Adams-Type Methods for the Numerical Solution of Stochastic Ordinary Differential Equations

Stochastic differential equations (SDEs) arise fi om physical systems where the parameters describing the system can only be estimated or are subject to noise. There has been much work done recently on developing numerical methods for solving SDEs. This paper will focus on stability issues and variable stepsize implementation techniques for numerically solving SDEs effectively. (C) 2000 Elsevier Science B.V. All rights reserved.

Stochastic linear multistep methods for the simulation of chemical kinetics

In this paper, we introduce the Stochastic Adams-Bashforth (SAB) and Stochastic Adams-Moulton (SAM) methods as an extension of the tau-leaping framework to past information. Using the theta-trapezoidal tau-leap method of weak order two as a starting procedure, we show that the k-step SAB method with k >= 3 is order three in the mean and correlation, while a predictor-corrector implementation of the SAM method is weak order three in the mean but only order one in the correlation. These convergence results have been derived analytically for linear problems and successfully tested numerically for both linear and non-linear systems. A series of additional examples have been implemented in order to demonstrate the efficacy of this approach.

The IFITM5 mutation c.-14C > T results in an elongated transcript expressed in human bone; And causes varying phenotypic severity of osteogenesis imperfecta type V

Background The genetic mutation resulting in osteogenesis imperfecta (OI) type V was recently characterised as a single point mutation (c.-14C > T) in the 5' untranslated region (UTR) of IFITM5, a gene encoding a transmembrane protein with expression restricted to skeletal tissue. This mutation creates an alternative start codon and has been shown in a eukaryotic cell line to result in a longer variant of IFITM5, but its expression has not previously been demonstrated in bone from a patient with OI type V. Methods Sanger sequencing of the IFITM5 5' UTR was performed in our cohort of subjects with a clinical diagnosis of OI type V. Clinical data was collated from referring clinicians. RNA was extracted from a bone sample from one patient and Sanger sequenced to determine expression of wild-type and mutant IFITM5. Results: All nine subjects with OI type V were heterozygous for the c.-14C > T IFITM5 mutation. Clinically, there was heterogeneity in phenotype, particularly in the manifestation of bone fragility amongst subjects. Both wild-type and mutant IFITM5 mRNA transcripts were present in bone. Conclusions The c.-14C > T IFITM5 mutation does not result in an RNA-null allele but is expressed in bone. Individuals with identical mutations in IFITM5 have highly variable phenotypic expression, even within the same family.

Risedronate in adults with osteogenesis imperfecta type I: Increased bone mineral density and decreased bone turnover, but high fracture rate persists

Summary Bisphosphonates can increase bone mineral density (BMD) in children with osteogenesis imperfecta (OI). In this study of adults with OI type I, risedronate increased BMD at lumbar spine (but not total hip) and decreased bone turnover. However, the fracture rate in these patients remained high. Introduction Intravenous bisphosphonates given to children with OI can increase BMD and reduce fracture incidence. Oral and/or intravenous bisphosphonates may have similar effects in adults with OI. We completed an observational study of the effect of risedronate in adults with OI type I. Methods Thirty-two adults (mean age, 39 years) with OI type I were treated with risedronate (total dose, 35 mg weekly) for 24 months. Primary outcome measures were BMD changes at lumbar spine (LS) and total hip (TH). Secondary outcome measures were fracture incidence, bone pain, and change in bone turnover markers (serum procollagen type I aminopropeptide (P1NP) and bone ALP). A meta-analysis of published studies of oral bisphosphonates in adults and children with OI was performed. Results Twenty-seven participants (ten males and seventeen females) completed the study. BMD increased at LS by 3.9% (0.815 vs. 0.846 g/cm 2, p=0.007; mean Z-score, -1.93 vs. -1.58, p=0.002), with no significant change at TH. P1NP fell by 37% (p=0.00041), with no significant change in bone ALP (p=0.15). Bone pain did not change significantly (p=0.6). Fracture incidence remained high, with 25 clinical fractures and 10 major fractures in fourteen participants (0.18 major fractures per person per year), with historical data of 0.12 fractures per person per year. The meta-analysis did not demonstrate a significant difference in fracture incidence in patients with OI treated with oral bisphosphonates. Conclusions Risedronate in adults with OI type I results in modest but significant increases in BMD at LS, and decreased bone turnover. However, this may be insufficient to make a clinically significant difference to fracture incidence.

