A preconditioned numerical solver for stiff nonlinear reaction-diffusion equations with fractional Laplacians that avoids dense matrices

The numerical solution of fractional partial differential equations poses significant computational challenges in regard to efficiency as a result of the spatial nonlocality of the fractional differential operators. The dense coefficient matrices that arise from spatial discretisation of these operators mean that even one-dimensional problems can be difficult to solve using standard methods on grids comprising thousands of nodes or more. In this work we address this issue of efficiency for one-dimensional, nonlinear space-fractional reaction–diffusion equations with fractional Laplacian operators. We apply variable-order, variable-stepsize backward differentiation formulas in a Jacobian-free Newton–Krylov framework to advance the solution in time. A key advantage of this approach is the elimination of any requirement to form the dense matrix representation of the fractional Laplacian operator. We show how a banded approximation to this matrix, which can be formed and factorised efficiently, can be used as part of an effective preconditioner that accelerates convergence of the Krylov subspace iterative solver. Our approach also captures the full contribution from the nonlinear reaction term in the preconditioner, which is crucial for problems that exhibit stiff reactions. Numerical examples are presented to illustrate the overall effectiveness of the solver.

A new single-phase frequency adaptive Phase-Locked Loop (PLL) for harmonic measurement

The paper presents an improved Phase-Locked Loop (PLL) for measuring the fundamental frequency and selective harmonic content of a distorted signal. This information can be used by grid interfaced devices and harmonic compensators. The single-phase structure is based on the Synchronous Reference Frame (SRF) PLL. The proposed PLL needs only a limited number of harmonic stages by incorporating Moving Average Filters (MAF) for eliminating the undesired harmonic content at each stage. The frequency dependency of MAF in effective filtering of undesired harmonics is also dealt with by a proposed method for adaptation to frequency variations of input signal. The method is suitable for high sampling rates and a wide frequency measurement range. Furthermore, an extended model of this structure is proposed which includes the response to both the frequency and phase angle variations. The proposed algorithm is simulated and verified using Hardware-in-the-Loop (HIL) testing.

Fourier spectral methods for fractional-in-space reaction-diffusion equations

Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction-diffusion equations described by the fractional Laplacian in bounded rectangular domains ofRn. The main advantages of the proposed schemes is that they yield a fully diagonal representation of the fractional operator, with increased accuracy and efficiency when compared to low-order counterparts, and a completely straightforward extension to two and three spatial dimensions. Our approach is illustrated by solving several problems of practical interest, including the fractional Allen–Cahn, FitzHugh–Nagumo and Gray–Scott models, together with an analysis of the properties of these systems in terms of the fractional power of the underlying Laplacian operator.

Increasing functional variability in the preparatory phase of the takeoff improves elite springboard diving performance

PURPOSE: Previous research demonstrating that specific performance outcome goals can be achieved in different ways is functionally significant for springboard divers whose performance environment can vary extensively. This body of work raises questions about the traditional approach of balking (terminating the takeoff) by elite divers aiming to perform only identical, invariant movement patterns during practice. METHOD: A 12-week training program (2 times per day; 6.5 hr per day) was implemented with 4 elite female springboard divers to encourage them to adapt movement patterns under variable takeoff conditions and complete intended dives, rather than balk. RESULTS: Intraindividual analyses revealed small increases in variability in the board-work component of each diver's pretraining and posttraining program reverse-dive takeoffs. No topological differences were observed between movement patterns of dives completed pretraining and posttraining. Differences were noted in the amount of movement variability under different training conditions (evidenced by higher normalized root mean square error indexes posttraining). An increase in the number of completed dives (from 78.91%-86.84% to 95.59%-99.29%) and a decrease in the frequency of balked takeoffs (from 13.16%-19.41% to 0.63%-4.41%) showed that the elite athletes were able to adapt their behaviors during the training program. These findings coincided with greater consistency in the divers' performance during practice as scored by qualified judges. CONCLUSION: Results suggested that on completion of training, athletes were capable of successfully adapting their movement patterns under more varied takeoff conditions to achieve greater consistency and stability of performance outcomes.

