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This operation is computationally expensive and generally cannot benefit from the mathematical simplifications available for true convolutions.
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The difference with other models consists in the complete absence of mathematical simplifications or other physical assumptions.
First, continuous thermodynamics results in mathematical simplifications, which can considerably reduce computer-time requirements in chemical engineering.
However, even with the considerable mathematical simplifications afforded by the assumptions of firing-rate models, the immense dimensionality of the brain requires further assumptions and approximations.
Differences between theoretical predictions and experimental results arise from differences between the true and the assumed genetic model, and from mathematical simplifications applied in the prediction methods.
In this paper, the surprisal is calculated with the natural logarithm (base e) for the sake of mathematical simplification.
The paper was circulated among only a handful of scientists; one issue may have been that the mathematical simplification doesn't exactly match the way the physical proteins seem to behave.
We use the product-inference rule in our FIS, since it allows a mathematical simplification in the defuzzification process and is commonly used in practice.
She identified a mathematical simplification, in which the non-planar six-membered rings of atoms can be represented by planar "median hexagon"s made from the midpoints of the chemical bonds.
The biological to mathematical mapping allows for separate use of biological and mathematical components, and includes automatic mathematical simplification using pseudo-steady approximations and mass conservation relationships.
Such understanding may prove useful for those cases where an explicit mathematical simplification is not feasible.
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