Oral fingolimod for relapsing-remitting multiple sclerosis

Background: Most people with multiple sclerosis have the relapsing-remitting type. Objective/methods: The objective was to evaluate two clinical trials of fingolimod in relapsing multiple sclerosis. Results: FREEDOMS (FTY720 Research Evaluation Effects of Daily Oral therapy in Multiple Sclerosis), a Phase III placebo-controlled trial, showed that fingolimod (0.5 or 1.25 mg) reduced the relapse rate and disability in multiple sclerosis, compared to placebo. Fingolimod (0.5 or 1.25 mg) has been compared to interferon β-1a in a Phase III clinical trial (TRANSFORMS; Trial Assessing Injectable Interferon versus FTY720 Oral in Relapsing-Remitting Multiple Sclerosis) and shown to be more efficacious than interferon β-1a in reducing relapse rates. However, fingolimod did increase the risk of infections and skin cancers. Conclusions: Only the lower dose of fingolimod (0.5 mg), which possibly has less toxicity, should be considered for prevention of relapses in relapsing-remitting multiple sclerosis.

Missing in space: An evaluation of imputation methods for missing data in spatial analysis of risk factors for type II diabetes

Background Spatial analysis is increasingly important for identifying modifiable geographic risk factors for disease. However, spatial health data from surveys are often incomplete, ranging from missing data for only a few variables, to missing data for many variables. For spatial analyses of health outcomes, selection of an appropriate imputation method is critical in order to produce the most accurate inferences. Methods We present a cross-validation approach to select between three imputation methods for health survey data with correlated lifestyle covariates, using as a case study, type II diabetes mellitus (DM II) risk across 71 Queensland Local Government Areas (LGAs). We compare the accuracy of mean imputation to imputation using multivariate normal and conditional autoregressive prior distributions. Results Choice of imputation method depends upon the application and is not necessarily the most complex method. Mean imputation was selected as the most accurate method in this application. Conclusions Selecting an appropriate imputation method for health survey data, after accounting for spatial correlation and correlation between covariates, allows more complete analysis of geographic risk factors for disease with more confidence in the results to inform public policy decision-making.

Cyclic plastic deformation characteristics of subgrade under moving train wheel load

Cyclic plastic deformation of subgrade and other engineered layers is generally not taken into account in the design of railway bridge transition zones, although the plastic deformation is the governing factor of frequent track deterioration. Actual stress behavior of fine grained subgrade/embankment layers under train traffic is, however, difficult to replicate using the conventional laboratory test apparatus and techniques. A new type of torsional simple shear apparatus, known as multi-ring shear apparatus, was therefore developed to evaluate the actual stress state and the corresponding cyclic plastic deformation characteristics of subgrade materials under moving wheel load conditions. Multi-ring shear test results has been validated using a theoretical model test results; the capability of the multi-ring shear apparatus for replicating the cyclic plastic deformation characteristics of subgrade under moving train wheel load conditions is thus established. This paper describes the effects of principal stress rotation (PSR) of the subgrade materials to the cyclic plastic deformation in a railroad and impacts of testing methods in evaluating the influence of principal stress rotation to the track deterioration of rail track.

Sound radiation characteristics of a box-type structure

The finite element and boundary element methods are employed in this study to investigate the sound radiation characteristics of a box-type structure. It has been shown [T.R. Lin, J. Pan, Vibration characteristics of a box-type structure, Journal of Vibration and Acoustics, Transactions of ASME 131 (2009) 031004-1–031004-9] that modes of natural vibration of a box-type structure can be classified into six groups according to the symmetry properties of the three panel pairs forming the box. In this paper, we demonstrate that such properties also reveal information about sound radiation effectiveness of each group of modes. The changes of radiation efficiencies and directivity patterns with the wavenumber ratio (the ratio between the acoustic and the plate bending wavenumbers) are examined for typical modes from each group. Similar characteristics of modal radiation efficiencies between a box structure and a corresponding simply supported panel are observed. The change of sound radiation patterns as a function of the wavenumber ratio is also illustrated. It is found that the sound radiation directivity of each box mode can be correlated to that of elementary sound sources (monopole, dipole, etc.) at frequencies well below the critical frequency of the plates of the box. The sound radiation pattern on the box surface also closely related to the vibration amplitude distribution of the box structure at frequencies above the critical frequency. In the medium frequency range, the radiated sound field is dominated by the edge vibration pattern of the box. The radiation efficiency of all box modes reaches a peak at frequencies above the critical frequency, and gradually approaches unity at higher frequencies.

Is liraglutide or exenatide better in type 2 diabetes?

