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Mathieu function. In mathematics, Mathieu functions, sometimes called angular Mathieu functions, are solutions of Mathieu's differential equation. where a, q are real -valued parameters. Since we may add π/2 to x to change the sign of q, it is a usual convention to set q ≥ 0.
Inverted pendulum. Balancing cart, a simple robotics system circa 1976. The cart contains a servo system that monitors the angle of the rod and moves the cart back and forth to keep it upright. An inverted pendulum is a pendulum that has its center of mass above its pivot point. It is unstable and falls over without additional help.
β = 0 , {\displaystyle \beta =0,} the Duffing equation describes a damped and driven simple harmonic oscillator, γ {\displaystyle \gamma } is the amplitude of the periodic driving force; if. γ = 0 {\displaystyle \gamma =0} the system is without a driving force, and. ω {\displaystyle \omega } is the angular frequency of the periodic driving ...
The polyhedral model (also called the polytope method) is a mathematical framework for programs that perform large numbers of operations -- too large to be explicitly enumerated -- thereby requiring a compact representation. Nested loop programs are the typical, but not the only example, and the most common use of the model is for loop nest ...
A hyperparameter is a parameter whose value is used to control the learning process, which must be configured before the process starts. [2] Hyperparameter optimization determines the set of hyperparameters that yields an optimal model which minimizes a predefined loss function on a given data set. [3] The objective function takes a set of ...
Dual-coding theory is a theory of cognition that suggests that the mind processes information along two different channels; verbal and nonverbal. It was hypothesized by Allan Paivio of the University of Western Ontario in 1971. In developing this theory, Paivio used the idea that the formation of mental imagery aids learning through the picture ...
The use of mathematical models to solve problems in business or military operations is a large part of the field of operations research. Mathematical models are also used in music, [3] linguistics, [4] and philosophy (for example, intensively in analytic philosophy). A model may help to explain a system and to study the effects of different ...
List of datasets in computer vision and image processing. Outline of machine learning. v. t. e. These datasets are used in machine learning (ML) research and have been cited in peer-reviewed academic journals. Datasets are an integral part of the field of machine learning. Major advances in this field can result from advances in learning ...