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

An exploration of the use of simple statistics to measure consensus and stability in Delphi studies

<p>Abstract</p> <p>Background</p> <p>The criteria for stopping Delphi studies are often subjective. This study aimed to examine whether consensus and stability in the Delphi process can be ascertained by descriptive evaluation of trends in participants' views.</p> <p>Methods</p> <p>A three round email-based Delphi required participants (n = 12) to verify their level of agreement with 8 statements, write comments on each if they considered it necessary and rank the statements for importance. Each statement was analysed quantitatively by the percentage of agreement ratings, importance rankings and the amount of comments made for each statement, and qualitatively using thematic analysis. Importance rankings between rounds were compared by calculating Kappa values to observe trends in how the process impacts on subject's views.</p> <p>Results</p> <p>Evolution of consensus was shown by increase in agreement percentages, convergence of range with standard deviations of importance ratings, and a decrease in the number of comments made. Stability was demonstrated by a trend of increasing Kappa values.</p> <p>Conclusion</p> <p>Following the original use of Delphi in social sciences, Delphi is suggested to be an effective way to gain and measure group consensus in healthcare. However, the proposed analytical process should be followed to ensure maximum validity of results in Delphi methodology for improved evidence of consensual decision-making.</p

Incidence of first primary central nervous system tumors in California, 2001–2005

We examined the incidence of first primary central nervous system tumors (PCNST) in California from 2001–2005. This study period represents the first five years of data collection of benign PCNST by the California Cancer Registry. California’s age-adjusted incidence rates (AAIR) for malignant and benign PCNST (5.5 and 8.5 per 100,000, respectively). Malignant PCNST were highest among non-Hispanic white males (7.8 per 100,000). Benign PCNST were highest among African American females (10.5 per 100,000). Hispanics, those with the lowest socioeconomic status, and those who lived in rural California were found to be significantly younger at diagnosis. Glioblastoma was the most frequent malignant histology, while meningioma had the highest incidence among benign histologies (2.6 and 4.5 per 100,000, respectively). This study is the first in the US to compare malignant to benign PCNST using a population-based data source. It illustrates the importance of PCNST surveillance in California and in diverse communities

Hierarchical Models in the Brain

This paper describes a general model that subsumes many parametric models for continuous data. The model comprises hidden layers of state-space or dynamic causal models, arranged so that the output of one provides input to another. The ensuing hierarchy furnishes a model for many types of data, of arbitrary complexity. Special cases range from the general linear model for static data to generalised convolution models, with system noise, for nonlinear time-series analysis. Crucially, all of these models can be inverted using exactly the same scheme, namely, dynamic expectation maximization. This means that a single model and optimisation scheme can be used to invert a wide range of models. We present the model and a brief review of its inversion to disclose the relationships among, apparently, diverse generative models of empirical data. We then show that this inversion can be formulated as a simple neural network and may provide a useful metaphor for inference and learning in the brain

Algebraic estimation in partial derivatives systems: parameters and differentiation problems

International audienceTwo goals are sought in this paper: namely, to provide a succinct overview on algebraic techniques for numerical differentiation and parameter estimation for linear systems and to present novel algebraic methods in the case of several variables. The state-of-art in the introduction is followed by a brief description of the methodology in the subsequent sections. Our new algebraic methods are illustrated by two examples in the multidimensional case. Some algebraic preliminaries are given in the appendix