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torchtree: Flexible Phylogenetic Model Development and Inference Using PyTorch. [PDF]

Syst Biol
Fourment M, Macaulay M, Swanepoel CJ, Ji X, Suchard MA, Matsen Iv FA.   +5 more
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Normal Multiresolution Approximation of Curves

Constructive Approximation, 2004
Subdivision is a powerful procedure for iteratively creating smooth curves and surfaces. Combined with wavelet methods, subdivision can be used to approximate functions, curves, and surfaces. The authors discuss the multiresolution approximation of a plane curve \(\Gamma\) in detail. A multiresolution approximation of \(\Gamma\) is called normal if all
Daubechies, Ingrid, Runborg, Olof, Sweldens, Wim   +2 more
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Multivariate Normal Approximation

2011
Chapter 12 considers multivariate normal approximation, extending both the size bias and exchangeable pair methods to this setting. In the latter case it is shows how in some instances the exchangeable pair ‘linearity condition’ can be achieved by embedding the problem in a higher dimension.
Louis H. Y. Chen, Larry Goldstein, Qi-Man Shao   +2 more
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Discretized Normal Approximation

2011
Returning to the independent case, and inspired by use of the continuity correction for the normal approximation of the binomial, Chap. 7 considers the approximation of independent sums of integer valued random variables by the discretized normal distribution, in the total variation metric.
Louis H. Y. Chen, Larry Goldstein, Qi-Man Shao   +2 more
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Normal Approximation in Hilbert Space. II

Theory of Probability & Its Applications, 1989
This paper contains the proofs of the main results stated in the first part [ibid., No.2, 225-245 (1988; Zbl 0649.60005)].
Zalesskij, B. A., Sazonov, V. V., Ul'yanov, V. V.   +2 more
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Non-normal Approximation

2011
Momentarily departing from the normal case, approximations by continuous distributions for which the methods of the previous chapters may be extended are considered in Chap. 13. The bounds developed are applied to the approximation of the distribution of the total spin of the Curie–Weiss model from statistical physics, at the critical inverse ...
Louis H. Y. Chen, Larry Goldstein, Qi-Man Shao   +2 more
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Approximate normalized cuts without Eigen-decomposition

Information Sciences, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jia, Hongjie, Ding, Shifei, Du, Mingjing, Xue, Yu   +3 more
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Normalizing Vogel's Approximation Method

Mathematics Magazine, 1972
This paper describes an approximation method for determining an initial basic feasible solution to transportation type problems. The paper presents a "cost normalization" which is easily performed with the aid of a computer. In over 200 random problems tested, this normalizing (while using little time itself) has reduced the average number of ...
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