High strong order methods for non-commutative stochastic ordinary differential equation systems and the Magnus formula

In recent years considerable attention has been paid to the numerical solution of stochastic ordinary differential equations (SODEs), as SODEs are often more appropriate than their deterministic counterparts in many modelling situations. However, unlike the deterministic case numerical methods for SODEs are considerably less sophisticated due to the difficulty in representing the (possibly large number of) random variable approximations to the stochastic integrals. Although Burrage and Burrage [High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations, Applied Numerical Mathematics 22 (1996) 81-101] were able to construct strong local order 1.5 stochastic Runge-Kutta methods for certain cases, it is known that all extant stochastic Runge-Kutta methods suffer an order reduction down to strong order 0.5 if there is non-commutativity between the functions associated with the multiple Wiener processes. This order reduction down to that of the Euler-Maruyama method imposes severe difficulties in obtaining meaningful solutions in a reasonable time frame and this paper attempts to circumvent these difficulties by some new techniques. An additional difficulty in solving SODEs arises even in the Linear case since it is not possible to write the solution analytically in terms of matrix exponentials unless there is a commutativity property between the functions associated with the multiple Wiener processes. Thus in this present paper first the work of Magnus [On the exponential solution of differential equations for a linear operator, Communications on Pure and Applied Mathematics 7 (1954) 649-673] (applied to deterministic non-commutative Linear problems) will be applied to non-commutative linear SODEs and methods of strong order 1.5 for arbitrary, linear, non-commutative SODE systems will be constructed - hence giving an accurate approximation to the general linear problem. Secondly, for general nonlinear non-commutative systems with an arbitrary number (d) of Wiener processes it is shown that strong local order I Runge-Kutta methods with d + 1 stages can be constructed by evaluated a set of Lie brackets as well as the standard function evaluations. A method is then constructed which can be efficiently implemented in a parallel environment for this arbitrary number of Wiener processes. Finally some numerical results are presented which illustrate the efficacy of these approaches. (C) 1999 Elsevier Science B.V. All rights reserved.

Segmentation of cone-beam CT using a hidden Markov random field with informative priors

Purpose: Flat-detector, cone-beam computed tomography (CBCT) has enormous potential to improve the accuracy of treatment delivery in image-guided radiotherapy (IGRT). To assist radiotherapists in interpreting these images, we use a Bayesian statistical model to label each voxel according to its tissue type. Methods: The rich sources of prior information in IGRT are incorporated into a hidden Markov random field (MRF) model of the 3D image lattice. Tissue densities in the reference CT scan are estimated using inverse regression and then rescaled to approximate the corresponding CBCT intensity values. The treatment planning contours are combined with published studies of physiological variability to produce a spatial prior distribution for changes in the size, shape and position of the tumour volume and organs at risk (OAR). The voxel labels are estimated using the iterated conditional modes (ICM) algorithm. Results: The accuracy of the method has been evaluated using 27 CBCT scans of an electron density phantom (CIRS, Inc. model 062). The mean voxel-wise misclassification rate was 6.2%, with Dice similarity coefficient of 0.73 for liver, muscle, breast and adipose tissue. Conclusions: By incorporating prior information, we are able to successfully segment CBCT images. This could be a viable approach for automated, online image analysis in radiotherapy.

Metabolomics coupled with proteomics advancing drug discovery toward more agile development of targeted combination therapies

To enhance the therapeutic efficacy and reduce the adverse effects of traditional Chinese medicine, practitioners often prescribe combinations of plant species and/or minerals, called formulae. Unfortunately, the working mechanisms of most of these compounds are difficult to determine and thus remain unknown. In an attempt to address the benefits of formulae based on current biomedical approaches, we analyzed the components of Yinchenhao Tang, a classical formula that has been shown to be clinically effective for treating hepatic injury syndrome. The three principal components of Yinchenhao Tang are Artemisia annua L., Gardenia jasminoids Ellis, and Rheum Palmatum L., whose major active ingredients are 6,7-dimethylesculetin (D), geniposide (G), and rhein (R), respectively. To determine the mechanisms underlying the efficacy of this formula, we conducted a systematic analysis of the therapeutic effects of the DGR compound using immunohistochemistry, biochemistry, metabolomics, and proteomics. Here, we report that the DGR combination exerts a more robust therapeutic effect than any one or two of the three individual compounds by hitting multiple targets in a rat model of hepatic injury. Thus, DGR synergistically causes intensified dynamic changes in metabolic biomarkers, regulates molecular networks through target proteins, has a synergistic/additive effect, and activates both intrinsic and extrinsic pathways.

