Number Of Cusps Research Articles

Morphogenesis of defects and tactoids during isotropic–nematic phase transition in self-assembled lyotropic chromonic liquid crystals

We explore the structure of nuclei and topological defects in the first-order phase transition between the nematic (N) and isotropic (I) phases in lyotropic chromonic liquid crystals (LCLCs). The LCLCs are formed by self-assembled molecular aggregates of various lengths and show a broad biphasic region. The defects emerge as a result of two mechanisms: (1) surface-anisotropy that endows each N nucleus (‘tactoid’) with topological defects thanks to preferential (tangential) orientation of the director at the closed I–N interface, and (2) Kibble mechanism with defects forming when differently oriented N tactoids merge with each other. Different scenarios of phase transition involve positive (N-in-I) and negative (I-in-N) tactoids with nontrivial topology of the director field and also multiply connected tactoid-in-tactoid configurations. The closed I–N interface limiting a tactoid shows a certain number of cusps; the lips of the interface on the opposite sides of the cusp make an angle different from π. The N side of each cusp contains a point defect-boojum. The number of cusps shows how many times the director becomes perpendicular to the I–N interface when one circumnavigates the closed boundary of the tactoid. We derive conservation laws that connect the number of cusps c to the topological strength m of defects in the N part of the simply connected and multiply connected tactoids. We demonstrate how the elastic anisotropy of the N phase results in non-circular shape of the disclination cores. A generalized Wulff construction is used to derive the shape of I and N tactoids as a function of I–N interfacial tension anisotropy in the approximation of frozen director field of various topological charges m. The complex shapes and structures of tactoids and topological defects demonstrate an important role of surface anisotropy in morphogenesis of phase transitions in liquid crystals.

Human Internal Jugular Valve M-mode Ultrasound Characterization

In humans the mechanism governing the internal jugular vein (IJV) valve opening and closure is still unclear. M-mode is used in echo-cardiology for the heart valves assessment. Sometimes it was performed also in deep peripheral veins and in vena cava assessment, but never in the IJV valve. Aim of the present study is to investigate the IJV valves physiology in healthy volunteers, by means of both B and M-mode ultrasound. Eighty-three (83) healthy volunteers (35 Male, 48 Female, 25.7±6.7 y.o.), for a total of 166 IJVs, were enrolled. The entire cohort underwent IJVs high-resolution B and M-mode evaluation, in standardized postural and respiratory conditions. Presence, motility, and number of cusps, as well as their opening and closure mechanism have been assessed. Bilateral valve absence occurred in 13/83 (16%), whereas at least a one side absence was recorded in 38/83 (46‰ of the cohort) (p<0.0356). Valve leaflets were always mobile and respectively bi-cusps in 34%, or mono-cusp in 27%. The latter was significantly more frequent on the left side (35%) than on the right side (19%) (p<0.0013). In supine, M-mode valve opening was synchronous with the cardiac cycle. To the contrary, in an upright position, the valve remained always open and saddled to the wall, independently from the cardiac cycle. In healthy subjects, the IJV valve leaflets are always mobile, but the significant rate of mono and bilateral absence could suggest a progressive phylogenetic importance loss of such apparatus. M-mode ultrasound enhances the characterization of IJV valve, for this reason it should be taken into consideration to routinely add it to the cerebral venous return investigation.

Bounding the j-invariant of Integral Points on Modular Curves

In this paper, we give some effective bounds for the $j$-invariant of integral points on arbitrary modular curves over arbitrary number fields assuming that the number of cusps is not less than 3.

Coagulation disorders and aortic stenosis: a chicken and egg question?

Coagulation disorders and aortic stenosis: a chicken and egg question?

Manipulation of Fgf and Bmp signaling in teleost fishes suggests potential pathways for the evolutionary origin of multicuspid teeth.

