Application of mixed formulations of quasi-reversibility to solve ill-posed problems for heat and wave equations: the 1d case

International audienceIn this paper we address some ill-posed problems involving the heat or the wave equation in one dimension, in particular the backward heat equation and the heat/wave equation with lateral Cauchy data. The main objective is to introduce some variational mixed formulations of quasi-reversibility which enable us to solve these ill-posed problems by using some classical La-grange finite elements. The inverse obstacle problems with initial condition and lateral Cauchy data for heat/wave equation are also considered, by using an elementary level set method combined with the quasi-reversibility method. Some numerical experiments are presented to illustrate the feasibility for our strategy in all those situations. 1. Introduction. The method of quasi-reversibility has now a quite long history since the pioneering book of Latt es and Lions in 1967 [1]. The original idea of these authors was, starting from an ill-posed problem which satisfies the uniqueness property, to introduce a perturbation of such problem involving a small positive parameter ε. This perturbation has essentially two effects. Firstly the perturbation transforms the initial ill-posed problem into a well-posed one for any ε, secondly the solution to such problem converges to the solution (if it exists) to the initial ill-posed problem when ε tends to 0. Generally, the ill-posedness in the initial problem is due to unsuitable boundary conditions. As typical examples of linear ill-posed problems one may think of the backward heat equation, that is the initial condition is replaced by a final condition, or the heat or wave equations with lateral Cauchy data, that is the usual Dirichlet or Neumann boundary condition on the boundary of the domain is replaced by a pair of Dirichlet and Neumann boundary conditions on the same subpart of the boundary, no data being prescribed on the complementary part of the boundary

ITERATED QUASI-REVERSIBILITY METHOD APPLIED TO ELLIPTIC AND PARABOLIC DATA COMPLETION PROBLEMS

International audienceWe study the iterated quasi-reversibility method to regularize ill-posed elliptic and parabolic problems: data completion problems for Poisson's and heat equations. We define an abstract setting to treat both equations at once. We demonstrate the convergence of the regularized solution to the exact one, and propose a strategy to deal with noise on the data. We present numerical experiments for both problems: a two-dimensional corrosion detection problem and the one-dimensional heat equation with lateral data. In both cases, the method prove to be efficient even with highly corrupted data

Novel synthesis and electrochemical investigations of ZnO/C composites for lithium-ion batteries

For the first time, ZnO/C composites were synthesized using zinc glycerolate as a precursor through one-step calcination under a nitrogen atmosphere. The effect of the heat treatment conditions on the structure, composition, morphology as well as on the electrochemical properties regarding application in lithium-ion batteries are investigated. The products obtained by calcination of the precursor in nitrogen at 400—800 °C consist of zinc oxide nanoparticles and amorphous carbon that is in-situ generated from organic components of the glycerolate precursor. When used as anode material for lithium-ion batteries, the as-prepared ZnO/C composite synthesized at a calcination temperature of 700 °C delivers initial discharge and charge capacities of 1061 and 671 mAh g−1 at a current rate of 100 mA g−1 and hence 1.5 times more than bare ZnO, which reaches only 749/439 mAh g−1. The native carbon improves the conductivity, allowing efficient electronic conductivity and Li-ion diffusion. By means of ex-situ XRD studies a two-step storage mechanism is proven. © 2021, The Author(s).This work was supported by the Deutsche Forschungsgemeinschaft through projects KL1824/12-1 and KL 1824/14-1. G.Z. acknowledges support of the state order via the Ministry of Science and Higher Education of Russia (No AAAA-A19-119031890025-9). E.T. acknowledges support by the BMWi through project 03ET6095C (HiKoMat). The authors thank I. Glass for experimental support

Adult onset asthma and interaction between genes and active tobacco smoking: The GABRIEL consortium.

BACKGROUND: Genome-wide association studies have identified novel genetic associations for asthma, but without taking into account the role of active tobacco smoking. This study aimed to identify novel genes that interact with ever active tobacco smoking in adult onset asthma. METHODS: We performed a genome-wide interaction analysis in six studies participating in the GABRIEL consortium following two meta-analyses approaches based on 1) the overall interaction effect and 2) the genetic effect in subjects with and without smoking exposure. We performed a discovery meta-analysis including 4,057 subjects of European descent and replicated our findings in an independent cohort (LifeLines Cohort Study), including 12,475 subjects. RESULTS: First approach: 50 SNPs were selected based on an overall interaction effect at p<10-4. The most pronounced interaction effect was observed for rs9969775 on chromosome 9 (discovery meta-analysis: ORint = 0.50, p = 7.63*10-5, replication: ORint = 0.65, p = 0.02). Second approach: 35 SNPs were selected based on the overall genetic effect in exposed subjects (p <10-4). The most pronounced genetic effect was observed for rs5011804 on chromosome 12 (discovery meta-analysis ORint = 1.50, p = 1.21*10-4; replication: ORint = 1.40, p = 0.03). CONCLUSIONS: Using two genome-wide interaction approaches, we identified novel polymorphisms in non-annotated intergenic regions on chromosomes 9 and 12, that showed suggestive evidence for interaction with active tobacco smoking in the onset of adult asthma

