Similarity, Eigenvalues, Matrix Decompositions, and Linear Transformations

Clinicians often encounter thyroid function tests (TFT) comprising serum/plasma free thyroxine (FT4) and thyroid stimulating hormone (TSH) measured using different assay platforms during the course of follow-up evaluations which complicates reliable comparison and interpretation of TFT changes. Although interconversion between concentration units is straightforward, the validity of interconversion of FT4/TSH values from one assay platform to another with different reference intervals remains questionable. This study aims to establish an accurate and reliable methodology of interconverting FT4 by any laboratory to an equivalent FT4 value scaled to a reference range of interest via linear transformation methods. As a proof-of-concept, FT4 was simultaneously assayed by direct analog immunoassay, tandem mass spectrometry and equilibrium dialysis. Both linear and piecewise linear transformations proved relatively accurate for FT4 inter-scale conversion. Linear transformation performs better when FT4 are converted from a more accurate to a less accurate assay platform. The converse is true, whereby piecewise linear transformation is superior to linear transformation when converting values from a less accurate method to a more robust assay platform. Such transformations can potentially apply to other biochemical analytes scale conversions, including TSH. This aids interpretation of TFT trends while monitoring the treatment of patients with thyroid disorders.

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Conversion Between Cubic Bezier Curves and Catmull–Rom Splines

SN Computer Science ◽

10.1007/s42979-021-00770-x ◽

2021 ◽

Vol 2 (5) ◽

Author(s):

Soroosh Tayebi Arasteh ◽

Adam Kalisz

Keyword(s):

Computer Graphics ◽

Geometric Design ◽

The Other ◽

Control Points ◽

Complex Surfaces ◽

Linear Transformations ◽

Computer Aided Geometric Design ◽

Cubic Curves ◽

Original Curve ◽

Computer Aided

AbstractSplines are one of the main methods of mathematically representing complicated shapes, which have become the primary technique in the fields of Computer Graphics (CG) and Computer-Aided Geometric Design (CAGD) for modeling complex surfaces. Among all, Bézier and Catmull–Rom splines are the most common in the sub-fields of engineering. In this paper, we focus on conversion between cubic Bézier and Catmull–Rom curve segments, rather than going through their properties. By deriving the conversion equations, we aim at converting the original set of the control points of either of the Catmull–Rom or Bézier cubic curves to a new set of control points, which corresponds to approximately the same shape as the original curve, when considered as the set of the control points of the other curve. Due to providing simple linear transformations of control points, the method is very simple, efficient, and easy to implement, which is further validated in this paper using some numerical and visual examples.

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Linear transformations extract parameters of ionic currents and action potential features from pseudo-ECG in cardiomyocyte models

10.1063/5.0035269 ◽

2020 ◽

Author(s):

Salim Baigildin ◽

Konstantin Ushenin ◽

Aigul Fabarisova ◽

Marat Bogdanov ◽

Olga Solovyeva

Keyword(s):

Action Potential ◽

Ionic Currents ◽

Linear Transformations

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Zero-diminishing linear transformations

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-1980-0587923-5 ◽

1980 ◽

Vol 80 (4) ◽

pp. 544-544 ◽

Cited By ~ 4

Author(s):

Thomas Craven ◽

George Csordas

Keyword(s):

Linear Transformations

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Principal Component Analysis and Matrix Decompositions

Signals and Communication Technology - The Variational Bayes Method in Signal Processing ◽

10.1007/3-540-28820-1_4 ◽

2006 ◽

pp. 57-88

Keyword(s):

Principal Component Analysis ◽

Principal Component ◽

Component Analysis ◽

Matrix Decompositions

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THE NATURAL PARTIAL ORDER ON LINEAR SEMIGROUPS WITH NULLITY AND CO-RANK BOUNDED BELOW

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972714000793 ◽

2014 ◽

Vol 91 (1) ◽

pp. 104-115 ◽

Cited By ~ 1

Author(s):

SUREEPORN CHAOPRAKNOI ◽

TEERAPHONG PHONGPATTANACHAROEN ◽

PONGSAN PRAKITSRI

Keyword(s):

Semigroup Forum ◽

Partial Order ◽

Lower Bounds ◽

Partial Orders ◽

Natural Partial Order ◽

Linear Transformations ◽

Bounded Below

AbstractHiggins [‘The Mitsch order on a semigroup’, Semigroup Forum 49 (1994), 261–266] showed that the natural partial orders on a semigroup and its regular subsemigroups coincide. This is why we are interested in the study of the natural partial order on nonregular semigroups. Of particular interest are the nonregular semigroups of linear transformations with lower bounds on the nullity or the co-rank. In this paper, we determine when they exist, characterise the natural partial order on these nonregular semigroups and consider questions of compatibility, minimality and maximality. In addition, we provide many examples associated with our results.

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