Asymmetric Objects Research Articles

Angular reconstitution: A posteriori assignment of projection directions for 3D reconstruction

In computerized tomography as well as in most problems of three-dimensional reconstruction from projections, one knows from the experimental set-up the angular relationships between the projections from which the reconstruction is to be calculated. A serious difficulty is encountered when the angles are not known. In this paper, a method of “angular reconstitution” is described, which allows the a posteriori determination of the relative angular orientations of the projections and thus enables the three-dimensional reconstruction of the object to be calculated. For asymmetric objects, a minimum of three projections is required, which should not be related by a tilt around a single rotation axis. The method can be applied to determine the three-dimensional structure of biological macromolecules based on electron micrographs of randomly oriented individual molecules. Angular reconstitution, in combination with multivariate statistical techniques to classify and average the characteristic views of a molecule forms a complete, self-contained methodology for molecular structure analysis by electron microscopy.

Methods for three-dimensional reconstruction of cellular components within a thick section

The tomographic reconstruction from multiple projections of cellular components, within a thick section, offers a way of visualizing and quantifying their three-dimensional (3D) structure. However, asymmetric objects require as many views from the widest tilt range as possible; otherwise the reconstruction may be uninterpretable. Even if not for geometric obstructions, the increasing pathway of electrons, as the tilt angle is increased, poses the ultimate upper limitation to the projection range. With the maximum tilt angle being fixed, the only way to improve the faithfulness of the reconstruction is by changing the mode of the tilting from single-axis to conical; a point within the object projected with a tilt angle of 60° and a full 360° azimuthal range is then reconstructed as a slightly elliptic (axis ratio 1.2 : 1) sphere.

On symmetry and asymmetry in literature

An attempt is made to investigate whether or not the principles of symmetry and asymmetry operate in literature. The result of the analysis is that certain (near) symmetric and/or asymmetric patterns may be found in literary works. Commonly, the authors use some convenient symmetric (asymmetric) figure, either as a descriptive means or as an underlying core around which their stories unfold. A structure of a literary work may also be interpreted in terms of symmetric and/or asymmetric objects. Sometimes a graphic shape of a work, most often of a poem, possesses symmetry. The content of a literary work may likewise be associated with some symmetric or asymmetric configuration. The citations from several literary works are included.

The Rotational Mode of Asymmetric Objects in Quantum Field Theory

The Rotational Mode of Asymmetric Objects in Quantum Field Theory

Universal Bundles for Deformations of Asymmetric Structures

Riemannian parallel transport of frames and Cartan connections can be considered as special cases of a type of structure in which the connection form on the principal bundle can transform by an arbitrary extension of the adjoint representation of the fiber group; there always exist universal deformations for asymmetric objects in any of these geometries.

Universal bundles for deformations of asymmetric structures

Riemannian parallel transport of frames and Cartan connections can be considered as special cases of a type of structure in which the connection form on the principal bundle can transform by an arbitrary extension of the adjoint representation of the fiber group; there always exist universal deformations for asymmetric objects in any of these geometries.

Imaging system using an intensity triple correlator

A new imaging system for incoherent objects is constructed. In this system, the coherence function of the diffracted field is derived from the signals of three scanning intensity detectors by using computational manipulations. The concrete optical and electronic systems, the details of the signal processings for the derivation of the coherence function, and calculations for image reconstruction are shown. The reconstructed images of asymmetric objects show the usefulness of the system.

Numerical analysis of interferograms of asymmetric plasma objects

Interferometric studies of dense rapidly expanding plasmas require the use of lasers emitting pulses of ~10–10–10–11 sec duration. Since the emission lines are wide, it is necessary to analyze interferograms by methods which ensure the maximum precision for a small number N of experimental points. Moreover, it is important to know the error resulting from such analysis and the optimal number Nopt of points to be analyzed. The present paper reports the results of numerical calculations, carried out on an M-220 computer, of the values of Nopt and of the error in the Van Voorhis method for three typical profiles of electron density in a plasma focus. The values of Nopt and of the errors in the parabola and Van Voorhis methods arerefined for a plasma jet (these parameters have been estimated earlier analytically). A diagnostic method is suggested for asymmetric plasmas and typical electron density profiles are calculated for Rayleigh–Taylor instability modes, which develop in pinches.

Algorithms for reproducing objects from their X-rays

A problem of considerable importance in biology is the reconstruction of three-dimensional biological structures from electron micrographs. The problem is mathematically equivalent to that of reconstructing a three-dimensional object from x-rays taken at several angles. Solutions to these problems by Fourier methods have been proposed; unfortunately, the techniques are only applicable to highly symmetric objects; otherwise they require an unrealistic number of electron micrographs. More recently, some Monte Carlo and algebraic reconstruction techniques have been proposed. They are applicable to asymmetric objects with a realistic number of electron micrographs and less computer time; however, their performance with unknown objects is difficult to evaluate. In this eaper we discuss the first steps towards linear-least-mean-squares techniques which can be used to develop rapid reconstruction algorithms that are also applicable to asymmetric objects with any number of electron micrographs. Such algorithms have the advantage of being the best of a class; in addition, their performance can be evaluated.

Algebraic Reconstruction Techniques (ART) for three-dimensional electron microscopy and X-ray photography

We give a new method for direct reconstruction of three-dimensional objects from a few electron micrographs taken at angles which need not exceed a range of 60 degrees. The method works for totally asymmetric objects, and requires little computer time or storage. It is also applicable to X-ray photography, and may greatly reduce the exposure compared to current methods of body-section radiography.