SLC11A1 (NRAMP1) Polymorphisms and Tuberculosis Susceptibility: Updated Systematic Review and Meta-Analysis

Background: Natural resistance associated macrophage protein 1 (NRAMP1), encoded by the SLC11A1 gene, has been described to regulate macrophage activation and be associated with infectious and autoimmune diseases. The relation between SLC11A1 polymorphisms and tuberculosis susceptibility has been studied in different populations. Methods: We systematically reviewed published studies on SLC11A1 polymorphisms and tuberculosis susceptibility until September 15, 2010 and quantitatively summarized associations of the most widely studied polymorphisms using metaanalysis. Results: In total, 36 eligible articles were included in this review. In Meta-analysis, significant associations were observed between tuberculosis risk and widely studied SLC11A1 polymorphisms with summarized odds ratio of 1.35 (95%CI, 1.17– 1.54), 1.25 (95 % CI, 1.04–1.50), 1.23 (95 % CI, 1.04–1.44), 1.31 (95%CI, 1.08–1.59) for 39 UTR, D543N, INT4, and 59 (GT)n, respectively. Heterogeneity between studies was not pronounced, and the associations did not remarkably vary in the stratified analysis with respect to study population and study base. Conclusions: The association between SLC11A1 polymorphisms and tuberculosis susceptibility observed in our analyses supports the hypothesis that NRAMP1 might play an important role in the host defense to the development of tuberculosis

Analysis of eight genes modulating interferon gamma and human genetic susceptibility to tuberculosis: a case-control association study

<p>Abstract</p> <p>Background</p> <p>Interferon gamma is a major macrophage-activating cytokine during infection with <it>Mycobacterium tuberculosis</it>, the causative pathogen of tuberculosis, and its role has been well established in animal models and in humans. This cytokine is produced by activated T helper 1 cells, which can best deal with intracellular pathogens such as <it>M. tuberculosis</it>. Based on the hypothesis that genes which regulate interferon gamma may influence tuberculosis susceptibility, we investigated polymorphisms in eight candidate genes.</p> <p>Methods</p> <p>Fifty-four polymorphisms in eight candidate genes were genotyped in over 800 tuberculosis cases and healthy controls in a population-based case-control association study in a South African population. Genotyping methods used included the SNPlex Genotyping System™, capillary electrophoresis of fluorescently labelled PCR products, TaqMan^®SNP genotyping assays or the amplification mutation refraction system. Single polymorphisms as well as haplotypes of the variants were tested for association with TB using statistical analyses.</p> <p>Results</p> <p>A haplotype in interleukin 12B was nominally associated with tuberculosis (p = 0.02), but after permutation testing, done to assess the significance for the entire analysis, this was not globally significant. In addition a novel allele was found for the interleukin 12B D5S2941 microsatellite.</p> <p>Conclusions</p> <p>This study highlights the importance of using larger sample sizes when attempting validation of previously reported genetic associations. Initial studies may be false positives or may propose a stronger genetic effect than subsequently found to be the case.</p

Meta-analysis identifies seven susceptibility loci involved in the atopic March

Eczema often precedes the development of asthma in a disease course called the a 'atopic march'. To unravel the genes underlying this characteristic pattern of allergic disease, we conduct a multi-stage genome-wide association study on infantile eczema followed by childhood asthma in 12 populations including 2,428 cases and 17,034 controls. Here we report two novel loci specific for the combined eczema plus asthma phenotype, which are associated with allergic disease for the first time; rs9357733 located in EFHC1 on chromosome 6p12.3 (OR 1.27; P=2.1 × 10 a'8) and rs993226 between TMTC2 and SLC6A15 on chromosome 12q21.3 (OR 1.58; P=5.3 × 10 a'9). Additional susceptibility loci identified

Sex- and age-dependent association of SLC11A1 polymorphisms with tuberculosis in Chinese: a case control study

