Chebyshev model arithmetic for factorable functions

This article presents an arithmetic for the computation of Chebyshev models for factorable functions and an analysis of their convergence properties. Similar to Taylor models, Chebyshev models consist of a pair of a multivariate polynomial approximating the factorable function and an interval remainder term bounding the actual gap with this polynomial approximant. Propagation rules and local convergence bounds are established for the addition, multiplication and composition operations with Chebyshev models. The global convergence of this arithmetic as the polynomial expansion order increases is also discussed. A generic implementation of Chebyshev model arithmetic is available in the library MC++. It is shown through several numerical case studies that Chebyshev models provide tighter bounds than their Taylor model counterparts, but this comes at the price of extra computational burden

Guaranteed parameter estimation in nonlinear dynamic systems using improved bounding techniques

This paper is concerned with guaranteed parameter estimation in nonlinear dynamic systems in a context of bounded measurement error. The problem consists of finding - or approximating as closely as possible - the set of all possible parameter values such that the predicted outputs match the corresponding measurements within prescribed error bounds. An exhaustive search procedure is applied, whereby the parameter set is successively partitioned into smaller boxes and exclusion tests are performed to eliminate some of these boxes, until a prespecified threshold on the approximation level is met. Exclusion tests rely on the ability to bound the solution set of the dynamic system for a given parameter subset and the tightness of these bounds is therefore paramount. Equally important is the time required to compute the bounds, thereby defining a trade-off. It is the objective of this paper to investigate this trade-off by comparing various bounding techniques based on interval arithmetic, Taylor model arithmetic and ellipsoidal calculus. When applied to a simple case study, ellipsoidal and Taylor model approaches are found to reduce the number of iterations significantly compared to interval analysis, yet the overall computational time is only reduced for tight approximation levels due to the computational overhead. © 2013 EUCA

The Politics of Municipal Reform

When modernization of city government is proposed in a community in which taxes ore going up, administrative authority is fragmented, municipal structure is clumsy, and citizen estimate of the city council is somewhat low, popular attitudes toward municipal reform are favorable. But those persons who have empires to defend and interests to protect in the city hall, will defend the status quo and resist the introduction of proposed innovations. Some may even fight back with all the fury irrational men can have at their command, and thus the reform movement produces strange side effects and unfortunate after effects

A Gross Election Data Analysis by Simple Statistical and Stochastic Processes

By statistical analysis correlations were found to exist between voting in certain types of local elections and voting in specific kinds of state elections. But such correlations do not explain the behavior of individuals. By simple stochastic process, the author supports Ulmer\u27s theory that, over a given time sequence, the outcome of an election depends upon the outcomes of preceding elections

The effect of wave conditions and surfer ability on performance and the physiological response of recreational surfers.

This study investigated the effects of wave conditions on performance and the physiological responses of surfers. After institutional ethical approval 39 recreational surfers participated in 60 surfing sessions where performance and physiological response were measured using global positioning system (GPS) heart rate monitors. Using GPS, the percentage time spent in surfing activity categories was on average 41.6, 47.0, 8.1, and 3.1% for waiting, paddling, riding, and miscellaneous activities, respectively. Ability level of the surfers, wave size, and wave period are significantly associated with the physiological, ride, and performance parameters during surfing. As the ability level of the surfers increases there is a reduction in the relative exercise intensity (e.g., average heart rate as a percentage of laboratory maximum, rpartial = -0.412, p < 0.01) which is in contrast to increases in performance parameters (e.g., maximum ride speed (0.454, p < 0.01). As the wave size increased there were reductions in physiological demand (e.g., total energy expenditure rpartial = -0.351, p ≤ 0.05) but increases in ride speed and distance measures (e.g., the maximum ride speed, 0.454, p < 0.01). As the wave period increased there were increases in intensity (e.g., average heart rate as a percentage of laboratory maximum, rp = 0.490, p < 0.01) and increases in ride speed and distance measures (e.g., the maximum ride speed, rpartial = 0.371, p < 0.01). This original study is the first to show that wave parameters and surfer ability are significantly associated with the physiological response and performance characteristics of surfing