Teeth with two or more cusps have arisen independently from an ancestral unicuspid condition in a variety of vertebrate lineages, including sharks, teleost fishes, amphibians, lizards, and mammals. One potential explanation for the repeated origins of multicuspid teeth is the existence of multiple adaptive pathways leading to them, as suggested by their different uses in these lineages. Another is that the addition of cusps required only minor changes in genetic pathways regulating tooth development. Here we provide support for the latter hypothesis by demonstrating that manipulation of the levels of Fibroblast growth factor (Fgf) or Bone morphogenetic protein (Bmp) signaling produces bicuspid teeth in the zebrafish (Danio rerio), a species lacking multicuspid teeth in its ancestry. The generality of these results for teleosts is suggested by the conversion of unicuspid pharyngeal teeth into bicuspid teeth by similar manipulations of the Mexican Tetra (Astyanax mexicanus). That these manipulations also produced supernumerary teeth in both species supports previous suggestions of similarities in the molecular control of tooth and cusp number. We conclude that despite their apparent complexity, the evolutionary origin of multicuspid teeth is positively constrained, likely requiring only slight modifications of a pre-existing mechanism for patterning the number and spacing of individual teeth.

Prevalence of cusp 7 in permanent mandibular first molars in an Indian population: a comparative study of variations in occlusal morphology

The aims of the present study were to determine the prevalence of cusp 7 in permanent mandibular first molars in an Indian population, and to comparatively evaluate the variations in occlusal morphology of these teeth, including the difference in the number of cusps and fissure patterns. A total of 1123 Indian participants from the Government College of Dentistry, Indore, Madhya Pradesh, India, were selected for the study. For the analyses of cusp 6 and cusp 7 in permanent mandibular first molars, the Arizona State University Dental Anthropology System was used. Groove patterns were analyzed and classified as Y, +, X, and Ұ. Of the 1123 individuals, 132 (11.75%) were found to have cusp 7, while 78 (6.95%) had cusp 6. Thus, a total of 210 participants had the six-cusped mandibular first molars, 98 (8.73%) had the four-cusped mandibular first molars, and two had the seven-cusped variant. Overall, the most common fissure pattern was the Y pattern (50.36%), while the least common was the X pattern (1.25%). Mandibular first molars with cusp 7 demonstrated a highly significant (P<0.05) dominance of the Ұ pattern (36.80%) over the Y (30.74%), + (27.71%), and X (4.46%) fissure patterns. A significant prevalence of cusp 7 (11.25%) in permanent mandibular first molars was found in the present study in an Indian population.

Making three-dimensional Monson's sphere using virtual dental models

ObjectivesThe Monson's sphere and curve of Wilson can be used as reference for prosthetic reconstructions or orthodontic treatments. This study aimed to generate and measure the three-dimensional (3-D) Monson's sphere and curve of Wilson using virtual dental models and custom software. MethodsMandibular dental casts from 79 young adults of Korean descent were scanned and rendered as virtual dental models using a 3-D digitizing scanner. 26 landmarks were digitized on the virtual dental models using a custom made software program. The Monson's sphere was estimated by fitting a sphere to the cusp tips using a least-squares method. Two curves of Wilson were generated by finding the intersecting circle between the Monson's sphere and two vertical planes orthogonal to a virtual occlusal plane. Non-parametric Mann–Whitney and Kruskal–Wallis tests were performed to test for difference between sex and in cusp number within tooth position. ResultsThe mean radius of Monson's sphere was 110.89±25.75mm. There were significant differences between males and females in all measurements taken (p<0.01), within 16.87–17.27mm. Furthermore, morphological variation derived from variability in cusp number in the second premolar and second molar were not found to influence occlusal curvature (p>0.05). ConclusionsThis study describes a best-fit algorithm for generating 3-D Monson's sphere using occlusal curves quantified from virtual dental models. The radius of Monson's sphere in Korean subjects was greater than the original four-inch value suggested by Monson. Clinical significanceThe Monson's sphere and curve of Wilson can be used as a reference for prosthetic reconstruction and orthodontic treatment. The data found in this study may be applied to improve dental treatment results.

Metamerism, morphogenesis, and the expression of carabelli and other dental traits in humans

The patterning cascade model of tooth morphogenesis has emerged as a useful tool in explaining how tooth shape develops and how tooth evolution may occur. Enamel knots, specialized areas of dental epithelium where cusps initiate, act as signaling centers that direct the growth of surrounding tissues. For a new cusp to form, an enamel knot must form beyond the inhibition fields of other enamel knots. The model predicts that the number and size of cusps depends on the spacing between enamel knots, reflected in the spacing between cusps. Recently, work by our group demonstrated that the model predicted Carabelli trait expression in human first molars. Here we test whether differences in Carabelli trait expression along the molar row can also be predicted by the model. Crown areas and intercusp distances were measured from dental casts of 316 individuals with a digital microscope. Although absolute cusp spacing is similar in first and second molars, the smaller size and more triangular shape of second molars results in larger cusp spacing relative to size and, likely, less opportunity for the Carabelli trait to form. The presence and size of the hypocone (HY) and a range of small accessory cusps in a larger sample of 340 individuals were also found to covary with the Carabelli trait in a complex way. The results of this study lend further support to the view that the dentition develops, varies, and evolves as a single functional complex.

