Angular Variances Research Articles

A Computational Tool for Detection of Soft Tissue Landmarks and Cephalometric Analysis

In facial aesthetics, soft tissue landmark recognition and linear and angular measurement play a critical role in treatment planning. Visual identification and judgment by hand are time-consuming and prone to errors. As a result, user-friendly software solutions are required to assist healthcare practitioners in improving treatment planning. Our first goal in this paper is to create a computational tool that may be used to identify and save critical landmarks from patient X-ray pictures. The second goal is to create automated software that can assess the soft tissue facial profiles of patients in both linear and angular directions using the landmarks that have been identified. To boost the contrast, we employ gamma correction and a client-server web-based model to display the input images. Furthermore, we use the client-side to record landmarks in pictures and save the annotated landmarks to the database. The linear and angular measurements from the recorded landmarks are then calculated computationally and displayed to the user. Annotation and validation of 13 soft tissue landmarks were completed. The results reveal that our software accurately locates landmarks with a maximum deviation of 1.5 mm to 5 mm for the majority of landmarks. Furthermore, the linear and angular measurement variances across users are not large, indicating that the procedure is reliable.

2D DOA Estimation of Coherently Distributed Sources for Planar Arrays Based on Blind Signal Separation

A novel method is presented to estimate the direction-of-arrival (DOA) of coherently distributed (CD) sources for planar arrays. In the proposed method, the two-dimensional (2D) angular parameters are obtained by making use of the estimated generalized array manifold matrix, which is separated from the received observation data based on blind signal separation algorithm. The proposed method offers a number of advantages. First, the 2D central DOAs and angular spread variances can be estimated simultaneously. Second, the deterministic angular distributed functions (DADFs) of the CD sources do not need to know. Third, the special array geometries are not required, as the method is applicable to planar arrays. Computer simulations are shown to verify the efficacy of the proposed method.

ANALISIS OF THE INFLUENCE OF THE MAIN PARAMETERS AND CONDITION OF WORK OF AIRCRAFT CESN ON THE EFFICENCY OF THEIR USE METHODS OF MATHEMATICAL MODELING

The article describes the results of the numerical experiments on the mathematical model of the correlation-extreme navigation system (CESN) of the aircraft (LA) using microwave radiation of the earth's cover. The aim of the numerical experiments was the analysis of the influence of the main parameters (characteristics of the radiometer and antenna, a means of reviewing the space, parameters of the current image and the reference image, methods for image processing (algorithms for image correlation), conditions of the equipment operation (the speed and altitude of aircraft, the evolution of media) on the efficiency of CESN. The experiments were carried out with the fields of the underlying surface of three types-with an artificially synthesized map (CLAIM) containing several objects of different thermal contrast; with a homogeneous random field (OSP), with fragments of a digital map object structure (TSKOS) of real surface area of the earth. As a result of numerical experiments the author studied the influence on exactness characteristics of CESN navigation parameters (bank angles, pitch, yaw), flight altitude and speed, the noise of the radiometer, the pattern width, the width of the review sector, mis-scaling and angular misalignment of the current and reference images. Comparison of different methods of surface scanning was made based on the simulation results. During the experiments, the variation of one of the parameters with respect to the base variants of the parameters was carried out and the values and variances of errors of the CESN were estimated. All three main methods of beam scanning (longitudinal with a multi-beam radiometer, conical and transverse) were considered. The operation of the maximum search was made up of two procedures: searching for the global maximum area of the correlation matrix by enumerating all matrix entries and refining the location of the true maximum point by quadratic interpolation of the function. The implementation of errors is considered for various trajectories of the aircraft's motion, as well as for various angular variances. The implementation processing showed that an increase in the angular dispersion leads to a simultaneous increase in both the error modulus and the variance of the error modulus. The analysis of the obtained dependences shows a fairly stable tendency to reduce errors of CESN with a decrease in navigation angles. This dependence is demonstrated graphically. In order to estimate only the influence of the fluctuation noise of the radiometer on the magnitude of the CESN errors, a series of experiments was performed in which all other random fluctuations in the channel were eliminated.

12C-induced multifragmentation of heavy-ion reactions

Multifragmentation of carbon-induced fission is considered following the statistical scission model. The fragment products in the exit channel are two different deformed nuclei, as well as some nucleons and / or alpha particles. The angular distributions and variances of this multifragmentation process, including two deformed heavy fragments, have been numerically calculated. The present calculations show the strong dependence of these values on the nuclear temperature. The present calculated differential cross-sections are in good agreements with the experimental data for an incident carbon energy of 84 A MeV.

