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Cameron Potter. School of Engineering. University of Tasmania. Sandy Bay, Tasmania, Australia. [email protected]. Michael Negnevitsky. School of ...
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optimal distribution network. Index TermsâFacility location, Lagrangian relaxation, opti- mization, supply chain design. Manuscript received February 12, 2007; ...
Abstract. The feasibility of using ultrasound to investigate the bubble size distribution in dough is addressed. A model for the propagation of ultrasound in a ...
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Keywords and phrases: gene expression, stochastic processes, Pareto-like distributions, ..... the Cancer Research Anatomy Project including X-profiling,.
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distribution network. A multiobjective optimization model simultaneously minimizing the system expansion costs while achieving the best reliability (optimal ...
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solutions. This paper presents a new application of genetic algorithm .... formulation of non linear mixed-integer programming, ... employed alphabet represents, in the distribution net design, .... New York: Addison Wesley Publishing Inc., 1989.
GEOHORIZONS December 2009/54. Stochastic modeling of facies distribution in a carbonate reservoir in the Gulf of Mexico. Sanjay Srinivasan and Mrinal Sen.
Using the Fisher-Bingham distribution in stochastic ... - CiteSeerX
model is the Fisher-Bingham distribution on the 3D sphere (Kent, 1982), .... Physiology, University of Copenhagen, whose support is acknowledged. References.
Using the Fisher-Bingham distribution in stochastic models for protein structure John T. Kent* and Thomas Hamelryck
University of Leeds University of Copenhagen
1 Introduction Protein structure prediction is at present an unsolved problem, partly due to lack of a suitable energy function and partly due to the high number of conformational parameters involved. Many protein structure prediction methods therefore use simplified models (Buchete et al., 2004). A popular approach is to represent a protein by its C atoms only, ie. by its C trace. Thus a protein can be regarded as a sequence of edges in . To a first approximation ˚ The angles the length of each edge is constant (in practice one unit of length is about 3.8 A). between successive edges determine the shape of the protein. Here we introduce a probabilistic model of the geometry of a random protein’s C trace. Such a model has many applications, like for example steering the proposal of protein conformations in a Markov Chain Monte Carlo (MCMC) simulation. The model is based on machine learning techniques, and is trained from a set of representative protein structures. Central to the model is the Fisher-Bingham distribution on the 3D sphere (Kent, 1982), an analogue of the bivariate normal equation in the plane.
2 Simulating the FB distribution The FB
distribution, where and are real concentration parameters and is a orthogonal matrix representing orientation, was introduced in Kent (1982) and defines a statistical model on the unit sphere in . Its pdf in polar coordinates is given by
