Nonstationary Markov chains and convergence of the annealing algorithm

We study the asymptotic behavior as timet + of certain nonstationary Markov chains, and prove the convergence of the annealing algorithm in Monte Carlo simulations. We find that in the limitt + , a nonstationary Markov chain may exhibit phase transitions. Nonstationary Markov chains in general, and the annealing algorithm in particular, lead to biased estimators for the expectation values of the process. We compute the leading terms in the bias and the variance of the sample-means estimator. We find that the annealing algorithm converges if the temperatureT(t) goes to zero no faster thanC/log(t/t ₀) ast+, with a computable constantC andt ₀ the initial time. The bias and the variance of the sample-means estimator in the annealing algorithm go to zero likeO(t^–1+) for some 0<1, with =0 only in very special circumstances. Our results concerning the convergence of the annealing algorithm, and the rate of convergence to zero of the bias and the variance of the sample-means estimator, provide a rigorous procedure for choosing the optimal annealing schedule. This optimal choice reflects the competition between two physical effects: (a) The adiabatic effect, whereby if the temperature is loweredtoo abruptly the system may end up not in a ground state but in a nearby metastable state, and (b) the super-cooling effect, whereby if the temperature is loweredtoo slowly the system will indeed approach the ground state(s) but may do so extremely slowly.     

内噪声作用下的随机共振算法对弱信号的检测

基于随机共振理论提出了一种简便、有效地检测弱信号的方法。在内噪声协同作用下，通过调节输入噪声信号的大小能较好地提高系统输出信号的信噪比，从而实现检测背景噪声很强的弱信号的目的。应用于模拟信号和实验信号的结果证明了方法是可行的。     

Automated molecular design: A new fragment-joining algorithm

Summary A popular first step in the problem of structure-based, de novo molecule design is to identify regions where specific functional groups or chemical entities would be expected to interact strongly. When the three-dimensional structure of the receptor is not available, it may be possible to derive a pharmacophore giving the three-dimensional relationships between such chemical groups. The task then is to design synthetically feasible molecules which not only contain the required groups, but which can also position them in the desired relative orientation. One way to do this is to first link the groups using an acyclic chain. We have investigated the application of the tweak algorithm [Shenkin, P.S. et al., Biopolymers, 26 (1987) 2053] for generating families of acyclic linkers. These linking structures can subsequently be braced using a ring-joining algorithm [Leach, A.R. and Lewis, R.A., J. Comput. Chem., 15 (1994) 233], giving rise to an even wider variety of molecular skeletons for further studies.     

Aligning Text and Phonemes for Speech Technology Applications Using an EM-Like Algorithm

A common requirement in speech technology is to align two different symbolic representations of the same linguistic ‘message’. For instance, we often need to align letters of words listed in a dictionary with the corresponding phonemes specifying their pronunciation. As dictionaries become ever bigger, manual alignment becomes less and less tenable yet automatic alignment is a hard problem for a language like English. In this paper, we describe the use of a form of the expectation-maximization (EM) algorithm to learn alignments of English text and phonemes, starting from a variety of initializations. We use the British English Example Pronunciation (BEEP) dictionary of almost 200,000 words in this work. The quality of alignment is difficult to determine quantitatively since no ‘gold standard’ correct alignment exists. We evaluate the success of our algorithm indirectly from the performance of a pronunciation by analogy system using the aligned dictionary data as a knowledge base for inferring pronunciations. We find excellent performance—the best so far reported in the literature. There is very little dependence on the start point for alignment, indicating that the EM search space is strongly convex. Since the aligned BEEP dictionary is a potentially valuable resource, it is made freely available for research use.     

Numerical comparison of several variable-metric algorithms

The paper compares the numerical performances of the LDL decomposition of the BFGS variable-metric algorithm, the Dennis-Mei dogleg algorithm on the BFGS update, and Davidon's projections with the BFGS update with the straight BFGS update on a number of standard test problems. Numerical results indicate that the standard BFGS algorithm is superior to all of the more complex strategies.This research was supported by the National Science Foundation under Research Grant No. MCS77-07327.     

Quantitative determination of Malathion in pesticide by modified attenuated total reflectance-Fourier transform infrared spectrometry applying genetic algorithm wavelength selection method

A simple and environment friendly method was developed for determination of Malathion content of analytical and commercial insecticide samples with no special preparation. Attenuated total reflectance-Fourier transform infrared (ATR-FTIR) spectra were characterized and 1000-2000 cm⁻¹ region was selected for quantitative analysis utilizing partial least square (PLS) and two wavelength selection methods: (a) principal component regression (PCR) and (b) genetic algorithm (GA). Relative error of prediction (REP) was calculated in PLS, PCR-PLS and GA-PLS methods and was 3.536, 1.656 and 0.188, respectively. Proposed method is successfully applicable for quantification of Malathion in commercial grade samples and reliable results in comparison with known methods, confirms this idea.     

SPE – Microwave‐assisted extraction coupled system for the extraction of pesticides from water samples

SPE is a commonly applied technique for preconcentration of pesticides from water samples. Microwave‐assisted extraction (MAE) technique is the extraction applied for preconcentration of different compounds from solid samples. SPE coupled with MAE is capable of preconcentrating these compounds from water samples too. This investigation was aimed at improving the efficiency of atrazine, alachlor, and α‐cypermethrin pesticide extraction from the spiked water samples applying SPE followed by MAE. In this way, MAE served for elution of pesticides from C₁₈‐extraction disks with solvent heated by microwave energy. Various elution conditions were tested for their effects on the extraction efficiency of the SPE–MAE combined technique. Several parameters, such as elution solvent volume (mL), elution temperature (°C), and duration of elution (min), affect the extraction efficiency of the SPE–MAE coupled system and need to be optimized for the selected pesticides. In order to develop a mathematical model, 15 experiments were performed in the central composite design. The equation was then used to predict recoveries of the pesticides under specific experimental conditions. Optimization of microwave extraction was accomplished using the genetic algorithm approach. Best results were achieved using 20 mL of ethanol at 60°C. Optimal hold time was 5 min and 24 s. The SPE–MAE combination was also compared with the conventional SPE extraction technique with elution of a nonpolar or a moderately polar compound with nonpolar solvents.     

The Enhancement of Efficiency of High-order Harmonic in Intense Laser Field Based on Asymptotic Boundary Conditions and Symplectic Algorithm

Asymptotic boundary condition (ABC) of laser-atom interaction presented recently is applied to transform the initial value problem of the time-dependent Schrödinger equation (TDSE) in infinite space into the initial and boundary value problem in the finite space, and then the TDSE is discretized into linear canonical equations by substituting the symmetry difference quotient for the 2-order partial derivative. The canonical equation is solved by symplectic algorithm. The ground state and the equal weight coherent superposition of the ground state and the first excited state have been taken as the initial conditions, respectively, while we calculate the population of bound states, the evolution of average distance and the high-order harmonic generation (HHG). The conversion efficiency of HHG can be enhanced by initial coherent superposition state and moderate laser intensities     

Density functional calculations of large systems containing heavy elements by means of the regionalization algorithm

The compounds containing transition metals orother heavy elements play important roles in chemistry.They possess diverse properties which have been util-ized in numerous functional materials. Some of theseproperties are also involved in biological processes.However, it is very difficult to study these compoundsdeeply by means of quantum chemical methods, be-cause in these systems usually there are a large amountof electrons, the distribution of the frontier orbitals isdense, the correlation be…