Spatial discretization for stochastic semilinear superdiffusion driven by fractionally integrated multiplicative space-time white noise

We investigate the spatial discretization of a stochastic semilinear superdiffusion problem driven by fractionally integrated multiplicative space-time white noise. The white noise is characterized by its properties of being white in both space and time and the time fractional derivative is considered in the Caputo sense with an order $\alpha \in (1, 2)$. A spatial discretization scheme is introduced by approximating the space-time white noise with the Euler method in the spatial direction and approximating the second-order space derivative with the central difference scheme. By using the Green functions, we obtain both exact and approximate solutions for the proposed problem. The regularities of both the exact and approximate solutions are studied and the optimal error estimates that depend on the smoothness of the initial values are established. This paper builds upon the research presented in Mathematics. 2021. 9, 1917, where we originally focused on error estimates in the context of subdiffusion with $\alpha \in (0, 1)$. We extend our investigation to the spatial approximation of stochastic superdiffusion with $\alpha \in (1, 2)$ and place particular emphasis on refining our understanding of the superdiffusion phenomenon by analyzing the error estimates associated with the time derivative at the initial point

Numerical Approximation for a Stochastic Fractional Differential Equation Driven by Integrated Multiplicative Noise

From Crossref journal articles via Jisc Publications RouterHistory: epub 2024-01-23, issued 2024-01-23Article version: VoRPublication status: PublishedWe consider a numerical approximation for stochastic fractional differential equations driven by integrated multiplicative noise. The fractional derivative is in the Caputo sense with the fractional order α∈(0,1), and the non-linear terms satisfy the global Lipschitz conditions. We first approximate the noise with the piecewise constant function to obtain the regularized stochastic fractional differential equation. By applying Minkowski’s inequality for double integrals, we establish that the error between the exact solution and the solution of the regularized problem has an order of O(Δtα) in the mean square norm, where Δt denotes the step size. To validate our theoretical conclusions, numerical examples are presented, demonstrating the consistency of the numerical results with the established theory

Spatial Discretization for Stochastic Semi-Linear Subdiffusion Equations Driven by Fractionally Integrated Multiplicative Space-Time White Noise

From MDPI via Jisc Publications RouterHistory: accepted 2021-08-03, pub-electronic 2021-08-12Publication status: PublishedSpatial discretization of the stochastic semi-linear subdiffusion equations driven by fractionally integrated multiplicative space-time white noise is considered. The nonlinear terms f and σ satisfy the global Lipschitz conditions and the linear growth conditions. The space derivative and the fractionally integrated multiplicative space-time white noise are discretized by using the finite difference methods. Based on the approximations of the Green functions expressed by the Mittag–Leffler functions, the optimal spatial convergence rates of the proposed numerical method are proved uniformly in space under some suitable smoothness assumptions of the initial value

Ambient vibration re-testing and operational modal analysis of the Humber Bridge

An ambient vibration survey of the Humber Bridge was carried out in July 2008 by a combined team from the UK, Portugal and Hong Kong. The exercise had several purposes that included the evaluation of the current technology for instrumentation and system identification and the generation of an experimental dataset of modal properties to be used for validation and updating of finite element models for scenario simulation and structural health monitoring. The exercise was conducted as part of a project aimed at developing online diagnosis capabilities for three landmark European suspension bridges. Ten stand-alone tri-axial acceleration recorders were deployed at locations along all three spans and in all four pylons during five days of consecutive one-hour recordings. Time series segments from the recorders were merged, and several operational modal analysis techniques were used to analyse these data and assemble modal models representing the global behaviour of the bridge in all three dimensions for all components of the structure. The paper describes the equipment and procedures used for the exercise, compares the operational modal analysis (OMA) technology used for system identification and presents modal parameters for key vibration modes of the complete structure. The results obtained using three techniques, natural excitation technique/eigensystem realisation algorithm, stochastic subspace identification and poly-Least Squares Frequency Domain method, are compared among themselves and with those obtained from a 1985 test of the bridge, showing few significant modal parameter changes over 23 years in cases where direct comparison is possible. The measurement system and the much more sophisticated OMA technology used in the present test show clear advantages necessary due to the compressed timescales compared to the earlier exercise. Even so, the parameter estimates exhibit significant variability between different methods and variations of the same method, while also varying in time and having inherent variability. (C) 2010 Elsevier Ltd. All rights reserved

