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相关概念视频

Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

7.5K
A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half...
7.5K
Gauss's Law: Problem-Solving01:10

Gauss's Law: Problem-Solving

1.7K
Gauss's law helps determine electric fields even though the law is not directly about electric fields but electric flux. In situations with certain symmetries (spherical, cylindrical, or planar) in the charge distribution, the electric field can be deduced based on the knowledge of the electric flux. In these systems, we can find a Gaussian surface S over which the electric field has a constant magnitude. Furthermore, suppose the electric field is parallel (or antiparallel) to the area...
1.7K
Region of Convergence of Laplace Tarnsform01:20

Region of Convergence of Laplace Tarnsform

519
The Region of Convergence (ROC) is a fundamental concept in signal processing and system analysis, particularly associated with the Laplace transform. The ROC represents an area in the complex plane where the Laplace transform of a given signal converges, determining the transform's applicability and utility.
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This...
519
Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

7.5K
A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
7.5K
Gauss's Law01:07

Gauss's Law

7.2K
If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.
7.2K
Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

7.9K
A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
7.9K

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相关实验视频

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Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
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Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

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一个高斯过程的近似空间SIR过程使用时刻关闭和模拟器.

Parker Trostle1, Joseph Guinness2, Brian J Reich1

  • 1Department of Statistics, North Carolina State University, Raleigh, NC, 27607, United States.

Biometrics
|July 22, 2024
PubMed
概括

这项研究引入了一种新的高斯过程方法来建模复杂的空间疾病传播动态,改进了现有的流行病学模型. 该方法准确地模拟了传染病在不同地点的传播,这对于公共卫生规划至关重要.

科学领域:

  • 流行病学 流行病学
  • 计算生物学 计算生物学
  • 统计建模 统计建模

背景情况:

  • 由于病原体和行为因素,模拟传染病传播是复杂的.
  • 空间流行病学模型通常涉及准确性,确定性和计算成本之间的权衡.

研究的目的:

  • 开发一种灵活且计算效率高的方法来建模空间疾病动态.
  • 通过高斯过程对复杂的空间分布进行近似推理,以改善推理.

主要方法:

  • 开发了一个空间扩展可感-传染-恢复 (SIR) 随机过程.
  • 导出了一个时刻闭关近似,产生普通微分方程 (ODE).
  • 采用低级模拟器来近似ODEs,并为杂的感染数据构建了一个层次模型.

主要成果:

  • 成功推断了模拟的空间SIR跳跃过程感染.
  • 将模型应用于巴西 (2015-2016年) 寨卡病毒感染的真实数据.

结论:

  • 高斯过程近似为复杂的空间流行病学建模提供了一种可行的方法.
  • 该方法提供了一个强大的框架,用于在空间和时间上分析报告不足的传染病数据.
关键词:
这些SIR模型是SIR模型.模拟器模型 模拟器模型关闭时刻的近似值.时间空间流行病学

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