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Collisions in Multiple Dimensions: Introduction01:05

Collisions in Multiple Dimensions: Introduction

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It is far more common for collisions to occur in two dimensions; that is, the initial velocity vectors are neither parallel nor antiparallel to each other. Let's see what complications arise from this. The first idea is that momentum is a vector. Like all vectors, it can be expressed as a sum of perpendicular components (usually, though not always, an x-component and a y-component, and a z-component if necessary). Thus, when the statement of conservation of momentum is written for a...
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Collisions in Multiple Dimensions: Problem Solving01:06

Collisions in Multiple Dimensions: Problem Solving

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In multiple dimensions, the conservation of momentum applies in each direction independently. Hence, to solve collisions in multiple dimensions, we should write down the momentum conservation in each direction separately. To help understand collisions in multiple dimensions, consider an example.
A small car of mass 1,200 kg traveling east at 60 km/h collides at an intersection with a truck of mass 3,000 kg traveling due north at 40 km/h. The two vehicles are locked together. What is the...
4.5K
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...
785
Sequence Networks of Rotating Machines01:24

Sequence Networks of Rotating Machines

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A Y-connected synchronous generator, grounded through a neutral impedance, is designed to produce balanced internal phase voltages with only positive-sequence components. The generator's sequence networks include a source voltage that is exclusively in the positive-sequence network. The sequence components of line-to-ground voltages at the generator terminals illustrate this configuration.
Zero-sequence current induces a voltage drop across the generator's neutral impedance and other...
592
Discrete Fourier Transform01:15

Discrete Fourier Transform

1.3K
The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...
1.3K
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
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Related Experiment Video

Updated: Apr 30, 2026

Mining Spatial Transcriptomics Datasets using DeepSpaceDB
10:16

Mining Spatial Transcriptomics Datasets using DeepSpaceDB

Published on: September 5, 2025

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Mining recurring concepts in a dynamic feature space.

João Bártolo Gomes, Mohamed Medhat Gaber, Pedro A C Sousa

    IEEE Transactions on Neural Networks and Learning Systems
    |May 9, 2014
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a novel data stream classification system (MReC-DFS) that efficiently handles changing features and reappearing concepts. It achieves high accuracy and memory efficiency by dynamically adapting models and selecting relevant features.

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    Area of Science:

    • Machine Learning
    • Data Mining
    • Artificial Intelligence

    Background:

    • Traditional data stream classification assumes static feature spaces, which is unrealistic for real-world applications where features evolve.
    • Concept drift and recurring concepts pose challenges for maintaining accuracy and efficiency in data stream mining.
    • Storing past models for concept reuse can be memory-intensive, limiting practical application.

    Purpose of the Study:

    • To propose mining recurring concepts in a dynamic feature space (MReC-DFS), a system for data stream classification.
    • To address the challenges of learning recurring concepts within a dynamic feature space while minimizing memory consumption.
    • To enhance learning accuracy and processing time by reusing previously learned models.

    Main Methods:

    • MReC-DFS detects and adapts to concept changes using learning performance and contextual information.
    • A dynamically weighted ensemble combines stored models to handle recurring concepts.
    • Incremental feature selection reduces the feature space, storing only relevant features for memory efficiency.

    Main Results:

    • MReC-DFS demonstrates high accuracy compared to state-of-the-art techniques on diverse real-world datasets.
    • The system exhibits superior memory efficiency by storing only the most relevant features.
    • An incremental feature selection method effectively determines the threshold for relevant features.

    Conclusions:

    • MReC-DFS effectively addresses concept drift and recurring concepts in dynamic feature spaces.
    • The proposed system offers a significant improvement in memory efficiency for data stream classification.
    • MReC-DFS provides a robust and efficient solution for real-world data stream mining applications.