Rapid and Recoverable in vivo Magnetic Resonance Imaging of the Adult Zebrafish at 7 T

Increasing scientific interest in the zebrafish as a model organism across a range of biomedical and biological research areas raises the need for the development of in vivo imaging tools appropriate to this subject. Development of the embryonic and early stage forms of the subject can currently be assessed using optical based techniques due to the transparent nature of the species at these early stages. However this is not an option during the juvenile and adult stages when the subjects become opaque. Magnetic Resonance Imaging (MRI) techniques would allow for the longitudinal and non-invasive assessment of development and health in these later life stages. However, the small size of the zebrafish and its aquatic environment represent considerable challenges for the technique. We have developed a suitable flow cell system that incorporates a dedicated MRI imaging coil to solve these challenges. The system maintains and monitors a zebrafish during a scan and allows for it to be fully recovered. The imaging properties of this system compare well with those of other preclinical MRI coils used in rodent models. This enables the rapid acquisition of MRI data which is comparable in terms of quality and acquisition time. This would allow the many unique opportunities of the zebrafish as a model organism to be combined with the benefits of non-invasive MRI

Prediction of acute myeloid leukaemia risk in healthy individuals

The incidence of acute myeloid leukaemia (AML) increases with age and mortality exceeds 90% when diagnosed after age 65. Most cases arise without any detectable early symptoms and patients usually present with the acute complications of bone marrow failure(1). The onset of such de novo AML cases is typically preceded by the accumulation of somatic mutations in preleukaemic haematopoietic stem and progenitor cells (HSPCs) that undergo clonal expansion(2,3). However, recurrent AML mutations also accumulate in HSPCs during ageing of healthy individuals who do not develop AML, a phenomenon referred to as age-related clonal haematopoiesis (ARCH)(4-8). Here we use deep sequencing to analyse genes that are recurrently mutated in AML to distinguish between individuals who have a high risk of developing AML and those with benign ARCH. We analysed peripheral blood cells from 95 individuals that were obtained on average 6.3 years before AML diagnosis (pre-AML group), together with 414 unselected age- and gender-matched individuals (control group). Pre-AML cases were distinct from controls and had more mutations per sample, higher variant allele frequencies, indicating greater clonal expansion, and showed enrichment of mutations in specific genes. Genetic parameters were used to derive a model that accurately predicted AML-free survival; this model was validated in an independent cohort of 29 pre-AML cases and 262 controls. Because AML is rare, we also developed an AML predictive model using a large electronic health record database that identified individuals at greater risk. Collectively our findings provide proof-of-concept that it is possible to discriminate ARCH from pre-AML many years before malignant transformation. This could in future enable earlier detection and monitoring, and may help to inform intervention

Ten-year mortality, disease progression, and treatment-related side effects in men with localised prostate cancer from the ProtecT randomised controlled trial according to treatment received

