On the General Analytical Solution of the Kinematic Cosserat Equations

Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies a simple explicitly given algebraic relation. As our main theoretical result, in addition to the construction of the solution, we proof its generality. Based on this observation, a hybrid semi-analytical solver for highly viscous two-way coupled fluid-rod problems is developed which allows for the interactive high-fidelity simulations of flagellated microswimmers as a result of a substantial reduction of the numerical stiffness.Comment: 14 pages, 3 figure

Thomas Decomposition and Nonlinear Control Systems

This paper applies the Thomas decomposition technique to nonlinear control systems, in particular to the study of the dependence of the system behavior on parameters. Thomas' algorithm is a symbolic method which splits a given system of nonlinear partial differential equations into a finite family of so-called simple systems which are formally integrable and define a partition of the solution set of the original differential system. Different simple systems of a Thomas decomposition describe different structural behavior of the control system in general. The paper gives an introduction to the Thomas decomposition method and shows how notions such as invertibility, observability and flat outputs can be studied. A Maple implementation of Thomas' algorithm is used to illustrate the techniques on explicit examples

Worst-case analysis of heap allocations

Abstract. In object oriented languages, dynamic memory allocation is a fundamental concept. When using such a language in hard real-time systems, it becomes important to bound both the worst-case execution time and the worst-case memory consumption. In this paper, we present an analysis to determine the worst-case heap allocations of tasks. The analysis builds upon techniques that are well established for worst-case execution time analysis. The difference is that the cost function is not the execution time of instructions in clock cycles, but the allocation in bytes. In contrast to worst-case execution time analysis, worst-case heap allocation analysis is not processor dependent. However, the cost function depends on the object layout of the runtime system. The analysis is evaluated with several real-time benchmarks to establish the usefulness of the analysis, and to compare the memory consumption of different object layouts.

Basic Module Theory over Non-Commutative Rings with Computational Aspects of Operator Algebras

The present text surveys some relevant situations and results where basic Module Theory interacts with computational aspects of operator algebras. We tried to keep a balance between constructive and algebraic aspects.Comment: To appear in the Proceedings of the AADIOS 2012 conference, to be published in Lecture Notes in Computer Scienc

A constructive study of the module structure of rings of partial differential operators

The purpose of this paper is to develop constructive versions of Stafford's theorems on the module structure of Weyl algebras A n (k) (i.e., the rings of partial differential operators with polynomial coefficients) over a base field k of characteristic zero. More generally, based on results of Stafford and Coutinho-Holland, we develop constructive versions of Stafford's theorems for very simple domains D. The algorithmization is based on the fact that certain inhomogeneous quadratic equations admit solutions in a very simple domain. We show how to explicitly compute a unimodular element of a finitely generated left D-module of rank at least two. This result is used to constructively decompose any finitely generated left D-module into a direct sum of a free left D-module and a left D-module of rank at most one. If the latter is torsion-free, then we explicitly show that it is isomorphic to a left ideal of D which can be generated by two elements. Then, we give an algorithm which reduces the number of generators of a finitely presented left D-module with module of relations of rank at least two. In particular, any finitely generated torsion left D-module can be generated by two elements and is the homomorphic image of a projective ideal whose construction is explicitly given. Moreover, a non-torsion but non-free left D-module of rank r can be generated by r+1 elements but no fewer. These results are implemented in the Stafford package for D=A n (k) and their system-theoretical interpretations are given within a D-module approach. Finally, we prove that the above results also hold for the ring of ordinary differential operators with either formal power series or locally convergent power series coefficients and, using a result of Caro-Levcovitz, also for the ring of partial differential operators with coefficients in the field of fractions of the ring of formal power series or of the ring of locally convergent power series. © 2014 Springer Science+Business Media

The Development of Practice Recommendations for Drug-Disease Interactions by Literature Review and Expert Opinion

Background Drug-disease interactions negatively affect the benefit/risk ratio of drugs for specific populations. In these conditions drugs should be avoided, adjusted, or accompanied by extra monitoring. The motivation for many drug-disease interactions in the Summary of Product Characteristics (SmPC) is sometimes insufficiently supported by (accessible) evidence. As a consequence the translation of SmPC to clinical practice may lead to non-specific recommendations. For the translation of this information to the real world, it is necessary to evaluate the available knowledge about drug-disease interactions, and to formulate specific recommendations for prescribers and pharmacists. The aim of this paper is to describe a standardized method how to develop practice recommendations for drug-disease interactions by literature review and expert opinion. Methods The development of recommendations for drug-disease interactions will follow a six-step plan involving a multidisciplinary expert panel (1). The scope of the drug-disease interaction will be specified by defining the disease and by describing relevant effects of this drug-disease interaction. Drugs possibly involved in this drug-disease interaction are selected by checking the official product information, literature, and expert opinion (2). Evidence will be collected from the official product information, guidelines, handbooks, and primary literature (3). Study characteristics and outcomes will be evaluated and presented in standardized reports, including preliminary conclusions on the clinical relevance and practice recommendations (4). The multidisciplinary expert panel will discuss the reports and will either adopt or adjust the conclusions (5). Practice recommendations will be integrated in clinical decision support systems and published (6). The results of the evaluated drug-disease interactions will remain up-to-date by screening new risk information, periodic literature review, and (re)assessments initiated by health care providers. Actionable Recommendations The practice recommendations will result in advices for specific DDSI. The content and considerations of these DDSIs will be published and implemented in all Clinical Decision Support Systems in the Netherlands. Discussion The recommendations result in professional guidance in the context of individual patient care. The professional will be supported in the decision making in concerning pharmacotherapy for the treatment of a medical problem, and the clinical risks of the proposed medication in combination with specific diseases

Au Sujet des Approches Symboliques des Équations Intégro-Différentielles

International audienceRecent progress in computer algebra has opened new opportunities for the parameter estimation problem in nonlinear control theory, by means of integro-differential input-output equations. This paper recalls the origin of integro-differential equations. It presents new opportunities in nonlinear control theory. Finally, it reviews related recent theoretical approaches on integro-differential algebras, illustrating what an integro-differential elimination method might be and what benefits the parameter estimation problem would gain from it.Un résultat récent en calcul formel a ouvert de nouvelles opportunités pour l'estimation de paramètres en théorie du contrôle non linéaire, via des équations entrée-sortie intégro-différentielles. Ce chapitre rappelle les origines des équations intégro-différentielles. Il présente de nouvelles opportunités en théorie du contrôle non linéaire. Finalement, il passe en revue des approches théoriques récentes sur les algèbres intégro-différentielles, illustrant ce qu'une méthode d'élimination intégro-différentielle pourrait être et les bénéfices que le problème de l'estimation de paramètres pourrait en tirer

Linear Control Systems over Ore Algebras: Effective Algorithms for the Computation of Parametrizations

In this paper, we study linear control systems over Ore algebras. Within this mathematical framework..