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Related Concept Videos

State Space Representation01:27

State Space Representation

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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.
Consider an RLC circuit, a...
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Synthetic Disvision of Polynomials01:28

Synthetic Disvision of Polynomials

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Synthetic division is an efficient algorithmic approach for dividing a polynomial by a linear binomial of the form x - c, where c is a real number. This method is helpful due to its streamlined process, which avoids the more cumbersome steps involved in the traditional long division of polynomials. It simplifies computation and serves as a practical tool for evaluating polynomials and identifying their factors.To perform synthetic division, one begins by listing the coefficients of the...
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State Space to Transfer Function01:21

State Space to Transfer Function

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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.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
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Statically Indeterminate Problem Solving01:16

Statically Indeterminate Problem Solving

587
Statically indeterminate problems are those where statics alone can not determine the internal forces or reactions. Consider a structure comprising two cylindrical rods made of steel and brass. These rods are joined at point B and restrained by rigid supports at points A and C. Now, the reactions at points A and C and the deflection at point B are to be determined. This rod structure is classified as statically indeterminate as the structure has more supports than are necessary for maintaining...
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Constraints and Statical Determinacy01:26

Constraints and Statical Determinacy

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In structural engineering, the equilibrium of a system is not only determined by its equations of equilibrium but also with the help of constraints. Constraints refer to restrictions on the motion of a system. The proper combinations of constraints can minimize the total number of constraints needed to maintain a system in mechanical equilibrium. When this happens, the system is said to be statically determinate. For such systems, the unknown reaction supports can be estimated using equilibrium...
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Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...
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Active inference on discrete state-spaces: A synthesis.

Lancelot Da Costa1,2, Thomas Parr2, Noor Sajid2

  • 1Department of Mathematics, Imperial College London, London, SW7 2RH, United Kingdom.

Journal of Mathematical Psychology
|December 21, 2020
PubMed
Summary
This summary is machine-generated.

Active inference, a principle for perception and action, is mathematically synthesized for discrete models. This work clarifies its theory, neuronal dynamics, and practical applications in simulating behavior and predicting neurophysiological responses.

Keywords:
Active inferenceFree energy principleMarkov decision processMathematical reviewProcess theoryVariational Bayesian inference

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Area of Science:

  • Computational Neuroscience
  • Artificial Intelligence
  • Cognitive Science

Background:

  • Active inference is a unifying principle for perception, action, and learning in biological and artificial systems.
  • Its process theory has evolved with complex generative models, but the link between principles and implementation can be unclear.

Purpose of the Study:

  • To provide a comprehensive mathematical synthesis of active inference for discrete state-space models.
  • To bridge the gap between active inference theory and its practical implementation.
  • To offer a foundation for understanding active inference with mixed generative models.

Main Methods:

  • Mathematical synthesis of active inference on discrete state-space models.
  • Derivation of neuronal dynamics from first principles.
  • Integration of continuous sensations with discrete representations.

Main Results:

  • A unified mathematical framework for active inference on discrete models.
  • Derivation of neuronal dynamics linked to biological processes.
  • A foundational understanding for mixed generative models in active inference.

Conclusions:

  • This synthesis clarifies active inference principles and their relation to process theories.
  • The work serves as a practical guide for implementing active inference and simulating behavior.
  • It provides insights for empirical predictions of neurophysiological responses.