Stochastic Order and Generalized Weighted Mean Invariance

In this paper, we present order invariance theoretical results for weighted quasi-arithmetic means of a monotonic series of numbers. The quasi-arithmetic mean, or Kolmogorov–Nagumo mean, generalizes the classical mean and appears in many disciplines, from information theory to physics, from economics to traffic flow. Stochastic orders are defined on weights (or equivalently, discrete probability distributions). They were introduced to study risk in economics and decision theory, and recently have found utility in Monte Carlo techniques and in image processing. We show in this paper that, if two distributions of weights are ordered under first stochastic order, then for any monotonic series of numbers their weighted quasi-arithmetic means share the same order. This means for instance that arithmetic and harmonic mean for two different distributions of weights always have to be aligned if the weights are stochastically ordered, this is, either both means increase or both decrease. We explore the invariance properties when convex (concave) functions define both the quasi-arithmetic mean and the series of numbers, we show its relationship with increasing concave order and increasing convex order, and we observe the important role played by a new defined mirror property of stochastic orders. We also give some applications to entropy and cross-entropy and present an example of multiple importance sampling Monte Carlo technique that illustrates the usefulness and transversality of our approach. Invariance theorems are useful when a system is represented by a set of quasi-arithmetic means and we want to change the distribution of weights so that all means evolve in the same direction.     

Exact Recovery of Stochastic Block Model by Ising Model

In this paper, we study the phase transition property of an Ising model defined on a special random graph—the stochastic block model (SBM). Based on the Ising model, we propose a stochastic estimator to achieve the exact recovery for the SBM. The stochastic algorithm can be transformed into an optimization problem, which includes the special case of maximum likelihood and maximum modularity. Additionally, we give an unbiased convergent estimator for the model parameters of the SBM, which can be computed in constant time. Finally, we use metropolis sampling to realize the stochastic estimator and verify the phase transition phenomenon thfough experiments.     

Determination of Rosiglitazone by Direct Analysis in Real-Time Mass Spectrometry

The determination of rosiglitazone in dietary supplements by direct analysis in real-time mass spectrometry normally provides low repeatability. The [M+H]⁺ signal sharply decreased in the presence of strong-base and weak-acid ionic compounds because rosiglitazone decomposition occurred due to the hydrolysis of strong-base and weak-acid anions. The repeatability was improved and the influence of ionic compounds was minimized by the use of pioglitazone as an internal standard. Orbitrap mass spectrometry was used to provide high resolution in which isotopic interferences from M?+?1 of pioglitazone upon M of rosiglitazone were eliminated. This approach was used to determine rosiglitazone in tablet and dietary supplements in 1?min per sample.     

Assessment of model chemistries for hydrofluoropolyethers: A DFT/M08‐HX benchmark study

In this work, we report the first detailed theoretical comparative conformational investigation between two different classes of hydrofluoropolyethers: dihydro‐ and dimethoxyfluoropolyethers. The main objective was to determine a cost‐effective computational methodology that could accurately reproduce the energetic rankings and thermal weight factors of the simplest examples of those two classes calculated with M08‐HX/triple‐ζ//M08‐HX/double‐ζ benchmark model chemistries. Between the tested methodologies, M08‐HX/aug‐pcseg‐2//M08‐HX/pcseg‐1 was found to be the most appropriate, exhibiting a good accuracy and considerable reduction in computational cost with respect to the benchmark, being more than three times faster than M08‐HX/aug‐pcseg‐2//M08‐HX/aug‐pcseg‐1. This cost‐effective approach will be essential in future work when studying larger hydrofluoropolyethers, where the computational complexity associated with increasing number of conformers will require such approximations.     

Elemental Analysis of Stone Fruits by Inductively Coupled Plasma Mass Spectrometry and Direct Mercury Analysis

This study reports the concentrations of eight trace essential (Zn, Mn, Cu, Ni, Cr, Co, V, and Se) and four toxic elements (Pb, As, Cd, and Hg) in commonly consumed stone fruits from South Korea. The samples were digested by microwave-induced combustion and analyzed by inductively coupled plasma mass spectrometry (ICP-MS). The concentrations of mercury were analyzed by direct mercury analysis (DMA). The analytical techniques were validated by linearity, limits of detection and quantification, precision, recovery, and for accuracy by analyzing a spinach leave-certified reference material; satisfactory results were obtained in all cases. The concentrations of essential trace elements varied considerably among the stone fruits. Generally stone fruits contained comparatively high concentrations of Zn (0.946 to 7.86?µg/g) and Mn (below the limit of detection to 1.66?µg/g), while lower contents of Cu (0.214 to 1.24?µg/g), Cr (0.032 to 0.114?µg/g), Ni (0.006 to 0.091?µg/g), Co (0.004 to 0.016?µg/g), V (below the limit of detection to 0.023?µg/g), and Se (0.0002 to 0.005?µg/g) were obtained. The concentrations (µg/g) of toxic metals were 0.007 (peach) to 0.016 (cherry) for Pb, 0.001 (plum) to 0.007 (cherry) for As, 0.002 (apricot and cherry) to 0.003 (peach) for Cd, and 0.0003 (peach) to 0.0016 (jujube) for Hg. The values for the estimated dietary intakes, target hazard quotients, and hazard indices were lower than the recommended safety limits by World Health Organization. Therefore, the analyzed stone fruits were deemed to be safe for human consumption.     

