General method for reducing adaptive laser pulse-shaping experiments to a single control variable

Adaptive laser pulse shaping has proven to be expeditious for discovering laser pulse shapes capable of manipulating complex systems. However, if adaptive control is to be a valuable interrogative technique that informs physical and chemical research, methods that make it possible to infer mechanistic information from experimental results must be developed. Here, we demonstrate multivariate statistical analysis to extract a single control variable from results of a 137-parameter adaptive laser pulse-shaping optimization of multiphoton electronic excitation in a ruthenium(II) coordination complex in solution. We show that this single variable can be used to linearly manipulate the observed fitness, which is determined by the ratio of molecular emission to second harmonic generation of the laser pulse, over the range explored during the adaptive optimization. Further, manipulation of this variable reveals the latent control mechanism. For this system, that mechanism entails focusing the second harmonic power spectrum of the laser field in a spectral region where the probability of two-photon absorption by the molecule is also large. The statistical tools developed are general and will help elucidate control mechanisms in future adaptive pulse-shaping experiments.     

The invariant constrained equilibrium edge preimage curve method for the dimension reduction of chemical kinetics

This work addresses the construction and use of low-dimensional invariant manifolds to simplify complex chemical kinetics. Typically, chemical kinetic systems have a wide range of time scales. As a consequence, reaction trajectories rapidly approach a hierarchy of attracting manifolds of decreasing dimension in the full composition space. In previous research, several different methods have been proposed to identify these low-dimensional attracting manifolds. Here we propose a new method based on an invariant constrained equilibrium edge (ICE) manifold. This manifold (of dimension nr) is generated by the reaction trajectories emanating from its (nr-1)-dimensional edge, on which the composition is in a constrained equilibrium state. A reasonable choice of the nr represented variables (e.g., nr "major" species) ensures that there exists a unique point on the ICE manifold corresponding to each realizable value of the represented variables. The process of identifying this point is referred to as species reconstruction. A second contribution of this work is a local method of species reconstruction, called ICE-PIC, which is based on the ICE manifold and uses preimage curves (PICs). The ICE-PIC method is local in the sense that species reconstruction can be performed without generating the whole of the manifold (or a significant portion thereof). The ICE-PIC method is the first approach that locally determines points on a low-dimensional invariant manifold, and its application to high-dimensional chemical systems is straightforward. The "inputs" to the method are the detailed kinetic mechanism and the chosen reduced representation (e.g., some major species). The ICE-PIC method is illustrated and demonstrated using an idealized H2O system with six chemical species. It is then tested and compared to three other dimension-reduction methods for the test case of a one-dimensional premixed laminar flame of stoichiometric hydrogen/air, which is described by a detailed mechanism containing nine species and 21 reactions. It is shown that the error incurred by the ICE-PIC method with four represented species is small across the whole flame, even in the low temperature region.     

Taxonomy dimension reduction for colorectal cancer prediction

A growing number of people suffer from colorectal cancer, which is one of the most common cancers. It is essential to diagnose and treat the cancer as early as possible. The disease may change the microorganism communities in the gut, and it could be an efficient method to employ gut microorganisms to predict colorectal cancer. In this study, we selected operational taxonomic units that include several kinds of microorganisms to predict colorectal cancer. To find the most important microorganisms and obtain the best prediction performance, we explore effective feature selection methods. We employ three main steps. First, we use a single method to reduce features. Next, to reduce the number of features, we integrate the dimension reduction methods correlation-based feature selection and maximum relevance–maximum distance (MRMD 1.0 and MRMD 2.0). Then, we selected the important features according to the taxonomy files. In this study, we created training and test sets to obtain a more objective evaluation. Random forest, naïve Bayes, and decision tree classifiers were evaluated. The results show that the methods proposed in this study are better than hierarchical feature engineering. The proposed method, which combines correlation-based feature selection with MRMD 2.0, performed the best on the CRC2 dataset. The dataset and methods can be found in http://lab.malab.cn/data/microdata/data.html.     

A L1-regularized feature selection method for local dimension reduction on microarray data

Dimension reduction is a crucial technique in machine learning and data mining, which is widely used in areas of medicine, bioinformatics and genetics. In this paper, we propose a two-stage local dimension reduction approach for classification on microarray data. In first stage, a new L1-regularized feature selection method is defined to remove irrelevant and redundant features and to select the important features (biomarkers). In the next stage, PLS-based feature extraction is implemented on the selected features to extract synthesis features that best reflect discriminating characteristics for classification. The suitability of the proposal is demonstrated in an empirical study done with ten widely used microarray datasets, and the results show its effectiveness and competitiveness compared with four state-of-the-art methods. The experimental results on St Jude dataset shows that our method can be effectively applied to microarray data analysis for subtype prediction and the discovery of gene coexpression.     

