A posteriori error control for discontinuous Galerkin methods for parabolic problems

We derive energy-norm a posteriori error bounds for an Euler time-stepping method combined with various spatial discontinuous Galerkin schemes for linear parabolic problems. For accessibility, we address first the spatially semidiscrete case, and then move to the fully discrete scheme by introducing the implicit Euler time-stepping. All results are presented in an abstract setting and then illustrated with particular applications. This enables the error bounds to hold for a variety of discontinuous Galerkin methods, provided that energy-norm a posteriori error bounds for the corresponding elliptic problem are available. To illustrate the method, we apply it to the interior penalty discontinuous Galerkin method, which requires the derivation of novel a posteriori error bounds. For the analysis of the time-dependent problems we use the elliptic reconstruction technique and we deal with the nonconforming part of the error by deriving appropriate computable a posteriori bounds for it.Comment: 6 figure

Parameter identification problems in the modelling of cell motility

We present a novel parameter identification algorithm for the estimation of parameters in models of cell motility using imaging data of migrating cells. Two alternative formulations of the objective functional that measures the difference between the computed and observed data are proposed and the parameter identification problem is formulated as a minimisation problem of nonlinear least squares type. A Levenberg–Marquardt based optimisation method is applied to the solution of the minimisation problem and the details of the implementation are discussed. A number of numerical experiments are presented which illustrate the robustness of the algorithm to parameter identification in the presence of large deformations and noisy data and parameter identification in three dimensional models of cell motility. An application to experimental data is also presented in which we seek to identify parameters in a model for the monopolar growth of fission yeast cells using experimental imaging data. Our numerical tests allow us to compare the method with the two different formulations of the objective functional and we conclude that the results with both objective functionals seem to agree

A model for selection of eyespots on butterfly wings

The development of eyespots on the wing surface of butterflies of the family Nympalidae is one of the most studied examples of biological pattern formation.However, little is known about the mechanism that determines the number and precise locations of eyespots on the wing. Eyespots develop around signaling centers, called foci, that are located equidistant from wing veins along the midline of a wing cell (an area bounded by veins). A fundamental question that remains unsolved is, why a certain wing cell develops an eyespot, while other wing cells do not. We illustrate that the key to understanding focus point selection may be in the venation system of the wing disc. Our main hypothesis is that changes in morphogen concentration along the proximal boundary veins of wing cells govern focus point selection. Based on previous studies, we focus on a spatially two-dimensional reaction-diffusion system model posed in the interior of each wing cell that describes the formation of focus points. Using finite element based numerical simulations, we demonstrate that variation in the proximal boundary condition is sufficient to robustly select whether an eyespot focus point forms in otherwise identical wing cells. We also illustrate that this behavior is robust to small perturbations in the parameters and geometry and moderate levels of noise. Hence, we suggest that an anterior-posterior pattern of morphogen concentration along the proximal vein may be the main determinant of the distribution of focus points on the wing surface. In order to complete our model, we propose a two stage reaction-diffusion system model, in which an one-dimensional surface reaction-diffusion system, posed on the proximal vein, generates the morphogen concentrations that act as non-homogeneous Dirichlet (i.e., fixed) boundary conditions for the two-dimensional reaction-diffusion model posed in the wing cells. The two-stage model appears capable of generating focus point distributions observed in nature. We therefore conclude that changes in the proximal boundary conditions are sufficient to explain the empirically observed distribution of eyespot focus points on the entire wing surface. The model predicts, subject to experimental verification, that the source strength of the activator at the proximal boundary should be lower in wing cells in which focus points form than in those that lack focus points. The model suggests that the number and locations of eyespot foci on the wing disc could be largely controlled by two kinds of gradients along two different directions, that is, the first one is the gradient in spatially varying parameters such as the reaction rate along the anterior-posterior direction on the proximal boundary of the wing cells, and the second one is the gradient in source values of the activator along the veins in the proximal-distal direction of the wing cell

Analysis and simulations of coupled bulk-surface reaction-diffusion systems on exponentially evolving volumes

In this article we present a system of coupled bulk-surface reaction-diffusion equations on exponentially evolving volumes. Detailed linear stability analysis of the homogeneous steady state is carried out. It turns out that due to the nature of the coupling (linear Robin-type boundary conditions) the characterisation of the dispersion relation in the absence and presence of spatial variation (i.e. diffusion), can be decomposed as a product of the dispersion relation of the bulk and surface models thereby allowing detailed analytical tractability. As a result we state and prove the conditions for diffusion-driven instability for systems of coupled bulk-surface reaction-diffusion equations. Furthermore, we plot explicit evolving parameter spaces for the case of an exponential growth. By selecting parameter values from the parameter spaces, we exhibit pattern formation in the bulk and on the surface in complete agreement with theoretical predictions

Cervix Uteri Cancer in Lebanon: Incidence, Temporal Trends, and Comparison to Countries From Different Regions in the World

