Div-Curl Problems and H1\mathbf{H}^1-regular Stream Functions in 3D Lipschitz Domains

We consider the problem of recovering the divergence-free velocity field ${\mathbf U}\in\mathbf{L}^2(\Omega)$ of a given vorticity ${\mathbf F}=\mathrm{curl}\,{\mathbf U}$ on a bounded Lipschitz domain $\Omega\subset\mathbb{R}^3$. To that end, we solve the "div-curl problem" for a given ${\mathbf F}\in{\mathbf H}^{-1}(\Omega)$. The solution is expressed in terms of a vector potential (or stream function) ${\mathbf A}\in{\mathbf H}^1(\Omega)$ such that ${\mathbf U}=\mathrm{curl}\,{\mathbf A}$. After discussing existence and uniqueness of solutions and associated vector potentials, we propose a well-posed construction for the stream function. A numerical method based on this construction is presented, and experiments confirm that the resulting approximations display higher regularity than those of another common approach

Ontology Design Patterns for bio-ontologies: a case study on the Cell Cycle Ontology

<p>Abstract</p> <p>Background</p> <p>Bio-ontologies are key elements of knowledge management in bioinformatics. Rich and rigorous bio-ontologies should represent biological knowledge with high fidelity and robustness. The richness in bio-ontologies is a prior condition for diverse and efficient reasoning, and hence querying and hypothesis validation. Rigour allows a more consistent maintenance. Modelling such bio-ontologies is, however, a difficult task for bio-ontologists, because the necessary richness and rigour is difficult to achieve without extensive training.</p> <p>Results</p> <p>Analogous to design patterns in software engineering, Ontology Design Patterns are solutions to typical modelling problems that bio-ontologists can use when building bio-ontologies. They offer a means of creating rich and rigorous bio-ontologies with reduced effort. The concept of Ontology Design Patterns is described and documentation and application methodologies for Ontology Design Patterns are presented. Some real-world use cases of Ontology Design Patterns are provided and tested in the Cell Cycle Ontology. Ontology Design Patterns, including those tested in the Cell Cycle Ontology, can be explored in the Ontology Design Patterns public catalogue that has been created based on the documentation system presented (<url>http://odps.sourceforge.net/</url>).</p> <p>Conclusions</p> <p>Ontology Design Patterns provide a method for rich and rigorous modelling in bio-ontologies. They also offer advantages at different development levels (such as design, implementation and communication) enabling, if used, a more modular, well-founded and richer representation of the biological knowledge. This representation will produce a more efficient knowledge management in the long term.</p

Long-term follow-up of IPEX syndrome patients after different therapeutic strategies : an international multicenter retrospective study

Background: Immunodysregulation polyendocrinopathy enteropathy x-linked(IPEX) syndrome is a monogenic autoimmune disease caused by FOXP3 mutations. Because it is a rare disease, the natural history and response to treatments, including allogeneic hematopoietic stem cell transplantation (HSCT) and immunosuppression (IS), have not been thoroughly examined. Objective: This analysis sought to evaluate disease onset, progression, and long-term outcome of the 2 main treatments in long-term IPEX survivors. Methods: Clinical histories of 96 patients with a genetically proven IPEX syndrome were collected from 38 institutions worldwide and retrospectively analyzed. To investigate possible factors suitable to predict the outcome, an organ involvement (OI) scoring system was developed. Results: We confirm neonatal onset with enteropathy, type 1 diabetes, and eczema. In addition, we found less common manifestations in delayed onset patients or during disease evolution. There is no correlation between the site of mutation and the disease course or outcome, and the same genotype can present with variable phenotypes. HSCT patients (n = 58) had a median follow-up of 2.7 years (range, 1 week-15 years). Patients receiving chronic IS (n 5 34) had a median follow-up of 4 years (range, 2 months-25 years). The overall survival after HSCT was 73.2% (95% CI, 59.4-83.0) and after IS was 65.1% (95% CI, 62.8-95.8). The pretreatment OI score was the only significant predictor of overall survival after transplant (P = .035) but not under IS. Conclusions: Patients receiving chronic IS were hampered by disease recurrence or complications, impacting long-term.disease-free survival. When performed in patients with a low OI score, HSCT resulted in disease resolution with better quality of life, independent of age, donor source, or conditioning regimen

