A preconditioned Lanczos method for space-fractional reaction-diffusion equations on two-dimensional unstructured meshes

We consider a two-dimensional space-fractional reaction diffusion equation with a fractional Laplacian operator and homogeneous Neumann boundary conditions. The finite volume method is used with the matrix transfer technique of Ilić et al. (2006) to discretise in space, yielding a system of equations that requires the action of a matrix function to solve at each timestep. Rather than form this matrix function explicitly, we use Krylov subspace techniques to approximate the action of this matrix function. Specifically, we apply the Lanczos method, after a suitable transformation of the problem to recover symmetry. To improve the convergence of this method, we utilise a preconditioner that deflates the smallest eigenvalues from the spectrum. We demonstrate the efficiency of our approach for a fractional Fisher’s equation on the unit disk.

On the prediction of simultaneous inbreeding coefficients at multiple loci

A new deterministic method for predicting simultaneous inbreeding coefficients at three and four loci is presented. The method involves calculating the conditional probability of IBD (identical by descent) at one locus given IBD at other loci, and multiplying this probability by the prior probability of the latter loci being simultaneously IBD. The conditional probability is obtained applying a novel regression model, and the prior probability from the theory of digenic measures of Weir and Cockerham. The model was validated for a finite monoecious population mating at random, with a constant effective population size, and with or without selfing, and also for an infinite population with a constant intermediate proportion of selfing. We assumed discrete generations. Deterministic predictions were very accurate when compared with simulation results, and robust to alternative forms of implementation. These simultaneous inbreeding coefficients were more sensitive to changes in effective population size than in marker spacing. Extensions to predict simultaneous inbreeding coefficients at more than four loci are now possible.

Analysis of stream cipher based authenticated encryption schemes

Authenticated Encryption (AE) is the cryptographic process of providing simultaneous confidentiality and integrity protection to messages. This approach is more efficient than applying a two-step process of providing confidentiality for a message by encrypting the message, and in a separate pass providing integrity protection by generating a Message Authentication Code (MAC). AE using symmetric ciphers can be provided by either stream ciphers with built in authentication mechanisms or block ciphers using appropriate modes of operation. However, stream ciphers have the potential for higher performance and smaller footprint in hardware and/or software than block ciphers. This property makes stream ciphers suitable for resource constrained environments, where storage and computational power are limited. There have been several recent stream cipher proposals that claim to provide AE. These ciphers can be analysed using existing techniques that consider confidentiality or integrity separately; however currently there is no existing framework for the analysis of AE stream ciphers that analyses these two properties simultaneously. This thesis introduces a novel framework for the analysis of AE using stream cipher algorithms. This thesis analyzes the mechanisms for providing confidentiality and for providing integrity in AE algorithms using stream ciphers. There is a greater emphasis on the analysis of the integrity mechanisms, as there is little in the public literature on this, in the context of authenticated encryption. The thesis has four main contributions as follows. The first contribution is the design of a framework that can be used to classify AE stream ciphers based on three characteristics. The first classification applies Bellare and Namprempre's work on the the order in which encryption and authentication processes take place. The second classification is based on the method used for accumulating the input message (either directly or indirectly) into the into the internal states of the cipher to generate a MAC. The third classification is based on whether the sequence that is used to provide encryption and authentication is generated using a single key and initial vector, or two keys and two initial vectors. The second contribution is the application of an existing algebraic method to analyse the confidentiality algorithms of two AE stream ciphers; namely SSS and ZUC. The algebraic method is based on considering the nonlinear filter (NLF) of these ciphers as a combiner with memory. This method enables us to construct equations for the NLF that relate the (inputs, outputs and memory of the combiner) to the output keystream. We show that both of these ciphers are secure from this type of algebraic attack. We conclude that using a keydependent SBox in the NLF twice, and using two different SBoxes in the NLF of ZUC, prevents this type of algebraic attack. The third contribution is a new general matrix based model for MAC generation where the input message is injected directly into the internal state. This model describes the accumulation process when the input message is injected directly into the internal state of a nonlinear filter generator. We show that three recently proposed AE stream ciphers can be considered as instances of this model; namely SSS, NLSv2 and SOBER-128. Our model is more general than a previous investigations into direct injection. Possible forgery attacks against this model are investigated. It is shown that using a nonlinear filter in the accumulation process of the input message when either the input message or the initial states of the register is unknown prevents forgery attacks based on collisions. The last contribution is a new general matrix based model for MAC generation where the input message is injected indirectly into the internal state. This model uses the input message as a controller to accumulate a keystream sequence into an accumulation register. We show that three current AE stream ciphers can be considered as instances of this model; namely ZUC, Grain-128a and Sfinks. We establish the conditions under which the model is susceptible to forgery and side-channel attacks.

