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Related Concept Videos

Approximate Integration01:24

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In many practical and theoretical contexts, the exact value of a definite integral may be inaccessible. This limitation typically arises when the antiderivative of a function is either unknown or cannot be expressed in a closed mathematical form. Alternatively, it can occur when a function is defined not by a formula but by a finite set of empirical data points, such as those collected during experiments. In these cases, approximate integration techniques provide a valuable solution.One of the...
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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...
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Optical Trapping of Nanoparticles
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Approximate Bayesian computation techniques for optical characterization of nanoparticle clusters.

Ozan Burak Ericok, Ali Taylan Cemgil, Hakan Erturk

    Journal of the Optical Society of America. A, Optics, Image Science, and Vision
    |January 13, 2018
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    Summary

    This study compares approximate Bayesian computation (ABC) methods for nanoparticle aggregate characterization. Adaptive population Monte Carlo (APMC) proved most efficient for analyzing soot aggregates using light scattering data.

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    Area of Science:

    • Nanoparticle science
    • Computational physics
    • Statistical modeling

    Background:

    • Characterizing nanoparticle aggregates via scattered light presents a complex inverse problem.
    • Classical likelihood-based inference is often infeasible due to the complexity of forward scattering models.
    • Likelihood-free methods, particularly approximate Bayesian computation (ABC), offer an alternative by relying solely on numerical simulations.

    Purpose of the Study:

    • To compare the accuracy and efficiency of four likelihood-free inference methods for nanoparticle aggregate characterization.
    • To evaluate the performance of rejection, Markov chain Monte Carlo, population Monte Carlo, and adaptive population Monte Carlo (APMC) algorithms.
    • To apply these methods to analyze soot aggregates using experimental light scattering data.

    Main Methods:

    • Utilized Filippov's particle-cluster algorithm to generate nanoparticle aggregates.
    • Employed discrete dipole approximation (DDA) to model light scattering behavior.
    • Implemented and compared four approximate Bayesian computation (ABC) algorithms: rejection, MCMC, population Monte Carlo, and APMC.

    Main Results:

    • The adaptive population Monte Carlo (APMC) algorithm demonstrated superior performance in terms of computational time and acceptance rates compared to other ABC methods.
    • All tested ABC algorithms yielded comparable posterior distributions for aggregate properties.
    • Successful characterization of soot aggregates was achieved, with deviations under 2 nm in nanoparticle radius and 3-4 in the number of constituent nanoparticles for monodisperse cases.
    • Promising results were also obtained for polydisperse aggregates with a log-normal particle size distribution.

    Conclusions:

    • Likelihood-free inference, specifically APMC, is a viable and efficient approach for complex nanoparticle aggregate characterization problems.
    • The developed methodology allows for accurate determination of aggregate size and composition from light scattering measurements.
    • The findings suggest broad applicability to both monodisperse and polydisperse nanoparticle systems.