Thyroxine and reserpine-induced changes in metabolic profiles of rat urine and the therapeutic effect of Liu Wei Di Huang Wan detected by UPLC-HDMS

The promise of metabonomics, a new "omics" technique, to validate Chinese medicines and the compatibility of Chinese formulas has been appreciated. The present study was undertaken to explore the excretion pattern of low molecular mass metabolites in the male Wistar-derived rat model of kidney yin deficiency induced with thyroxine and reserpine as well as the therapeutic effect of Liu Wei Di Huang Wan (LW) and its separated prescriptions, a classic traditional Chinese medicine formula for treating kidney yin deficiency in China. The study utilized ultra-performance liquid chromatography/electrospray ionization synapt high definition mass spectrometry (UPLC/ESI-SYNAPT-HDMS) in both negative and positive electrospray ionization (ESI). At the same time, blood biochemistry was examined to identify specific changes in the kidney yin deficiency. Distinct changes in the pattern of metabolites, as a result of daily administration of thyroxine and reserpine, were observed by UPLC-HDMS combined with a principal component analysis (PCA). The changes in metabolic profiling were restored to their baseline values after treatment with LW according to the PCA score plots. Altogether, the current metabonomic approach based on UPLC-HDMS and orthogonal projection to latent structures discriminate analysis (OPLS-DA) indicated 20 ions (14 in the negative mode, 8 in the positive mode, and 2 in both) as "differentiating metabolites".

Metabolic urinary profiling of alcohol hepatotoxicity and intervention effects of Yin Chen Hao Tang in rats using ultra-performance liquid chromatography/electrospray ionization quadruple time-of-flight mass spectrometry

This paper was designed to study metabonomic characters of the hepatotoxicity induced by alcohol and the intervention effects of Yin Chen Hao Tang (YCHT), a classic traditional Chinese medicine formula for treatment of jaundice and liver disorders in China. Urinary samples from control, alcohol- and YCHT-treated rats were analyzed by ultra-performance liquid chromatography/electrospray ionization quadruple time-of-flight mass spectrometry (UPLC/ESI-QTOF-MS) in positive ionization mode. The total ion chromatograms obtained from the control, alcohol- and YCHT-treated rats were easily distinguishable using a multivariate statistical analysis method such as the principal components analysis (PCA). The greatest difference in metabolic profiling was observed from alcohol-treated rats compared with the control and YCHT-treated rats. The positive ions m/z 664.3126 (9.00 min) was elevated in urine of alcohol-treated rats, whereas, ions m/z 155.3547 (10.96 min) and 708.2932 (9.01 min) were at a lower concentration compared with that in urine of control rats, however, these ions did not indicate a statistical difference between control rats and YCHT-treated rats. The ion m/z 664.3126 was found to correspond to ceramide (d18:1/25:0), providing further support for an involvement of the sphingomyelin signaling pathway in alcohol hepatotoxicity and the intervention effects of YCHT.

