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A POSTERIORI ENERGY-NORM ERROR ESTIMATES FOR ADVECTION-DIFFUSION EQUATIONS APPROXIMATED BY WEIGHTED INTERIOR PENALTY METHODS

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Journal of Computational Mathematics 2008年第4期26卷 488-510页

作者： alexandre Ern AnnetteF.Stephansen Université Paris-Est CermicsEcole des Ponts6 et 8 avenue Blaise PascalChamps sur Marne77455 Marne la Vallée Cedex 2France Université Paris-Est CermicsEcole des Ponts6 et 8 avenue Blaise PascalChamps sur Marne77455 Marne la Vallée Cedex 2France AndraParc de la Croix-Blanche1-7 rue Jean Monnet92298 Ch■tenay-Malabry cedexFrance

We propose and analyze a posteriori energy-norm error estimates for weighted interior penalty discontinuous Galerkin approximations of advection-diffusion-reaction equations with heterogeneous and anisotropic diffusion. The weights, which play a key role in the analysis, depend on the diffusion tensor and are used to formulate the consistency terms in the discontinuous Galerkin method. The error upper bounds, in which all the constants are specified, consist of three terms： a residual estimator which depends only on the elementwise fluctuation of the discrete solution residual, a diffusive flux estimator where the weights used in the method enter explicitly, and a non-conforming estimator which is nonzero because of the use of discontinuous finite element spaces. The three estimators can be bounded locally by the approximation error. A particular attention is given to the dependency on problem parameters of the constants in the local lower error bounds. For moderate advection, it is shown that full robustness with respect to diffusion heterogeneities is achieved owing to the specific design of the weights in the discontinuous Galerkin method, while diffusion anisotropies remain purely local and impact the constants through the square root of the condition number of the diffusion tensor. For dominant advection, it is shown, in the spirit of previous work by Verfiirth on continuous finite elements, that the local lower error bounds can be written with constants involving a cut-off for the ratio of local mesh size to the reciprocal of the square root of the lowest local eignevalue of the diffusion tensor.

关键词： Discontinuous Galerkin Weighted interior penalty A posteriori error estimate,Heterogeneous diffusion Advection-diffusion.

Colon mucus in colorectal neoplasia and beyond

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World Journal of Gastroenterology 2022年第32期28卷 4475-4492页

作者： alexandre Loktionov DiagNodus Ltd Cambridge CB40WSUnited Kingdom

Little was known about mammalian colon mucus(CM)until the beginning of the 21^(st) *** that time considerable progress has been made in basic research addressing CM structure and *** CM is formed by two distinct layers composed of gel-forming glycosylated mucins that are permanently secreted by goblet cells of the colonic *** inner layer is dense and impenetrable for bacteria,whereas the loose outer layer provides a habitat for abundant commensal *** barrier integrity is essential for preventing bacterial contact with the mucosal epithelium and maintaining homeostasis in the gut,but it can be impaired by a variety of factors,including CM-damaging switch of commensal bacteria to mucin glycan consumption due to dietary fiber *** is proven that impairments in CM structure and function can lead to colonic barrier deterioration that opens direct bacterial access to the ***-induced damage dysregulates epithelial proliferation and causes mucosal inflammatory responses that may expand to the loosened CM and eventually result in severe disorders,including colitis and neoplastic *** described formation of bacterial biofilms within the inner CM layer was shown to be associated with both inflammation and *** obvious gaps in our knowledge of human CM remain,its importance for the pathogenesis of major colorectal diseases,comprising inflammatory bowel disease and colorectal cancer,is already *** progress in CM exploration is likely to result in the development of a range of new useful clinical applications addressing colorectal disease diagnosis,prevention and therapy.

