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Related Concept Videos

Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

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In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
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Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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Uniform Depth Channel Flow: Problem Solving01:18

Uniform Depth Channel Flow: Problem Solving

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To calculate the flow rate for a trapezoidal channel, first, identify the bottom width, side slope, and flow depth of the channel. The cross-sectional area (A) corresponding to the depth of flow (y), channel bottom width (B), and side slope (θ) is determined by:Next, calculate the wetted perimeter, which includes the bottom width and the sloped side lengths in contact with the water. Using the values of the cross-sectional area and the wetted perimeter, determine the hydraulic radius by...
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Basic Discrete Time Signals01:16

Basic Discrete Time Signals

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The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
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State Space Representation01:27

State Space Representation

279
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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Transfer Function to State Space01:23

Transfer Function to State Space

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State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
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Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform
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A New Non-stationary High-order Spatial Sequential Simulation Method.

Amir Abbas Haji Abolhassani1,2, Roussos Dimitrakopoulos1, Frank P Ferrie2

  • 1COSMO - Stochastic Mine Planning Laboratory, McGill University, Montreal, QC Canada.

Mathematical Geosciences
|July 25, 2022
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A novel sequential simulation method models complex natural phenomena. This approach uses high-order statistics for accurate, non-stationary spatial attribute simulation.

Keywords:
High-order spatial statisticsNon-stationarySequential simulationTransformation-invariant and multi-point statistics

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Area of Science:

  • Geosciences and Environmental Modeling
  • Computational Statistics
  • Spatial Data Analysis

Background:

  • Modeling non-Gaussian, spatially distributed, and variant attributes of natural phenomena presents challenges.
  • Existing methods struggle with complex curvilinear patterns and non-stationarity in spatial data.

Purpose of the Study:

  • To introduce a new non-stationary, high-order sequential simulation method.
  • To accommodate complex curvilinear patterns in natural phenomena modeling.
  • To improve the simulation of variant spatial attributes.

Main Methods:

  • A multi-grid approach utilizing spatial templates, training images, and sample data.
  • A novel similarity measure based on high-order statistics of data events.
  • Calibration of replicate importance using conditioning data to address non-stationarity.

Main Results:

  • The method generates a non-stationary spatial distribution of weights for training patterns.
  • High-order statistics enable effective detection of similar patterns in various orientations.
  • The approach demonstrates robustness with additional training images.

Conclusions:

  • The proposed method effectively models complex, non-stationary spatial attributes.
  • High-order statistics provide a robust similarity measure for sequential simulation.
  • The technique offers improved accuracy for natural phenomena modeling.