Pharmacokinetic studies of a Chinese triple herbal drug formula

Yin Chen Hao Tang preparation (YCHTP) is a classic traditional Chinese medicine formula, which is commonly used for clinical treatment of hepatological diseases. In this study, a rapid and validated high-performance liquid chromatography (HPLC) method was developed to simultaneously identify 6,7-dimethylesculetin and geniposide in rat plasma. This assay was performed on a Dikma Diamonsil RP(18) column (200 mmx4.6 mm, 5 mum) with acetonitrile-methanol-water (0.1% formic acid) as the mobile phase, showing acceptable linearity, intra- and inter-day precision and accuracy (R.S.D.=5%), and absolute recovery for two analytes (74%); the limits of quantitation were 0.4 and 1.12 mug/ml, and the limits of detection were 0.06 and 0.09 mug/ml for two analytes. The developed method was successfully applied to study the effect of formula compatibility on the pharmacokinetics of 6,7-dimethylesculetin and geniposide in YCHTP when orally administrating an effective human daily dose of YCHTP to rats. We surmise that formula compatibility can significantly influence the pharmacokinetics of YCHTP, and we have elucidated and validated the compatible administration of YCHTP.

Pharmacokinetics-based elucidation on disparity in clinical effectiveness between varieties of Zhi Zhu Wan, a traditional Chinese medical formula

AIM: Zhi Zhu Wan (ZZW) is a classical Chinese medical formulation used for the treatment of functional dyspepsia that attributed to Spleen-deficiency Syndrome. ZZW contains Atractylodes Rhizome and Fructus Citrus Immaturus, the later originates from both Citrus aurantium L. (BZZW) and Citrus sinensis Osbeck (RZZW). The present study is designed to elucidate disparities in the clinical efficacy of two ZZW varieties based on the pharmacokinetics of naringenin and hesperetin. MEHTOD: After oral administration of ZZWs, blood sample was collected from healthy volunteers at designed time points. Naringenin and hesperetin were detected in plasma by RP-HPLC, pharmacokinetic parameters were processed using mode-independent methods with WINNONLIN. RESULTS: After oral administration of BZZW, both naringenin and hesperetin were detected in plasma, and demonstrated similar pharmacokinetic parameters. Ka was 0.384+/-0.165 and 0.401+/-0.159, T(1/2(ke))(h) was 5.491+/-3.926 and 5.824+/-3.067, the AUC (mg/Lh) was 34.886+/-22.199 and 39.407+/-19.535 for naringenin and hesperetin, respectively. However, in the case of RZZW, only hesperetin was found in plasma, but the pharmacokinetic properties for hesperetin in RZZW was different from that in BZZW. T(max) for hesperetin in RZZW is about 8.515h, and its C(max) is much larger than that of BZZW. Moreover, it was eliminated slowly as it possessed a much larger AUC value. CONCLUSION: The distinct therapeutic orientations of the Chinese medical formula ZZWs with different Fructus Citrus Immaturus could be elucidated based on the pharmacokinetic parameters of constituents after oral administration.

Principal component and linkage analysis of cardiovascular risk traits in the Norfolk isolate

OBJECTIVE(S): An individual's risk of developing cardiovascular disease (CVD) is influenced by genetic factors. This study focussed on mapping genetic loci for CVD-risk traits in a unique population isolate derived from Norfolk Island. METHODS: This investigation focussed on 377 individuals descended from the population founders. Principal component analysis was used to extract orthogonal components from 11 cardiovascular risk traits. Multipoint variance component methods were used to assess genome-wide linkage using SOLAR to the derived factors. A total of 285 of the 377 related individuals were informative for linkage analysis. RESULTS: A total of 4 principal components accounting for 83% of the total variance were derived. Principal component 1 was loaded with body size indicators; principal component 2 with body size, cholesterol and triglyceride levels; principal component 3 with the blood pressures; and principal component 4 with LDL-cholesterol and total cholesterol levels. Suggestive evidence of linkage for principal component 2 (h(2) = 0.35) was observed on chromosome 5q35 (LOD = 1.85; p = 0.0008). While peak regions on chromosome 10p11.2 (LOD = 1.27; p = 0.005) and 12q13 (LOD = 1.63; p = 0.003) were observed to segregate with principal components 1 (h(2) = 0.33) and 4 (h(2) = 0.42), respectively. CONCLUSION(S): This study investigated a number of CVD risk traits in a unique isolated population. Findings support the clustering of CVD risk traits and provide interesting evidence of a region on chromosome 5q35 segregating with weight, waist circumference, HDL-c and total triglyceride levels.

