presumably started after 2001 has lost headway after May 2006. Thus, it seems too early to conclude that dollarization changed its route to dedollarization.