Simultaneous determination by UPLC-ESI-MS of scoparone, capillarisin, rhein, and emodin in rat urine after oral administration of Yin Chen Hao Tang preparation

A simple, sensitive, and validated method was developed for simultaneous determination of scoparone, capillarisin, rhein, and emodin in rat urine by ultra-performance liquid chromatography/electrospray ionization quadruple time-of-flight mass spectrometry (UPLC-MS). The urinary samples were analyzed on an Acquity UPLC BEH C18 1.7 microm 2.1x50 mm column. Scoparone, capillarisin, rhein, and emodin in rat urine were simultaneously analyzed with good separation. The lower limits of detection were 6.0, 9.0, 7.0, and 3.0 ng/mL, and the lower limits of quantification were 20.0, 33.0, 24.0, and 12.0 ng/mL for scoparone, capillarisin, rhein, and emodin, respectively. The intra- and inter-day precisions (RSD) were less than 9%. The intra- and inter-accuracies were found to be in the range of 94.14-104.54% for scoparone, 101.72-107.34% for capillarisin, 95.24-103.59% for rhein, and 101.32-107.82% for emodin at three concentration levels. The absolute recoveries for scoparone, capillarisin, rhein, and emodin were not less than 77.0%. The developed method has been applied to determine scoparone, capillarisin, rhein, and emodin in rat urine after oral administration of Yin Chen Hao Tang preparation, a traditional Chinese medicine formulation widely used in China for treatment of jaundice and liver disorders.

Quality evaluation of Yin Chen Hao Tang extract based on fingerprint chromatogram and simultaneous determination of five bioactive constituents

A completely validated method based on HPLC coupled with photodiode array detector (HPLC-UV) was described for evaluating and controlling quality of Yin Chen Hao Tang extract (YCHTE). First, HPLC-UV fingerprint chromatogram of YCHTE was established for preliminarily elucidating amount and chromatographic trajectory of chemical constituents in YCHTE. Second, for the first time, five mainly bioactive constituents in YCHTE were simultaneously determined based on fingerprint chromatogram for furthermore controlling the quality of YCHTE quantitatively. The developed method was applied to analyze 12 batches of YCHTE samples which consisted of herbal drugs from different places of production, showed acceptable linearity, intraday (RSD <5%), interday precision (RSD <4.80%), and accuracy (RSD <2.80%). As a result, fingerprint chromatogram determined 15 representative general fingerprint peaks, and the fingerprint chromatogram resemblances are all better than 0.9996. The contents of five analytes in different batches of YCHTE samples do not indicate significant difference. So, it is concluded that the developed HPLC-UV method is a more fully validated and complete method for evaluating and controlling the quality of YCHTE.

Simultaneous determination of 6,7-dimethylesculetin and geniposide in rat plasma and its application to pharmacokinetic studies of Yin Chen Hao Tang preparation

A method for the rapid and simultaneous determination of 6,7-dimethylesculetin (CAS 120-08-1) and geniposide (CAS 24512-63-8) in rat plasma has been developed, using validated high performance liquid chromatography (HPLC) with solid phase extraction (SPE). The HPLC analysis was performed on a commercially available column (200 mm x 4.6 mm, 5 microm) with acetonitrile-methanol-0.1% aqueous formic acid as mobile phase and the UV detection at 343 nm and 238 nm for 6,7-dimethylesculetin and geniposide, respectively. The calibration curves for 6,7-dimethylesculetin and geniposide were linear over the range 0.4-25.6 microg/mL and 1.12-71.68 microg/mL, respectively. The lower limits of quantitation were 0.40 microg/ mL and 1.12 microg/mL, and the lower limits of detection were 0.06 microg/mL and 0.09 microg/ mL, respectively. The intra-day and inter-day precision for 6,7-dimethylesculetin and geniposide were < 5%, whereas the absolute recovery percentages were > 74%. A successful application of the developed HPLC analysis was demonstrated for the pharmacokinetic study of a Traditional Chinese Medicine formula of Yin Chen Hao Tang preparation.

A novel multiplex PCR-RFLP method for simultaneous detection of the MTHFR 677 C > T, eNOS +894 G > T and - eNOS -786 T > C variants among Malaysian Malays