Improved ultra-performance liquid chromatography with electrospray ionization quadrupole-time-of-flight high-definition mass spectrometry method for the rapid analysis of the chemical constituents of a typical medical formula: Liuwei Dihuang Wan

Liuwei Dihuang Wan (LWD), a classic Chinese medicinal formulae, has been used to improve or restore declined functions related to aging and geriatric diseases, such as impaired mobility, vision, hearing, cognition and memory. It has attracted increasingly much attention as one of the most popular and valuable herbal medicines. However, the systematic analysis of the chemical constituents of LDW is difficult and thus has not been well established. In this paper, a rapid, sensitive and reliable ultra-performance liquid chromatography with electrospray ionization quadrupole time-of-flight high-definition mass spectrometry (UPLC-ESI-Q-TOF-MS) method with automated MetaboLynx analysis in positive and negative ion mode was established to characterize the chemical constituents of LDW. The analysis was performed on a Waters UPLCTM HSS T3 using a gradient elution system. MS/MS fragmentation behavior was proposed for aiding the structural identification of the components. Under the optimized conditions, a total of 50 peaks were tentatively characterized by comparing the retention time and MS data. It is concluded that a rapid and robust platform based on UPLC-ESI-Q-TOF-MS has been successfully developed for globally identifying multiple-constituents of traditional Chinese medicine prescriptions. This is the first report on systematic analysis of the chemical constituents of LDW. This article is protected by copyright. All rights reserved.

Segmentation of cone-beam CT using a hidden Markov random field with informative priors

Cone-beam computed tomography (CBCT) has enormous potential to improve the accuracy of treatment delivery in image-guided radiotherapy (IGRT). To assist radiotherapists in interpreting these images, we use a Bayesian statistical model to label each voxel according to its tissue type. The rich sources of prior information in IGRT are incorporated into a hidden Markov random field model of the 3D image lattice. Tissue densities in the reference CT scan are estimated using inverse regression and then rescaled to approximate the corresponding CBCT intensity values. The treatment planning contours are combined with published studies of physiological variability to produce a spatial prior distribution for changes in the size, shape and position of the tumour volume and organs at risk. The voxel labels are estimated using iterated conditional modes. The accuracy of the method has been evaluated using 27 CBCT scans of an electron density phantom. The mean voxel-wise misclassification rate was 6.2\%, with Dice similarity coefficient of 0.73 for liver, muscle, breast and adipose tissue. By incorporating prior information, we are able to successfully segment CBCT images. This could be a viable approach for automated, online image analysis in radiotherapy.

Vision-based estimation of airborne target pseudobearing rate using hidden Markov model filters

The problem of estimating pseudobearing rate information of an airborne target based on measurements from a vision sensor is considered. Novel image speed and heading angle estimators are presented that exploit image morphology, hidden Markov model (HMM) filtering, and relative entropy rate (RER) concepts to allow pseudobearing rate information to be determined before (or whilst) the target track is being estimated from vision information.

Comparative study on the protective effects of Yinchenhao Decoction against liver injury induced by alpha-naphthylisothiocyanate and carbon tetrachloride

