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相关概念视频

Sampling Distribution01:12

Sampling Distribution

12.3K
Given simple random samples of size n from a given population with a measured characteristic such as mean, proportion, or standard deviation for each sample, the probability distribution of all the measured characteristics is called a sampling distribution. How much the statistic varies from one sample to another is known as the sampling variability of a statistic. You typically measure the sampling variability of a statistic by its standard error. The standard error of the mean is an example...
12.3K
Sampling Theorem01:15

Sampling Theorem

310
In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
310
Reaction Quotient02:35

Reaction Quotient

48.2K
The status of a reversible reaction is conveniently assessed by evaluating its reaction quotient (Q). For a reversible reaction described by m A + n B ⇌ x C + y D, the reaction quotient is derived directly from the stoichiometry of the balanced equation as
48.2K
Free Energy Changes for Nonstandard States03:25

Free Energy Changes for Nonstandard States

11.1K
The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; concentrations other than 1 M) is related to the standard free energy change according to this equation:
 
where R is the gas constant (8.314 J/K·mol), T is the absolute temperature in kelvin, and Q is the reaction quotient. This equation may be used to predict the spontaneity of a process under any given set of conditions.
Reaction Quotient...
11.1K
Estimating Population Standard Deviation01:26

Estimating Population Standard Deviation

3.0K
When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate of σ. However, it can sometimes under or overestimate the population standard deviation. To overcome this drawback, confidence intervals are determined to estimate population parameters and eliminate any calculation bias accurately. However, this only applies to random samples from normally distributed populations. Knowing the sample mean and...
3.0K
The Small x Assumption02:20

The Small x Assumption

46.0K
If a reaction has a small equilibrium constant, the equilibrium position favors the reactants. In such reactions, a negligible change in concentration may occur if the initial concentrations of reactants are high and the Kc value is small. In such circumstances, the equilibrium concentration is approximately equal to its initial concentration.  This estimation can be used to simplify the equilibrium calculations by assuming that some equilibrium concentrations are equal to the initial...
46.0K

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相关实验视频

Updated: Jun 12, 2025

The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

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对于在中度偏差调节中的随机反应-扩散方程的重要性抽样.

Ioannis Gasteratos1, Michael Salins2, Konstantinos Spiliopoulos2

  • 1Department of Mathematics, Imperial College London, London, UK.

Stochastic partial differential equations : analysis and computations
|September 19, 2024
PubMed
概括

我们开发了一种高效的重要性抽样方法,以估计随机反应-扩散方程的退出概率. 这种方法准确地预测系统如何远离稳定状态,即使噪声小.

科学领域:

  • 应用数学 应用数学 应用数学
  • 随机分析 随机分析
  • 计算科学 计算科学

背景情况:

  • 随机反应-扩散方程模型复杂的系统与固有的随机性.
  • 估计从稳定状态中逃脱的概率对于理解系统动态至关重要.
  • 经常使用小噪声近似,但可能缺乏准确性.

研究的目的:

  • 开发一个可证明有效的重要性抽样计划.
  • 估计从稳定平衡的缩放社区的退出概率.
  • 在中度偏差缩放下分析随机反应-扩散方程的行为.

主要方法:

  • 采用进口量抽样的方式.
  • 适度偏差缩放的缩放方式
  • 非线性动力学的线性化.
  • 随机控制 随机控制 随机控制
  • 变量方法 变量方法

主要成果:

  • 开发了一个被证明是有效的重要抽样计划.
  • 该方案准确地估计了小噪音随机反应-扩散方程的退出概率.
  • 性能在零噪声极限和预异象验证时得到验证.
关键词:
进口量抽样采集方式适度的偏差 适度的偏差蒙特卡洛方法 蒙特卡洛方法最佳的控制控制是最好的控制.模拟罕见事件的模拟.随机反应扩散方程 随机反应扩散方程

更多相关视频

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

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Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
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Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

Published on: April 12, 2019

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相关实验视频

Last Updated: Jun 12, 2025

The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

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Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
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Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

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  • 确定了用于高概率出口的有限维子空间.

    • 结论:

    • 开发的重要性采样方案对于分析随机反应-扩散系统是有效的.
    • 该方法提供出口概率的准确估计,通过理论和模拟验证.
    • 识别的子空间为系统逃生动态提供了洞察力.