Background: Subjects with type 2 diabetes have high circulating levels of glucose. Glucagon-like peptide-1 (GLP-1) is an intestinal hormone that has a major role in glucose homeostasis. Exenatide and liraglutide are both agonists at the GLP-1 receptor, and are effective at reducing circulating glucose levels (measured as HbA1c levels), but they have not been compared. Objectives/methods: This evaluation is of a clinical trial comparing liraglutide once a day with exenatide twice a day in subjects with type 2 diabetes. Results: In the Liraglutide Effect and Action in Diabetes (LEAD)-6 trial, subcutaneous liraglutide 1.8 mg once a day was compared with exenatide 10 μg twice a day. The primary efficacy outcome was change in HbA1c levels, and this was significantly greater with liraglutide (1.12%) than with exenatide (0.79%). Liraglutide and exenatide had similar small abilities to reduce body weight, blood pressure and LDL-cholesterol. Conclusions: Liraglutide was more effective than exenatide for overall glycaemic control in subjects with type 2 diabetes. However, this is only true for the preparations and doses tested, that is liraglutide 1.8 mg once weekly and exenatide 10 μg b.i.d., and may not apply when the comparison is undertaken with the new longer-lasting preparation of exenatide once weekly.

Experimental and theoretical studies of the redox potentials of cyclic nitroxides

The redox potentials of 25 cyclic nitroxides from four different structural classes (pyrrolidine, piperidine, isoindoline, and azaphenalene) were determined experimentally by cyclic voltammetry in acetonitrile, and also via high-level ab initio molecular orbital calculations. It is shown that the potentials are influenced by the type of ring system, ring substituents and/or groups surrounding the radical moiety. For the pyrrolidine, piperidine, and isoindolines there is excellent agreement (mean absolute deviation of 0.05 V) between the calculated and experimental oxidation potentials; for the azaphenalenes, however, there is an extraordinary discrepancy (mean absolute deviation of 0.60 V), implying that their one-electron oxidation might involve additional processes not considered in the theoretical calculations. This recently developed azaphenalene class of nitroxide represents a new variant of a nitroxide ring fused to an aromatic system and details of the synthesis of five derivatives involving differing aryl substitution are also presented.

The impact of delayed blood centrifuging, choice of collection tube, and type of assay on 25-hydroxyvitamin D concentrations

Studies have examined the associations between cancers and circulating 25-hydroxyvitamin D [25(OH)D], but little is known about the impact of different laboratory practices on 25(OH)D concentrations. We examined the potential impact of delayed blood centrifuging, choice of collection tube, and type of assay on 25(OH)D concentrations. Blood samples from 20 healthy volunteers underwent alternative laboratory procedures: four centrifuging times (2, 24, 72, and 96 h after blood draw); three types of collection tubes (red top serum tube, two different plasma anticoagulant tubes containing heparin or EDTA); and two types of assays (DiaSorin radioimmunoassay [RIA] and chemiluminescence immunoassay [CLIA/LIAISON®]). Log-transformed 25(OH)D concentrations were analyzed using the generalized estimating equations (GEE) linear regression models. We found no difference in 25(OH)D concentrations by centrifuging times or type of assay. There was some indication of a difference in 25(OH)D concentrations by tube type in CLIA/LIAISON®-assayed samples, with concentrations in heparinized plasma (geometric mean, 16.1 ng ml−1) higher than those in serum (geometric mean, 15.3 ng ml−1) (p = 0.01), but the difference was significant only after substantial centrifuging delays (96 h). Our study suggests no necessity for requiring immediate processing of blood samples after collection or for the choice of a tube type or assay.

Driving-related eye and head movements are changed by the type of presbyopic correction

Purpose: To investigate whether wearing different presbyopic vision corrections alters the pattern of eye and head movements when viewing dynamic driving-related traffic scenes. Methods: Participants included 20 presbyopes (mean age: 56±5.7 years) who had no experience of wearing presbyopic vision corrections (i.e. all were single vision wearers). Eye and head movements were recorded while wearing five different vision corrections: single vision lenses (SV), progressive addition spectacle lenses (PALs), bifocal spectacle lenses (BIF), monovision (MV) and multifocal contact lenses (MTF CL) in random order. Videotape recordings of traffic scenes of suburban roads and expressways (with edited targets) were presented as dynamic driving-related stimuli and digital numeric display panels included as near visual stimuli (simulating speedometer and radio). Eye and head movements were recorded using the faceLAB™ system and the accuracy of target identification was also recorded. Results: The magnitude of eye movements while viewing the driving-related traffic scenes was greater when wearing BIF and PALs than MV and MTF CL (p≤0.013). The magnitude of head movements was greater when wearing SV, BIF and PALs than MV and MTF CL (p<0.0001) and the number of saccades was significantly higher for BIF and PALs than MV (p≤0.043). Target recognition accuracy was poorer for all vision corrections when the near stimulus was located at eccentricities inferiorly and to the left, rather than directly below the primary position of gaze (p=0.008), and PALs gave better performance than MTF CL (p=0.043). Conclusions: Different presbyopic vision corrections alter eye and head movement patterns. In particular, the larger magnitude of eye and head movements and greater number of saccades associated with the spectacle presbyopic corrections, may impact on driving performance.

