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Titolo: The likelihood function in fiber diffraction
Autore: Mu, XQ; Makowski, L;
 Indirizzi:
 Florida State Univ, Inst Mol Biophys, Tallahassee, FL 32306 USA Florida State Univ Tallahassee FL USA 32306 ys, Tallahassee, FL 32306 USA
 Titolo Testata:
 ACTA CRYSTALLOGRAPHICA SECTION A
,
volume: 56,
anno: 2000,
parte:, 2
pagine: 168  177
 SICI:
 01087673(200003)56:<168:TLFIFD>2.0.ZU;20
 Fonte:
 ISI
 Lingua:
 ENG
 Soggetto:
 TOBACCO MOSAICVIRUS; LIKELY RFACTORS; PHASE DETERMINATION; REFINEMENT; DISTRIBUTIONS; MAXIMIZATION; RESOLUTION; ENTROPY;
 Tipo documento:
 Article
 Natura:
 Periodico
 Settore Disciplinare:
 Physical, Chemical & Earth Sciences
 Citazioni:
 23
 Recensione:
 Indirizzi per estratti:
 Indirizzo: Mu, XQ Florida State Univ, Inst Mol Biophys, Tallahassee, FL 32306 USA Florida State Univ Tallahassee FL USA 32306 lahassee, FL 32306 USA



 Citazione:
 X.Q. Mu e L. Makowski, "The likelihood function in fiber diffraction", ACT CRYST A, 56, 2000, pp. 168177
Abstract
The likelihood function is an appropriate target function fur refinement of molecular structures using tiber diffraction data. However, its practicalapplication to fiber diffraction faces two significant obstacles: (i) the intensities of layer lines in a fiber diffraction pattern usually arise from the superposition of several terms, each equivalent to a crystallographicstructure factor, thereby making the calculation significantly more complex than for the crystallographic case: (ii) to describe a molecular structure at the atomic level based on fiber diffraction data, the radial and phaseparts of the atomic coordinates must be treated separately owing to the uniaxial symmetry of the structure. These issues are addressed here in order to derive equations of likelihood functions for fiber diffraction. The special case of a single term on a layer line is treated first followed by extension of the method to the multiterm case, A practical difficulty in implementation of likelihood for the multiterm case is that each term has a different variance. An analytical technique is described that allows the conversion of the unequalvariance case to an equalvariance case. This makes it possible to express the likelihood by an explicit formula, allowing a directimplementation of the likelihood calculation. A cylindrically symmetric model is proposed for error distribution of the atomic coordinates in a helical structure. Variances and offset coefficients of the contributing terms in the likelihood functions are expressed in terms of the variance of the atomic coordinates in the cylindrical reference system.
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Documento generato il 05/12/20 alle ore 10:25:51