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Related Concept Videos

Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Linearization and Approximation01:26

Linearization and Approximation

Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

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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

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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Linear Approximations01:23

Linear Approximations

For a differentiable function of two variables, linear approximation estimates values near a known point by replacing the curved surface with its tangent plane. Consider the function\begin{equation*}f(x,y)=x^2+3y^2\end{equation*}near the point (2, 1). The exact value at this point is f(2, 1) = 22 + 3(1)2 = 4 + 3 = 7.The linear approximation of f(x, y)) near (a, b) is\begin{equation*}L(x,y)=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)\end{equation*}First, compute the partial derivatives: fx(x, y) = 2x and...
Propagation of Uncertainty from Random Error00:59

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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...

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The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
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Published on: August 12, 2013

Optical linear algebra processors: noise and error-source modeling.

D Casasent, A Ghosh

    Optics Letters
    |September 3, 2009
    PubMed
    Summary
    This summary is machine-generated.

    This study models noise and errors in optical linear algebra processors (OLAPs), focusing on frequency-multiplexed designs. It provides general expressions for output variations due to component errors and noise, and discusses a digital simulator for this model.

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    Published on: January 28, 2019

    Area of Science:

    • Optical computing
    • Linear algebra processing
    • Signal processing

    Background:

    • Optical linear algebra processors (OLAPs) offer potential for high-speed computation.
    • Understanding and quantifying noise and error sources is crucial for OLAP performance and reliability.
    • Frequency-multiplexed OLAPs present unique challenges and opportunities in optical signal processing.

    Purpose of the Study:

    • To develop a comprehensive model for system and component noise and error sources in optical linear algebra processors (OLAPs).
    • To specifically analyze noise and error effects in frequency-multiplexed OLAP architectures.
    • To derive general mathematical expressions quantifying the impact of these errors on OLAP output.

    Main Methods:

    • Development of a mathematical model to represent noise and error sources within OLAPs.
    • Derivation of analytical expressions linking component errors and noise to system output.
    • Design and discussion of a digital simulator for validating the developed OLAP error model.

    Main Results:

    • General expressions were obtained for OLAP output as a function of various component errors and noise.
    • The model provides a framework for understanding the sensitivity of OLAPs to imperfections.
    • A digital simulator was discussed for practical evaluation and refinement of the model.

    Conclusions:

    • The developed model effectively captures the impact of noise and errors on OLAP performance.
    • Frequency-multiplexed OLAPs can be analyzed for their robustness against system and component imperfections.
    • The digital simulator facilitates further research and development in reliable optical computing systems.