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相关概念视频

Maxwell-Boltzmann Distribution: Problem Solving01:20

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Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
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Convolution: Math, Graphics, and Discrete Signals01:24

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In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...
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Convolution Properties I01:20

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Convolution computations can be simplified by utilizing their inherent properties.
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Applications of Integration to Probability Density Functions01:27

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Continuous probability distributions are used to model random variables that can take on any real value within a specified range. These variables do not take on isolated or countable values but rather exist on a continuum. For example, the height of an individual can be measured with increasing precision—such as 163.5 or 165.25 centimeters—demonstrating that height is a continuous random variable.The behavior of such variables is described using a probability density function (PDF),...
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Probability Distributions01:32

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 The probability of a random variable x  is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
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State Space Representation01:27

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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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Morphology-Based Distinction Between Healthy and Pathological Cells Utilizing Fourier Transforms and Self-Organizing Maps
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一般化卷积多体分布的功能表示.

Danish Khan1,2, O Anatole von Lilienfeld1,2,3,4,5,6,7

  • 1Department of Chemistry, Chemical Physics Theory Group, University of Toronto, St. George Campus, Toronto, ON M5R 0A3, Canada.

Proceedings of the National Academy of Sciences of the United States of America
|October 6, 2025
PubMed
概括
此摘要是机器生成的。

一般化的卷积多体分布函数 (cMBDF) 为化学中的机器学习提供了一个计算效率高的替代方案. 这些紧的原子表示显著减少了对准确材料性质预测的数据和计算需求.

关键词:
化学物理化学物理机器学习是机器学习.量子化学是一种量子化学.

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科学领域:

  • 计算化学是一种计算化学.
  • 材料科学是一种材料科学.
  • 机器学习 机器学习

背景情况:

  • 现代机器学习 (ML) 模型需要大量的数据和计算资源,导致高碳足迹.
  • 轻量化方法提供更快的培训和减少环境影响.

研究的目的:

  • 引入一般化的卷积多体分布函数 (cMBDF) 作为有效的原子表示.
  • 提高化学和材料系统的机器学习的精度并降低计算成本,特别是在低数据场景中.

主要方法:

  • 通过使用翻译和旋转不变函数来概括MBDF框架开发了cMBDF.
  • 用互动潜力加权的光滑原子密度紧地编码了局部化学环境.
  • 利用快速的富里埃变换,在预定义的网格上高效地评估和存储功能值.

主要成果:

  • 实现了高计算和数据效率的原子表示 (cMBDF),在低数据模式中表现出色.
  • 证明cMBDF向量是紧的和尺寸不变的,独立于系统大小或组成.
  • 显示的cMBDF比在有机和无机数据集 (QM7b,QM9,VQM24) 中学习量子性质的流行的表示更准确.

结论:

  • cMBDF可显著减少模型培训和测试时间 (例如23小时至8分钟),降低碳足迹.
  • 由于cMBDF的紧性和高效性,它适用于广泛的化学和材料应用.
  • 这种方法促进了科学发现中可持续和高效的机器学习模型的开发.