Temperature‐shuffled parallel cascade selection molecular dynamics accelerates the structural transitions of proteins

Parallel cascade selection molecular dynamics (PaCS‐MD) is an enhanced conformational sampling method for searching structural transition pathways from a given reactant to a product. Recently, a temperature‐aided PaCS‐MD (Vinod et al., Eur. Biophys. J. 2016, 45, 463) has been proposed as its extension, in which the temperatures were introduced as additional parameters in conformational resampling, whereas the temperature is fixed in the original PaCS‐MD. In the present study, temperature‐shuffled PaCS‐MD is proposed as a further extension of temperature‐aided PaCS‐MD in which the temperatures are shuffled among different replicas at the beginning of each cycle of conformational resampling. To evaluate their conformational sampling efficiencies, the original, temperature‐aided, and temperature‐shuffled PaCS‐MD were applied to a protein‐folding process of Trp‐cage, and their minimum computational costs to identify the native state were addressed. Through the evaluation, it was confirmed that temperature‐shuffled PaCS‐MD remarkably accelerated the protein‐folding process of Trp‐cage compared with the other methods. © 2017 Wiley Periodicals, Inc.     

Adaptive‐numerical‐bias metadynamics

A metadynamics scheme is presented in which the free energy surface is filled with progressively adding adaptive biasing potentials, obtained from the accumulated probability distribution of the collective variables. Instead of adding Gaussians with assigned height and width in conventional metadynamics method, here we add a more realistic adaptive biasing potential to the Hamiltonian of the system. The shape of the adaptive biasing potential is adjusted on the fly by sampling over the visited states. As the top of the barrier is approached, the biasing potentials become wider. This decreases the problem of trapping the system in the niches, introduced by the addition of Gaussians of fixed height in metadynamics. Our results for the free energy profiles of three test systems show that this method is more accurate and converges more quickly than the conventional metadynamics, and is quite comparable (in accuracy and convergence rate) with the well‐tempered metadynamics method. © 2017 Wiley Periodicals, Inc.     

Structural dissimilarity sampling with dynamically self‐guiding selection

Structural dissimilarity sampling (SDS) has been proposed as an enhanced conformational sampling method for reproducing the structural transitions of a given protein. SDS consists of cycles of two steps: (1) Selections of initial structures with structural dissimilarities by referring to a measure. (2) Conformational resampling by restarting short‐time molecular dynamics (MD) simulations from the initial structures. In the present study, an efficient measure is proposed as a dynamically self‐guiding selection to accelerate the structural transitions from a reactant state to a product state as an extension to the original SDS. In the extended SDS, the inner product (IP ) between the reactant and the snapshots generated by short‐time MD simulations are evaluated and ranked according to the IP s at every cycle. Then, the snapshots with low IP s are selected as initial structures for the short‐time MD simulations. This scheme enables one to choose dissimilar and distant initial structures from the reactant, and thus the initial structures dynamically head towards the product, promoting structural transitions from the reactant. To confirm the conformational sampling efficiency, the extended SDS was applied to maltodextrin binding protein (MBP), and we successfully reproduced the structural transition from the open to closed states with submicrosecond‐order simulation times. However, a conventional long‐time MD simulation failed to reproduce the same structural transition. We also compared the performance with that obtained by the ordinary SDS and other sampling techniques that have been developed by us to characterize the possible utility of the extended SDS for actual applications. © 2017 Wiley Periodicals, Inc.     

N_2-DART-Orbitrap中的特征气相离子反应及在西药快速检测中的应用

采用实时直接分析(DART)离子源串联高分辨质谱Orbitrap技术(DART-Orbitrap MS),对8种市售常见西药进行有效成分分析,建立了一种快速、简便、准确测定西药中有效成分的方法.对DART离子源的离子化温度、扫描模式、操作气体种类、辅助溶剂种类及其酸碱性等实验条件进行了优化,得到最佳实验条件.实验结果表明,正谱条件下,采用N_2气作为操作气体时,待测组分准分子离子峰[M+H]+同样具有较高的灵敏度和谱图辨识度.因此,N2气可以替代昂贵的He气作为DART离子源的操作气体用于8种药物有效成分的现场实时检测.该方法具备成本低、快速和操作简便的特点.通过分析待测组分的特征碎片离子,发现了N2-DART离子源中的特征离子反应,包括氧化反应和重排反应.根据获得的特征碎片离子对N_2-DART-MS中发生的反应机理进行推导,并结合理论计算对其进行验证.N_2-DART-MS技术有望应用于复杂基质混合物的现场快速检测中.