Number Of Cusps Research Articles

Stable functions and common stabilizations of Heegaard splittings

We present a new proof of Reidemeister and Singer's Theorem that any two Heegaard splittings of the same 3-manifold have a common stabilization. The proof leads to an upper bound on the minimal genus of a common stabilization in terms of the number of negative slope inflection points and type-two cusps in a Rubinstein-Scharlemann graphic for the two splittings.

Cranial morphology and systematics of an extraordinary sample of the Late Neogene dwarf tapir,Tapirus polkensis(Olsen)

The previously poorly known“Tapiravus” polkensisOlsen, 1960 (Mammalia, Perissodactyla, Tapiridae) is now known from abundant, well preserved specimens from both the type area in central Florida and from the Gray Fossil Site (GFS) in eastern Tennessee. The latter has produced over 75 individuals, the greatest number of tapirids from a single fossil site, including many articulated skeletons. Almost all linear measurements taken on skulls, mandibles, and cheek teeth from GFS have coefficients of variation less than 10 (most between 3 and 7), indicating the presence of a single species. However, the sample reveals considerable intraspecific variation for a few key morphologic features, including development of the sagittal crest, outline shape of the nasals, and number and relative strength of lingual cusps on the P1. The Florida sample ofT. polkensisis more limited, but has the same state as the GFS sample for all preserved characters of systematic significance, and while the Florida teeth are on average smaller (especially narrower lower cheek teeth), they fall either within or just below the observed range of the Gray Fossil Site population. The new material supports a reassignment of“Tapiravus” polkensisto the genusTapirus, and demonstrates that the geologic age of the species is significantly younger than previously thought, Hemphillian rather than Barstovian.Tapirus polkensisis the smallest known North AmericanTapirus, and smaller than any of the extant species in the genus, with an estimated average mass of 125 kg.

Morphometric and immunohistochemical investigation of tooth development in rats prenatally exposed to ethanol

The purpose of this study was to clarify the effect of ethanol on rat molar tooth development. Pregnant rats were fed 25%-ethanol solutions or ethanol-free water up to delivery, and tooth germs, as well as fully developed teeth, obtained from the offspring (ethanol-exposed rats or control rats) were subjected to morphometric analysis and immunohistochemistry. No significant differences were observed in terms of tooth size between the ethanol-exposed and control rats. Moreover, no abnormalities in cusp number, form or dental surface structure was noted in the ethanol-exposed rats. In the ethanol-exposed rats, the tooth development showed a slight retardation in comparison to the controls. Morphological alteration in tooth germs was not observed in the experimental rats. Both bone morphogenetic protein-4 and basic fibroblast growth factor-2 were immunolocalized in the cells composing the tooth germs in the ethanol-exposed rats. No differences, however, were found in immunostaining intensity between the ethanol-exposed and control rats. Taken together, the results indicate that the effect of ethanol on tooth development was weaker than expected in the rat FAS model.

APPARENT CONTOURS WITH MINIMAL NUMBER OF SINGULARITIES

For a stable map φ: M →S2 of a closed and connected surface into the sphere, let c(φ), i(φ) and n(φ) denote the numbers of cusps, fold curve components and nodes respectively. In this paper, in a given homotopy class, we will determine the minimal triples (c, i, n), (n, c, i) and (i, n, c) with respect to the lexicographic order.

