Adaptation of Cardinal Points Symmetry Landmarks Distribution Model to in-vivo B-Mode Ultrasound Images of Transverse Cross-section of Carotid Arteries

The geometry of the imaged transverse cross-section of carotid arteries in in-vivo B-mode ultrasound images are most times irregular, unsymmetrical, full of speckles and usually non-uniform. We had earlier developed a technique of cardinal point symmetry landmark distribution model (CPS-LDM) to completely characterize the Region of Interest (ROI) of the geometric shape of thick-walled simulated B-mode ultrasound images of carotid artery imaged in the transverse plane, but this was based on the symmetric property of the image. In this paper, this developed technique was applied to completely characterize the region of interest of the geometric shape of in-vivo B-mode ultrasound images of non-uniform carotid artery imaged in the transverse plane. In order to adapt the CPS-LD Model to the in-vivo carotid artery images, the single VS-VS vertical symmetry line common to the four ROIs of the symmetric image is replaced with each ROI having its own VS-VS vertical symmetry line. This adjustment enables the in-vivo carotid artery images possess symmetric properties, hence, ensuring that all mathematical operations of the CPS-LD Model are conveniently applied to them. This adaptability was observed to work well in segmenting the in-vivo carotid artery images. This paper shows the adaptive ability of the developed CPS-LD Model to successfully annotate and segment in-vivo B-mode ultrasound images of carotid arteries in the transverse cross-sectional plane either they are symmetrical or unsymmetrical.

Reliability evaluation of consecutive k-out-of-m: F balanced systems with a symmetry line

Based on some real backgrounds, a new balanced system structure, a consecutive k-out-of- m: F system with a symmetry line, is proposed in this paper. Considering different state numbers of a subsector, the new balanced system is analyzed under two situations respectively: the subsector with binary-state and the subsector with multi-state, while the multi-state balanced systems have not been studied in the previous research. Besides, two models are developed in terms of assumptions for the two situations, respectively. For this system, several methods, such as the finite Markov chain imbedding approach, the order statistics technique and the phase-type distributions, are used on the models. In addition to system reliability formulas, the means and variances of the system lifetimes under two models for different situations are given. Finally, numerical examples are presented to illustrate the results obtained in this paper.

Influence of Substrate Material on Flow in Freezing Water Droplets—An Experimental Study

Freezing water droplets are a natural phenomenon that occurs regularly in the Arctic climate. It affects areas such as aircrafts, wind turbine blades and roads, where it can be a safety issue. To further scrutinize the freezing process, the main objective of this paper is to experimentally examine the influence of substrate material on the internal flow of a water droplet. The secondary goal is to reduce uncertainties in the freezing process by decreasing the randomness of the droplet size and form by introducing a groove in the substrate material. Copper, aluminium and steel was chosen due to their differences in thermal conductivities. Measurements were performed with Particle Image Velociometry (PIV) to be able to analyse the velocity field inside the droplet during the freezing process. During the investigation for the secondary goal, it could be seen that by introducing a groove in the substrate material, the contact radius could be controlled with a standard deviation of 0.85%. For the main objective, the velocity profile was investigated during different stages of the freezing process. Five points along the symmetry line of the droplet were compared and copper, which also has the highest thermal conductivity, showed the highest internal velocity. The difference between aluminium and steel was in their turn more difficult to distinguish, since the maximum velocity switched between the two materials along the symmetry line.

Line of approximate SU(3) symmetry inside the symmetry triangle of the Interacting Boson Model

The U(5), SU(3), and O(6) symmetries of the Interacting Boson Model (IBM) have been traditionally placed at the vertices of the symmetry triangle, while an O(5) symmetry is known to hold along the U(5)–O(6) side of the triangle. We construct [1] for the first time a symmetry line in the interior of the triangle, along which the SU(3) symmetry is preserved. This is achieved by using the contraction of the SU(3) algebra to the algebra of the rigid rotator in the large boson number limit of the IBM. The line extends from the SU(3) vertex to near the critical line of the first order shape/phase transition separating the spherical and prolate deformed phases. It lies within the Alhassid–Whelan arc of regularity, the unique valley of regularity connecting the SU(3) and U(5) vertices amidst chaotic regions, thus providing an explanation for its existence.

ANALYSIS OF SKIN PATTERNS OF GERMAN SHEPHERD’S RHINARIUM IN COMPARATIVE ASPECT

The popularity of the German Shepherd breed and its use in many areas of human life creates the need to search for new identification methods to establish ownership. The identification methods available, such as chipping and marking, have several disadvantages. The method of dogs’ identification by rhinarium’s imprint is comparatively cheap and reliable. Papillary patterns reflected on rhinarium’s imprint are relatively constant, and have common and particular signs of difference, which make it possible to distinguish the impression of one dog from another. Dogs of the same breed have a standardized exterior, that is, similarity in external characters, which suggests that there are similarities between common and particular characteristics within the same breed. It is found that imprints of the rhinarium of German shepherd breed dogs, obtained from dogs of different origin, housing and feeding conditions, have common features of papillary patterns peculiar to the given breed. The presented results of the comparison of skin patterns of the rhinarium show that this breed is characterized by a straight, straight round-pointed and V-shaped forms of the nose symmetry line, the majority of the representatives of the breed have prints heavily spotted with lines and, as a rule, have 2 branches of the line of symmetry, which proves the presence of breed characteristics and allows for the use of prints in forensic and forensic veterinary identification of dogs.

Induced Voltage in an Open Wire

A puzzle arising from Faraday’s law has been considered and solved concerning the question which voltage will be induced in an open wire with a time-varying homogeneous magnetic field. In contrast to closed wires where the voltage is determined by the time variance of the magnetic field and the enclosed area, in an open wire we have to integrate the electric field along the wire. It is found that the longitudinal electric field with respect to the wave vector contributes with 1/3 and the transverse field with 2/3 to the induced voltage. In order to find the electric fields the sources of the magnetic fields are necessary to know. The representation of a spatially homogeneous and time-varying magnetic field implies unavoidably a certain symmetry point or symmetry line which depend on the geometry of the source. As a consequence the induced voltage of an open wire is found to be the area covered with respect to this symmetry line or point perpendicular to the magnetic field. This in turn allows to find the symmetry points of a magnetic field source by measuring the voltage of an open wire placed with different angles in the magnetic field. We present exactly solvable models of the Maxwell equations for a symmetry point and for a symmetry line, respectively. The results are applicable to open circuit problems like corrosion and for astrophysical applications.