关键词： Colon Colon mucus Mucins Goblet cells Gut microbiota Inflammatory bowel disease Colorectal cancer

Eosinophils in the gastrointestinal tract and their role in the pathogenesis of major colorectal disorders

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World Journal of Gastroenterology 2019年第27期25卷 3503-3526页

作者： alexandre Loktionov DiagNodus Ltd Babraham Research Campus

Eosinophils are currently regarded as versatile mobile cells controlling and regulating multiple biological pathways and responses in health and *** cells store in their specific granules numerous biologically active substances(cytotoxic cationic proteins, cytokines, growth factors, chemokines,enzymes) ready for rapid release. The human gut is the main destination of eosinophils that are produced and matured in the bone marrow and then transferred to target tissues through the circulation. In health the most important functions of gut-residing eosinophils comprise their participation in the maintenance of the protective mucosal barrier and interactions with other immune cells in providing immunity to microbiota of the gut lumen. Eosinophils are closely involved in the development of inflammatory bowel disease(IBD),when their cytotoxic granule proteins cause damage to host tissues. However,their roles in Crohn’s disease and ulcerative colitis appear to follow different immune response patterns. Eosinophils in IBD are especially important in altering the structure and protective functions of the mucosal barrier and modulating massive neutrophil influx to the lamina propria followed by transepithelial migration to colorectal mucus. IBD-associated inflammatory process involving eosinophils then appears to expand to the mucus overlaying the internal gut surface. The author hypothesises that immune responses within colorectal mucus as well as ETosis exerted by both neutrophils and eosinophils on the both sides of the colonic epithelial barrier act as additional pathogenetic factors in IBD. Literature analysis also shows an association between elevated eosinophil levels and better colorectal cancer(CRC) prognosis, but mechanisms behind this effect remain to be elucidated. In conclusion, the author emphasises the importance of investigating colorectal mucus in IBD and CRC patients as a previously unexplored milieu of disease-related inflammatory responses.

关键词： Eosinophils Eosinophilopoiesis Gut lamina propria Colorectal mucus Normal human small intestine Normal human colon Inflammatory bowel disease Crohn’s disease Ulcerative colitis Colorectal cancer

Biomarkers for detecting colorectal cancer non-invasively: DNA,RNA or proteins?

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World Journal of Gastrointestinal Oncology 2020年第2期12卷 124-148页

作者： alexandre Loktionov Diag Nodus Ltd Babraham Research Campus

Colorectal cancer(CRC)is a global problem affecting millions of people *** disease is unique because of its slow progress that makes it preventable and often *** symptoms usually emerge only at advanced stages of the disease,consequently its early detection can be achieved only through active population screening,which markedly reduces mortality due to this *** screening tests that employ non-invasively detectable biomarkers are currently being actively developed and,in most cases,samples of either stool or blood are ***,alternative biological substances that can be collected non-invasively(colorectal mucus,urine,saliva,exhaled air)have now emerged as new sources of diagnostic *** main categories of currently explored CRC biomarkers are:(1)Proteins(comprising widely used haemoglobin);(2)DNA(including mutations and methylation markers);(3)RNA(in particular microRNAs);(4)Low molecular weight metabolites(comprising volatile organic compounds)detectable by metabolomic techniques;and(5)Shifts in gut microbiome *** tests for early CRC detection employing such non-invasive biomarkers have been proposed and clinically *** some of these studies generated promising early results,very few of the proposed tests have been transformed into clinically validated diagnostic/screening *** DNA-based tests as Food and Drug Administration-approved multitarget stool test(marketed as Cologuard®)or blood test for methylated septin 9(marketed as Epi proColon®2.0 CE)show good diagnostic performance but remain too expensive and technically complex to become effective CRC screening *** can be concluded that,despite its deficiencies,the protein(haemoglobin)detection-based faecal immunochemical test(FIT)today presents the most cost-effective option for non-invasive CRC *** combination of non-invasive FIT and confirmatory invasive colonoscopy is the current strategy of choice for CRC ***

关键词： Colorectal cancer screening Biomarkers Non-invasive testing Stool Colorectal mucus Blood

Dynamical machine learning volumetric reconstruction of objects’ interiors from limited angular views

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Light(Science & Applications) 2021年第5期10卷 824-844页

作者： Iksung Kang alexandre Goy George Barbastathis Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology77 Massachusetts AveCambridgeMAUSA Department of Mechanical Engineering Massachusetts Institute of TechnologyCambridgeMA 02139USA Singapore-MIT Alliance for Research and Technology(SMART)Centre 1 Create WaySingapore 117543Singapore Omnisens SA Morges 1110Switzerland