OBJECTIVE: To optimize the animal model of liver injury that can properly represent the pathological characteristics of dampness-heat jaundice syndrome of traditional Chinese medicine. METHODS: The liver injury in the model rat was induced by alpha-naphthylisothiocyanate (ANIT) and carbon tetrachloride (CCl(4) ) respectively, and the effects of Yinchenhao Decoction (, YCHD), a proved effective Chinese medical formula for treating the dampness-heat jaundice syndrome in clinic, on the two liver injury models were evaluated by analyzing the serum level of alanine aminotransferase (ALT), asparate aminotransferase (AST), alkaline phosphatase (ALP), malondialchehyche (MDA), total bilirubin (T-BIL), superoxide dismutase (SOD), glutathione peroxidase (GSH-PX) as well as the ratio of liver weight to body weight. The experimental data were analyzed by principal component analytical method of pattern recognition. RESULTS: The ratio of liver weight to body weight was significantly elevated in the ANIT and CCl(4) groups when compared with that in the normal control (P<0.01). The contents of ALT and T-BIL were significantly higher in the ANIT group than in the normal control (P<0.05,P<0.01), and the levels of AST, ALT and ALP were significantly elevated in CCl(4) group relative to those in the normal control P<0.01). In the YCHD group, the increase in AST, ALT and ALP levels was significantly reduced (P<0.05, P<0.01), but with no significant increase in serum T-BIL. In the CCl(4) intoxicated group, the MDA content was significantly increased and SOD, GSH-PX activities decreased significantly compared with those in the normal control group, respectively (P<0.01). The increase in MDA induced by CCl(4) was significantly reduced by YCHD P<0.05). CONCLUSION: YCHD showed significant effects on preventing liver injury progression induced by CCl(4), and the closest or most suitable animal model for damp-heat jaundice syndrome may be the one induced by CCl(4).

Efficiency comparison of Markov Chain Monte Carlo simulation with subset simulation (MCMC/ss) to standard Monte Carlo Simulation (sMC) for extreme event scenarios

Standard Monte Carlo (sMC) simulation models have been widely used in AEC industry research to address system uncertainties. Although the benefits of probabilistic simulation analyses over deterministic methods are well documented, the sMC simulation technique is quite sensitive to the probability distributions of the input variables. This phenomenon becomes highly pronounced when the region of interest within the joint probability distribution (a function of the input variables) is small. In such cases, the standard Monte Carlo approach is often impractical from a computational standpoint. In this paper, a comparative analysis of standard Monte Carlo simulation to Markov Chain Monte Carlo with subset simulation (MCMC/ss) is presented. The MCMC/ss technique constitutes a more complex simulation method (relative to sMC), wherein a structured sampling algorithm is employed in place of completely randomized sampling. Consequently, gains in computational efficiency can be made. The two simulation methods are compared via theoretical case studies.

Understanding the abnormal brain activity in epilepsy as a potential predictor of the onset of an epileptic seizure

The Brain Research Institute (BRI) uses various types of indirect measurements, including EEG and fMRI, to understand and assess brain activity and function. As well as the recovery of generic information about brain function, research also focuses on the utilisation of such data and understanding to study the initiation, dynamics, spread and suppression of epileptic seizures. To assist with the future focussing of this aspect of their research, the BRI asked the MISG 2010 participants to examine how the available EEG and fMRI data and current knowledge about epilepsy should be analysed and interpreted to yield an enhanced understanding about brain activity occurring before, at commencement of, during, and after a seizure. Though the deliberations of the study group were wide ranging in terms of the related matters considered and discussed, considerable progress was made with the following three aspects. (1) The science behind brain activity investigations depends crucially on the quality of the analysis and interpretation of, as well as the recovery of information from, EEG and fMRI measurements. A number of specific methodologies were discussed and formalised, including independent component analysis, principal component analysis, profile monitoring and change point analysis (hidden Markov modelling, time series analysis, discontinuity identification). (2) Even though EEG measurements accurately and very sensitively record the onset of an epileptic event or seizure, they are, from the perspective of understanding the internal initiation and localisation, of limited utility. They only record neuronal activity in the cortical (surface layer) neurons of the brain, which is a direct reflection of the type of electrical activity they have been designed to record. 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The sphynx's new riddle : how to relate the canonical formula of myth to quantum interaction

We introduce Claude Lévi Strauss' canonical formula (CF), an attempt to rigorously formalise the general narrative structure of myth. This formula utilises the Klein group as its basis, but a recent work draws attention to its natural quaternion form, which opens up the possibility that it may require a quantum inspired interpretation. We present the CF in a form that can be understood by a non-anthropological audience, using the formalisation of a key myth (that of Adonis) to draw attention to its mathematical structure. The future potential formalisation of mythological structure within a quantum inspired framework is proposed and discussed, with a probabilistic interpretation further generalising the formula