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Related Concept Videos

Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

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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...
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Gauss's Law: Problem-Solving01:10

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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...
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Region of Convergence of Laplace Tarnsform01:20

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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...
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Gauss's Law: Cylindrical Symmetry01:20

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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,...
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Gauss's Law01:07

Gauss's Law

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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.
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Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

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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...
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Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
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A Gaussian-process approximation to a spatial SIR process using moment closures and emulators.

Parker Trostle1, Joseph Guinness2, Brian J Reich1

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

Biometrics
|July 22, 2024
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Summary
This summary is machine-generated.

This study introduces a novel Gaussian process approach to model complex spatial disease spread dynamics, improving upon existing epidemiological models. The method accurately simulates infectious disease transmission across locations, crucial for public health planning.

Keywords:
SIR modelsemulator modelsmoment-closure approximationsspatiotemporal epidemiology

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Area of Science:

  • Epidemiology
  • Computational Biology
  • Statistical Modeling

Background:

  • Modeling infectious disease spread is complex due to pathogen and behavioral factors.
  • Spatial epidemiological models often involve trade-offs between accuracy, determinism, and computational cost.

Purpose of the Study:

  • To develop a flexible and computationally efficient approach for modeling spatial disease dynamics.
  • To approximate complex spatial spread with a Gaussian process for improved inference.

Main Methods:

  • Developed a spatial extension to the Susceptible-Infectious-Recovered (SIR) stochastic process.
  • Derived a moment-closure approximation yielding ordinary differential equations (ODEs).
  • Employed a low-rank emulator to approximate ODEs and built a hierarchical model for noisy infection data.

Main Results:

  • Successfully inferred simulated spatial SIR jump process infections.
  • Applied the model to real-world data on Zika infections in Brazil (2015-2016).

Conclusions:

  • The Gaussian process approximation offers a viable method for complex spatial epidemiological modeling.
  • The approach provides a robust framework for analyzing underreported infectious disease data across space and time.