A resampling-based test to detect person-to-person transmission of infectious disease

Early detection of person-to-person transmission of emerging infectious diseases such as avian influenza is crucial for containing pandemics. We developed a simple permutation test and its refined version for this purpose. A simulation study shows that the refined permutation test is as powerful as or outcompetes the conventional test built on asymptotic theory, especially when the sample size is small. In addition, our resampling methods can be applied to a broad range of problems where an asymptotic test is not available or fails. We also found that decent statistical power could be attained with just a small number of cases, if the disease is moderately transmissible between humans.Comment: Published at http://dx.doi.org/10.1214/07-AOAS105 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Relational Approach to Quantum Mechanics, Part I: Formulation

Non-relativistic quantum mechanics is reformulated here based on the idea that relational properties among quantum systems, instead of the independent properties of a quantum system, are the most fundamental elements to construct quantum mechanics. This idea, combining with the emphasis that measurement of a quantum system is a bidirectional interaction process, leads to a new framework to calculate the probability of an outcome when measuring a quantum system. In this framework, the most basic variable is the relational probability amplitude. Probability is calculated as summation of weights from the alternative measurement configurations. The properties of quantum systems, such as superposition and entanglement, are manifested through the rules of counting the alternatives. Wave function and reduced density matrix are derived from the relational probability amplitude matrix. They are found to be secondary mathematical tools that equivalently describe a quantum system without explicitly calling out the reference system. Schr\"{o}dinger Equation is obtained when there is no entanglement in the relational probability amplitude matrix. Feynman Path Integral is used to calculate the relational probability amplitude, and is further generalized to formulate the reduced density matrix. In essence, quantum mechanics is reformulated as a theory that describes physical systems in terms of relational properties.Comment: 19 pages, 2 figures, article split into 3 parts during refereeing, minor correction. Adding journal reference for part

Asteroseismic constraints on the OPAL opacity interpolation

The frequency difference between a model used only two-point interpolation of opacity and a model used piecewise linear interpolation of opacity is of the order of several microHertz at a certain stage, which is almost 10 times worse than the observational precision of p-modes of solar-like stars. Therefore, the two-point interpolation of opacity is unsuitable in modelling of solar-like stars with element diffusion.Comment: 2 pages, 1 figure; to appear in the Proceedings of IAU Symp. 252 "The Art of Modelling Stars in the 21st Century", Sanya, China, 6th-11th April 2008, (L. Deng, K.L. Chan & C. Chiosi, eds.