Limited-angle tomography of an interior volume is a challenging, highly ill-posed problem with practical implications in medical and biological imaging, manufacturing, automation, and environmental and food security. Regularizing priors are necessary to reduce artifacts by improving the condition of such problems. Recently, it was shown that one effective way to learn the priors for strongly scattering yet highly structured 3D objects, e.g. layered and Manhattan, is by a static neural network [Goy et al. Proc. Natl. Acad. Sci. 116, 19848–19856 (2019)]. Here, we present a radically different approach where the collection of raw images from multiple angles is viewed analogously to a dynamical system driven by the object-dependent forward scattering operator. The sequence index in the angle of illumination plays the role of discrete time in the dynamical system analogy. Thus, the imaging problem turns into a problem of nonlinear system identification, which also suggests dynamical learning as a better fit to regularize the reconstructions. We devised a Recurrent Neural Network (RNN) architecture with a novel Separable-Convolution Gated Recurrent Unit (SC-GRU) as the fundamental building block. Through a comprehensive comparison of several quantitative metrics, we show that the dynamic method is suitable for a generic interior-volumetric reconstruction under a limited-angle scheme. We show that this approach accurately reconstructs volume interiors under two conditions: weak scattering, when the Radon transform approximation is applicable and the forward operator well defined;and strong scattering, which is nonlinear with respect to the 3D refractive index distribution and includes uncertainty in the forward operator.

关键词： interior dynamical angular

Bacteriological Profile of Infections Encountered in a Pneumology Service in a Moderate-Income Country [Pneumology Department of CHU Cocody (Côte d’Ivoire)]

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Open Journal of Respiratory Diseases 2024年第1期14卷 1-11页

作者： Brou Jean Marcel Ahui Alitonde Eudoxie Djegbeton Alima Kone Marc-Olivier Koffi Kouame Clarisse Elogne Mobio Nancy Hermine Benjamin Kouraogo Erick Akouatia Constante Virginie Brou-Gode Kigninlman Horo Boko alexandre Kouassi Ngoran Koffi Pneumology Service Teaching Hospital of Cocody Abidjan C&#244te d’Ivoire Medical School of Abidjan University Félix Houphou&#235t Boigny Abidjan C&#244te d’Ivoire Pasteur Institute of Cô te d’Ivoire Abidjan C&#244te d’Ivoire

Introduction: Infections represent a real public health problem aggravating the morbidity and mortality of hospitalized patients. Methods: This was a retrospective study with descriptive purposes over a period of 05 years, in the Pneumology Department of the University Hospital of Cocody. Results: The average age in our population was 42 years. We observed a male predo- minance of 64.5%, with a sex ratio of 1.8. Medical history was dominated by HIV infection (23.5%), followed by tuberculosis (15.6%). Concerning lifestyle, smoking was found in 38% of cases. Symptoms progressed chronically in 80% of cases. An infectious syndrome was found in 75% of cases. Microbial culture was positive in 42% of cases. Pseudomonas aeruginosa and Klebsiella pneumoniae were encountered in 26.4% of cases each, followed by Echerichia coli in 10.4% of cases. Klebsiella pneumoniae in the first three years topped the list, but gradually. Pseudomonas aeruginosa maintained its leadership over the last three years. Pseudomonas aeruginosa isolates expressed a resistance rate of 9.8% to ceftazidime and 8.1% to imipenem;to aztreonam (36%), ticarcillin (33.3%) and levofloxacin. These strains were susceptible to fosfomycin (100%), mero- penem (96.6%) and amikacin (96%). For isolated strains of Entero- bacteria- ceae, resistance was observed about ticarcillin (83.3%) and amoxicillin clavula- nic acid (71.2%). Streptococcaceae showed resistance to tetracycline (69.2%) and erythromycin (50%). Over the years there has been an increase in re- sistance to amoxicillin-clavulanic acid ceftriaxone. The death rate was 14%. Conclusion: The bacterial profile of infections is dominated by germs respon- sible for nosocomial infection with significant mortality.

