Stochastic integration based on simple, symmetric random walks

A new approach to stochastic integration is described, which is based on an a.s. pathwise approximation of the integrator by simple, symmetric random walks. Hopefully, this method is didactically more advantageous, more transparent, and technically less demanding than other existing ones. In a large part of the theory one has a.s. uniform convergence on compacts. In particular, it gives a.s. convergence for the stochastic integral of a finite variation function of the integrator, which is not c\`adl\`ag in general.Comment: 16 pages, some typos correcte

Mild hypodontia is associated with reduced tooth dimensions and cusp numbers compared to controls in a Romanian sample

The associations seen clinically between variations in tooth number, size and shape reflect the repetitive genetic interactions occurring between the epithelium and mesenchyme during the initiation and morphogenetic stages of dental development. The aim of this study was to investigate this relationship further by comparing multiple crown parameters, including cusp numbers, between patients with mild hypodontia and controls. Digital images of dental casts of the permanent dentition from 28 Romanian subjects with mild hypodontia and 28 controls were used. Measurements of the vestibular and occlusal surfaces were performed using a 2D image analysis method. Seven dimensions were measured (mesio-distal, occluso-gingival, bucco-lingual, vestibular perimeter, vestibular area, occlusal perimeter and occlusal area) and cusps on premolars and first molars were counted. Multivariate analysis of variance was performed using SPSS V17 software. The results showed teeth in the hypodontia group were smaller than those of controls, with many measurements being significantly different (significance values varied from p=0.048 to p=0.0001). Lower first incisors and upper first premolar teeth presented the most reduced dimensions. Mesio-distal, bucco-lingual and occlusal area and perimeter dimensions were the most affected. Upper first molars presented the Carabelli trait in significantly less subjects in the hypodontia group than in controls. This variation was accompanied by a difference in tooth height. Lower premolars showed reduced cusp numbers in hypodontia subjects, accompanied by variation in tooth width or depth. In conclusion, this study demonstrated differences in multiple parameters of crown size and shape in patients with mild hypodontia compared to controls. The degree of these differences varied between different tooth types and dimensions. Acknowledgments: This study was supported by the Internal Research Grant no. 8/30.01.2013 of the University of Medicine and Pharmacy of Tîrgu Mureș, Romania. Keywords: tooth dimensions; mild hypodontia; cusp numbe