Background: Invasive cervix uteri cancer is the fourth most common malignancy in women globally. This study investigates the incidence and trends of cervix uteri cancer in Lebanon, a country in the Middle East, and compares these rates to regional and global ones. Methods: Data on cervix uteri were obtained from the Lebanese national cancer registry for the currently available years 2005 to 2016. The calculated age-standardized incidence and age-specific rates were expressed as per 100,000 population. Results: From 2005 to 2016, cervix uteri cancer was the tenth most common cancer among women. Its age-standardized incidence rate fluctuated narrowly between 3.5 and 5.7 per 100,000, with the lowest rate in 2013 and the highest rate in 2012. The age-specific incidence rate had 2 peaks, the highest peak at age group 70–74 years and the second at age group 50–59 years. The annual percent change (+.05%) showed a non-statistically significant trend of increase. The age-standardized incidence rate of cervix uteri cancer in Lebanon was comparable to that of the Western Asia region that has the lowest incidence rate worldwide. The rate was intermediate as compared to other countries in the Middle East and North Africa Region and relatively similar to the ones in Australia, North America, and some Western European countries. Conclusion: The incidence rates of invasive cervix uteri are low in Lebanon. This could be attributed to the low prevalence of human papilloma virus infection and other sexually transmitted infections among Lebanese women, and the opportunistic screening practices. It is important to adopt a comprehensive approach to decrease the potential burden of cervix uteri, especially with the rising patterns of risky sexual behaviors. This includes improving awareness, enhancing access to preventive services, developing clinical guidelines, and training health care providers on these guidelines. © The Author(s) 2022

Transitional B cell cytokines predict renal allograft outcomes

Early immunological biomarkers that predict rejection and chronic allograft loss are needed to inform preemptive therapy and improve long-term outcomes. Here, we prospectively examined the ratio of interleukin-10 (IL-10) to tumor necrosis factor–α (TNFα) produced by transitional-1 B cells (T1B) 3 months after transplantation as a predictive biomarker for clinical and subclinical renal allograft rejection and subsequent clinical course. In both Training (n = 162) and Internal Validation (n = 82) Sets, the T1B IL-10/TNFα ratio 3 months after transplantation predicted both clinical and subclinical rejection anytime in the first year. The biomarker also predicted subsequent late rejection with a lead time averaging 8 months. Among biomarker high-risk patients, 60% had early rejection, of which 48% recurred later in the first posttransplant year. Among high-risk patients without early rejection, 74% developed rejection later in the first year. In contrast, only 5% of low-risk patients had early and 5% late rejection. The biomarker also predicted rejection in an External Validation Set (n = 95) and in key patient subgroups, confirming generalizability. Biomarker high-risk patients exhibited progressively worse renal function and decreased 5-year graft survival compared to low-risk patients. Treatment of B cells with anti-TNFα in vitro augmented the IL-10/TNFα ratio, restored regulatory activity, and inhibited plasmablast differentiation. To conclude, the T1B IL-10/TNFα ratio was validated as a strong predictive biomarker of renal allograft outcomes and provides a rationale for preemptive therapeutic intervention with TNF blockade

Visualization of transcoronary ablation of septal hypertrophy in patients with hypertrophic obstructive cardiomyopathy: a comparison between cardiac MRI, invasive measurements and echocardiography

Hypertrophic obstructive cardiomyopathy (HOCM) is treated by surgical myectomy or transcoronary ablation of septal hypertrophy (TASH). The aim of this study was to visualize the feasibility, success and short-term results of TASH on the basis of cardiac MRI (CMR) in comparison with cardiac catheterization and echocardiography. In this in vivo study, nine patients with HOCM were treated with TASH. Patients were evaluated by transthoracic echocardiography, invasive cardiac angiography and CMR. Follow-up examinations were carried out after 1, 3 and 12 months. MR imaging was performed on a 1.5-T scanner. All images were processed using the semiautomatic Argus software and were evaluated by an attending thoracic radiologist and cardiologist. The echocardiographic pressure gradient (at rest) was 69.3 +/- A 15.3 mmHg before and 22.1 +/- A 5.7 mmHg after TASH (P < 0.01, n = 9). The flux acceleration over the aortic valve examined (V (max)) was 5.1 +/- A 0.6 m/s before and 3.4 +/- A 0.3 m/s after the TASH procedure (P < 0.05). Also, there was a decrease of septum thickness from 22.0 +/- A 1.2 to 20.2 +/- A 1.0 mm (P < 0.05) after 6 +/- A 3 weeks. The invasively assessed pressure gradient at rest was reduced from 63.7 +/- A 15.2 to 21.2 +/- A 11.1 mmHg (P < 0.01) and the post-extrasystolic gradient was reduced from 138.9 +/- A 12.7 to 45.6 +/- A 16.5 mmHg (P < 0.01). All differences as well as the quantity of injected ethanol were plotted against the size or amount of scar tissue as assessed in the MRI. There was a statistically significant correlation between the post-extrasystolic gradient decrease and the amount of scar tissue (P = 0.03, r (2) = 0.5). In addition, the correlation between the quantity of ethanol and scar tissue area was highly significant (P < 0.01, r (2) = 0.6), whereas the values for the gradient deviation (P = 0.10, r (2) = 0.34), Delta V (max) (P = 0.12, r (2) = 0.31), as well as the gradient at rest (P = 0.27, r (2) = 0.17) were not significant. TASH was consistently effective in reducing the gradient in all patients with HOCM. In contrast to the variables investigated by echocardiography, the invasively measured post-extrasystolic gradient correlated much better with the amount of scar tissue as assessed by CMR. We conclude that the optimal modality to visualize the TASH effect seems to be a combination of CMR and the invasive identification of the post-extrasystolic gradient.Deutsche Forschungsgemeinschaft (DFG) [MA 1982/2-2, MA 1982/4-1