A novel approach for dimension reduction of microarray

This paper proposes a new hybrid search technique for feature (gene) selection (FS) using Independent component analysis (ICA) and Artificial Bee Colony (ABC) called ICA + ABC, to select informative genes based on a Naïve Bayes (NB) algorithm. An important trait of this technique is the optimization of ICA feature vector using ABC. ICA + ABC is a hybrid search algorithm that combines the benefits of extraction approach, to reduce the size of data and wrapper approach, to optimize the reduced feature vectors. This hybrid search technique is facilitated by evaluating the performance of ICA + ABC on six standard gene expression datasets of classification. Extensive experiments were conducted to compare the performance of ICA + ABC with the results obtained from recently published Minimum Redundancy Maximum Relevance (mRMR) +ABC algorithm for NB classifier. Also to check the performance that how ICA + ABC works as feature selection with NB classifier, compared the combination of ICA with popular filter techniques and with other similar bio inspired algorithm such as Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). The result shows that ICA + ABC has a significant ability to generate small subsets of genes from the ICA feature vector, that significantly improve the classification accuracy of NB classifier compared to other previously suggested methods.     

Optimal non-linear dimension reduction scheme for classical molecular dynamics

The optimal creation of a reduced space that effectively captures the long timescale dynamics of a non-linear molecular system over a range of frequencies is described. The technique builds on a previously developed subspace method based on linear constant projective transformation of the original full space. The present work attempts to propose transformation that are spatially dependent thereby leading to an effective subspace for better representing the dynamics of interests. The algorithm seeks out an optimal transformation consistent with desired low frequency motion in a rather general way. The method is demonstrated for a six-dimensional nonlinear system reduced to two-dimensions. Superior performance is found in evaluating ensemble-averaged classical dynamical properties.     

New method for the reduction of benzofurans

A new method for the reduction of benzofurans with potassium and sodium borohydrides in CF₃COOH was developed. It is shown by gas-liquid chromatography and PMR spectroscopy that mixtures (23) of the cis and trans isomers of dihydro derivatives of benzofuran are formed in the reduction. The mechanism of the reduction includes intermolecular transfer of a hydride ion to the protonated form of the benzofuran.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1174–1176, September, 1981.     

A new timescale dimension for migration experiments in clay: proof of principle for the application of miniaturized clay column experiments (MCCE)

Geological clay formations are often considered as a host rock for a future nuclear waste repository. Many studies concerning sorption or desorption experiments with metal ions like radionuclides or other relevant substances (e.g. metal complexing ligands) onto/from geological clay samples are performed with the batch techniques where only small amounts of the homogenized clay is in contact with the appropriate metals diluted in high volumes of aqueous solutions. This unnatural contact of clay with water can lead to high bias or not transferable results for a risk assessment study of a future repository. Diffusion experiments as an alternative and more natural experimental tool have the lack of huge time consuming when the migration of higher valent metal ions is considered. With the herein described new miniaturized clay column setup a linker between the unnatural batch techniques and the time consuming diffusion experiments is installed. The presented miniaturized clay column experiments (MCCE) derived and modified from high performance liquid chromatography can be applied in a lot of geochemical studies. Using MCCE, migration experiments of inert tracers (iodide), natural organic matter as complexing ligands (lactate and salicylate) as well as trivalent metal ions (europium) in compacted clay can be performed within a short time span of a few minutes or hours only in contrast to several months by use of classical diffusion or column methods. As preliminary results, typical migration times through miniaturized clay columns (20 × 3.5 mm, L × ID) of iodide as inert tracer are in the range of 145 min, meanwhile increasing retention times of salicylate from about 390 min in the absence of Eu to migration times in the range of 420–470 min in the presence of different Eu concentration can be observed.     

Thermo-mechanical method for the determination of the fractal dimension of fat crystal networks

The physical properties of a fat are determined by its thermal history, processing conditions, chemical composition, polymorphism and spatial distribution of mass. The mass fractal dimension of a fat crystal network can be determined from the slope of the log–log plot of the storage modulus (G′) versus the solid fat content (SFC). Different SFCs were obtained by melting the fat, diluting it to different extents in liquid oil, and crystallizing the blends under specific conditions. One of the major drawbacks of this method is the inability of characterizing the native structure of an already crystallized fat. In the thermo-mechanical method developed in this study, SFC is changed via temperature variations instead. At each temperature, the G′ and SFC were measured and the fractal dimension calculated as described above. The thermomechanical method proved to be a simpler and more reliable estimator of the fractal dimension of a fat crystal network than the dilution method.     

An adaptive stepsize method for the chemical Langevin equation

Mathematical and computational modeling are key tools in analyzing important biological processes in cells and living organisms. In particular, stochastic models are essential to accurately describe the cellular dynamics, when the assumption of the thermodynamic limit can no longer be applied. However, stochastic models are computationally much more challenging than the traditional deterministic models. Moreover, many biochemical systems arising in applications have multiple time-scales, which lead to mathematical stiffness. In this paper we investigate the numerical solution of a stochastic continuous model of well-stirred biochemical systems, the chemical Langevin equation. The chemical Langevin equation is a stochastic differential equation with multiplicative, non-commutative noise. We propose an adaptive stepsize algorithm for approximating the solution of models of biochemical systems in the Langevin regime, with small noise, based on estimates of the local error. The underlying numerical method is the Milstein scheme. The proposed adaptive method is tested on several examples arising in applications and it is shown to have improved efficiency and accuracy compared to the existing fixed stepsize schemes.     