Abnormal tooth size and morphology in subjects with cleft lip and/or palate in the north of England

The aim of this study was to investigate tooth size and morphology in subjects with unilateral cleft palate (UCLP), bilateral cleft palate (BCLP), and isolated cleft palate (ICP) living in the north of England and to compare these with a control group. The measurements were undertaken retrospectively using dental study casts. To assess tooth size, the mesiodistal and buccolingual dimensions of each fully erupted permanent tooth were measured using digital Vernier callipers. The following morphological features of the teeth were assessed: upper incisor shovelling and crown form, the presence of Carabelli's tubercle on the upper molars, molar cusp number, and lower molar fissure pattern. Multilevel regression analysis was used to determine differences in tooth size, while chi-square tests and analysis of variance were used to assess differences in tooth morphology between the groups. Tooth size was reduced in all cleft groups in both jaws, with the smallest teeth being found in the ICP group. Upper lateral incisors on the cleft-affected side in UCLP and BCLP patients showed the greatest reduction in size. The upper central and lateral incisors on the cleft-affected side in the UCLP and BCLP groups were frequently hypoplastic or peg-shaped. Molar morphology in all the cleft groups was similar to that in the control group. Reduced tooth dimensions were found in both jaws in subjects with all types of clefts, suggesting a shared genetic basis. Additionally, the upper incisors were abnormal in morphology in UCLP and BCLP subjects with or without a cleft palate, suggesting shared local aetiological factors.

Effect of eda Loss of Function on Upper Jugal Tooth Morphology

The Tabby/eda mice, which bear a loss of function mutation for the eda (ectodysplasinA) gene, are known to display developmental anomalies in organs with an ectodermal origin. Although the lower jugal (cheek) teeth of Tabby/eda mice have been extensively studied, upper teeth have never been investigated in detail. However, this may help us to further understand the function of the eda gene in tooth development. In this work, the shape and size of both the crown and the radicular system were studied in the Tabby/eda mice upper jugal teeth. To deal with the high morphological variability, we defined several morphotypes based on cusp numbers and position. Statistical tests were then performed within and between the different morphotypes to test the correlation between tooth size and morphology. Our analysis reveals that, as in lower teeth, eda is necessary to segment the dental lamina into three teeth with the characteristic size and proportions of the mouse. Nevertheless, since strong effects are observed in heterozygous upper teeth while lower are only mildly affected, it seems that the upper jaw is more sensitive than the lower jaw to the loss of eda function. Modifications in cusp number and the abnormal crown size of the teeth are clearly linked, and our results indicate a role of eda in cusp patterning. Moreover, we found that the Tabby mutation induces variations in the dental root pattern, sometimes associated with hypercementosis, suggesting a newly uncovered role played by eda in root patterning and formation.

A multiscale computational comparison of the bicuspid and tricuspid aortic valves in relation to calcific aortic stenosis

Patients with bicuspid aortic valve (BAV) are more likely to develop a calcific aortic stenosis (CAS), as well as a number of other ailments, as compared to their cohorts with normal tricuspid aortic valves (TAV). It is currently unknown whether the increase in risk of CAS is caused by the geometric differences between the tricuspid and bicuspid valves or whether the increase in risk is caused by the same underlying factors that produce the geometric difference. CAS progression is understood to be a multiscale process, mediated at the cell level. In this study, we employ multiscale finite-element simulations of the valves. We isolate the effect of one geometric factor, the number of cusps, in order to explore its effect on multiscale valve mechanics, particularly in relation to CAS. The BAV and TAV are modeled by a set of simulations describing the cell, tissue, and organ length scales. These simulations are linked across the length scales to create a coherent multiscale model. At each scale, the models are three-dimensional, dynamic, and incorporate accurate nonlinear constitutive models of the valve leaflet tissue. We compare results between the TAV and BAV at each length scale. At the cell-scale, our region of interest is the location where calcification develops, near the aortic-facing surface of the leaflet. Our simulations show the observed differences between the tricuspid and bicuspid valves at the organ scale: the bicuspid valve shows greater flexure in the solid phase and stronger jet formation in the fluid phase relative to the tricuspid. At the cell-scale, however, we show that the region of interest is shielded against strain by the wrinkling of the fibrosa. Thus, the cellular deformations are not significantly different between the TAV and BAV in the calcification-prone region. This result supports the assertion that the difference in calcification observed in the BAV versus TAV may be due primarily to factors other than the simple geometric difference between the two valves.