Variation in Morphology of Permanent Mandibular First Molars - A Rare Case Report

Dental size and morphology are easily recorded aspects of phenotypic variations. The majority of pathological variations in shape affect the crown of the tooth. The variations in the crown of the mandibular permanent molars include the occurrence of the sixth and cusp 7 on the first molars and the fifth cusp on the second molars. Cusp numbers and patterns are of great interest to the anthropologist, not only on account of variation in modern human groups, but because they show marked changes throughout the primate evolution. As the variations are always varied, we present a unique case of bilateral, unusual morphology of mandibular first permanent molars with an oblique ridge.

Mitral valve size measurement in North Karnataka by using cardiac sizer: A cadaveric study

Background: Heart is a vital organ of circulatory system. Valves maintain the unidirectional flow of blood. Mitral valve (MV) prevents the backflow of blood into the left atrium. For the proper functioning of the heart, all valves should be intact. MV prolapse and regurgitation is the main cause of MV replacement. Mean circumference of MV varies from person to person. Aim of the present study is to measure the average size of the valve in the cadavers of North Karnataka region by using cardiac sizer, which would help in the selection of prosthetic valve in the cardiac surgery. Materials and Methods: This study was carried out on 50 cadaveric adult human hearts. Left atrium was opened along the left border of heart so as to expose the mitral orifice. Then, the diameter of the valve was measured by using cardiac sizer, whereas circumference was calculated manually. Number of mitral valve cusps and papillary muscles were observed. Results: The mean annular circumference and diameter of the mitral valve was found to be 8.03 ± 0.82 cm and 2.56 ± 0.32 cm, respectively. Majority (72%) of the mitral valves had the circumference ranging from 7.53 to 8.47 cm and the diameter ranging from 2.4 to 2.7 cm. Conclusion: The size of mitral valve in the North Karnataka region was found to be less as compared to the other studies. This study might help cardio-thoracic surgeon as well the prosthetic valve manufacturing companies for the rough estimation of the mitral valve size.

Plane algebraic curves with many cusps, with an appendix by Eugenii Shustin

The maximum number $$k(d)$$ of cusps on a plane algebraic curve of degree $$d$$ is an open classical problem that dates back to the nineteenth century. A related open problem is the asymptotic value ( $$a.v.$$ ) of the number of cusps on plane curves, that is $$a.v.=\limsup _{d\rightarrow \infty } k(d)/{d^2}$$ . In this paper, we improve the best known lower bound for the asymptotic value by constructing curves with the largest known number of cusps for infinitely many degrees. Some particular curves of relatively low degree with many cusps are constructed too. The “Appendix” to this paper is devoted to the case of degree 11 and it is due to E. Shustin.

Complex multicusped postcanine teeth from the Lower Triassic of South Africa

ABSTRACT Two incisors and five postcanine teeth of complex crown morphology were found in the lower levels of the Burgersdorp Formation of the Beaufort Group, corresponding to the basal Subzone A of the Cynognathus Assemblage Zone (late Olenekian). All the teeth bear a single root and the postcanines show two rows of mesiodistally aligned cusps and a central basin or groove. Among the postcanines, two general patterns of crown morphology are recognized on the basis of relative length of the cusp rows, number of cusps per row, and width of the central area. Phylogenetic affinities of the described specimens remain unclear, and thus they are regarded as Eucynodontia incertae sedis. However, comparisons with non-mammalian cynodonts with labiolingually expanded postcanines show that they are most similar to those of Aleodon, Candelariodon, and some haramiyids. Many cynodont taxa such as Aleodon, Candelariodon, Cromptodon, haramiyids, and tritylodontids, which are probably not closely related to each other, have labiolingually expanded postcanines with cusps arranged mesiodistally in rows and a central basin; thus pointing to the homoplastic nature of dental morphologies in the cynodont lineage. The teeth presented here are the oldest record of therapsid teeth with crowns having parallel rows of cusps, representing a temporal extension of approximately 10 million years for this crown pattern.