General and efficient method for the synthesis of alkoxymethylsilanes

Although alkoxymethylsilanes serve as useful building blocks, various efforts to synthesize them by substitution reaction with an alkoxide ion at the carbon adjacent to the silicon failed. To solve this synthetic problem a new route which is very simple to perform was developed. Bromination of (methoxymethyl)trimethylsilane by using N‐bromosuccinimide/2,2′‐azobisisobutyronitrile (NBS/AIBN) was followed by a substitution by alcohols in the presence of triethylamine to give the corresponding [alkoxy‐­(methoxy)methyl]trimethylsilanes. These acetals can be used directly for the next reduction with di‐isobutylaluminium hydride (DIBAL‐H) or Et₃SiH/BF₃·OEt₂ to give alkoxymethylsilanes in good to moderate yields. The success of the substitution reaction with the alcohols suggests that the mechanism is of somewhat S_N1 by nature and formation of the cationic intermediate seems to release the steric hindrance around the carbon, allowing the attack of alcohols. Copyright © 1999 John Wiley & Sons, Ltd.     

General method for the palladium-catalyzed allylation of aliphatic alcohols

A palladium catalysis-mediated approach to coupling aliphatic alcohols with allyl carbonates has been developed. The method allows for the allylation of primary, secondary, and tertiary alcohols efficiently under mild conditions. Limitations were explored as well as the asymmetric application of the chemistry. Regiochemical and olefin geometry was controlled in the coupling of unsymmetrical allylating agents. Transient allyl carbonates were observed in the coupling, which comprised the trans-carboxylation of the allyl-carbonate with the requisite alcohol.     

A new method for the reduction of nitronyl nitroxides

Reduction of nitronyl nitroxides using hexamethylenetetramine is a very convenient method for preparing the corresponding imino nitroxides and 2-imidazoline N-oxides.     

A method for the evaluation of the activation energy from relaxation experiments

A method is proposed for calculating the activation energy over the entire temperature range from relaxation measurements at two frequencies as a function of temperature by taking into account the entire experimental curve. The method is independent of the distribution of relaxation times, but assumes the validity of the time-temperature superposition principle.     

General method for the synthesis of 8-arylsulfanyl adenine derivatives

We report a general method for the synthesis of 8-arylsulfanyl adenine derivatives using a mild protocol of coupling 8-mercaptoadenine with a variety of aryl iodides.     

An adaptive pseudospectral method for wave packet dynamics

We solve the time-dependent Schro?dinger equation for molecular dynamics using a pseudospectral method with global, exponentially decaying, Hagedorn basis functions. The approximation properties of the Hagedorn basis depend strongly on the scaling of the spatial coordinates. Using results from control theory we develop a time-dependent scaling which adaptively matches the basis to the wave packet. The method requires no knowledge of the Hessian of the potential. The viability of the method is demonstrated on a model for the photodissociation of IBr, using a Fourier basis in the bound state and Hagedorn bases in the dissociative states. Using the new approach to adapting the basis we are able to solve the problem with less than half the number of basis functions otherwise necessary. We also present calculations on a two-dimensional model of CO(2) where the new method considerably reduces the required number of basis functions compared to the Fourier pseudospectral method.     

A superior method for the reduction of secondary phosphine oxides

[reaction: see text] Diisobutylaluminum hydride (DIBAL-H) and triisobutylaluminum have been found to be outstanding reductants for secondary phosphine oxides (SPOs). All classes of SPOs can be readily reduced, including diaryl, arylalkyl, and dialkyl members. Many SPOs can now be reduced at cryogenic temperatures, and conditions for preservation of reducible functional groups have been found. Even the most electron-rich and sterically hindered phosphine oxides can be reduced in a few hours at 50-70 degrees C. This new reduction has distinct advantages over existing technologies.     

A rapid and efficient method for the reduction of quinoxalines

Mono and di‐substituted alkyl and aryl quinoxalines are rapidly reduced in high yield to their respective 1,2,3,4‐tetrahydro‐derivatives by borane in THF solution. In the case of the 2,3‐di‐substituted compounds, reduction is stereoselective yielding exclusively the cis‐isomers. Sodium borohydride in acetic acid also reduces alkyl and aryl quinoxalines, but proceeds with lower yields and often produces side products. Sodium borohydride in ethanol reduces quinoxaline and 2‐methylquinoxaline in high yield; however, the reaction is very slow, whereas 2,3‐dialkyl and 2‐aryl quinoxalines are not efficiently reduced by sodium borohydride in ethanol.