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X-ray Crystallography02:18

X-ray Crystallography

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The size of the unit cell and the arrangement of atoms in a crystal may be determined from measurements of the diffraction of X-rays by the crystal, termed X-ray crystallography.
Diffraction
Diffraction is the change in the direction of travel experienced by an electromagnetic wave when it encounters a physical barrier whose dimensions are comparable to those of the wavelength of the light. X-rays are electromagnetic radiation with wavelengths about as long as the distance between neighboring...
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Prediction Intervals01:03

Prediction Intervals

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The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y. 
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Confidence Intervals01:21

Confidence Intervals

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An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a  sample proportion. However, unlike the point estimate which is a single value, the confidence interval  contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
A...
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Improper Integrals: Infinite Intervals01:29

Improper Integrals: Infinite Intervals

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An integral is classified as improper due to an infinite interval when at least one of its limits of integration extends to positive or negative infinity. In such cases, the region under the curve is unbounded, and standard techniques for evaluating definite integrals are not directly applicable. Instead, the improper integral is defined through a limiting process that allows one to determine whether the accumulated area remains finite despite the infinite domain.Application to Exponential...
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Interval Level of Measurement00:55

Interval Level of Measurement

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For effective statistical analysis, data are classified into four levels of measurement—nominal, ordinal, interval, and ratio.
Data measured using the interval scale are similar to ordinal level data because they have a definite arrangement. However, in the interval level of measurement, the differences between data values are meaningful even though the data does not have a starting point.
Temperature is measured using the interval scale. It is measurable data, and the difference between...
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Interpretation of Confidence Intervals01:19

Interpretation of Confidence Intervals

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A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.
Confidence intervals have confidence coefficients that are crucial for their interpretation. The most common confidence coefficients are 0.90, 0.95, and 0.99, which can be written as percentages–90%, 95%, and 99%, respectively.
Suppose a person calculates a confidence interval with a confidence coefficient of 0.95. In that case, they can...
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Related Experiment Video

Updated: Feb 8, 2026

Trace Fear Conditioning in Mice
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Time Interval Ray Tracing for Motion Blur.

Konstantin Shkurko, Cem Yuksel, Daniel Kopta

    IEEE Transactions on Visualization and Computer Graphics
    |July 11, 2018
    PubMed
    Summary
    This summary is machine-generated.

    This study presents a novel ray tracing method for realistic motion blur. It analytically approximates blur per ray, avoiding sampling for efficient, noise-free results in computer graphics.

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    Area of Science:

    • Computer Graphics
    • Computational Geometry
    • Image Processing

    Background:

    • Realistic motion blur is crucial for visual fidelity in computer graphics.
    • Existing methods often rely on computationally expensive sampling techniques.

    Purpose of the Study:

    • To develop an efficient and accurate method for computing motion blur in ray tracing.
    • To eliminate noise associated with sampling-based motion blur approximations.

    Main Methods:

    • Associating time intervals with rays for direct intersection evaluation with animated object faces.
    • Representing swept volumes using triangulations for intersection with stationary triangles.
    • Utilizing standard ray tracing acceleration structures without time-dimension modifications.

    Main Results:

    • Analytical approximation of motion blurred visibility per ray.
    • Noise-free motion blur for primary and secondary rays.
    • Framework for emulating camera shutter mechanisms and motion amplification.

    Conclusions:

    • The proposed method offers an efficient and high-quality solution for motion blur in ray tracing.
    • Enables improved visual realism and artistic control in rendering animated scenes.