Insights of Window-Based Mechanism Approach to Visualize Composite BioData Point in Feature Spaces

Mosaab Daoud1,2

  • 1Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada.

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Classifying Matter by Composition

Matter: Pure Substances and Mixtures
According to its composition, the matter can be classified into two broad categories — pure substances and mixtures. 
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Solution Composition During Acid/Base Titrations01:17

Solution Composition During Acid/Base Titrations

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State Space Representation01:27

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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Space Trusses01:25

Space Trusses

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Transfer Function to State Space

State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
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State Space to Transfer Function01:21

State Space to Transfer Function

The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
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