关键词： Bacterial Pleural Pneumonia Nosocomial Infection Sub-Saharan Africa Antibiotic Therapy

REAL-TIME OPTICAL MONITORING OF CAPILLARY GRID SPATIAL PATTERN IN EPITHELIUM BY SPATIALLY RESOLVED DIFFUSE REFLECTANCE PROBE

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Journal of Innovative Optical Health Sciences 2012年第2期5卷 10-18页

作者： GUENNADI SAIKO alexandre DOUPLIK Department of Physics Ryerson University TorontoON M5B 2K3Canada Clinical Photonics Lab School of Advanced Optical Technologies(SAOT)Friedrich-Alexander Erlangen-Nuremberg University ErlangenGermany Medical Photonics Engineering Group Chair of Photonics Technologies Friedrich-Alexander Erlangen-Nuremberg University Erlangen Germany

We developed a novel method for real-time monitoring of alteration of the local epithelium vessel/capillary and blood oxygenation spatial pattern in epithelium exploiting a compact fibre sensor system based on spatially and spectrally resolved diffuse *** method is based on collection of spatially resolved diffuse reflectance Re(λ)by fiber *** spatial resolution is provided as a dependence of Re(λ)on a set of distancesρbetween the source and detector(attenuation curve).It is expected that the new method can reasonably extract the minor spatial deviations of oxygenation and local blood volume fraction-parameters,directly related to the local vessel density and capillary spatial patterns in the *** scattering in visible range is naturally taken into account in the proposed method.

关键词： Spatially resolved diffuse reflectance fiber optics biospectroscopy diagnostics shock cancer

REGULARIZATION METHODS FOR THE NUMERICAL SOLUTION OF THE DIVERGENCE EQUATION △. u = f＊

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Journal of Computational Mathematics 2012年第4期30卷 354-380页

作者： alexandre Caboussat Roland Glowinski University of Houston Department of Mathematics Houston Texas USA

The problem of finding a L^∞-bounded two-dimensional vector field whose divergence is given in L2 is discussed from the numerical viewpoint. A systematic way to find such a vector field is to introduce a non-smooth variational problem involving a L^∞-norm. To solve this problem from calculus of variations, we use a method relying on a well- chosen augmented Lagrangian functional and on a mixed finite element approximation. An Uzawa algorithm allows to decouple the differential operators from the nonlinearities introduced by the L^∞-norm, and leads to the solution of a sequence of Stokes-like systems and of an infinite family of local nonlinear problems. A simpler method, based on a L2- regularization is also considered. Numerical experiments are performed, making use of appropriate numerical integration techniques when non-smooth data are considered; they allow to compare the merits of the two approaches discussed in this article and to show the ability of the related methods at capturing L^∞bounded solutions.

关键词： Divergence equation Bounded solutions Regularization methods AugmentedLagrangian Uzawa algorithm Nonlinear variational problems.

A Penalty-Regularization-Operator Splitting Method for the Numerical Solution of a Scalar Eikonal Equation

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Chinese Annals of Mathematics,Series B 2015年第5期36卷 659-688页

作者： alexandre CABOUSSAT Roland GLOWINSKI Haute Ecole de Gestion de Genève HES-SO//University of Applied Sciences Department of Mathematics University of Houston

In this article, we discuss a numerical method for the computation of the minimal and maximal solutions of a steady scalar Eikonal equation. This method relies on a penalty treatment of the nonlinearity, a biharmonic regularization of the resulting variational problem, and the time discretization by operator-splitting of an initial value problem associated with the Euler-Lagrange equations of the regularized variational problem. A low-order finite element discretization is advocated since it is well-suited to the low regularity of the solutions. Numerical experiments show that the method sketched above can capture efficiently the extremal solutions of various two-dimensional test problems and that it has also the ability of handling easily domains with curved boundaries.

关键词： Eikonal equation Minimal and maximal solutions Regularization methods Penalization of equality constraints Dynamical flow Operator splitting Finite element methods