Marco Maggesi and Carlos Simpson Laboratoire J. A. Dieudonné, CNRS UMR 6621 Université de Nice-Sophia Antipolis . . . la traduction en langage formalisé ne serait plus qu’un exercise de patience (sans doutes fort pénible). —Nicolas Bourbaki Hanc marginis exiguitas non caperet. —Pierre de Fermat We feel that this context has now changed. For a long time, “mathematics” and “computer science” have...

Kanji Hioka Graduate School of Science and Engineering, Yamaguchi University 1677-1 Yoshida, Yamaguchi 753-8512, Japan [email protected] Yoshimasa Miwa Graduate School of Science and Engineering, Yamaguchi University 1677-1 Yoshida, Yamaguchi 753-8512, Japan [email protected] Chen Li Human Genome Center, University of Tokyo 4-6-1 Shirokanedai, Minatoku, Tokyo 108-8639, Ja...

A sample size calculation for logistic regression involves complicated formulae. This paper suggests use of sample size formulae for comparing means or for comparing proportions in order to calculate the required sample size for a simple logistic regression model. One can then adjust the required sample size for a multiple logistic regression model by a variance inflation factor. This method re...

Exact power and sample size calculation for bioequivalence studies with high order crossover designs using statistical software nQuery are presented. Such calculation can be very easily performed, and thus provides a convenient tool for practical usage.

The use of Cone beam CT (CBCT) systems for Image Guided Radiotherapy is rapidly expanding in the developed world. With its use comes concern for the increased risks of additional radiation exposure. Quantification of the imaging dose is necessary in order to report, optimise and justify CBCT exposures. This article reviews the current methods of dose measurement and calculation including dose m...

In clinical research, parameters required for sample size calculation are usually unknown. A typical approach is to use estimates from some pilot studies as the true parameters in the calculation. This approach, however, does not take into consideration sampling error. Thus, the resulting sample size could be misleading if the sampling error is substantial. As an alternative, we suggest a Bayes...

BACKGROUND Incomplete revascularization negatively affects survival after coronary artery bypass surgery (CABG). Since gender and classification technique might impact outcome and reporting, we investigated their effect on revascularization patterns and mortality. METHODS A cohort of bypass patients (N = 1545, 23% women) was enrolled prospectively. The degree of revascularization was determin...

In an effort to clarify how deductive reasoning is accomplished, an fMRI study was performed to observe the neural substrates of logical reasoning and mathematical calculation. Participants viewed a problem statement and three premises, and then either a conclusion or a mathematical formula. They had to indicate whether the conclusion followed from the premises, or to solve the mathematical for...

We construct a bosonic quantum field on a general quantum graph. Consistency of the construction leads to the calculation of the total scattering matrix of the graph. This matrix is equivalent to the one already proposed using generalized star product approach. We give several examples and show how they generalize some of the scattering matrices computed in the mathematical or condensed matter ...

This paper shows how to compose differential equations describing the oscillations of mathematical spring-coupled pendulums in a Mathcad worksheet. The composed differential equations are solved using both symbolic calculation features of Mathcad and Laplace transform. On the basis of the obtained solution, a video clip is made to demonstrate the motion of mathematical spring-coupled pendulums....