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Multiple scientific articles were written, and the multiscale activities took different lives of their own. At SNL, the multiscale modeling effort was an engineering top-down approach starting from continuum mechanics perspective, which was already rich with a computational paradigm.
Merton believed that it is multiple discoveries, rather than unique ones, that represent the common pattern in science. [4] Merton contrasted a "multiple" with a "singleton"—a discovery that has been made uniquely by a single scientist or group of scientists working together. [5] The distinction may blur as science becomes increasingly ...
Multiple discoveries in the history of science provide evidence for evolutionary models of science and technology, such as memetics (the study of self-replicating units of culture), evolutionary epistemology (which applies the concepts of biological evolution to study of the growth of human knowledge), and cultural selection theory (which studies sociological and cultural evolution in a ...
In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives.. The function is often thought of as an "unknown" that solves the equation, similar to how x is thought of as an unknown number solving, e.g., an algebraic equation like x 2 − 3x + 2 = 0.
The optimization of portfolios is an example of multi-objective optimization in economics. Since the 1970s, economists have modeled dynamic decisions over time using control theory. [14] For example, dynamic search models are used to study labor-market behavior. [15] A crucial distinction is between deterministic and stochastic models. [16]
In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equation constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables). [1]
Example A occurs twice in set 1 because these are chosen with replacement. Bootstrap aggregation (bagging) involves training an ensemble on bootstrapped data sets. A bootstrapped set is created by selecting from original training data set with replacement. Thus, a bootstrap set may contain a given example zero, one, or multiple times.
The terminology of ABM tends to be used more often in the science, and MAS in engineering and technology. [5] Applications where multi-agent systems research may deliver an appropriate approach include online trading, [6] disaster response, [7] [8] target surveillance [9] and social structure modelling. [10]