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Related Concept Videos

Quadratic Equations01:29

Quadratic Equations

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A quadratic equation is an algebraic expression where a variable is raised to the second power and combined with its first power and a constant; all equated to zero. These equations are frequently used to model relationships involving area, motion, and optimization. The general representation of a quadratic equation iswhere a, b, and c are real values, and a is nonzero to ensure the presence of the squared term.One method for solving a quadratic equation involves rewriting it as a product of...
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Quadratic Models01:23

Quadratic Models

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Quadratic models are mathematical representations used to describe relationships in which the rate of change changes at a constant rate. These models appear in a wide variety of natural and engineered systems, especially those involving motion, forces, and optimization. One common application is analyzing the vertical motion of objects influenced by gravity, such as a ball thrown into the air.In such scenarios, the object's height changes over time in a curved pattern, rising to a maximum point...
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Graphs of Equations in Two Variables01:30

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An equation with two variables, typically written in the form y = f(x) or Ax + By = C, describes a relationship between quantities represented by x and y. Each solution to such an equation is an ordered pair (x, y) that satisfies the equation when substituted. These pairs can be represented graphically to understand the variables' relationship visually.A common technique for constructing the graph of a two-variable equation is to create a value table. Begin by choosing several values for the...
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Graphical Representation of Inequalities01:28

Graphical Representation of Inequalities

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The graph of the equation where y equals x squared forms a curve known as a parabola. This curve acts as a boundary in the coordinate plane, dividing it into distinct regions based on the relative position of points.When the equality sign in the equation is replaced with an inequality—such as greater than, less than, greater than or equal to, or less than or equal to—the graphical representation changes from a single curve into a broader shaded area that signifies the set of all...
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Solving Inequalities Graphically01:24

Solving Inequalities Graphically

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Solving inequalities graphically involves using a visual approach to determine where a mathematical expression meets a specific condition, such as being greater than or less than another value. By examining the position of a graph relative to the x-axis or another graph, it becomes possible to identify the range of x-values that satisfy the inequality. This method provides an intuitive understanding of solution intervals by showing where the inequality holds true.Graphical solutions to...
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Application of Nonlinear Inequalities01:29

Application of Nonlinear Inequalities

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A nonlinear inequality describes a comparison involving an expression that curves or behaves more complexly than a straight line. These inequalities often appear in forms that include squares, products, or variables in the denominator.To solve such an inequality, one starts by rewriting it so that zero appears on one side. For example, the inequality:  can be factored as: This form makes it easier to identify the values that cause the expression to equal zero. In this case, the...
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Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps
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Fast approximate quadratic programming for graph matching.

Joshua T Vogelstein1, John M Conroy2, Vince Lyzinski3

  • 1Department of Biomedical Engineering, Johns Hopkins University, Baltimore, MD, USA.

Plos One
|April 18, 2015
PubMed
Summary
This summary is machine-generated.

We developed a Fast Approximate Quadratic assignment algorithm for efficient graph matching in big data. This new algorithm outperforms the state-of-the-art in speed and accuracy on benchmark datasets and real-world brain-graph data.

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Area of Science:

  • Operations Research
  • Graph Theory
  • Computer Vision
  • Neuroscience

Background:

  • Quadratic assignment problems (QAP) are prevalent across multiple scientific domains.
  • Graph matching, a specific type of QAP, is crucial due to the rise of graph-valued data.
  • Existing methods struggle with the scale of large graphs common in big data.

Purpose of the Study:

  • To introduce a novel algorithm for efficient and accurate large graph matching.
  • To address the computational challenges posed by quadratic assignment problems in big data contexts.

Main Methods:

  • Development of the Fast Approximate Quadratic assignment algorithm.
  • Empirical evaluation using the QAPLIB benchmark library.
  • Application to matching C. elegans connectomes (brain-graphs).

Main Results:

  • The Fast Approximate Quadratic assignment algorithm demonstrates superior speed and lower objective values compared to state-of-the-art methods on over 80% of QAPLIB instances.
  • Efficient performance was achieved when applied to the C. elegans connectome matching task.

Conclusions:

  • The proposed algorithm offers a significant advancement for tackling large-scale graph matching problems.
  • This method provides an efficient and accurate solution for complex QAP instances, particularly in neuroscience applications.