Hemibrycon rafaelense n. sp. (Characiformes, Characidae), a new species from the upper Cauca River, with keys to Colombian species

A new fish species of Hemibrycon is described from the San Rafael River, upper Cauca River, Colombia. H. rafaelense canbe distinguished from other species of the genus by the number of cusps on the teeth in the internal premaxilla row (3-5 vs. 5-7 except H. surinamensis), by the number of predorsal scales (10-12 vs. 12-17, except H. jelskii and H. orcesi), and by poscleithrum 1 (much closer to postcleithrum 2 vs. postcleithrum 1 and 2 clearly separated). Ecological data of the aquatic habitat of the new taxon are presented and keys to help identify known Colombian species are included.

Implications of a congenitally abnormal valve: a study of 1025 consecutively excised aortic valves

Background:An increasing proportion of patients with congenitally abnormal aortic valves (AV) present for AV replacement.Aims:To review morphological changes in a large contemporary patient population undergoing AV replacement.Methods:A detailed review was...

Frequency and variability of the dental morphology in African-Colombian children of a school institution of Puerto Tejada, Cauca, Colombia.

Objectives: To assess the frequency and variability of eleven non-metric dental crown traits (winging, shovel-shape, double shovel shape, Carabelli trait, deflecting wrinkle, protostylid, groove pattern, cusp number, sixth and seventh cusps) in permanent (UI1/UI2/UM1/LM1) teeth, in order to understanding the ethnic influence and the biological distance of the sample in study. Materials and methods: In this descriptive and quantitative study, frequency and variability of twelve non-metric dental crown traits were analyzed, through the ASUDAS System, in dental casts from 84 African-Colombian children of both sexes (42 females and 42 males), in mixed-dentition from Puerto Tejada, Cauca (Colombia) inhabitants. Results: High frequencies of Carabelli trait in grade 5; and +5 y +6 groove patterns, suggests Western dental complex influence. High frequencies of protostylid (P point or foramen secum) and deflecting wrinkle that suggest Mongoloid influence from the miscegenation with regional indigenous groups were observed. Winging, shovel-shape, double shovel, cusp number and cusp 6 showed low frequencies. Bilateral symmetry and absence of sexual dimorphism were demonstrated (except winging, shovel-shape and protostylid).

Impact of Valvular Calcification on the Diagnostic Accuracy of Transesophageal Echocardiography for the Detection of Congenital Aortic Valve Malformation

Degeneration of congenital bicuspid or unicuspid aortic valves can progress more rapidly than that of tricuspid valves, and an early diagnosis significantly impacts decision making and outcome. We hypothesized that the extent of valvular calcification would negatively influence the diagnostic accuracy of multiplane transesophageal echocardiography (TEE) for the diagnosis of congenital aortic valve disease. TEE was performed in 57 patients undergoing aortic valve replacement surgery for aortic stenosis (n = 46), pure regurgitation (n = 9), or significant regurgitation with less than severe aortic stenosis (n = 2). The degree of aortic valve calcification and the number of valve cusps were determined at surgery. Surgical inspection confirmed 14 bicuspid and 43 tricuspid aortic valves. Sensitivity and specificity of TEE for the diagnosis of congenital aortic valve malformation was 93% (13/14) and 91% (39/43) (P = 0.0001), respectively. In patients with no or mild aortic valve calcification (n = 13), sensitivity and specificity of TEE for the diagnosis of congenitally malformed aortic valve was 100% (5/5) and 100% (8/8) (P = 0.001), respectively. In patients with moderate or marked aortic valve calcification (n = 44), sensitivity and specificity of TEE for the diagnosis of congenitally malformed aortic valve was 89% (8/9) and 89% (31/35) (P<0.0001), respectively. In this subgroup of 44 patients, there were four false-positive and one false-negative diagnoses due to valvular calcification. Although TEE is highly sensitive and specific for the detection of congenital aortic valve malformations, presence of moderate or marked calcification of the aortic valve may result in false positive and false negative diagnoses.

