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Volume 36 - Issue 2 - December 2011
We summarise the classical (gas diffusion) theory of decompression, which is an interesting application of elementary differential equations. We show that the derivation of recreational scuba diving tables from this theory is an ill-defined problem in optimisation.
• Shift scheduling with optimized service levels and employee
Tanja Van Hecke
This paper discusses the integer programming approach for dealing with resource allocation problems and employee satisfaction during shift scheduling. The ability to take into account the personal preferences of shift workers has an important impact on employee satisfaction. This paper describes an enhanced approach to this scheduling problem based on operations research.
• Optimal constrained confidence estimation of the Poisson mean via tail
Borek Puza, Mo Yang
A methodology is proposed for exact confidence estimation of the Poisson mean when that parameter is constrained. It is shown how tail functions can be used to construct a suitable confidence interval when the mean is bounded above, below, or both, and how this interval can be engineered for optimality in terms of prior expected length and other criteria. The theory is illustrated by way of comparison with the unified approach of Feldman and Cousins (1998).
• Understanding and using Fisher's p. Part 1: countering the p-statistic
K. R. W. Brewer, Genevieve Hayes
In September 2008 `Dr Fisher's casebook' in Significance was complaining `I have had it up to here with p-values', but by June 2009 this had softened to, `[S]ometimes a p-value is the only method available to assess the strength of evidence. Let us have one cheer for the p-value at least'. This four-part article suggests a way through the dilemma. In Part 1 it is shown that the Schwarz-inspired Bayesian information criterion can usefully be modified to take better account of the empirical information available when the implied null hypothesis is precise, and that in consequence substantially smaller values of two-sided p than currently envisaged are then required to establish a meaningful claim to significance.
• Understanding and using Fisher's p. Part 2: a reference Bayesian
K. R. W. Brewer, Genevieve Hayes
In Part 2 of this article, a reference Bayesian hypothesis test is constructed that corresponds exactly to the single-parameter ABIC1 of Part 1. An important role is played here by a hitherto rather neglected (and initially purely empirical) law of numbers (see Benford (1938)) that had first been propounded in 1881 (see Newcomb (1881)). This hypothesis test is then extended to small samples, where another important role is played by the p-statistic; this time in setting an upper bound to the false discovery rate, regardless of the number of degrees of freedom involved.
• Planar biarc curves – a geometric view
Tirupathi R. Chandrupatla, Thomas J. Osler
A biarc consists of two circular arcs which are tangential where they meet. This paper presents a geometric view of piecewise circular curves with continuously varying tangents (C1 or G1 curves). A smooth curve is divided into smaller segments by placing segment end points at various locations. In particular, these are placed at points of inflection of the curve. The curve is then approximated by biarcs in each of the segments. The geometric view provides a means of establishing all the needed relationships for constructing piecewise circular curves.
• Genetic algorithm and the pendulum problem
P. Kim, J. Latulippe, S. Muehlbacher, E. Shen, K. Shun
In this paper we present a mathematical model for a nonlinear damped pendulum. We compare the theoretical model with experimentally generated data recorded by a pendulum apparatus. We use a genetic algorithm to find the best fit model parameters. A detailed description of the algorithm is given and adapted for our pendulum model. We also illustrate that air friction and drag forces cannot always be ignored when modeling pendular motion.