Uncertainty estimation for linearised inverse problems comparing Bayesian inference and a pseudoinverse approach for acoustic transmission measurements

2017 ◽  
Vol 84 (4) ◽  
Author(s):  
Nadine Feldmann ◽  
Fabian Bause ◽  
Bernd Henning
Keyword(s):  
Inverse Problem ◽  
Bayesian Inference ◽  
Statistical Approach ◽  
Uncertainty Estimation ◽  
Acoustic Transmission ◽  
Model Function ◽  
Sources Of Uncertainty ◽  
Material Parameters ◽  
Transmission Measurements

AbstractThe determination of acoustic material parameters using ultrasonic transmission measurements can mathematically be described as an inverse problem. The question concerning the influence of uncertainties on the problem's solution can be answered using a statistical approach. Therefore, the sources of uncertainty have to be identified statistically. A method for linearising the model function using the

scholarly journals Determination of the geophysical model function of the ERS-1 scatterometer by the use of neural networks

1998 ◽  
Vol 103 (C6) ◽  
pp. 12853-12868 ◽  
Author(s):  
Carlos Mejia ◽  
Sylvie Thiria ◽  
Ngan Tran ◽  
Michel Crépon ◽  
Fouad Badran
Keyword(s):  
Neural Networks ◽  
Model Function ◽  
Geophysical Model ◽  
Geophysical Model Function

Determination of the Number of Conserved Chromosomal Segments Between Species

Genetics ◽  
2001 ◽  
Vol 157 (3) ◽  
pp. 1387-1395 ◽  
Author(s):  
Sudhir Kumar ◽  
Sudhindra R Gadagkar ◽  
Alan Filipski ◽  
Xun Gu
Keyword(s):  
Statistical Approach ◽  
Common Ancestor ◽  
Chromosomal Rearrangements ◽  
Structural Similarity ◽  
The Other ◽  
Segment Length ◽  
Human Genomes ◽  
Genomic Divergence ◽  
Human And Mouse

AbstractGenomic divergence between species can be quantified in terms of the number of chromosomal rearrangements that have occurred in the respective genomes following their divergence from a common ancestor. These rearrangements disrupt the structural similarity between genomes, with each rearrangement producing additional, albeit shorter, conserved segments. Here we propose a simple statistical approach on the basis of the distribution of the number of markers in contiguous sets of autosomal markers (CSAMs) to estimate the number of conserved segments. CSAM identification requires information on the relative locations of orthologous markers in one genome and only the chromosome number on which each marker resides in the other genome. We propose a simple mathematical model that can account for the effect of the nonuniformity of the breakpoints and markers on the observed distribution of the number of markers in different conserved segments. Computer simulations show that the number of CSAMs increases linearly with the number of chromosomal rearrangements under a variety of conditions. Using the CSAM approach, the estimate of the number of conserved segments between human and mouse genomes is 529 ± 84, with a mean conserved segment length of 2.8 cM. This length is <40% of that currently accepted for human and mouse genomes. This means that the mouse and human genomes have diverged at a rate of ∼1.15 rearrangements per million years. By contrast, mouse and rat are diverging at a rate of only ∼0.74 rearrangements per million years.

Determination of an impulsive diffusion operator from interior spectral data

Analysis ◽  
2020 ◽  
Vol 40 (1) ◽  
pp. 39-45
Author(s):  
Yasser Khalili ◽  
Dumitru Baleanu
Keyword(s):  
Inverse Problem ◽  
Spectral Data ◽  
Potential Functions ◽  
Half Line ◽  
Internal Point ◽  
Diffusion Operator ◽  
Impulsive Diffusion

AbstractIn the present work, the interior spectral data is used to investigate the inverse problem for a diffusion operator with an impulse on the half line. We show that the potential functions {q_{0}(x)} and {q_{1}(x)} can be uniquely established by taking a set of values of the eigenfunctions at some internal point and one spectrum.

Reconstructing Three-Dimensional Fluid Velocity Vector Fields from Acoustic Transmission Measurements

1977 ◽  
pp. 307-326 ◽  
Author(s):  
S. A. Johnson ◽  
J. F. Greenleaf ◽  
C. R. Hansen ◽  
W. F. Samayoa ◽  
M. Tanaka ◽  
...  
Keyword(s):  
Velocity Vector ◽  
Vector Fields ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Acoustic Transmission ◽  
Transmission Measurements
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