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Related Concept Videos

Biot-Savart Law: Problem-Solving00:59

Biot-Savart Law: Problem-Solving

The magnitude and direction of a magnetic field created by a steady current can be calculated using the Biot-Savart law.
Consider a mobile phone battery bank as a source of steady current, which flows through the wire connected between the two. What is the magnitude of the magnetic field created by this current at a field point P?
To estimate the magnitude of the total magnetic field, we first consider a small current element of length dl, at a distance r from the field point. Now the following...
Ampere-Maxwell's Law: Problem-Solving01:17

Ampere-Maxwell's Law: Problem-Solving

A parallel-plate capacitor with capacitance C, whose plates have area A and separation distance d, is connected to a resistor R and a battery of voltage V. The current starts to flow at t = 0. What is the displacement current between the capacitor plates at time t? From the properties of the capacitor, what is the corresponding real current?
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For the first part of the problem,...
Statically Indeterminate Problem Solving01:16

Statically Indeterminate Problem Solving

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...
Mason's Rule01:20

Mason's Rule

Mason's rule is a powerful tool in control systems and signal processing. It simplifies the calculation of transfer functions from signal-flow graphs. This method leverages various elements, including loop gains, forward-path gains, and non-touching loops, to determine the transfer function efficiently.
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The Chain Rule: Problem Solving01:23

The Chain Rule: Problem Solving

The thermal expansion of a metal rod shows the application of the Chain Rule when one physical quantity depends on another that varies with time. As the rod is heated, its length changes according to linear thermal expansion, while the temperature of the system varies quadratically with time.For linear thermal expansion, the length L of the rod depends on temperature T such that the rate of change of length with respect to temperature is constant:where L0 = 2 m is the initial length of the rod,...
Rationalizing Substitutions01:29

Rationalizing Substitutions

Integrals involving non-rational functions are often difficult to evaluate using standard techniques, especially when radicals appear in the integrand. Rationalizing substitution provides a systematic method for simplifying such integrals by converting them into rational forms that are easier to handle.Consider a rod whose linear mass density depends on a constant linear density, a characteristic length, and the distance from the left end of the rod. Determining the total mass requires...

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Updated: May 8, 2026

Operant Procedures for Assessing Behavioral Flexibility in Rats
08:30

Operant Procedures for Assessing Behavioral Flexibility in Rats

Published on: February 15, 2015

Abstracting Concept-Changing Rules for Solving Raven's Progressive Matrix Problems.

Fan Shi, Bin Li, Xiangyang Xue

    IEEE Transactions on Pattern Analysis and Machine Intelligence
    |January 21, 2026
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces CRAB, a new AI model that learns abstract rules for visual reasoning tasks like Raven's Progressive Matrices. CRAB effectively discovers concept-changing rules without needing extra human guidance.

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    Last Updated: May 8, 2026

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    RBDT: A Computerized Task System based in Transposition for the Continuous Analysis of Relational Behavior Dynamics in Humans

    Published on: July 17, 2021

    Area of Science:

    • Artificial Intelligence
    • Cognitive Science
    • Machine Learning

    Background:

    • Abstract visual reasoning is key to human intelligence for rule discovery.
    • Raven's Progressive Matrices (RPM) test this ability in AI.
    • Generative AI struggles with concept-changing rules in RPM without supervision.

    Purpose of the Study:

    • To develop a model capable of discovering global concept-changing rules in RPM.
    • To enable AI to perform abstract visual reasoning without auxiliary supervision.

    Main Methods:

    • Proposed a deep latent variable model named Concept-changing Rule ABstraction (CRAB).
    • CRAB learns interpretable concepts and parses rules in a latent space.
    • Employs an iterative learning process for automatic global rule abstraction.

    Main Results:

    • CRAB successfully abstracts global rules shared across concepts.
    • Achieved superior performance over baselines without auxiliary supervision.
    • Demonstrated comparable or better accuracy than models with supervision.

    Conclusions:

    • CRAB offers an interpretable approach to concept learning and rule abstraction.
    • The model effectively handles concept-changing rules in abstract visual reasoning.
    • CRAB advances generative AI's ability in complex rule discovery tasks.