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Related Concept Videos

Accelerators01:17

Accelerators

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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.
The effectiveness of calcium chloride can...
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Trial and Error and Algorithm01:12

Trial and Error and Algorithm

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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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Average Acceleration01:30

Average Acceleration

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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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Instantaneous Acceleration01:16

Instantaneous Acceleration

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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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Acceleration Vectors01:30

Acceleration Vectors

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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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Accelerating Fluids01:17

Accelerating Fluids

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When a fluid is in constant acceleration, the pressure and buoyant force equations are modified. Suppose a beaker is placed in an elevator accelerating upward with a constant acceleration, a. In the beaker, assume there is a thin cylinder of height h with an infinitesimal cross-sectional area, ΔS.
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Area-based Image Analysis Algorithm for Quantification of Macrophage-fibroblast Cocultures
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Accelerating MCMC algorithms.

Christian P Robert1,2, Víctor Elvira3,4, Nick Tawn2

  • 1Université Paris Dauphine PSL Research University Paris France.

Wiley Interdisciplinary Reviews. Computational Statistics
|September 1, 2018
PubMed
Summary
This summary is machine-generated.

Markov chain Monte Carlo (MCMC) algorithms simulate complex distributions locally. Techniques like tempering and Rao-Blackwellization accelerate MCMC convergence for high-dimensional data challenges.

Keywords:
Bayesian analysisHamiltonian Monte CarloMonte Carlo methodsRao‐Blackwellisationcomputational statisticsconvergence of algorithmsefficiency of algorithmssimulationtempering

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Area of Science:

  • Statistical and Graphical Methods of Data Analysis
  • Algorithms and Computational Methods

Background:

  • Markov chain Monte Carlo (MCMC) algorithms are essential for simulating complex statistical distributions.
  • Their local exploration approach simplifies understanding but can lead to lengthy simulations, especially with high-dimensional data.

Purpose of the Study:

  • To review and categorize techniques for accelerating MCMC algorithm convergence.
  • To provide an overview of methods that enhance both the exploration and exploitation phases of MCMC.

Main Methods:

  • Categorization of acceleration techniques into exploration-level (e.g., tempering, Hamiltonian Monte Carlo) and exploitation-level (e.g., Rao-Blackwellization, scalable methods).
  • Discussion of how these methods address the computational demands of MCMC.

Main Results:

  • Identified various strategies to improve the efficiency of MCMC simulations.
  • Highlighted the trade-offs between local exploration and computational cost.

Conclusions:

  • Accelerating MCMC convergence is crucial for tackling complex statistical problems.
  • A range of algorithmic enhancements exist to optimize MCMC performance across different computational challenges.