Aberrationless theory of self-focusing via spatial and angular variances for modal laser fields

We present a new, to the best of our knowledge, formalism based on the propagation of variances in an ABCD optical system to study nonlinear effect in a Kerr medium. This theory, developed for the first order in the beam power, is applied to modal laser fields (Gaussian, Hermite-Gaussian, and Laguerre-Gaussian beams) and permits one to obtain a simple analytical formulation for self-focusing and Z-scan experiments, whatever the thickness of the nonlinear medium.

Kinematic analysis of the hip and trunk during bilateral stance on firm, foam, and multiaxial support surfaces

Objective. To differentiate hip and trunk motion during double-leg stance. Design. Trunk and hip angular position variances were measured on different support surfaces with and without vision. Background. Postural control results from motion about the hips and trunk during bilateral stance. While the hip joint has been studied extensively, information concerning relative amounts of hip and trunk motions during postural control is limited. Methods. Trunk flexion/extension, trunk lateral flexion, right and left hip flexion/extension and abduction/adduction angular position variances were assessed in 14 normal subjects using an electromagnetic tracking system during bilateral stance on firm, foam, and multiaxial support surfaces with and without vision. Results. Significantly greater amounts of motion occurred at all joints for the multiaxial-eyes closed condition compared to all other surface–vision conditions. No significant differences were found between any other surface–vision conditions. Within the multiaxial-eyes closed condition, right and left hip flexion/extension and abduction/adduction magnitudes were significantly greater than those of trunk flexion and lateral flexion, and left hip flexion/extension motion was significantly greater than that of the right hip. Conclusions. Postural control mechanisms involve similar amounts of motion at the hips and trunk, except for conditions under which a rigid base of support becomes unstable and vision is eliminated. Relevance These results suggest that the trunk and hips should be considered separately during kinematic analysis of postural control. This information may be useful in providing a more sensitive assessment of postural control to identify balance-related pathologies associated with stroke, concussion, and somatosensory deficits.

The behavioural role of pit organs in the epaulette shark

Epaulette sharks Hemiscyllium ocellatum in three treatments, pit organs (free neuromasts) ablated, sham‐operated and normal (n = 8 for each treatment), showed a significant preference for facing upstream in a flume (P < 0·05). There were no significant differences in the mean angles or angular variances among treatments. Individuals with ablated pit organs, however, spent significantly less time moving around than controls (P < 0·05), suggesting that pit organs contributed to motivation for activity. Pit organs do not appear to make an important contribution to rheotaxis in H. ocellatum. It is suggested that this may be due to structural differences in the pit organs of H. ocellatum compared with other species.

Retrieval by Local Motion

Motion feature plays an important role in video retrieval. The current literature mostly addresses motion retrieval only by camera motion and global motion of individual video objects in a video scene. In this paper, we propose two new motion descriptors that capture the local motion of the video object within its bounding box. The proposed descriptors are rotation and scale invariant and based on the angular and circular area variances of the video object and the variances of the angular radial transform coefficients. Experiments show that ranking obtained by querying with our proposed descriptors closely match with the human ranking.

Internal motional amplitudes and correlated bond rotations in an alpha-helical peptide derived from 13C and 15N NMR relaxation.

Peptide GFSKAELAKARAAKRGGY folds in an alpha-helical conformation that is stabilized by formation of a hydrophobic staple motif and an N-terminal capping box (Munoz V. Blanco FJ, Serrano L, 1995, Struct Biol 2:380-385). To investigate backbone and side-chain internal motions within the helix and hydrophobic staple, residues F2, A5, L7, A8, and A10 were selectively 13C- and 15N-enriched and NMR relaxation experiments were performed in water and in water/trifluoroethanol (TFE) solution at four Larmor frequencies (62.5, 125, 150, and 200 MHz for 13C). Relaxation data were analyzed using the model free approach and an anisotropic diffusion model. In water, angular variances of motional vectors range from 10 to 20 degrees and backbone phi,psi bond rotations for helix residues A5, L7, A8, and A10 are correlated indicating the presence of Calpha-H, Calpha-Cbeta, and N-H rocking-type motions along the helix dipole axis. L7 side-chain CbetaH2 and CgammaH motions are also correlated and as motionally restricted as backbone CalphaH, suggesting considerable steric hindrance with neighboring groups. In TFE which stabilizes the fold, internal motional amplitudes are attenuated and rotational correlations are increased. For the side chain of hydrophobic staple residue F2, wobbling-in-a-cone type motions dominate in water, whereas in TFE, the Cbeta-Cgamma bond and phenyl ring fluctuate more simply about the Calpha-Cbeta bond. These data support the Daragan-Mayo model of correlated bond rotations (Daragan VA, Mayo KH, 1996, J Phys Chem 100:8378-8388) and contribute to a general understanding of internal motions in peptides and proteins.