Potential theory, path integrals and the Laplacian of the indicator

This paper links the field of potential theory -- i.e. the Dirichlet and Neumann problems for the heat and Laplace equation -- to that of the Feynman path integral, by postulating that the potential is equal to plus/minus the Laplacian of the indicator of the domain D. The Laplacian of the indicator is a generalized function: it is the d-dimensional analogue of the Dirac delta'-function. This function has -- according to the author's best knowledge -- not formally been defined before. We show, first, that the path integral's perturbation series (or Born series) matches the classical single and double boundary layer series of potential theory, thereby connecting two hitherto unrelated fields. Second, we show that the perturbation series is valid for all domains D that allow Green's theorem (i.e. with a finite number of corners, edges and cusps), thereby expanding the classical applicability of boundary layers. Third, we show that the minus (plus) in the potential holds for the Dirichlet (Neumann) boundary condition; showing for the first time a particularly close connection between these two classical problems. Fourth, we demonstrate that the perturbation series of the path integral converges in a monotone/alternating fashion, depending on the convexity/concavity of the domain. We also discuss the third boundary problem (which poses Robin boundary conditions) and discuss an extension to moving domains.

Gene clone and expression of Barx1 in different tooth of the mini-pig at embryonic day 40

To partially clone and compare the quantitative expression of tooth development-related gene Barx1 in different teeth of the mini-pig embryo at embryonic day 40, and to investigate the relationship between Barx1 spatial quantitative expression and tooth morphogenesis. The mini-pig Barx1 genes was partially cloned and the mRNA sequences of human Barx1 genes was aligned with expressed sequence tags (EST) of pig by basic local alignment search tool (BLAST), which were assembled with DNAman v5.2.2. With designed primers, Barx1 was partially cloned in use of reverse transcription polymerase chain reaction (PCR), and tested by BLAST with all the species in NCBI database and confirmed as one part of target gene. Laser capture microdissection was used to collect tooth samples from frozen sections which were prepared before in -80°C freezer. Real-time PCR was carried out to analyze quantitative expression in different teeth. Partial mini-pig Barx1 gene of 698 bp was cloned. Real-time PCR showed that, glyceraldehyde-3-phosphate dehydrogenase used as loading control, the figures of 2(-ΔCT) of lower deciduous incisor, canine, the third premolar and molar were 0.000 249, 0.000 715, 0.026 096 and 0.112 656, respectively. There was a trend of increasing expression from anterior to posterior teeth. Barx1 gene could be related to the number or differentiation of tooth cusps.

On the affine geometry of the graph of a real polynomial

Given a surface defined as the graph of a real polynomial in two variables, we analyze some basic subsets characterized by its tangential singularities. If the parabolic curve is compact we provide certain criteria to determine when the unbounded component of its complement is hyperbolic. Moreover, we obtain an upper bound of the number of Gaussian cusps that holds even if the parabolic curve is non compact.

Concepts and steps for the realization of a new domain wall based giant magnetoresistance nanowire device: From the available 24 multiturn counter to a 212 turn counter

Two concepts for new types of a magnetic domain wall (DW) based multiturn counter with true power on functionality are presented. Both counters use several closed loops of magnetic nanowires, each with different numbers of cusps. The turns are counted by the motion of domain walls through the loops, whereas a DW will move through one cusp during 90° external field rotation. Two concepts are introduced: a system based on binary logic, which is easy to integrate in digital electronics, and a system based on coprime numbers, which is useful to count large numbers. We have performed micromagnetic simulations in order to optimize the geometry of the cusp with respect to the operation margin of the device. Experimental verification of the domain wall motion through a giant magnetoresistance stack cusp is given. Furthermore, the read-out scheme for both systems is shown.