Self-efficacy, outcome expectations and self-care behaviour in people with type 2 diabetes in Taiwan

Aims. To explore differences in self-care behaviour according to demographic and illness characteristics; and relationships among self-care behaviour and demographic and illness characteristics, efficacy expectations and outcome expectations of people with type 2 diabetes in Taiwan. Background. Most people with diabetes do not control their disease appropriately in Taiwan. Enhanced self-efficacy towards managing diseases can be an effective way of improving disease control as proposed by the self-efficacy model which provides a useful framework for understanding adherence to self-care behaviours. Design and methods. The sample comprised 145 patients with type 2 diabetes aged 30 years or more from diabetes outpatient clinics in Taipei. Data were collected using a self-administered questionnaire for this study. One-way anova, t-tests, Pearson product moment correlation and hierarchical regression were analysed for the study. Results. Significant differences were found: between self-care behaviour and complications (t = −2·52, p < 0·01) and patient education (t = −1·96, p < 0·05). Self-care behaviour was significantly and positively correlated with duration of diabetes (r = 0·36, p < 0·01), efficacy expectations (r = 0·54, p < 0·01) and outcome expectations (r = 0·44, p < 0·01). A total of 39·1% of variance in self-care behaviour can be explained by duration of diabetes, efficacy expectations and outcome expectations. Conclusions. Findings support the use of the self-efficacy model as a framework for understanding adherence to self-care behaviour. Relevance to clinical practice. Using self-efficacy theory when designing patient education interventions for people with type 2 diabetes will enhance self-management routines and assist in reducing major complications in the future.

Design methods of rhombic tensegrity structures

As a special type of novel flexible structures, tensegrity holds promise for many potential applications in such fields as materials science, biomechanics, civil and aerospace engineering. Rhombic systems are an important class of tensegrity structures, in which each bar constitutes the longest diagonal of a rhombus of four strings. In this paper, we address the design methods of rhombic structures based on the idea that many tensegrity structures can be constructed by assembling one-bar elementary cells. By analyzing the properties of rhombic cells, we first develop two novel schemes, namely, direct enumeration scheme and cell-substitution scheme. In addition, a facile and efficient method is presented to integrate several rhombic systems into a larger tensegrity structure. To illustrate the applications of these methods, some novel rhombic tensegrity structures are constructed.

Novel analytical and numerical methods for solving fractional dynamical systems

During the past three decades, the subject of fractional calculus (that is, calculus of integrals and derivatives of arbitrary order) has gained considerable popularity and importance, mainly due to its demonstrated applications in numerous diverse and widespread fields in science and engineering. For example, fractional calculus has been successfully applied to problems in system biology, physics, chemistry and biochemistry, hydrology, medicine, and finance. In many cases these new fractional-order models are more adequate than the previously used integer-order models, because fractional derivatives and integrals enable the description of the memory and hereditary properties inherent in various materials and processes that are governed by anomalous diffusion. Hence, there is a growing need to find the solution behaviour of these fractional differential equations. However, the analytic solutions of most fractional differential equations generally cannot be obtained. As a consequence, approximate and numerical techniques are playing an important role in identifying the solution behaviour of such fractional equations and exploring their applications. The main objective of this thesis is to develop new effective numerical methods and supporting analysis, based on the finite difference and finite element methods, for solving time, space and time-space fractional dynamical systems involving fractional derivatives in one and two spatial dimensions. A series of five published papers and one manuscript in preparation will be presented on the solution of the space fractional diffusion equation, space fractional advectiondispersion equation, time and space fractional diffusion equation, time and space fractional Fokker-Planck equation with a linear or non-linear source term, and fractional cable equation involving two time fractional derivatives, respectively. One important contribution of this thesis is the demonstration of how to choose different approximation techniques for different fractional derivatives. Special attention has been paid to the Riesz space fractional derivative, due to its important application in the field of groundwater flow, system biology and finance. We present three numerical methods to approximate the Riesz space fractional derivative, namely the L1/ L2-approximation method, the standard/shifted Gr¨unwald method, and the matrix transform method (MTM). The first two methods are based on the finite difference method, while the MTM allows discretisation in space using either the finite difference or finite element methods. Furthermore, we prove the equivalence of the Riesz fractional derivative and the fractional Laplacian operator under homogeneous Dirichlet boundary conditions – a result that had not previously been established. This result justifies the aforementioned use of the MTM to approximate the Riesz fractional derivative. After spatial discretisation, the time-space fractional partial differential equation is transformed into a system of fractional-in-time differential equations. We then investigate numerical methods to handle time fractional derivatives, be they Caputo type or Riemann-Liouville type. This leads to new methods utilising either finite difference strategies or the Laplace transform method for advancing the solution in time. The stability and convergence of our proposed numerical methods are also investigated. Numerical experiments are carried out in support of our theoretical analysis. We also emphasise that the numerical methods we develop are applicable for many other types of fractional partial differential equations.