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State Space Representation01:27

State Space Representation

668
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...
668
Orthogonal Trajectories01:26

Orthogonal Trajectories

137
Orthogonal trajectories describe the geometric relationship between two families of curves that intersect each other at right angles. One illustrative case involves a family of parabolas that open sideways along the x-axis. These curves share a common shape but differ by a scaling parameter, resulting in a set of curves that all pass through the origin and widen at different rates.Determining Orthogonal TrajectoriesTo identify the orthogonal trajectories for these parabolas, the first step...
137
Space Trusses: Problem Solving01:29

Space Trusses: Problem Solving

946
A space truss is a three-dimensional counterpart of a planar truss. These structures consist of members connected at their ends, often utilizing ball-and-socket joints to create a stable and versatile framework. Due to its adaptability and capacity to withstand complex loads, the space truss is widely used in various construction projects.
Consider a tripod consisting of a tetrahedral space truss with a ball-and-socket joint at C. Suppose the height and lengths of the horizontal and vertical...
946
LTR Retrotransposons03:08

LTR Retrotransposons

20.3K
LTR retrotransposons are class I transposable elements with long terminal repeats flanking an internal coding region. These elements are less abundant in mammals compared to other class I transposable elements. About 8 percent of human genomic DNA comprises LTR retrotransposons. Some of the common examples of LTR retrotransposons are Ty elements in yeast and Copia elements in Drosophila.
The internal coding region of LTR retrotransposons and their mechanism of transposition closely resembles a...
20.3K
Statically Indeterminate Problem Solving01:16

Statically Indeterminate Problem Solving

815
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...
815
Escape Velocity01:26

Escape Velocity

8.6K
The escape velocity of an object is defined as the minimum initial velocity that it requires to escape the surface of another object to which it is gravitationally bound and never to return. For example, what would be the minimum velocity at which a satellite should be launched from the Earth's surface such that it just escapes the Earth's gravitational field?
To calculate the escape velocity, it is assumed that no energy is lost to any frictional forces. In practice, a satellite...
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Related Experiment Video

Updated: Mar 17, 2026

Application of Deep Learning-Based Medical Image Segmentation via Orbital Computed Tomography
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LSTM: A Search Space Odyssey.

Klaus Greff, Rupesh K Srivastava, Jan Koutnik

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    This study analyzed eight Long Short-Term Memory (LSTM) variants for machine learning tasks. Results show standard LSTM with its forget gate and output activation function remains optimal, offering guidelines for hyperparameter tuning.

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    Area of Science:

    • Artificial Intelligence
    • Machine Learning
    • Deep Learning

    Background:

    • Long Short-Term Memory (LSTM) networks are advanced recurrent neural networks.
    • Various LSTM architectures have been developed since 1995.
    • These networks are state-of-the-art for many machine learning tasks, driving interest in their components.

    Purpose of the Study:

    • To conduct a large-scale analysis of eight LSTM variants.
    • To evaluate the utility of different computational components within LSTM architectures.
    • To compare LSTM variants on speech recognition, handwriting recognition, and music modeling tasks.

    Main Methods:

    • Performed a large-scale analysis of 5400 experimental runs across eight LSTM variants.
    • Optimized hyperparameters for each variant and task using random search.
    • Assessed hyperparameter importance using functional ANalysis Of VAriance (fANOVA).

    Main Results:

    • No LSTM variant significantly outperformed the standard LSTM architecture.
    • The forget gate and output activation function were identified as the most critical LSTM components.
    • Studied hyperparameters demonstrated near-complete independence.

    Conclusions:

    • Standard LSTM architecture is highly effective for speech, handwriting, and music modeling.
    • Forget gate and output activation function are key to LSTM performance.
    • Derived guidelines for efficient hyperparameter adjustment in LSTMs.