On the initial angular variances of clinical electron beams

Electron beam radiotherapy treatment planning systems need to be fed with the characteristics of the high-energy electron beams (4-50 MeV) from the specifically applied accelerator. Beams can be characterized by their mean initial energy, effective initial angular variance, virtual source position and the resulting central axis depth dose distribution in water. This information is the only input to pencil beam dose calculation models. Newer calculation models like macro Monte Carlo, voxel Monte Carlo and phase space evolution require as input the full initial phase space or a parametrization of that initial phase space, generally consisting of a primary beam component and one or more scatter components. This primary beam component is often characterized by initial energy, primary beam initial angular variance and virtual source distance. The purpose of the present investigation was to investigate to what extent standard values can be used both for the effective initial angular variance as input to pencil beam models and for the primary beam initial angular variance. Comprehensive benchmark data were obtained on the initial angular variance of various types of accelerator, for various energies and field sizes. The initial angular variance has been derived from penumbra measurements in air by means of film dosimetry at various distances from the lower collimator. For the types of accelerator used in radiotherapy nowadays the measurements show values for of around 13 cm where T(E) is the ICRU-35 linear angular scattering power in air. This value can be chosen as standard value for the primary beam initial angular variance, only slightly compromising the dose calculation accuracy. As input to pencil beam models, an effective should be used incorporating the scatter from the lower collimator. For the case that the air gaps between lower collimator and patient are small (5-10 cm) an effective of 20 cm has been found and is recommended as the standard input for pencil beam models. Of the accelerators investigated, a different value was found only for the Elekta SL15, i.e. 50% higher for the effective .

Angular variances for internal bond rotations of side chains in GXG-based tripeptides derived from (13)C-NMR relaxation measurements: Implications to protein folding.

The study of backbone and side-chain internal motions in proteins and peptides is crucial to having a better understanding of protein/peptide "structure" and to characterizing unfolded and partially folded states of proteins and peptides. To achieve this, however, requires establishing a baseline for internal motions and motional restrictions for all residues in the fully, solvent-exposed "unfolded state." GXG-based tripeptides are the simpliest peptides where residue X is fully solvent exposed in the context of an actual peptide. In this study, a series of GXG-based tripeptides has been synthesized with X being varied to include all twenty common amino acid residues. Proton-coupled and -decoupled (13)C-nmr relaxation measurements have been performed on these twenty tripeptides and various motional models (Lipari-Szabo model free approach, rotational anisotropic diffusion, rotational fluctuations within a potential well, rotational jump model) have been used to analyze relaxation data for derivation of angular variances and motional correlation times for backbone and side-chain chi(1) and chi(2) bonds and methyl group rotations. At 298 K, backbone motional correlation times range from about 50 to 85 ps, whereas side-chain motional correlation times show a much broader spread from about 18 to 80 ps. Angular variances for backbone phi,psi bond rotations range from 11 degrees to 23 degrees and those for side chains vary from 5 degrees to 24 degrees for chi(1) bond rotations and from 5 degrees to 27 degrees for chi(2) bond rotations. Even in these peptide models of the "unfolded state," side-chain angular variances can be as restricted as those for backbone and beta-branched (valine, threonine, and isoleucine) and aromatic side chains display the most restricted motions probably due to steric hinderence with backbone atoms. Comparison with motional data on residues in partially folded, beta-sheet-forming peptides indicates that side-chain motions of at least hydrophobic residues are less restricted in the partially folded state, suggesting that an increase in side-chain conformational entropy may help drive early-stage protein folding. Copyright 1999 John Wiley & Sons, Inc.

Motional dynamics of residues in a beta-hairpin peptide measured by 13C-NMR relaxation.

