Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Fixed-scale wavelet-type approximation of periodic density distributions.

V Y Lunin1

  • 1Institute of Mathematical Problems of Biology, Russian Academy of Sciences, Pushchino, Moscow Region. lunin@impb.psn.ru

Acta Crystallographica. Section A, Foundations of Crystallography
|June 30, 2000
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Likelihood-based refinement. I. Irremovable model errors.

Acta crystallographica. Section A, Foundations of crystallography·2002
Same author

Fast differentiation algorithm and efficient calculation of the exact matrix of second derivatives.

Acta crystallographica. Section A, Foundations of crystallography·2001
Same author

Low-resolution data analysis for low-density lipoprotein particle.

Acta crystallographica. Section D, Biological crystallography·2001
Same author

Low-resolution ab initio phasing: problems and advances.

Acta crystallographica. Section D, Biological crystallography·2000
Same author

Density constraints and low-resolution phasing.

Acta crystallographica. Section D, Biological crystallography·2000
Same author

Ab initio low-resolution phasing in crystallography of macromolecules by maximization of likelihood.

Acta crystallographica. Section D, Biological crystallography·2000

This study introduces crystallographic wavelet-type functions for analyzing crystal structures. It explores fixed-scale decomposition for representing functions within unit cells, aiding in crystal structure analysis.

Area of Science:

  • Crystallography
  • Signal Processing
  • Materials Science

Background:

  • Crystallographic analysis often involves understanding functions within a unit cell.
  • Standard signals and their properties are crucial for signal localization in real and reciprocal space.
  • Periodical functions with symmetry are fundamental in crystallographic studies.

Purpose of the Study:

  • To define and analyze crystallographic wavelet-type functions.
  • To investigate the fixed-scale decomposition of functions within a unit cell.
  • To explore the representation of arbitrary functions using shifted standard signals.

Main Methods:

  • Definition of crystallographic wavelet-type functions based on localization and symmetry.
  • Fixed-scale analysis involving the decomposition of distributions into shifted standard signals.

Related Experiment Videos

  • Investigation of coefficient calculation and approximation methods for function decomposition.

    • Main Results:

    • Established criteria for identifying crystallographic wavelet-type functions.
    • Developed methods for fixed-scale decomposition of functions within unit cells.
    • Analyzed the conditions for exact and approximate function representation.

    Conclusions:

    • Crystallographic wavelet-type functions offer a novel approach to signal analysis in crystals.
    • Fixed-scale decomposition provides a framework for understanding function representation in crystallography.
    • The study highlights connections between fixed-scale decomposition and key crystallographic problems like the phase problem.