Background The ProtecT trial reported intention-to-treat analysis of men with localised prostate cancer randomly allocated to active monitoring (AM), radical prostatectomy, and external beam radiotherapy. Objective To report outcomes according to treatment received in men in randomised and treatment choice cohorts. Design, setting, and participants This study focuses on secondary care. Men with clinically localised prostate cancer at one of nine UK centres were invited to participate in the treatment trial comparing AM, radical prostatectomy, and radiotherapy. Intervention Two cohorts included 1643 men who agreed to be randomised and 997 who declined randomisation and chose treatment. Outcome measurements and statistical analysis Analysis was carried out to assess mortality, metastasis and progression and health-related quality of life impacts on urinary, bowel, and sexual function using patient-reported outcome measures. Analysis was based on comparisons between groups defined by treatment received for both randomised and treatment choice cohorts in turn, with pooled estimates of intervention effect obtained using meta-analysis. Differences were estimated with adjustment for known prognostic factors using propensity scores. Results and limitations According to treatment received, more men receiving AM died of PCa (AM 1.85%, surgery 0.67%, radiotherapy 0.73%), whilst this difference remained consistent with chance in the randomised cohort (p = 0.08); stronger evidence was found in the exploratory analyses (randomised plus choice cohort) when AM was compared with the combined radical treatment group (p = 0.003). There was also strong evidence that metastasis (AM 5.6%, surgery 2.4%, radiotherapy 2.7%) and disease progression (AM 20.35%, surgery 5.87%, radiotherapy 6.62%) were more common in the AM group. Compared with AM, there were higher risks of sexual dysfunction (95% at 6 mo) and urinary incontinence (55% at 6 mo) after surgery, and of sexual dysfunction (88% at 6 mo) and bowel dysfunction (5% at 6 mo) after radiotherapy. The key limitations are the potential for bias when comparing groups defined by treatment received and changes in the protocol for AM during the lengthy follow-up required in trials of screen-detected PCa. Conclusions Analyses according to treatment received showed increased rates of disease-related events and lower rates of patient-reported harms in men managed by AM compared with men managed by radical treatment, and stronger evidence of greater PCa mortality in the AM group. Patient summary More than 95 out of every 100 men with low or intermediate risk localised prostate cancer do not die of prostate cancer within 10 yr, irrespective of whether treatment is by means of monitoring, surgery, or radiotherapy. Side effects on sexual and bladder function are better after active monitoring, but the risks of spreading of prostate cancer are more common

Functional and quality of life outcomes of localised prostate cancer treatments (prostate testing for cancer and treatment [ProtecT] study)

Objective To investigate the functional and quality of life (QoL) outcomes of treatments for localised prostate cancer and inform treatment decision-making. Patients and Methods Men aged 50–69 years diagnosed with localised prostate cancer by prostate-specific antigen testing and biopsies at nine UK centres in the Prostate Testing for Cancer and Treatment (ProtecT) trial were randomised to, or chose one of, three treatments. Of 2565 participants, 1135 men received active monitoring (AM), 750 a radical prostatectomy (RP), 603 external-beam radiotherapy (EBRT) with concurrent androgen-deprivation therapy (ADT) and 77 low-dose-rate brachytherapy (BT, not a randomised treatment). Patient-reported outcome measures (PROMs) completed annually for 6 years were analysed by initial treatment and censored for subsequent treatments. Mixed effects models were adjusted for baseline characteristics using propensity scores. Results Treatment-received analyses revealed different impacts of treatments over 6 years. Men remaining on AM experienced gradual declines in sexual and urinary function with age (e.g., increases in erectile dysfunction from 35% of men at baseline to 53% at 6 years and nocturia similarly from 20% to 38%). Radical treatment impacts were immediate and continued over 6 years. After RP, 95% of men reported erectile dysfunction persisting for 85% at 6 years, and after EBRT this was reported by 69% and 74%, respectively (P < 0.001 compared with AM). After RP, 36% of men reported urinary leakage requiring at least 1 pad/day, persisting for 20% at 6 years, compared with no change in men receiving EBRT or AM (P < 0.001). Worse bowel function and bother (e.g., bloody stools 6% at 6 years and faecal incontinence 10%) was experienced by men after EBRT than after RP or AM (P < 0.001) with lesser effects after BT. No treatment affected mental or physical QoL. Conclusion Treatment decision-making for localised prostate cancer can be informed by these 6-year functional and QoL outcomes