Proof of algorithms by general snapshots

A constructive approach to the question of proofs of algorithms is to consider proofs that an object resulting from the execution of an algorithm possesses certain static characteristics. It is shown by an elementary example how this possibility may be used to prove the correctness of an algorithm written in ALGOL 60. The stepping stone of the approach is what is called General Snapshots, i.e. expressions of static conditions existing whenever the execution of the algorithm reaches particular points. General Snapshots are further shown to be useful for constructing algorithms.     

基于四组分同时测定的PARAFAC和SWATLD算法及比较

邻苯二酚和对苯二酚是有毒物质,酪氨酸和色氨酸是天然氨基酸中仅有的会发光的组分,由于四组分光谱重叠,很难用常规方法直接定量检测。实验中采用三维荧光光谱结合平行因子和自加权交替三线性分解算法,邻苯二酚、对苯二酚、酪氨酸和色氨酸进行直接定量测定;同时,比较两种算法在定性测定和定量测定上的差别。当测量体系的成分数预估计值为4时,两种方法分辨后的回收率分别为(101.2±2.7)%,(99.3±3.0)%,(98.7±4.5)%,(101.6±4.7)%和(109.0±8.0)%,(91.3±11)%,(99.7±13)%,(98.1±11)%。试验结果表明,两种方法可用于四组分直接快速定量测定;通过对两种算法的比较,PARAFAC算法更具优势。     

Modelling the dynamics of stochastic local search on <Emphasis Type="Italic">k</Emphasis>-<Emphasis Type="SmallCaps">sat</Emphasis>

A new analytical tool is presented to provide a better understanding of the search space of k-sat. This tool, termed the local value distribution , describes the probability of finding assignments of any value q′ in the neighbourhood of assignments of value q. The local value distribution is then used to define a Markov model to model the dynamics of a corresponding stochastic local search algorithm for k-sat. The model is evaluated by comparing the predicted algorithm dynamics to experimental results. In most cases the fit of the model to the experimental results is very good, but limitations are also recognised.     

红黑排序混合算法收敛速度分析

The algorithm of applying the block Gauss elimination to the Red-Black or-dering matrix to reduce the order of the system then solve the reduced system byiterative methods is called Hybrid Red-Black Ordering algorithm.In this paper,we discuss the convergence rate of the hybrid methods combined with JACOBI,CG,GMRES(m).Theoretical analysis shows that without preconditioner thesethree hybrid methods converge about 2 times as fast as the corresponding natural ordering methods.For the case that all the eigenvalues is near the real axis, the GMRES(m) algorithm converges about 3 times faster than the natural ordering GMRES(m).Various numerical experiments are presented.For large scale prob-lem with preconditioners, numerical experiments show that the GMRES(m) hybrid methods converge from about 3 times to even 5 times as fast as the natural order-ing methods and the computing time is reduced to about 1/3 even 1/6 of that of the natural ordering methods.     

相移阴影莫尔基于迭代LSM拟合

相移阴影莫尔技术相位高度存在着非线性关系,无法在全场获得均匀相移,因而致使经典的相移算法不能得到精确解.对此,提出了一种基于最小方差迭代的相移阴影莫尔技术,该技术通过垂直光栅面等间距移动光栅来产生相移,但光栅移动距离可不采用固定值,所以相移过程灵活|使用在高度解调过程中确定的逐点相移增量来抽取精确的测量相位,实现了相移阴影莫尔技术中固有的相位高度非线性误差补偿.结果表明,该方法可通过干涉图计算光栅的移动量,具有相移器的自标定特性.     

Elucidation of triacylglycerols in cod liver oil by liquid chromatography electrospray tandem ion-trap mass spectrometry

Though liquid chromatography electrospray tandem mass spectrometry (LC-ESI-MS²) has been widely used in the structural elucidation of triacylglycerols (TAG) in vegetable oils, its potentiality for the identification of TAG molecules in omega-3 rich oils remains unexplored till date. Hence, this article investigates the applicability of LC-ESI-MS² for the structural characterization of naturally occurring TAG in cod liver oil without the TAG fractionation during the sample preparation. A computational algorithm was developed to automatically interpret the mass spectra and elucidate the TAG structures respectively. The results were compared against the lipase benchmark method. A principal component analysis study revealed that it is possible to discriminate genuine from adulterated cod liver oil.     

A novel trilinear decomposition algorithm： Three-dimension non-negative matrix factorization

Non-negative matrix factorization(NMF)is a technique for dimensionality reduction by placing non-negativity constraints onthe matrix.Based on the PARAFAC model,NMF was extended for three-dimension data decomposition.The three-dimension non-negative matrix factorization(NMF3)algorithm,which was concise and easy to implement,was given in this paper.The NMF3algorithm implementation was based on elements but not on vectors.It could decompose a data array directly without unfolding,which was not similar to that the traditional algorithms do.It has been applied to the simulated data array decomposition andobtained reasonable results.It showed that NMF3 could be introduced for curve resolution in chemometrics.     

Real-time recursive estimation of statistical parameters

Recursive algorithms for the computation of standard deviation and average deviation are derived and their applications in data acquisition are discussed. The relative speeds and accuracies of the two algorithms are compared for synthetic data. The performance of recursive estimation under shot and proportional noise limitations is also described. As an example of the utility of these algorithms, absorbance data with constant confidence intervals are collected regardless of incident and transmitted intensities. The desired precision is specified prior to data acquisition and used to control signal-averaging of the data in real time.