Fractional diffusion models of cardiac electrical propagation: Role of structural heterogeneity in dispersion of repolarization

Impulse propagation in biological tissues is known to be modulated by structural heterogeneity. In cardiac muscle, improved understanding on how this heterogeneity influences electrical spread is key to advancing our interpretation of dispersion of repolarization. We propose fractional diffusion models as a novel mathematical description of structurally heterogeneous excitable media, as a means of representing the modulation of the total electric field by the secondary electrical sources associated with tissue inhomogeneities. Our results, analysed against in vivo human recordings and experimental data of different animal species, indicate that structural heterogeneity underlies relevant characteristics of cardiac electrical propagation at tissue level. These include conduction effects on action potential (AP) morphology, the shortening of AP duration along the activation pathway and the progressive modulation by premature beats of spatial patterns of dispersion of repolarization. The proposed approach may also have important implications in other research fields involving excitable complex media.

Proteogenomics of selective susceptibility to endotoxin using circulating acute phase biomarkers and bioassay development in sheep: a review

Scientists have injected endotoxin into animals to investigate and understand various pathologies and novel therapies for several decades. Recent observations have shown that there is selective susceptibility to Escherichia coli lipopolysaccharide (LPS) endotoxin in sheep, despite having similar breed characteristics. The reason behind this difference is unknown, and has prompted studies aiming to explain the variation by proteogenomic characterisation of circulating acute phase biomarkers. It is hypothesised that genetic trait, biochemical, immunological and inflammation marker patterns contribute in defining and predicting mammalian response to LPS. This review discusses the effects of endotoxin and host responses, genetic basis of innate defences, activation of the acute phase response (APR) following experimental LPS challenge, and the current approaches employed in detecting novel biomarkers including acute phase proteins (APP) and micro-ribonucleic acids (miRNAs) in serum or plasma. miRNAs are novel targets for elucidating molecular mechanisms of disease because of their differential expression during pathological, and in healthy states. Changes in miRNA profiles during a disease challenge may be reflected in plasma. Studies show that gel-based two-dimensional electrophoresis (2-DE) coupled with either matrix-assisted laser desorption/ionisation time-of-flight mass spectrometry (MALDI-TOF MS) or liquid chromatography-mass spectrometry (LC-MS/MS) are currently the most used methods for proteome characterisation. Further evidence suggests that proteomic investigations are preferentially shifting from 2-DE to non-gel based LC-MS/MS coupled with data extraction by sequential window acquisition of all theoretical fragment-ion spectra (SWATH) approaches that are able to identify a wider range of proteins. Enzyme-linked immunosorbent assay (ELISA), quantitative real-time polymerase chain reaction (qRT-PCR), and most recently proteomic methods have been used to quantify low abundance proteins such as cytokines. qRT-PCR and next generation sequencing (NGS) are used for the characterisation of miRNA. Proteogenomic approaches for detecting APP and novel miRNA profiling are essential in understanding the selective resistance to endotoxin in sheep. The results of these methods could help in understanding similar pathology in humans. It might also be helpful in the development of physiological and diagnostic screening assays for determining experimental inclusion and endpoints, and in clinical trials in future

A phase 1b study of placenta-derived mesenchymal stromal cells in patients with idiopathic pulmonary fibrosis

BACKGROUND AND OBJECTIVE: Idiopathic pulmonary fibrosis (IPF) is a degenerative disease characterized by fibrosis following failed epithelial repair. Mesenchymal stromal cells (MSC), a key component of the stem cell niche in bone marrow and possibly other organs including lung, have been shown to enhance epithelial repair and are effective in preclinical models of inflammation-induced pulmonary fibrosis, but may be profibrotic in some circumstances. METHODS: In this single centre, non-randomized, dose escalation phase 1b trial, patients with moderately severe IPF (diffusing capacity for carbon monoxide (DLCO ) ≥ 25% and forced vital capacity (FVC) ≥ 50%) received either 1 × 10(6) (n = 4) or 2 × 10(6) (n = 4) unrelated-donor, placenta-derived MSC/kg via a peripheral vein and were followed for 6 months with lung function (FVC and DLCO ), 6-min walk distance (6MWD) and computed tomography (CT) chest. RESULTS: Eight patients (4 female, aged 63.5 (57-75) years) with median (interquartile range) FVC 60 (52.5-74.5)% and DLCO 34.5 (29.5-40)% predicted were treated. Both dose schedules were well tolerated with only minor and transient acute adverse effects. MSC infusion was associated with a transient (1% (0-2%)) fall in SaO2 after 15 min, but no changes in haemodynamics. At 6 months FVC, DLCO , 6MWD and CT fibrosis score were unchanged compared with baseline. There was no evidence of worsening fibrosis. CONCLUSIONS: Intravenous MSC administration is feasible and has a good short-term safety profile in patients with moderately severe IPF.