BACKGROUND: Host genetic factors are important determinants in tuberculosis (TB). The SLC11A1 (or NRAMP1) gene has been studied extensively for genetic association with TB, but with inconsistent findings. In addition, no study has yet looked into the effect of sex and age on the relationship between SLC11A1 polymorphisms and TB. METHODS: A case-control study was conducted. In total, 278 pulmonary TB patients and 282 sex- and age-matched controls without TB were recruited. All subjects were ethnic Chinese. On the basis of linkage disequilibrium pattern, three genetic markers from SLC11A1 and one from the nearby IL8RB locus were selected and examined for association with TB susceptibility. These markers were genotyped using single strand conformation polymorphism analysis or fragment analysis of amplified products. RESULTS: Statistically significant differences in allele (P = 0.0165, OR = 1.51) and genotype (P = 0.0163, OR = 1.59) frequencies of the linked markers SLC6a/b (classically called D543N and 3'UTR) of the SLC11A1 locus were found between patients and controls. With stratification by sex, positive associations were identified in the female group for both allele (P = 0.0049, OR = 2.54) and genotype (P = 0.0075, OR = 2.74) frequencies. With stratification by age, positive associations were demonstrated in the young age group (age ≤65 years) for both allele (P = 0.0047, OR = 2.52) and genotype (P = 0.0031, OR = 2.92) frequencies. All positive findings remained significant even after correction for multiple comparisons. No significant differences were noted in either the male group or the older age group. No significant differences were found for the other markers (one SLC11A1 marker and one IL8RB marker) either. CONCLUSION: This study confirmed the association between SLC11A1 and TB susceptibility and demonstrated for the first time that the association was restricted to females and the young age group

Особенности репаративного синтеза ДНК и полиморфизма генов ферментов биотрансформации ксенобиотиков у больных раком легкого

This paper shows results of comparative study of DNA reparation system and gene polymorphism of biotransformation enzymes of xenobiotics in patients with lung cancer (LC), chronic obstructive pulmonary disease (COPD) and healthy adults. We examined 50 patients with central LC: 41 males, 9 females with the average age of 56.57 ± 7.96 yrs treated in Oncology Research Institute in Tomsk. Comparative groups involved 46 chronic bronchitis patients with preneoplastic lesions of bronchial epithelium proved by morphologic and endoscopic examinations and 50 healthy men of the same age without respiratory pathology. Cell reparative activity was studied in blood lymphocytes. DNA samples of the LC and COPD patients were typed for polymorphism of GSTT1, GSTM1 and CYP2C19 biotransformation genes. The results showed reduced functional activity of DNA reparation systems as well as in chronic bronchitis patients and LC patients. Investigation of DNA reparative synthesis intensity revealed significant inhibition of this process in most of the LC patients. This intensity was related to a histological type of the tumour and its stage. The LC patients had decreased rate of the GSTM1 null genotype that could be specific for this pathology. The genotype spread in the LC patients greatly differed from that in healthy (p = 0.047) but the spread in the COPD patients was close to that in healthy. A difference between the LC patients and COPD patients was not found because of a small size of the groups. Thus, studies with larger sizes are required. Practical importance of such studies could be development of genotyping test sets to predict an increased risk for neoplasm occurrence.В настоящей работе проведено сравнительное изучение показателей системы репарации ДНК и полиморфизма генов ферментов биотрансформации у больных раком легких (РЛ), хроническими обструктивными болезнями легких (ХОБЛ) и у здоровых лиц. Обследованы 50 больных центральным РЛ (41 мужчина, 9 женщин), которые находились на лечении в клинике НИИ онкологии ТНЦ СО РАМН г. Томска. Средний возраст пациентов равен 56,57 ± 7,96 лет. Группы сравнения составили 46 больных хроническим бронхитом с предопухолевыми (диспластическими) изменениями бронхиального эпителия (диагноз был подтвержден морфологически и эндоскопически) и 50 здоровых мужчин соответствующего возраста без бронхолегочной патологии. Репаративную активность клеток исследовали в лимфоцитах периферической крови. Образцы ДНК больных РЛ и ХОБЛ были протипированы по полиморфизму 3 генов биотрансформации: GSTT1, GSTM1 и CYP2C19. Полученные результаты указывают на снижение функциональной активности ДНК репарационных систем как у больных хроническим бронхитом, так и РЛ. Изучение интенсивности репаративного синтеза ДНК у больных РЛ в большинстве случаев выявило значительное ингибирование этого процесса. При этом установлена связь между интенсивностью репаративного синтеза ДНК с гистологическим типом опухоли и стадией заболевания. Больные РЛ характеризуются сниженной частотой нулевого генотипа гена GSTM1, и этот маркер может быть специфичен именно для данной нозологии. Распределение генотипов в выборке больных РЛ статистически значимо отличается от такового у здоровых лиц (p = 0,047). При этом распределение генотипов у больных ХОБЛ близко к таковому у здоровых. Отличий между больными ХОБЛ и больными РЛ не получено из-за малого размера выборок. Необходимы дальнейшие исследования на больших по объему выборках. Практическим выходом такого рода исследований может быть создание генотипических тест-систем предиктивной диагностики повышенной подверженности к онкологической патологии в конкретных средовых условиях