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Geometric Approach (geometric + approach)

Distribution by Scientific Domains
Mathematics and Statistics28%

Selected Abstracts

A Geometric Approach to Comparing Treatments for Rapidly Fatal Diseases

BIOMETRICS, Issue 1 2006
Peter F. Thall
Summary In therapy of rapidly fatal diseases, early treatment efficacy often is characterized by an event, "response," which is observed relatively quickly. Since the risk of death decreases at the time of response, it is desirable not only to achieve a response, but to do so as rapidly as possible. We propose a Bayesian method for comparing treatments in this setting based on a competing risks model for response and death without response. Treatment effect is characterized by a two-dimensional parameter consisting of the probability of response within a specified time and the mean time to response. Several target parameter pairs are elicited from the physician so that, for a reference covariate vector, all elicited pairs embody the same improvement in treatment efficacy compared to a fixed standard. A curve is fit to the elicited pairs and used to determine a two-dimensional parameter set in which a new treatment is considered superior to the standard. Posterior probabilities of this set are used to construct rules for the treatment comparison and safety monitoring. The method is illustrated by a randomized trial comparing two cord blood transplantation methods. [source]

A geometric approach for the design of MIMO sliding controllers.

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 1 2009
Application to a wind-driven doubly fed induction generator
Abstract This paper presents a systematic methodology to design controllers for a general class of nonlinear MIMO systems affine in the control in the presence of bounded uncertainties and disturbances. The design method is developed using a theoretical framework based on the combination of a geometric approach and sliding mode techniques. The resulting robust control law guarantees finite time convergence, whereas chattering reduction is achieved by utilizing the minimum discontinuous action required to ensure disturbance rejection. The proposed methodology is applied to the control of a grid-connected wind energy generation system based on a doubly fed induction generator. The control objectives considered in this paper are maximization of the wind energy conversion and reactive power regulation to minimize machine losses. Copyright © 2008 John Wiley & Sons, Ltd. [source]

A geometric approach to robust performance of parametric uncertain systems

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 14 2003
J. Bondia
Abstract A new approach for the robust performance problem for parametric uncertain systems is presented. Contrary to the classical approach, where specifications must be given in the frequency domain, this approach allows to deal with classical time specifications such as bounds on the overshoot, settling time and steady state error, which are matched to an uncertain reference model. Controller synthesis is then formulated as a set inclusion problem with a clear geometrical interpretation. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Clifford geometric parameterization of inequivalent vacua

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 12 2001
Bertfried Fauser
Abstract We propose a geometric method to parameterize inequivalent vacua by dynamical data. Introducing quantum Clifford algebras with arbitrary bilinear forms we distinguish isomorphic algebras,as Clifford algebras,by different filtrations (resp. induced gradings). The idea of a vacuum is introduced as the unique algebraic projection on the base field embedded in the Clifford algebra, which is however equivalent to the term vacuum in axiomatic quantum field theory and the GNS construction in C* -algebras. This approach is shown to be equivalent to the usual picture which fixes one product but employs a variety of GNS states. The most striking novelty of the geometric approach is the fact that dynamical data fix uniquely the vacuum and that positivity is not required. The usual concept of a statistical quantum state can be generalized to geometric meaningful but non-statistical, non-definite, situations. Furthermore, an algebraization of states takes place. An application to physics is provided by an U (2)-symmetry producing a gap equation which governs a phase transition. The parameterization of all vacua is explicitly calculated from propagator matrix elements. A discussion of the relation to BCS theory and Bogoliubov,Valatin transformations is given. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Unfolding the fold of cyclic cysteine-rich peptides

PROTEIN SCIENCE, Issue 3 2008
Amarda Shehu
Abstract We propose a method to extensively characterize the native state ensemble of cyclic cysteine-rich peptides. The method uses minimal information, namely, amino acid sequence and cyclization, as a topological feature that characterizes the native state. The method does not assume a specific disulfide bond pairing for cysteines and allows the possibility of unpaired cysteines. A detailed view of the conformational space relevant for the native state is obtained through a hierarchic multi-resolution exploration. A crucial feature of the exploration is a geometric approach that efficiently generates a large number of distinct cyclic conformations independently of one another. A spatial and energetic analysis of the generated conformations associates a free-energy landscape to the explored conformational space. Application to three long cyclic peptides of different folds shows that the conformational ensembles and cysteine arrangements associated with free energy minima are fully consistent with available experimental data. The results provide a detailed analysis of the native state features of cyclic peptides that can be further tested in experiment. [source]

A framework for the study of macronutrient intake in fish

AQUACULTURE RESEARCH, Issue 6 2001
S J Simpson
Abstract A good understanding of the capabilities of commercially reared fish species to regulate intake of specific macronutrients has potential economic, welfare and environmental benefits. We present a conceptual and experimental framework for studying macronutrient intake in fish. This ,geometric' approach addresses the multidimensional and interactive nature of nutrition. It was developed from work on insect herbivores and has successfully been applied to mammals and birds. The various components of the framework are introduced in simple outlines, and key experimental designs are described for assessing whether or not fish specifically regulate their intake of macronutrients, how they balance over-ingesting some nutrients against undereating others when provided with suboptimal diets, and how they regulate growth post-ingestively. [source]