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Related Concept Videos

Collisions in Multiple Dimensions: Introduction01:05

Collisions in Multiple Dimensions: Introduction

6.4K
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...
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Computed Tomography01:10

Computed Tomography

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Tomography refers to imaging by sections. Computed tomography (CT) is a non-invasive imaging technique that uses computers to analyze several cross-sectional X-rays to reveal minute details about structures in the body.
The technique was invented in the 1970s and is based on the principle that as X-rays pass through the body, they are absorbed or reflected at different levels. In the technique, a patient lies on a motorized platform while a computerized axial tomography (CAT) scanner rotates...
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Scalar and Vector Triple Products01:06

Scalar and Vector Triple Products

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Two vectors can be multiplied using a scalar product or a vector product. The resultant of a scalar product is scalar, while with vector products, the resultant is a vector. These rules of the scalar or vector product between two vectors can be applied to multiple vectors to obtain meaningful combinations. The scalar triple product is the dot product of a vector with the cross product of two vectors.
The scalar triple product is the dot product of a vector with the cross product of two vectors....
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Three-Dimensional Analysis of Strain01:29

Three-Dimensional Analysis of Strain

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Three-dimensional strain analysis is crucial for understanding how materials deform under stress, particularly in elastic, homogeneous materials. This method employs principal stress axes to simplify complex stress states into more understandable forms. Subjected to stress, a small cubic element within a material either expands or contracts along these axes, transforming into a rectangular parallelepiped. This transformation effectively illustrates the material's deformation. The principal...
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Histogram01:05

Histogram

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The histogram is a graphical representation in the x-y form of data distribution in a data set. The horizontal x-axis is labeled with what the data represents (for instance, distance from your home to school). The vertical y-axis is labeled either frequency or relative frequency (or percent frequency or probability).
A histogram graph consists of contiguous (adjoining) boxes. The heights of the bars correspond to frequency values. The graph will have the same shape with respective labels. The...
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Related Experiment Videos

TTHRESH: Tensor Compression for Multidimensional Visual Data.

Rafael Ballester-Ripoll, Peter Lindstrom, Renato Pajarola

    IEEE Transactions on Visualization and Computer Graphics
    |March 15, 2019
    PubMed
    Summary
    This summary is machine-generated.

    This study presents a new lossy compression algorithm for multidimensional data, utilizing higher-order singular value decomposition (HOSVD) and other coding techniques. The method offers smooth data degradation and superior performance at low-to-medium bit rates for visualization applications.

    Related Experiment Videos

    Area of Science:

    • Computer Science
    • Data Compression
    • Scientific Visualization

    Background:

    • High-resolution multidimensional data sets in visualization applications face memory and network bandwidth limitations.
    • Efficient data compression strategies are crucial for managing and archiving large datasets.

    Purpose of the Study:

    • To introduce a novel lossy compression algorithm for multidimensional data over regular grids.
    • To address the bottlenecks in memory and network bandwidth for visualization applications.

    Main Methods:

    • The algorithm leverages higher-order singular value decomposition (HOSVD) to decompose multidimensional data.
    • It employs bit-plane, run-length, and arithmetic coding to compress the HOSVD transform coefficients.
    • The compression scheme is designed for regular grid data.

    Main Results:

    • The proposed algorithm achieves smoother data degradation compared to existing methods.
    • It demonstrates lower mean squared error at low-to-medium bit rates.
    • The method offers fine bit rate selection granularity.

    Conclusions:

    • The novel lossy compression algorithm effectively reduces data size for visualization applications.
    • It provides advantages in data archiving, management, and manipulation within the compressed domain.
    • The algorithm is suitable for applications requiring efficient handling of high-resolution multidimensional data.