A simple stochastic mechanism that produces exact and approximate power-law distributions is presented. The model considers radially symmetric Gaussian, exponential and power-law functions inn= 1, 2, 3 dimensions. Ran...A simple stochastic mechanism that produces exact and approximate power-law distributions is presented. The model considers radially symmetric Gaussian, exponential and power-law functions inn= 1, 2, 3 dimensions. Randomly sampling these functions with a radially uniform sampling scheme produces heavy-tailed distributions. For two-dimensional Gaussians and one-dimensional exponential functions, exact power-laws with exponent –1 are obtained. In other cases, densities with an approximate power-law behaviour close to the origin arise. These densities are analyzed using Padé approximants in order to show the approximate power-law behaviour. If the sampled function itself follows a power-law with exponent –α, random sampling leads to densities that also follow an exact power-law, with exponent -n/a – 1. The presented mechanism shows that power-laws can arise in generic situations different from previously considered specialized systems such as multi-particle systems close to phase transitions, dynamical systems at bifurcation points or systems displaying self-organized criticality. Thus, the presented mechanism may serve as an alternative hypothesis in system identification problems.展开更多
Bone mass is important for dental implant success and is regulated by mechanoresponsive osteocytes. We aimed to investigate the relationship between the levels and orientation of tensile strain and morphology and orie...Bone mass is important for dental implant success and is regulated by mechanoresponsive osteocytes. We aimed to investigate the relationship between the levels and orientation of tensile strain and morphology and orientation of osteocytes at different dental implant positions in the maxillary bone. Bone biopsies were retrieved from eight patients who underwent maxillary sinus-floor elevation with β-tricalcium phosphate prior to implant placement. Gap versus free-ending locations were compared using 1) a three-dimensional finite-element model of the maxilla to predict the tensile strain magnitude and direction and 2) histology and histomorphometric analyses. The finite-element model predicted larger, differently directed tensile strains in the gap versus freeending locations. The mean percentage of mineralised residual native-tissue volume, osteocyte number(mean ± standard deviations:97 ± 40/region-of-interest), and osteocyte shape(90% elongated,10% round) were similar for both locations. However, the osteocyte surface area was 1.5-times larger in the gap than in the free-ending locations, and the elongated osteocytes in these locations were more cranially caudally oriented. In conclusion, significant differences in the osteocyte surface area and orientation seem to exist locally in the maxillary bone, which may be related to the tensile strain magnitude and orientation. This might reflect local differences in the osteocyte mechanosensitivity and bone quality, suggesting differences in dental implant success based on the location in the maxilla.展开更多
文摘A simple stochastic mechanism that produces exact and approximate power-law distributions is presented. The model considers radially symmetric Gaussian, exponential and power-law functions inn= 1, 2, 3 dimensions. Randomly sampling these functions with a radially uniform sampling scheme produces heavy-tailed distributions. For two-dimensional Gaussians and one-dimensional exponential functions, exact power-laws with exponent –1 are obtained. In other cases, densities with an approximate power-law behaviour close to the origin arise. These densities are analyzed using Padé approximants in order to show the approximate power-law behaviour. If the sampled function itself follows a power-law with exponent –α, random sampling leads to densities that also follow an exact power-law, with exponent -n/a – 1. The presented mechanism shows that power-laws can arise in generic situations different from previously considered specialized systems such as multi-particle systems close to phase transitions, dynamical systems at bifurcation points or systems displaying self-organized criticality. Thus, the presented mechanism may serve as an alternative hypothesis in system identification problems.
基金supported by a grant from the University of Amsterdam for the stimulation of a research priority area in Oral Regenerative Medicinelogistic support from the Research Office of the University of San Carlos, Cebu City
文摘Bone mass is important for dental implant success and is regulated by mechanoresponsive osteocytes. We aimed to investigate the relationship between the levels and orientation of tensile strain and morphology and orientation of osteocytes at different dental implant positions in the maxillary bone. Bone biopsies were retrieved from eight patients who underwent maxillary sinus-floor elevation with β-tricalcium phosphate prior to implant placement. Gap versus free-ending locations were compared using 1) a three-dimensional finite-element model of the maxilla to predict the tensile strain magnitude and direction and 2) histology and histomorphometric analyses. The finite-element model predicted larger, differently directed tensile strains in the gap versus freeending locations. The mean percentage of mineralised residual native-tissue volume, osteocyte number(mean ± standard deviations:97 ± 40/region-of-interest), and osteocyte shape(90% elongated,10% round) were similar for both locations. However, the osteocyte surface area was 1.5-times larger in the gap than in the free-ending locations, and the elongated osteocytes in these locations were more cranially caudally oriented. In conclusion, significant differences in the osteocyte surface area and orientation seem to exist locally in the maxillary bone, which may be related to the tensile strain magnitude and orientation. This might reflect local differences in the osteocyte mechanosensitivity and bone quality, suggesting differences in dental implant success based on the location in the maxilla.