Background Hyperhomocysteinemia as a consequence of the MTHFR 677 C > T variant is associated with cardiovascular disease and stroke. Another factor that can potentially contribute to these disorders is a depleted nitric oxide level, which can be due to the presence of eNOS +894 G > T and eNOS −786 T > C variants that make an individual more susceptible to endothelial dysfunction. A number of genotyping methods have been developed to investigate these variants. However, simultaneous detection methods using polymerase chain reaction-restriction fragment length polymorphism (PCR-RFLP) analysis are still lacking. In this study, a novel multiplex PCR-RFLP method for the simultaneous detection of MTHFR 677 C > T and eNOS +894 G > T and eNOS −786 T > C variants was developed. A total of 114 healthy Malay subjects were recruited. The MTHFR 677 C > T and eNOS +894 G > T and eNOS −786 T > C variants were genotyped using the novel multiplex PCR-RFLP and confirmed by DNA sequencing as well as snpBLAST. Allele frequencies of MTHFR 677 C > T and eNOS +894 G > T and eNOS −786 T > C were calculated using the Hardy Weinberg equation. Methods The 114 healthy volunteers were recruited for this study, and their DNA was extracted. Primer pair was designed using Primer 3 Software version 0.4.0 and validated against the BLAST database. The primer specificity, functionality and annealing temperature were tested using uniplex PCR methods that were later combined into a single multiplex PCR. Restriction Fragment Length Polymorphism (RFLP) was performed in three separate tubes followed by agarose gel electrophoresis. PCR product residual was purified and sent for DNA sequencing. Results The allele frequencies for MTHFR 677 C > T were 0.89 (C allele) and 0.11 (T allele); for eNOS +894 G > T, the allele frequencies were 0.58 (G allele) and 0.43 (T allele); and for eNOS −786 T > C, the allele frequencies were 0.87 (T allele) and 0.13 (C allele). Conclusions Our PCR-RFLP method is a simple, cost-effective and time-saving method. It can be used to successfully genotype subjects for the MTHFR 677 C > T and eNOS +894 G > T and eNOS −786 T > C variants simultaneously with 100% concordance from DNA sequencing data. This method can be routinely used for rapid investigation of the MTHFR 677 C > T and eNOS +894 G > T and eNOS −786 T > C variants.

Identification and simultaneous analysis of harmane, harmol, isovitexin and vitexin in Passiflora incarnata extracts with a novel HLPC method

A high performance liquid chromatographic method for the simultaneous analysis of two flavonoids (iso-vitexin and vitexin), and three indole alkaloids (harmane, harmine, and harmol) was developed. This method was then utilised to quantitate levels of these five constituents in methanolic extracts of Australian Passiflora incarnata. HPLC analysis was performed using a Waters™ Novapak C18 (150 × 4 mm, 4 μm) column, with a gradient solvent system of methanol-water-acetic acid. Detection was achieved by PDA UV (254 nm) and fluorescence (excitation 254 nm, emission 414 nm), utilising the external standard method to obtain quantification.

Simultaneous determination of aldrin, dieldrin, endrin, heptachlor, and p,p'-DDT in medicinal plant extracts using a novel high performance liquid chromatography method

A high performance liquid chromatographic method for the simultaneous determination of five organochlorine pesticides (aldrin, p,p’-DDT, dieldrin, endrin, and heptachlor) was developed. The method was used to determine the levels of these pesticides in medicinal plant samples. Analysis was carried out using a Merck LiChrospher 100 RP C18 (5 μm) column with a gradient solvent system of acetonitrile-water and PDA UV detection (224 nm). Quantification was carried out by the external standard method. The limit of detection for the utilized method was below the local legal limits (ANZFA) for similar plant materials for all 5 pesticides excepting endrin. Medicinal plant extracts were further analyzed by conventional GC-ECD and GC-NPD means using SPE and GPC cleanup as required.

A simplified approach for calculating the moments of action for linear reaction-diffusion equations

The mean action time is the mean of a probability density function that can be interpreted as a critical time, which is a finite estimate of the time taken for the transient solution of a reaction-diffusion equation to effectively reach steady state. For high-variance distributions, the mean action time under-approximates the critical time since it neglects to account for the spread about the mean. We can improve our estimate of the critical time by calculating the higher moments of the probability density function, called the moments of action, which provide additional information regarding the spread about the mean. Existing methods for calculating the nth moment of action require the solution of n nonhomogeneous boundary value problems which can be difficult and tedious to solve exactly. Here we present a simplified approach using Laplace transforms which allows us to calculate the nth moment of action without solving this family of boundary value problems and also without solving for the transient solution of the underlying reaction-diffusion problem. We demonstrate the generality of our method by calculating exact expressions for the moments of action for three problems from the biophysics literature. While the first problem we consider can be solved using existing methods, the second problem, which is readily solved using our approach, is intractable using previous techniques. The third problem illustrates how the Laplace transform approach can be used to study coupled linear reaction-diffusion equations.