Structurally characterizing partially folded peptides is problematic given the nature of their transient conformational states. 13C-NMR relaxation data can provide information on the geometry of bond rotations, motional restrictions, and correlated bond rotations of the backbone and side chains and, therefore, is one approach that is useful to assess the presence of folded structure within a conformational ensemble. A peptide 12mer, R1GITVNG7KTYGR12, has been shown to partially fold in a relatively stable beta-hairpin conformation centered at NG. Here, five residues, G2, V5, G7, Y10, G11, were selectively 13C-enriched, and 13C-NMR relaxation experiments were performed to obtain auto- and cross-correlation motional order parameters, correlation times, bond rotation angular variances, and bond rotational correlation coefficients. Our results indicate that, of the three glycines, G7 within the hairpin beta-turn displays the most correlated phi(t),psi(t) rotations with its axis of rotation bisecting the angle defined by the H-C-H bonds. These positively correlated bond rotations give rise to "twisting" type motions of the HCH group. V5 and Y10 phi,psi bond rotations are also positively correlated, with their CbetaCalphaH groups undergoing similar "twisting" type motions. Motions of near-terminal residues G2 and G11 are less restricted and less correlated and are best described as wobbling-in-a-cone. V5 and Y10 side-chain motions, aside from being highly restricted, were found to be correlated with phi,psi bond rotations. At 303 K, where the hairpin is considered "unfolded," the peptide exists in a transient, collapsed state because backbone and side-chain motions of V5, G7, and Y10 remain relatively restricted, unlike their counterparts in GXG-based tripeptides. These results provide unique information toward understanding conformational variability in the unfolded state of proteins, which is necessary to solve the protein folding problem.

What Statistics Determine Segmentation of Orientation-Defined Textures?

Beck suggested that texture segmentation is based upon differences in the first-order statistics of stimulus features such as orientation, size, and contrast. However, this theory does not indicate how these differences might be quantified, or what properties of the statistics might be used. Some alternative models postulate that texture segmentation is determined by the responses of spatial-frequency channels, where the channels contain both a linear filtering mechanism and various nonlinearities. Such models do a good job of predicting human performance, but do not give us much insight into what textures will segment, since the comparison carried out by the model is often obscured by the details of the filtering, nonlinearity, and image-based decision processes. It is suggested here that, for orientation-defined textures (eg in which each ‘texel’ has a single orientation), segmentation is well-described by something like the ‘significance’ of the differences between (1) the mean orientations, and (2) the angular variances of the two textures. The ‘significance’ of the difference in means takes into account the variability in the texture, so that two homogeneous textures with means differing by 30° may easily segment, while two heterogeneous textures with the same difference in mean may not. Furthermore, it is shown that these statistics may be computed in a biologically plausible way, which greatly resembles the typical filter-based approaches to texture segmentation. Thus the connection between statistical theories of texture segmentation and spatial-frequency channel models becomes more transparent.

Multifragmentation of24Mg+24Mg heavy-ion reactions leading to alpha-particles

Angular distributions of alpha-particles emitted from magnesium + magnesium reactions are calculated at different incident energies. The alpha-particles are sequentially emitted from long-lived states of primary fragments populated in direct reactions. The present reaction yields to multifragmentation with the result of twelve alpha-particles which are dealt with using the cluster model. The statistical scission model is used in developing the angular distributions of the fragments. The angular distributions and variances of this multifragmentation process have been numerically calculated. The obtained results are in good agreement with previous calculations.

Application of some statistical methods for comparing samples of Hue-Angle data

Several color spaces utilize angular measures of hue:for example, CIE 1976 u, v hue-angle; CIE 1976 a, b hueangle. Such measures are not amenable to conventional statistical analysis, unless a categorization of hue-angles has previously been decided upon, in which case nonparametric tests are appropriate. In this article we present two recently established methods that are appropriate for the parametric statistical analysis of hue-angle data from two or more samples: [i] a test of the equality of angular variances; [ii] a test of the equality of mean angles. These tests may be performed easily on a microcomputer and produce statistics conforming approximately to well known distributions. We envisage that the tests will be of interest to psychologists and others working in the field of color research. © 1992 John Wiley & Sons, Inc.

Wide-Band Monopulse Sonar: Processor Performance in the Remote Profiling Application

Monopulse radars are used extensively to track isolated targets to within angular error variances that are very small in comparison with antenna beamwidth. Analogous active sonar configurations (e.g., split-beam sonar) have been in use for several decades, although very little attention has been paid to adaptation of the monopulse concept to accommodate wide-hand operation, or to the angular error variance that is due to a wave phenomenon known in the radar community as "glint." The wide-band adaptation is relatively simple, and permits adjustments in the design of the array processor to reduce glint errors and to avoid anomalous magnification of errors due to ambient noise. This adaptation also has the advantage of being free of angle ambiguities, regardless of the transmitted pulse spectrum. Performance is analyzed for the particular application of remotely measuring the depth/structure profile of the seafloor. Sensitivity to various design parameters is analyzed in detail.