Complexity in 15- and 30-sectors polygonal serpentine: Longitudinal sections, intrasector stacking faults and XRPD satellites

Pale-green massive serpentine veins cutting the Yugoslavian serpentinites consist of 15- and 30-sectors polygonal serpentine in random orientation but becoming stress-oriented close to the vein walls. [100] cross-sections show ordered one-layer and two-layer projected polytype sequences, as well as disordered multilayer sequences. From sector to sector, these sections have systematically alternating polytypes that obey the O-L-R and O-R-L alternation rules in 15- and 30-sectors polygonal serpentine, respectively. Furthermore, [010] longitudinal sections systematically show a unique two-layer sequence. By combining the two projections, we reconstruct the basic 3D polytype assemblage that from sector to sector consists of alternating M5-M15-M15 or M5-M16-M16 polytypes. The individual fibers may be described as cyclical pseudo-twins, based upon continuous 1:1 layers, with possible octahedral rotation from one sector to the other. Continuous curved sector boundaries join adjacent sectors, with no tetrahedral sheet inversion; the curved boundaries behave as similar folds and have variable interplanar spacings. Simulated electron diffraction patterns reproduce all the observed diffraction geometries, even for faulted stacking sequences, and explain numbers of diffraction cusps and chords. Additional XRPD reflections are indexed based on polytypes present in 15- and 30-sectors polygonal serpentines.

A geometric classification of the path components of the space of locally stable maps [formula omitted

Locally stable maps S 3 → R 4 are classified up to homotopy through locally stable maps. The equivalence class of a map f is determined by three invariants: the isotopy class σ ( f ) of its framed singularity link, the generalized normal degree ν ( f ) , and the algebraic number of cusps κ ( f ) of any extension of f to a locally stable map of the 4-disk into R 5 . Relations between the invariants are described, and it is proved that for any σ , ν , and κ which satisfy these relations, there exists a map f : S 3 → R 4 with σ ( f ) = σ , ν ( f ) = ν , and κ ( f ) = κ . It follows in particular that every framed link in S 3 is the singularity set of some locally stable map into R 4 .

Patterning the size and number of tooth and its cusps

Mice and rats, two species of rodents, show some dental similarities such as tooth number and cusp number, and differences such as tooth size and cusp size. In this study, the tooth size, tooth number, cusp size and cusp number, which are four major factors of the tooth patterning, were investigated by the heterospecific recombinations of tissues from the molar tooth germs of mice and rats. Our results suggest that the dental epithelium and mesenchyme determine the cusp size and tooth size respectively and the cusp number is co-regulated by the tooth size and cusp size. It is also suggested that the mesenchymal cell number regulates not the tooth size but the tooth number. The relationships among these factors in tooth patterning including micropatterning (cusp size and cusp number) and macropatterning (tooth size and tooth number) were analyzed in a reaction diffusion mechanism. Key molecules determining the patterning of teeth remains to be elucidated for controlling the tooth size and cusp size of bioengineered tooth.

COBORDISMS OF FOLD MAPS AND MAPS WITH A PRESCRIBED NUMBER OF CUSPS

A generic smooth map of a closed $2k$-manifold into $(3k-1)$-space has a finite number of cusps ($\Sigma^{1,1}$-singularities). We determine the possible numbers of cusps of such maps. A fold map is a map with singular set consisting of only fold singularities ($\Sigma^{1,0}$-singularities). Two fold maps are fold bordant if there are cobordisms between their source- and target manifolds with a fold map extending the two maps between the boundaries, if the two targets agree and the target cobordism can be taken as a product with a unit interval then the maps are fold cobordant. We compute the cobordism groups of fold maps of $(2k-1)$-manifolds into $(3k-2)$-space. Analogous cobordism semi-groups for arbitrary closed $(3k-2)$-dimensional target manifolds are endowed with Abelian group structures and described. Fold bordism groups in the same dimensions are described as well.

