Introduction to Overdetermined Systems

Branham, Richard L.

doi:10.1007/978-1-4612-3362-6_4

Cited by 28 publications

(17 citation statements)

References 5 publications

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“…The C j values are different for each probe sequence; the X j values are the same for all probes. The least-squares parameters X j are found by solving the normal equations by Cholesky decomposition (Branham 1990). Then the corrected ratio for each probe, R corrected , is given by the residual to the fit: log R corrected = log R measured ‫מ‬ log R fit .…”

Section: Sequence Normalization Algorithmsmentioning

confidence: 99%

Strategies for Mutational Analysis of the Large Multiexon ATM Gene Using High-Density Oligonucleotide Arrays

Hacia¹,

Sun²,

Hunt³

et al. 1998

Genome Res.

103

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Mutational analysis of large genes with complex genomic structures plays an important role in medical genetics. Technical limitations associated with current mutation screening protocols have placed increased emphasis on the development of new technologies to simplify these procedures. High-density arrays of >90,000-oligonucleotide probes, 25 nucleotides in length, were designed to screen for all possible heterozygous germ-line mutations in the 9.17-kb coding region of the ATM gene. A strategy for rapidly developing multiexon PCR amplification protocols in DNA chip-based hybridization analysis was devised and implemented in preparing target for the 62 ATM coding exons. Improved algorithms for interpreting data from two-color experiments, where reference and test samples are cohybridized to the arrays, were developed. In a blinded study, 17 of 18 distinct heterozygous and 8 of 8 distinct homozygous sequence variants in the assayed region were detected accurately along with five false-positive calls while scanning >200 kb in 22 genomic DNA samples. Of eight heterozygous sequence changes found in more than one sample, six were detected in all cases. Five previously unreported sequence changes, not found by other mutational scanning methodologies on these same samples, were detected that led to either amino acid changes or premature truncation of the ATM protein. DNA chip-based assays should play a valuable role in high throughput sequence analysis of complex genes.

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Section: Sequence Normalization Algorithmsmentioning

confidence: 99%

Strategies for Mutational Analysis of the Large Multiexon ATM Gene Using High-Density Oligonucleotide Arrays

Hacia¹,

Sun²,

Hunt³

et al. 1998

Genome Res.

103

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show abstract

“…The problem here is that cross-hole tomography is not a well posed problem because of the relative distribution of sources and receivers (Branham, 1990;Tarantola, 2005) that involves rays almost parallel which increase condition number of associated S matrix.…”

Section: Forward and Inverse Problemmentioning

confidence: 99%

“…Geometrically, the maximum and minimum values represent the axes of an ellipse (Branham, 1990). If the ratio tends to unity the correlation is null (independent) and if it is very large, that is almost perfect (dependent) and so ill conditioned.…”

Section: Conditioning Of a Matrixmentioning

confidence: 99%

Seismic data inversion by cross-hole tomography using geometrically uniform spatial coverage

Imhof¹,

Calvo²,

Santamarina³

2010

Rev. Bras. Geof.

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ABSTRACT.One of the inversion schemes most employed in seismic tomography processing is least squares and derived algorithms, using as input data the vector of first arrivals. A division of the whole space between sources and receivers is performed, constructing a pixel model with its elements of the same size. Spatial coverage is defined, then, as the sum of traveled length by all rays through every pixel that conform the medium considered. It is related, therefore, with the source-receiver's distribution and the form of the domain among them. In cross-hole array, rays do not evenly sample the properties of the medium, leading to non-uniform spatial coverage. It is known that this affects the inversion process. The purpose of this paper, then, was to study the problem of spatial coverage uniformity to obtain travel path matrices leading to inversion algorithms with better convergence. The medium was divided in elements of different size but with an even spatial coverage (named as 'ipixels'), and then it was explored how this improved the inversion process. A theoretical model was implemented with added noise to emulate real data; and then the vector of measured times was generated with known velocity distribution. Afterwards an inversion method using minimum length solution was performed to test the two domain divisions. The results showed that the fact of using ipixels not only improved the inversion scheme used in all cases; but in addition allowed to get convergence where it was impossible to do using pixels; particularly through the method considered. This is a direct result of the improvement of condition number of the associated matrices.Keywords: seismic tomography, cross-hole, spatial coverage, pixel, ipixel. RESUMEN.Uno de los esquemas de inversión más empleados en el procesamiento de datos de tomografía sísmica es el de mínimos cuadrados y algoritmos relacionados, utilizando el vector de primeros arribos como datos de entrada. Se lleva a cabo una división del dominio completo entre emisores y receptores, con el objeto de diseñar un modelo de píxeles del mismo tamaño. Se define la cobertura espacial como la suma de los tiempos de viaje de todos los rayos en cada uno de los píxeles que conforman el medio. Por lo tanto este parámetro está relacionado con la distribución emisor-receptor y con la forma del dominio entre los mismos. En el dispositivo cross-hole los rayos no muestrean de igual forma al medio, conduciendo a una cobertura espacial no uniforme. Se sabe que este inconveniente afecta el proceso de inversión. El propósito de este artículo fué el de estudiar el problema de la uniformidad de la cobertura espacial a fin de lograr matrices de tiempo de viaje que conduzcan a algoritmos de inversión con mejor convergencia. El medio se dividió en elementos de diferente tamaño pero con cobertura espacial uniforme (denominados 'ipixels'). Se implementó un modelo teórico con ruido a fin de simular datos reales; y el vector de tiempos se calculó con una distribución conocida de velocidades. Luego se probó la...

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“…Estimation of area values during the closure may be possible by surface modeling of the area values during the preceding and the following transition segments. As an empirical approach to surface modeling, least-squares based bivariate polynomial approximation [36], [37], [39]- [44] on the area values is investigated. The polynomial function is used for interpolating the area values during the closure and for estimating the place of maximum constriction.…”

Section: Estimation Of Vocal Tract Shape During Stop Closuresmentioning

confidence: 99%

Estimation of Place of Articulation During Stop Closures of Vowel–Consonant–Vowel Utterances

Pandey

Shah²

2009

IEEE Trans. Audio Speech Lang. Process.

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Introduction to Overdetermined Systems

Cited by 28 publications

References 5 publications

Strategies for Mutational Analysis of the Large Multiexon ATM Gene Using High-Density Oligonucleotide Arrays

Strategies for Mutational Analysis of the Large Multiexon ATM Gene Using High-Density Oligonucleotide Arrays

Seismic data inversion by cross-hole tomography using geometrically uniform spatial coverage

Estimation of Place of Articulation During Stop Closures of Vowel–Consonant–Vowel Utterances

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