The behavior of the axial next-nearest-neighbor Ising (ANNNI) model in an external magnetic field is investigated using a low-temperature expansion of the free energy. Unusual cascades of phase transitions and “compl...
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The behavior of the axial next-nearest-neighbor Ising (ANNNI) model in an external magnetic field is investigated using a low-temperature expansion of the free energy. Unusual cascades of phase transitions and “complete devil's staircases,” unexpected for the ANNNI model, are fo
Mathematically testing the validity of a theoretical model with an observed physical system is an important step in understanding and utilizing such a system. Perhaps even more useful is the generation of computationa...
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Mathematically testing the validity of a theoretical model with an observed physical system is an important step in understanding and utilizing such a system. Perhaps even more useful is the generation of computational techniques which use input-output data from physical systems to automatically construct mathematical models which, in some sense, provide the ''best'' descriptions of the real systems. This paper briefly discusses a few of the more recent mathematical techniques available for model generation and testing. A new identification method based upon convex and linearprogramming is discussed in detail and a number of examples indicating its applicability are given. The linear programming method is basically an approximation to a convex programming problem, the solution of which determines the coefficients of the differential equation describing the observed system data. A number of extensions of the identification method indicate some of its most useful properties. The order of the assumed model differential equation can be larger than that of the unknown system and the identification process will either assign zero values to the superfluous coefficients of the model or pole-zero cancellations will occur in the factored form of the Laplace transform of the model transfer function. ''Best'' lowest order models may be selected automatically. linear constraints among the coefficients of the model differential equation may be used to restrict the allowable ranges of the coefficients. Multiple sets of data for a single system may be used simultaneously in the indentification process. Multiple input-output systems or systems described by difference equations or with transportation lag can also be identified. Coefficients of time varying and/or nonlinear models may be determined. Review on some recent identification methods and a new convex and linear programming method is presented which is particularly applicable to biological and medical experimentation.
A new method for detecting negative cycles in a graph is proposed. This method is based upon the primal - dual relationships of a linear program formulated from an assign- ment problem type network. A computer program...
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A new method for detecting negative cycles in a graph is proposed. This method is based upon the primal - dual relationships of a linear program formulated from an assign- ment problem type network. A computer program is developed for this new method to include the complete solution of the assignment problem. Results are given on program efficiency
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