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Related Concept Videos

Area Problem01:26

Area Problem

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Determining the area of a region with straight edges is straightforward, as geometric formulas for rectangles, triangles, and polygons can be applied directly. However, traditional geometric methods are insufficient when a region has a curved boundary, such as the area under a function.fromThe area problem involves finding a systematic way to measure such regions. One approach to solving this problem is through approximation. Instead of attempting to compute the area exactly at the outset, the...
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Area Between Curves: Integrating With Respect to x01:25

Area Between Curves: Integrating With Respect to x

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Consider two continuous functions defined on a closed interval from a to b. The region between these curves is bounded vertically by their graphs and horizontally by the endpoints of the interval. The objective is to measure the area of this region.An initial estimate of the area can be obtained by dividing the interval into a large number of narrow vertical strips of equal width. Each strip is approximated by a rectangle whose height is given by the vertical difference between the two...
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The moment of inertia is a fundamental concept in mechanical engineering that plays a significant role in designing rotationally symmetric objects such as flywheels, gears, and other mechanical systems. In this context, we will discuss the moment of inertia of a flywheel rotating about its centroidal axis and how it relates to the moment of inertia about an axis parallel to it.
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Area Computation by the Alternative Coordinate Method01:24

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The alternative coordinate method, also known as the Shoelace Formula, is a technique for determining the area of a traverse using Cartesian coordinates. This method relies on the sequential arrangement of x and y coordinates for each point of the shape, ensuring accuracy and ease of application.In this approach, each corner's x and y coordinates are listed as fractions, with the x-coordinate as the numerator and the y-coordinate as the denominator. These coordinates are arranged sequentially...
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Area Between Curves: Problem Solving01:27

Area Between Curves: Problem Solving

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A region can be enclosed by three curves: a square root function, a reflected cube root function, and a linear function. The linear function intersects each of the other two curves, and these intersection points determine where the boundary of the enclosed region changes. Because different curves serve as the upper and lower boundaries in different parts of the graph, the area cannot be found using a single setup over the entire interval.To compute the area, the region is first divided into two...
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A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
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Related Experiment Video

Updated: Mar 31, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
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A polynomial time algorithm for computing the area under a GDT curve.

Aleksandar Poleksic1

  • 1Department of Computer Science, University of Northern Iowa, 305 ITTC, Cedar Falls, Iowa, 50613 USA.

Algorithms for Molecular Biology : AMB
|October 28, 2015
PubMed
Summary

This study introduces a novel algorithm for accurately estimating the area under the GDT (Global Distance Test) function, a key metric for assessing protein model quality. This advancement offers a more reliable measure than existing methods for protein structure prediction.

Keywords:
Model qualityProtein structureStructure modelingStructure prediction

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Area of Science:

  • Computational Biology
  • Structural Bioinformatics
  • Algorithm Development

Background:

  • Protein structure prediction quality assessment is crucial for advancing the field.
  • The Global Distance Test (GDT) function is a primary descriptor of protein model quality.
  • Accurate estimation of the area under the GDT function (GDT_A) is needed, as current metrics like GDT_TS are approximations.

Purpose of the Study:

  • To develop and present the first algorithm for computing near-optimal estimates of GDT_A.
  • To establish GDT_A as a reliable single numerical measure for protein model quality.

Main Methods:

  • Proving that GDT_A is well-defined.
  • Approximating GDT_A using Riemann sums with accurate GDT function values.
  • Developing an algorithm with cubic asymptotic time complexity.

Main Results:

  • GDT_A is robust to coordinate changes, unlike GDT_TS.
  • The computation of GDT_A is tractable and achievable in cubic time.
  • The new algorithm provides near-optimal estimates for GDT_A.

Conclusions:

  • The presented algorithm is the first capable of computing near-optimal GDT_A estimates.
  • The implemented techniques are expected to foster more reliable protein 3D model quality assessment procedures.