Functional regression modeling via regularized Gaussian basis expansions

We consider the problem of constructing functional regression models for scalar responses and functional predictors, using Gaussian basis functions along with the technique of regularization. An advantage of our regularized Gaussian basis expansions to functional data analysis is that it creates a much more flexible instrument for transforming each individual’s observations into functional form. In constructing functional regression models there remains the problem of how to determine the number of basis functions and an appropriate value of a regularization parameter. We present model selection criteria for evaluating models estimated by the method of regularization in the context of functional regression models. The proposed functional regression models are applied to Canadian temperature data. Monte Carlo simulations are conducted to examine the efficiency of our modeling strategies. The simulation results show that the proposed procedure performs well especially in terms of flexibility and stable estimates.     

Ultrasound therapy modulates osteocalcin expression during bone repair in rats

The aim of this study was to measure the temporal pattern of the protein expression of RUNX2, RANKL, OPG, and osteocalcin after ultrasound therapy during the process of bone healing by immunohistochemistry. The animals were randomly distributed into two groups: control or ultrasound-treated group. A non-critical size bone defects were surgically created at the upper third of the tibia. The treatments started 24 h post-surgery, and they are performed for 3, 6, and 12 sessions, with an interval of 48 h. A low-intensity pulsed ultrasound (1.5 MHz, 1:4 duty cycle, intensity SATA 30 mW/cm², 20 min/session, stationary mode application) was used. On days 7, 13, and 25 post-injury, rats were killed individually by carbon dioxide asphyxia. The tibias were removed for analysis. The histopathological analysis pointed out no remarkable differences between groups for all periods evaluated. However, immunohistochemical data revealed that ultrasound therapy produced an up-regulation of osteocalcin at day 7th and 13th post-surgery. Taken together, our results indicate that ultrasound therapy modulates osteocalcin expression during bone repair in rats as depicted by differential immunopression at the initial and intermediate stages of recovery.