Manufacturing and use of human placenta-derived mesenchymal stromal cells for phase I clinical trials: Establishment and evaluation of a protocol

Background/Aim. Mesenchymal stromal cells (MSCs) have been utilised in many clinical trials as an experimental treatment in numerous clinical settings. Bone marrow remains the traditional source tissue for MSCs but is relatively hard to access in large volumes. Alternatively, MSCs may be derived from other tissues including the placenta and adipose tissue. In an initial study no obvious differences in parameters such as cell surface phenotype, chemokine receptor display, mesodermal differentiation capacity or immunosuppressive ability, were detected when we compared human marrow derived- MSCs to human placenta-derived MSCs. The aim of this study was to establish and evaluate a protocol and related processes for preparation placenta-derived MSCs for early phase clinical trials. Methods. A full-term placenta was taken after delivery of the baby as a source of MSCs. Isolation, seeding, incubation, cryopreservation of human placentaderived MSCs and used production release criteria were in accordance with the complex regulatory requirements applicable to Code of Good Manufacturing Practice manufacturing of ex vivo expanded cells. Results. We established and evaluated instructions for MSCs preparation protocol and gave an overview of the three clinical areas application. In the first trial, MSCs were co-transplanted iv to patient receiving an allogeneic cord blood transplant as therapy for treatmentrefractory acute myeloid leukemia. In the second trial, MSCs were administered iv in the treatment of idiopathic pulmonary fibrosis and without serious adverse effects. In the third trial, MSCs were injected directly into the site of tendon damage using ultrasound guidance in the treatment of chronic refractory tendinopathy. Conclusion. Clinical trials using both allogeneic and autologous cells demonstrated MSCs to be safe. A described protocol for human placenta-derived MSCs is appropriate for use in a clinical setting, relatively inexpensive and can be relatively easily adjusted to a different set of regulatory requirements, as applicable to early phase clinical trials.

Determination of tricyclazole in water using solid phase extraction and liquid chromatography

A method for determination of tricyclazole in water using solid phase extraction and high performance liquid chromatography (HPLC) with UV detection at 230nm and a mobile phase of acetonitrile:water (20:80, v/v) was developed. A performance comparison between two types of solid phase sorbents, the C18 sorbent of Supelclean ENVI-18 cartridge and the styrene-divinyl benzene copolymer sorbent of Sep-Pak PS2-Plus cartridge was conducted. The Sep-Pak PS2-Plus cartridges were found more suitable for extracting tricyclazole from water samples than the Supelclean ENVI-18 cartridges. For this cartridge, both methanol and ethyl acetate produced good results. The method was validated with good linearity and with a limit of detection of 0.008gL-1 for a 500-fold concentration through the SPE procedure. The recoveries of the method were stable at 80% and the precision was from 1.1-6.0% within the range of fortified concentrations. The validated method was also applied to measure the concentrations of tricyclazole in real paddy water.

Functional localization of the human color center by decreased water displacement using diffusion-weighted fMRI

Introduction Decreased water displacement following increased neural activity has been observed using diffusion-weighted functional MRI (DfMRI) at high b-values. The physiological mechanisms underlying the diffusion signal change may be unique from the standard blood oxygenation level-dependent (BOLD) contrast and closer to the source of neural activity. Whether DfMRI reflects neural activity more directly than BOLD outside the primary cerebral regions remains unclear. Methods Colored and achromatic Mondrian visual stimuli were statistically contrasted to functionally localize the human color center Area V4 in neurologically intact adults. Spatial and temporal properties of DfMRI and BOLD activation were examined across regions of the visual cortex. Results At the individual level, DfMRI activation patterns showed greater spatial specificity to V4 than BOLD. The BOLD activation patterns were more prominent in the primary visual cortex than DfMRI, where activation was localized to the ventral temporal lobe. Temporally, the diffusion signal change in V4 and V1 both preceded the corresponding hemodynamic response, however the early diffusion signal change was more evident in V1. Conclusions DfMRI may be of use in imaging applications implementing cognitive subtraction paradigms, and where highly precise individual functional localization is required.