Efecto del método de sincronización de la ovulación en búfalas de agua (Bubalus bubalis)

El presente trabajo se realizo en tres explotaciones localizadas en Panzós, Alta Verapaz, Cuyuta, Masagua, Escuintla y San Lucas Toliman Solola. Los resultados fueron 6.25%, 19%, 5.8% respectivamente, el porcentaje global fue de un 15.9%. Las búfalas destinadas a la producción de leche tuvieron una mejor tasa de preñez que las destinadas a la producción de carne (12% vrs 1%) Se discuten los factores que puedan estar afectando este parámetro tales como manejo de los animales durante el experimento, el propósito, época, la poca renovación genética, y el abuso en la rusticidad de los mismos. Se discute además, que bajo las condiciones actuales de las explotaciones de búfalos en Guatemala deben mejorase las condiciones de manejo sanitario, nutricional y general

Boundary Integral Exterior Calculus

In this thesis, we ultimately develop first-kind boundary integral equations for boundary value problems involving the Hodge--Dirac and Hodge--Laplace operators associated with the de Rham Hilbert complex on compact Riemannian manifolds and in Euclidean space. We show that first-kind boundary integral operators associated with these boundary value problems posed on submanifolds with Lipschitz boundaries are Hodge--Dirac and Hodge--Laplace operators as well, but associated with trace de Rham complexes on the boundary whose spaces are equipped with non-local inner products defined through boundary potentials. The correspondence is to some extent structure-preserving in the sense that adding zero-order terms to these operators lead to the addition of zero-order terms in the trace de Rham complexes at the level of boundary integral operators. We put forth Boundary Integral Exterior Calculus (BIEC), a calculus of boundary potentials that significatively ease the derivation of boundary integral equations for (possibly perturbed) Hodge--Dirac, Hodge--Yukawa and possibly other boundary value problems. The ability to appeal to the powerful theory of Hilbert complexes greatly simplifies their analysis. This paves the way for the developement of Boundary Element Exterior Calculus (BEEC), where Galerkin discretizations of variational boundary integral equations could be studied in the language of differential forms

Convergence of discrete exterior calculus

Discrete exterior calculus (DEC) is a fairly recent structure-preserving discretization of exterior calculus. It is based on the algebraic geometry of simplicial complexes, and exploits the interplay between a triangulation and its dual to reproduce the key geometric features of differential forms that are useful for computational purposes. It has been used to tackle problems ranging from homology, riemannian geometry, fluid dynamics and discrete mechanics, including variational problems in computer vision and animation. However, establishing a convergence theory for DEC remains an open problem. In this thesis, we will share recent advancements towards such a theory for the case of boundary value problems on 0-forms (real-valued functions), and the main difficulties one encounters in trying to extend these results to higher-order settings will be discussed."Discrete exterior calculus" (DEC) est une théorie assez récente obtenue par le developpément d'opérateurs discrets permettant un calcul simplicial analogue au calcul différentiel et intégral des formes différentielles. DEC est fondé sur la géometrie algébrique des complexes simplicials et exploite la reciprocité entre une triangulation et sa construction duale de façon à reproduire les propriétées geométriques clés des formes differentielles utiles pour le calcul scientifique. Dans la littérature, la théorie fut dejà utilisée pour affronter des problèmes variés appartenant à des domaines tels que l'homologie, la geométrie riemannienne, la dynamique des fluides, la méchanique discrète, incluant le calcul des variations en vision par ordinateur et en animation. Jusqu'à présent, établir la convergence des methodes produites par DEC reste un problème non resolu. Dans cette thèse, nous partagerons de récentes découvertes qui élargissent notre compréhension de cette question dans le cas des probèmes d'équations différentielles avec conditions limites pour des formes de degré zero (fonctions à valeurs réeles). Nous discuterons également des difficultés encontrées lorsqu'on tente d'étendre ces résultats à des ordres supérieurs

Diesel equipment, jil. 1/ Schulz

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