Towards an end-to-end analysis and prediction system for weather, climate, and Marine applications in the Red Sea

AbstractThe Red Sea, home to the second-longest coral reef system in the world, is a vital resource for the Kingdom of Saudi Arabia. The Red Sea provides 90% of the Kingdom’s potable water by desalinization, supporting tourism, shipping, aquaculture, and fishing industries, which together contribute about 10%–20% of the country’s GDP. All these activities, and those elsewhere in the Red Sea region, critically depend on oceanic and atmospheric conditions. At a time of mega-development projects along the Red Sea coast, and global warming, authorities are working on optimizing the harnessing of environmental resources, including renewable energy and rainwater harvesting. All these require high-resolution weather and climate information. Toward this end, we have undertaken a multipronged research and development activity in which we are developing an integrated data-driven regional coupled modeling system. The telescopically nested components include 5-km- to 600-m-resolution atmospheric models to address weather and climate challenges, 4-km- to 50-m-resolution ocean models with regional and coastal configurations to simulate and predict the general and mesoscale circulation, 4-km- to 100-m-resolution ecosystem models to simulate the biogeochemistry, and 1-km- to 50-m-resolution wave models. In addition, a complementary probabilistic transport modeling system predicts dispersion of contaminant plumes, oil spill, and marine ecosystem connectivity. Advanced ensemble data assimilation capabilities have also been implemented for accurate forecasting. Resulting achievements include significant advancement in our understanding of the regional circulation and its connection to the global climate, development, and validation of long-term Red Sea regional atmospheric–oceanic–wave reanalyses and forecasting capacities. These products are being extensively used by academia, government, and industry in various weather and marine studies and operations, environmental policies, renewable energy applications, impact assessment, flood forecasting, and more.</jats:p

Induction chemotherapy followed by chemoradiotherapy versus chemoradiotherapy alone as neoadjuvant treatment for locally recurrent rectal cancer: Study protocol of a multicentre, open-label, parallel-arms, randomized controlled study (PelvEx II)

Background: A resection with clear margins (R0 resection) is the most important prognostic factor in patients with locally recurrent rectal cancer (LRRC). However, this is achieved in only 60 per cent of patients. The aim of this study is to investigate whether the addition of induction chemotherapy to neoadjuvant chemo(re)irradiation improves the R0 resection rate in LRRC. Methods: Thismulticentre, international, open-label, phase III, parallel-arms study will enrol 364 patients with resectable LRRC after previous partial or total mesorectal resection without synchronous distant metastases or recent chemo- and/or radiotherapy treatment. Patients will be randomized to receive either induction chemotherapy (three 3-week cycles of CAPOX (capecitabine, oxaliplatin), four 2- week cycles of FOLFOX (5-fluorouracil, leucovorin, oxaliplatin) or FOLFORI (5-fluorouracil, leucovorin, irinotecan)) followed by neoadjuvant chemoradiotherapy and surgery (experimental arm) or neoadjuvant chemoradiotherapy and surgery alone (control arm). Tumours will be restaged usingMRI and, in the experimental arm, a further cycle of CAPOX or two cycles of FOLFOX/FOLFIRI will be administered before chemoradiotherapy in case of stable or responsive disease. The radiotherapy dose will be 25 × 2.0 Gy or 28 × 1.8Gy in radiotherapy-naive patients, and 15 × 2.0Gy in previously irradiated patients. The concomitant chemotherapy agent will be capecitabine administered twice daily at a dose of 825mg/m2 on radiotherapy days. The primary endpoint of the study is the R0 resection rate. Secondary endpoints are long-termoncological outcomes, radiological and pathological response, toxicity, postoperative complications, costs, and quality of life. Discussion: This trial protocol describes the PelvEx II study. PelvEx II, designed as a multicentre, open-label, phase III, parallel-arms study, is the first randomized study to compare induction chemotherapy followed by neoadjuvant chemo(re)irradiation and surgery with neoadjuvant chemo(re)irradiation and surgery alone in patients with locally recurrent rectal cancer, with the aim of improving the number of R0 resections