Prediction of muscular architecture of the rectus femoris and vastus lateralis from EMG during isometric contractions in soccer players

Objectives The purpose of the study was to establish regression equations that could be used to predict muscle thickness and pennation angle at different intensities from electromyography (EMG) based measures of muscle activation during isometric contractions. Design Cross-sectional study. Methods Simultaneous ultrasonography and EMG were used to measure pennation angle, muscle thickness and muscle activity of the rectus femoris and vastus lateralis muscles, respectively, during graded isometric knee extension contractions performed on a Cybex dynamometer. Data form fifteen male soccer players were collected in increments of approximately 25% intensity of the maximum voluntary contraction (MVC) ranging from rest to MVC. Results There was a significant correlation (P < 0.05) between ultrasound predictors and EMG measures for the muscle thickness of rectus femoris with an R2 value of 0.68. There was no significant correlation (P > 0.05) between ultrasound pennation angle for the vastus lateralis predictors for EMG muscle activity with an R2 value of 0.40. Conclusions The regression equations can be used to characterise muscle thickness more accurately and to determine how it changes with contraction intensity, this provides improved estimates of muscle force when using musculoskeletal models.

Structure-preserving Runge-Kutta methods for stochastic Hamiltonian equations with additive noise

There has been considerable recent work on the development of energy conserving one-step methods that are not symplectic. Here we extend these ideas to stochastic Hamiltonian problems with additive noise and show that there are classes of Runge-Kutta methods that are very effective in preserving the expectation of the Hamiltonian, but care has to be taken in how the Wiener increments are sampled at each timestep. Some numerical simulations illustrate the performance of these methods.

Flexural capacity of hollow flange beams

The hollow flange beam (HFB) is a unique cold-formed steel section developed in Australia for use as a flexural member. Research has identified that the HFB section's flexural capacity for intermediate span members is limited by lateral distortional buckling, which is characterized by simultaneous lateral deflection, twist, and web distortion. This buckling behaviour is mainly due to the unique geometry of the section, comprising two torsionally stiff triangular flanges connected by a slender web. This paper presents a finite element analytical model suitable for non-linear analysis of HFB flexural members. The model includes all significant effects that may influence the ultimate capacity of such members, including material inelasticity, local buckling, member instability, web distortion, residual stresses, and geometric imperfections. It was found to accurately predict both the elastic lateral distortional buckling moments and the ultimate capacities of HFB flexural members, and was therefore used in the development of design curves and suitable design procedures.

Experimental studies of hollow flange channel beams subject to combined bending and shear actions

This paper presents the details of an experimental study of a cold-formed steel hollow flange channel beam known as LiteSteel Beam (LSB) subject to combined bending and shear actions. The LSB sections are produced by a patented manufacturing process involving simultaneous cold-forming and electric resistance welding. Due to the geometry of the LSB, as well as its unique residual stress characteristics and initial geometric imperfections resultant of manufacturing processes, much of the existing research for common cold-formed steel sections is not directly applicable to LSB. Experimental and numerical studies have been carried out to evaluate the behaviour and design of LSBs subject to pure bending actions and predominant shear actions. To date, however, no investigation has been conducted into the strength of LSB sections under combined bending and shear actions. Combined bending and shear is especially prevalent at the supports of continuous span and cantilever beams, where the interaction of high shear force and bending moment can reduce the capacity of a section to well below that for the same section subject only to pure shear or moment. Hence experimental studies were conducted to assess the combined bending and shear behaviour and strengths of LSBs. Eighteen tests were conducted and the results were compared with current AS/NZS 4600 and AS 4100 design rules. AS/NZS 4600 design rules were shown to grossly underestimate the combined bending and shear capacities of LSBs and hence two lower bound design equations were proposed based on experimental results. Use of these equations will significantly improve the confidence and cost-effectiveness of designing LSBs for combined bending and shear actions.

Development and validation of anthropometric prediction equations for estimation of lean body mass and appendicular lean soft tissue in Indian men and women

Lean body mass (LBM) and muscle mass remains difficult to quantify in large epidemiological studies due to non-availability of inexpensive methods. We therefore developed anthropometric prediction equations to estimate the LBM and appendicular lean soft tissue (ALST) using dual energy X-ray absorptiometry (DXA) as a reference method. Healthy volunteers (n= 2220; 36% females; age 18-79 y) representing a wide range of body mass index (14-44 kg/m2) participated in this study. Their LBM including ALST was assessed by DXA along with anthropometric measurements. The sample was divided into prediction (60%) and validation (40%) sets. In the prediction set, a number of prediction models were constructed using DXA measured LBM and ALST estimates as dependent variables and a combination of anthropometric indices as independent variables. These equations were cross-validated in the validation set. Simple equations using age, height and weight explained > 90% variation in the LBM and ALST in both men and women. Additional variables (hip and limb circumferences and sum of SFTs) increased the explained variation by 5-8% in the fully adjusted models predicting LBM and ALST. More complex equations using all the above anthropometric variables could predict the DXA measured LBM and ALST accurately as indicated by low standard error of the estimate (LBM: 1.47 kg and 1.63 kg for men and women, respectively) as well as good agreement by Bland Altman analyses. These equations could be a valuable tool in large epidemiological studies assessing these body compartments in Indians and other population groups with similar body composition.