Designs for phase I clinical trials with multiple courses of subjects at different doses

The goal of this article is to provide a new design framework and its corresponding estimation for phase I trials. Existing phase I designs assign each subject to one dose level based on responses from previous subjects. Yet it is possible that subjects with neither toxicity nor efficacy responses can be treated at higher dose levels, and their subsequent responses to higher doses will provide more information. In addition, for some trials, it might be possible to obtain multiple responses (repeated measures) from a subject at different dose levels. In this article, a nonparametric estimation method is developed for such studies. We also explore how the designs of multiple doses per subject can be implemented to improve design efficiency. The gain of efficiency from "single dose per subject" to "multiple doses per subject" is evaluated for several scenarios. Our numerical study shows that using "multiple doses per subject" and the proposed estimation method together increases the efficiency substantially.

Preliminary investigations into the use of a functionalised polymer to reduce diffusion in Fricke gel dosimeters

Purpose A modification of the existing PVA-​FX hydrogel has been made to investigate the use of a functionalised polymer in a Fricke gel dosimetry system to decrease Fe3+ diffusion. Methods The chelating agent, xylenol orange, was chem. bonded to the gelling agent, polyvinyl alc. (PVA) to create xylenol orange functionalised PVA (XO-​PVA)​. A gel was created from the XO-​PVA (20​% w​/v) with ferrous sulfate (0.4 mM) and sulfuric acid (50 mM)​. Results This resulted in an optical d. dose sensitivity of 0.014 Gy-​1, an auto-​oxidn. rate of 0.0005 h-​1, and a diffusion rate of 0.129 mm2 h-​1; an 8​% redn. compared to the original PVA-​FX gel, which in practical terms adds approx. 1 h to the time span between irradn. and accurate read-​out. Conclusions Because this initial method of chem. bonding xylenol orange to polyvinyl alc. has inherently low conversion, the improvement on existing gel systems is minimal when compared to the drawbacks. More efficient methods of functionalising polyvinyl alc. with xylenol orange must be developed for this system to gain clin. relevance.

A Bayesian decision approach for sample size determination in phase II trials

Stallard (1998, Biometrics 54, 279-294) recently used Bayesian decision theory for sample-size determination in phase II trials. His design maximizes the expected financial gains in the development of a new treatment. However, it results in a very high probability (0.65) of recommending an ineffective treatment for phase III testing. On the other hand, the expected gain using his design is more than 10 times that of a design that tightly controls the false positive error (Thall and Simon, 1994, Biometrics 50, 337-349). Stallard's design maximizes the expected gain per phase II trial, but it does not maximize the rate of gain or total gain for a fixed length of time because the rate of gain depends on the proportion: of treatments forwarding to the phase III study. We suggest maximizing the rate of gain, and the resulting optimal one-stage design becomes twice as efficient as Stallard's one-stage design. Furthermore, the new design has a probability of only 0.12 of passing an ineffective treatment to phase III study.

Isotonic designs for phase I trials

The purpose of a phase I trial in cancer is to determine the level (dose) of the treatment under study that has an acceptable level of adverse effects. Although substantial progress has recently been made in this area using parametric approaches, the method that is widely used is based on treating small cohorts of patients at escalating doses until the frequency of toxicities seen at a dose exceeds a predefined tolerable toxicity rate. This method is popular because of its simplicity and freedom from parametric assumptions. In this payer, we consider cases in which it is undesirable to assume a parametric dose-toxicity relationship. We propose a simple model-free approach by modifying the method that is in common use. The approach assumes toxicity is nondecreasing with dose and fits an isotonic regression to accumulated data. At any point in a trial, the dose given is that with estimated toxicity deemed closest to the maximum tolerable toxicity. Simulations indicate that this approach performs substantially better than the commonly used method and it compares favorably with other phase I designs.

Predicting a new phase (T′′) of two-dimensional transition metal di-chalcogenides and strain-controlled topological phase transition

Single layered transition metal dichalcogenides have attracted tremendous research interest due to their structural phase diversities. By using a global optimization approach, we have discovered a new phase of transition metal dichalcogenides (labelled as T′′), which is confirmed to be energetically, dynamically and kinetically stable by our first-principles calculations. The new T′′ MoS2 phase exhibits an intrinsic quantum spin Hall (QSH) effect with a nontrivial gap as large as 0.42 eV, suggesting that a two-dimensional (2D) topological insulator can be achieved at room temperature. Most interestingly, there is a topological phase transition simply driven by a small tensile strain of up to 2%. Furthermore, all the known MX2 (M = Mo or W; X = S, Se or Te) monolayers in the new T′′ phase unambiguously display similar band topologies and strain controlled topological phase transitions. Our findings greatly enrich the 2D families of transition metal dichalcogenides and offer a feasible way to control the electronic states of 2D topological insulators for the fabrication of high-speed spintronics devices.