An exhaustive study of the workspace topologies of all 3R orthogonal manipulators with geometric simplifications

This paper proposes a classification of three-revolute orthogonal manipulators that have at least one of their DH parameters equal to zero. This classification is based on the topology of their workspace. The workspace is characterized in a half cross-section by the singular curves. The workspace topology is defined by the number of cusps and nodes that appear on these singular curves. The manipulators are classified into different types with similar kinematic properties. Each type is evaluated according to interesting kinematic properties such as, whether the workspace is fully reachable with four inverse kinematic solutions or not, the existence of voids, and the feasibility of continuous trajectories in the workspace. It is found that several orthogonal manipulators have a “well-connected” workspace, that is, their workspace is fully accessible with four inverse kinematic solutions and any continuous trajectory is feasible. This result is of interest for the design of alternative manipulator geometries.

Cobordism of Morse functions on surfaces, the universal complex of singular fibers and their application to map germs

We give a new and simple proof for the computation of the oriented and the unoriented fold cobordism groups of Morse functions on surfaces. We also compute similar cobordism groups of Morse functions based on simple stable maps of 3-manifolds into the plane. Furthermore, we show that certain cohomology classes associated with the universal complexes of singular fibers give complete invariants for all these cobordism groups. We also discuss invariants derived from hypercohomologies of the universal homology complexes of singular fibers. Finally, as an application of the theory of universal complexes of singular fibers, we show that for generic smooth map germs g: (R^3, 0) --> (R^2, 0) with R^2 being oriented, the algebraic number of cusps appearing in a stable perturbation of g is a local topological invariant of g.

Evolution of novelty in the cichlid dentition

The shape of teeth occupies a central position in various biological disciplines, from paleo-ecology to molecular biology to cosmetic and reconstructive dentistry. Despite a long tradition of study in mammals, important questions remain regarding the genetic and developmental basis of differences in tooth shape. Here, we use natural mutants of cichlid fish from East Africa, which exhibit tremendous dental diversity, to help fill the gaps in our understanding of vertebrate odontogenesis. We employ an expanded genetic linkage map to demonstrate that cusp number segregates as a gene of major effect, which explains approximately 40% of the phenotypic variance, on cichlid chromosome 5. Furthermore, we examine patterns of Bmp4 expression in early odontogenesis to address and refine predictions of models linking tooth shape and tooth number. Mutations in the Bmp4 cistron do not control tooth shape in this mapping cross. Our data suggest that the evolution of novelty in the cichlid dentition is galvanized by a small number of genetic changes, echoing similar conclusions from recent studies of other vertebrate adaptive morphologies.

Cytotaxonomy of Parodon nasus and Parodon tortuosus (Pisces, Characiformes): A case of synonymy confirmed by cytogenetic analyses

Morphological and cytogenetical studies were carried out on the freshwater fish Parodon nasus and Parodon tortuosus in order to evaluate a putative synonymy. The diploid chromosome number observed in both species was 2n = 54 (48M/SM and 6ST) with no differences between the sexes. Despite slight differences in the pattern of heterochromatin distribution and the number of cusps in symphysean teeth, the location of nucleolar organizer regions (NORs) and 5S rRNA genes (both species-specific features) were similar in both species. The remarkable similarity observed between these allopatric species supports recent taxonomical reviews indicating that P. tortuosus is a synonym for P. nasus.

Minimizing singularities of generic plane disks with immersed boundaries

A cooriented circle immersion into the plane can be extended to a stable map of the disk which is an immersion in a neighborhood of the boundary and with outward normal vector field along the boundary equal to the given coorienting normal vector field. We express the minimal number of fold components of such a stable map as a function of its number of cusps and of the normal degree of its boundary. We also show that this minimum is attained for any cooriented circle immersion of normal degree not equal to one.