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Accelerators in concrete serve as admixtures to speed up the hardening process, enabling the concrete to achieve early strength faster. Although accelerators do not necessarily impact the time it takes concrete to set, they reduce this time in practice. A common accelerator is calcium chloride, which is particularly useful for hastening early strength development in cold weather or for rapid repair jobs that require quick heat generation after mixing.
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A problem-solving strategy is a plan of action used to find a solution. Different strategies have distinct action plans. Trial and error involves trying different solutions until one works. For instance, to fix a broken printer, you might check ink levels, ensure the paper tray isn't jammed, and verify the printer's connection to your laptop. This method can be time-consuming but is commonly used. Thomas Edison, for example, used trial and error to find a suitable filament for the light...
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The importance of understanding acceleration spans our day-to-day experiences, as well as the vast reaches of outer space and the tiny world of subatomic physics. In everyday conversation, to accelerate means to speed up. For instance, we are familiar with the acceleration of our car; the harder we apply our foot to the gas pedal, the faster we accelerate. The greater the acceleration, the greater the change in velocity over a given time. Acceleration is widely seen in experimental physics. In...
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Acceleration is in the direction of the change in velocity, but it is not always in the direction of motion. When an object slows down, its acceleration is opposite to the direction of its motion. Although commonly referred to as deceleration, this causes confusion in our analysis as deceleration is not a vector, and does not point to a specific direction with respect to a coordinate system. Therefore, the term deceleration is not used. For example, when a subway train slows down, it...
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In everyday conversation, accelerating means speeding up. Acceleration is a vector in the same direction as the change in velocity, Δv, therefore the greater the acceleration, the greater the change in velocity over a given time. Since velocity is a vector, it can change in magnitude, direction, or both. Thus acceleration is a change in speed or direction, or both. For example, if a runner traveling at 10 km/h due east slows to a stop, reverses direction, and continues their run at 10 km/h...
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Updated: Jan 31, 2026

Strategic Endothelial Cell Tube Formation Assay: Comparing Extracellular Matrix and Growth Factor Reduced Extracellular Matrix
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Accelerating Nonnegative Matrix Factorization Algorithms Using Extrapolation.

Andersen Man Shun Ang1, Nicolas Gillis2

  • 1Department of Mathematics and Operational Research, Faculté Polytechnique, Université de Mons, 7000 Mons, Belgium manshun.ang@umons.ac.be.

Neural Computation
|December 22, 2018
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Summary
This summary is machine-generated.

We introduce a novel framework to accelerate nonnegative matrix factorization (NMF) algorithms. This approach enhances speed for NMF, a key technique in data analysis, using extrapolation methods.

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Area of Science:

  • Machine Learning
  • Optimization Algorithms
  • Data Science

Background:

  • Nonnegative matrix factorization (NMF) is a widely used dimensionality reduction technique.
  • Existing NMF algorithms can be computationally intensive, limiting their application on large datasets.
  • Accelerating NMF algorithms is crucial for efficient data analysis.

Purpose of the Study:

  • To propose a general framework for significantly accelerating NMF algorithms.
  • To introduce a novel application of extrapolation schemes in nonconvex NMF.
  • To demonstrate the effectiveness of the proposed framework on existing NMF methods.

Main Methods:

  • A general framework inspired by extrapolation schemes from convex optimization and the method of parallel tangents.
  • Application of extrapolation to exact coordinate descent algorithms for nonconvex NMF problems.
  • Integration with state-of-the-art NMF algorithms like hierarchical alternating least squares (HALS) and alternating nonnegative least squares (ANLS).

Main Results:

  • Significant acceleration of NMF algorithms.
  • Demonstrated performance improvements on synthetic, image, and document datasets.
  • Novel application of extrapolation techniques to nonconvex NMF.

Conclusions:

  • The proposed framework offers a general and effective approach to accelerate NMF algorithms.
  • Extrapolation methods can be successfully applied to nonconvex NMF problems.
  • The accelerated NMF algorithms show improved performance across various data types.