The arrangement of the interproximal interfaces in the human permanent dentition

The interproximal interface (IPI) is the interface between two adjacent teeth, i.e., the site where forces are transmitted along the dental arch. We investigated the IPI arrangement of the human permanent dentition. Specifically, the IPI morphometrical characteristics were studied and interpreted within a biomechanical framework. A novel in vivo IPI measurement was developed based on diversity in transillumination of Polyvinyl siloxane impression of the interproximal region. The study group included 30 subjects, aged 27, ±4.0 years. Eleven parameters were examined in each of the 26 IPIs of the permanent dentition. The IPI showed intra-arch similarity and interarch diversity between the tooth groups. The IPI shape was predominantly oval (60-100%), yet kidney-shaped in some molars (22-40%). From incisors to molars: the IPI increased significantly (p < 0.001) in size (1.72 to 6.05 mm(2)), occupied more of the proximal wall (7.8-12%), changed its orientation from vertical to horizontal (88.66-14.80°), and was mainly located in the buccal-occlusal quadrant of the proximal wall, chiefly in the molar teeth. The IPI is a product of proximal wall attrition and is dictated by the mastication forces, number of cusps, and crown inclination. IPI arrangement counteracts the adverse crowding effect of the anterior component of the mastication forces. The IPI characteristics found in the present study provide guidelines for crown and proximal filling restorations to meet dental physiology requirements. Further, IPI determines correct tooth alignment and proximal wall stripping applied to resolve arch length deficiency.

On the difficulty of increasing dental complexity

One of the fascinating aspects of the history of life is the apparent increase in morphological complexity through time, a well known example being mammalian cheek tooth evolution. In contrast, experimental studies of development more readily show a decrease in complexity, again well exemplified by mammalian teeth, in which tooth crown features called cusps are frequently lost in mutant and transgenic mice. Here we report that mouse tooth complexity can be increased substantially by adjusting multiple signalling pathways simultaneously. We cultured teeth in vitro and adjusted ectodysplasin (EDA), activin A and sonic hedgehog (SHH) pathways, all of which are individually required for normal tooth development. We quantified tooth complexity using the number of cusps and a topographic measure of surface complexity. The results show that whereas activation of EDA and activin A signalling, and inhibition of SHH signalling, individually cause subtle to moderate increases in complexity, cusp number is doubled when all three pathways are adjusted in unison. Furthermore, the increase in cusp number does not result from an increase in tooth size, but from an altered primary patterning phase of development. The combination of a lack of complex mutants, the paucity of natural variants with complex phenotypes, and our results of greatly increased dental complexity using multiple pathways, suggests that an increase may be inherently different from a decrease in phenotypic complexity.

Study of mitral valve in human cadaveric hearts

Objectives:The mitral valve is a complex structure that is altered by disease states. The classical image of the mitral valve is a bicuspid valve with two leaflets and two papillary muscles. The reason for the present study is to study the morphology and morphometry of the mitral valve.Materials and Methods:This study was carried out on 116 human cadaveric hearts. Hearts were opened along the left border through the atrioventricular valve. The diameter and circumference of the annulus was measured and the number of valve leaflets was observed.Results:The mean annular diameter was 2.22 cm. The mean circumference of mitral valve annulus was 9.12 cm. The standard description of the mitral valve is bicuspid. In the present study, we found the number of cusps to be variable, from monocuspid to hexacuspid and classified them accordingly.Conclusions:The mitral valve is not always a bicuspid valve. The number of cusps varies greatly. An increase in the number of the cusp and their improper approximation most likely causes various valvular disorders.

The intercusp patterns on the mandibular M1 and M2 teeth

The existence and contact types between MB and DL cusps (Protoconid-Entoconid contact), as well as the reduction of cusp numbers and their interrelationship, determine the shape of intercusp patterns. According to Hellman, there are three shapes (types) of patterns: 'y', '+' and 'x'. This research was conducted on 552 orthodontic patients study models at the Clinic of Stomatology of Nis, with the aim of determining the frequency of shapes (types) of intercusp patterns on the permanent mandibular M1 and M2 teeth. The lower M1 teeth of the examined patients are characterized by the 'y' shape (70,11%) and the lower M2 teeth by the '+' shape (90,76%). The second frequent on M1 is the '+' shape (27,35%) and the 'x' shape on M2 (4,89%). On the mandibular M1 teeth, the most frequent type is the 'y 5' type (69,75%) , then the '+ 4' type (23,35%). For M2, the '+ 4' type is characteristic in 89,85%, while the 'y 5' type is found only in 3,44%.