On the numerical inversion of the Laplace transform and similar Fredholm integral equations of the first kind

McWhirter, J.G.; Pike, E. R.

doi:10.1088/0305-4470/11/9/007

Cited by 305 publications

(177 citation statements)

References 6 publications

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“…Second, we calculate a nonlinear fit to g 2 (τ ) − 1 by using a constrained regularization method [34][35][36], employing a CONTIN algorithm [37,38] in a standard implementation (ALV-Correlator Software ALV-7004 for Windows, V.3.0.4.5) by ALV GmbH, Langen, Germany. For the data analysis, several settings are specified within the ALV-Regularized fit setup of the ALV-Correlator Software.…”

Section: (B)mentioning

confidence: 99%

Synaptic vesicles studied by dynamic light scattering

et al. 2011

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Abstract. The size polydispersity distribution of synaptic vesicles (SVs) is characterized under quasiphysiological conditions by dynamic light scattering (DLS). Highly purified fractions of SVs obtained from rat brain still contain a small amount of larger contaminant structures, which can be quantified by DLS and further reduced by asymmetric-flow field-flow (AFFF) fractionation. The intensity autocorrelation functions g 2(τ ) recorded from these samples are analyzed by a constrained regularization method as well as by an alternative direct modeling approach. The results are in quantitative agreement with the polydispersity obtained from cryogenic electron microscopy of vitrified SVs. Next, different vesicle fusion assays based on samples composed of SVs and small unilamellar proteoliposomes with the fusion proteins syntaxin 1 and SNAP-25A are characterized by DLS. The size increase of the proteoliposomes due to SNARE-dependent fusion with SVs is quantified by DLS under quasi-physiological conditions.

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Section: (B)mentioning

confidence: 99%

Synaptic vesicles studied by dynamic light scattering

et al. 2011

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“…Chemically speaking, in this scenario, we assume that the molecule has to challenge an energy barrier with distributed barrier height at each reaction step, but the distributions of barrier heights in distinct reaction steps are independent. From the kinetic data in the t-domain p(t) = [∫ke −kt dF 1 (k)]* ··· *[∫ke −kt dF m (k)], which is a convolution of m factors, one can get the frequency spectrum in the ω-domain as the product of m singlestep reaction frequency spectra: (21) Because the function p(ω) given in eq 21 satisfies 0 < |p(ω)| < +∞ for Reω < 0, it is possible to define a single-valued phase function ψ(ω) = Imln p(ω) as (22) (See Supporting Information A.2 for a proof of the above statement.) According to eq 21, the phase ψ(ω) further decomposes to the sum of m terms:…”

Section: Fourier Transform Ofmentioning

confidence: 99%

Kinetic Analysis of Sequential Multistep Reactions

Zhou

Zhuang

2007

J. Phys. Chem. B

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Many processes in biology and chemistry involve multi-step reactions or transitions. The kinetic data associated with these reactions are manifested by superpositions of exponential decays that are often difficult to dissect. Two major challenges have hampered the kinetic analysis of multi-step chemical reactions: (1) Reliable and unbiased determination of the number of reaction steps, (2) Stable reconstruction of the distribution of kinetic rate constants. Here, we introduce two numerically stable integral transformations to solve these two challenges. The first transformation enables us to deduce the number of rate-limiting steps from kinetic measurements, even when each step has arbitrarily distributed rate constants. The second transformation allows us to reconstruct the distribution of rate constants in the multi-step reaction using the phase function approach, without fitting the data. We demonstrate the stability of the two integral transformations by both analytic proofs and numerical tests. These new methods will help providing robust and unbiased kinetic analysis for many complex chemical and biochemical reactions.

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“…There is a well-known intrinsic problem in AR-XPS analysis related to the difficulty in inverse Laplace transformation. [4] Cumpson showed that the number of degrees of freedom in AR-XPS data fitting is very small under usual conditions, e.g. only four parameters can be determined even if the experimental precision is as high as 0.3%.…”

Section: Introductionmentioning

confidence: 99%

Combination of high‐resolution RBS and angle‐resolved XPS: accurate depth profiling of chemical states

Kimura

Nakajima

Zhao

et al. 2008

Surface & Interface Analysis

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A new method for the combination analysis of high-resolution Rutherford backscattering spectroscopy (HRBS) and angleresolved X-ray photoelectron spectroscopy (AR-XPS) is proposed for accurate depth profiling of chemical states. In this method, attenuation lengths (ALs) for the photoelectrons are first determined so that the AR-XPS result is consistent with the HRBS result. Depth profiling of the chemical states are then performed in the AR-XPS analysis using the composition-depth profiles obtained by HRBS as constrained conditions. This method is successfully applied to Hf-based gate stack structures demonstrating its feasibility.

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On the numerical inversion of the Laplace transform and similar Fredholm integral equations of the first kind

Cited by 305 publications

References 6 publications

Synaptic vesicles studied by dynamic light scattering

Synaptic vesicles studied by dynamic light scattering

Kinetic Analysis of Sequential Multistep Reactions

Combination of high‐resolution RBS and angle‐resolved XPS: accurate depth profiling of chemical states

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