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Jaanson, A. A New Approach to Mathematical Modelling of Metal
Jaanson, A. A New Approach to Mathematical Modelling of Metal

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... marginal independence properties of the bi-directed graph imply P (XA = 0, XB = 0) = P (XA = 0)P (XB = 0) if no element in XA is adjacent to any element in XB in G. Therefore, the set of independent parameters in this parameterization is given by {qA }, for all XA that forms a connected set in G. Th ...
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Computer simulation



A computer simulation is a simulation, run on a single computer, or a network of computers, to reproduce behavior of a system. The simulation uses an abstract model (a computer model, or a computational model) to simulate the system. Computer simulations have become a useful part of mathematical modeling of many natural systems in physics (computational physics), astrophysics, climatology, chemistry and biology, human systems in economics, psychology, social science, and engineering. Simulation of a system is represented as the running of the system's model. It can be used to explore and gain new insights into new technology and to estimate the performance of systems too complex for analytical solutions.Computer simulations vary from computer programs that run a few minutes to network-based groups of computers running for hours to ongoing simulations that run for days. The scale of events being simulated by computer simulations has far exceeded anything possible (or perhaps even imaginable) using traditional paper-and-pencil mathematical modeling. Over 10 years ago, a desert-battle simulation of one force invading another involved the modeling of 66,239 tanks, trucks and other vehicles on simulated terrain around Kuwait, using multiple supercomputers in the DoD High Performance Computer Modernization ProgramOther examples include a 1-billion-atom model of material deformation; a 2.64-million-atom model of the complex maker of protein in all organisms, a ribosome, in 2005;a complete simulation of the life cycle of Mycoplasma genitalium in 2012; and the Blue Brain project at EPFL (Switzerland), begun in May 2005 to create the first computer simulation of the entire human brain, right down to the molecular level.Because of the computational cost of simulation, computer experiments are used to perform inference such as uncertainty quantification.
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