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相关概念视频

Convolution: Math, Graphics, and Discrete Signals01:24

Convolution: Math, Graphics, and Discrete Signals

218
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...
218
Discrete-Time Fourier Series01:20

Discrete-Time Fourier Series

204
The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
For a discrete-time periodic signal x[n]...
204
Discrete-time Fourier transform01:26

Discrete-time Fourier transform

247
The Discrete-Time Fourier Transform (DTFT) is an essential mathematical tool for analyzing discrete-time signals, converting them from the time domain to the frequency domain. This transformation allows for examining the frequency components of discrete signals, providing insights into their spectral characteristics. In the DTFT, the continuous integral used in the continuous-time Fourier transform is replaced by a summation to accommodate the discrete nature of the signal.
One of the notable...
247

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相关实验视频

Updated: May 21, 2025

Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases
09:33

Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases

Published on: July 28, 2013

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没有随机微分方程的离散生成扩散模型:一个张量网络方法.

Luke Causer1,2, Grant M Rotskoff3, Juan P Garrahan1,2

  • 1University of Nottingham, School of Physics and Astronomy, Nottingham, NG7 2RD, UK.

Physical review. E
|March 19, 2025
PubMed
概括
此摘要是机器生成的。

本研究介绍了使用张量网络 (TN) 的离散扩散模型 (DDM),以高效地采样复杂分布. 通过与蒙特卡洛方法集成,TN可以准确地表示和无偏见地生成离散数据.

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Diffusion Imaging in the Rat Cervical Spinal Cord
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Co-analysis of Brain Structure and Function using fMRI and Diffusion-weighted Imaging
17:06

Co-analysis of Brain Structure and Function using fMRI and Diffusion-weighted Imaging

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相关实验视频

Last Updated: May 21, 2025

Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases
09:33

Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases

Published on: July 28, 2013

28.2K
Diffusion Imaging in the Rat Cervical Spinal Cord
10:46

Diffusion Imaging in the Rat Cervical Spinal Cord

Published on: April 7, 2015

11.6K
Co-analysis of Brain Structure and Function using fMRI and Diffusion-weighted Imaging
17:06

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科学领域:

  • 机器学习 机器学习
  • 统计物理 统计物理
  • 计算科学 计算科学

背景情况:

  • 扩散模型 (DMs) 通过通过学习得分函数逆转噪声加法来生成数据.
  • 标准的DM在使用随机微分方程的连续分布上运行.
  • 具有离散自由度的格子系统对标准的DM方法构成挑战.

研究的目的:

  • 将扩散模型通用化为离散的格子系统.
  • 使用张量网络开发一种有效的抽样方法,用于使用离散数据.
  • 整合离散扩散模型与蒙特卡洛方法用于统计物理应用.

主要方法:

  • 参数化数据和演变运算符作为张量网络 (TN).
  • 开发了利用马尔科夫链跳动力学的离散扩散模型 (DDM).
  • 利用TN的自动回归特性进行样本生成.

主要成果:

  • 准确地表示使用TN的无声化动态.
  • 从离散分布生成高效且无偏见的样本.
  • 通过TNs和蒙特卡洛集成,为博尔茨曼式分布构建了一个高效的学习方案.

结论:

  • 张量网络为离散扩散模型提供了一个有效的框架.
  • 拟议的方法可以准确地采样复杂的离散分布.
  • 证明适用于研究平衡在与非微不足道的热力学模型.