Analysis of a growth model inspired by Gompertz and Korf laws, and an analogous birth-death process.

We propose a new deterministic growth model which captures certain features of both the Gompertz and Korf laws. We investigate its main properties, with special attention to the correction factor, the relative growth rate, the inflection point, the maximum specific growth rate, the lag time and the threshold crossing problem. Some data analytic examples and their performance are also considered. Furthermore, we study a stochastic counterpart of the proposed model, that is a linear time-inhomogeneous birth-death process whose mean behaves as the deterministic one. We obtain the transition probabilities, the moments and the population ultimate extinction probability for this process. We finally treat the special case of a simple birth process, which better mimics the proposed growth model.

The sit up test to exhaustion as a test for muscular endurance evaluation.

AIMS/HYPOTHESIS: The aim of this study was to examine the sit up test to exhaustion as a field test for muscular endurance evaluation in a sample of sedentary people of both sexes. METHODS: A cross-sectional study was performed. Three-hundred-eighty-one participants volunteered for the study (28.5 ± 10.0 years; 168.2 ± 8.9 cm; 65.1 ± 11.1 kg), of which 194 males (27.5 ± 10.2 years; 173.6 ± 7.0 cm; 71.2 ± 5.2 kg) and 187 females (29.6 ± 10.1 years; 162.6 ± 7.1 cm; 58.7 ± 8.9 kg). Each subject voluntarily and randomly performed: a sit up test (SUT), a push up test (PUT), and a free weight squat test (ST), all till exhaustion. A multiple regression analysis was adopted for data analysis. Subsequently a percentile model for muscle endurance was developed. The 25th, 50th, and 75th percentile were identified as upper limit for low muscular endurance, average muscular endurance, and lower limit for high muscular endurance, respectively. RESULTS: Considering the sit up test as the dependent variable, the coefficients (R(2) = 0.23; r = 0.49; p < 0.001), and (R(2) = 0.31; r = 0.57; p < 0.001) emerged from a multiple regression analysis applied with respect to the push up test and the squat test, respectively. Gender stratification showed regression coefficients of (R(2) = 0.19; r = 0.44; p < 0.001) for SUT vs. PUT, and (R(2) = 0.30; r = 0.56; p < 0.001) for SUT vs. ST in male; and (R(2) = 0.23; r = 0.49; p < 0.001) for SUT vs. PUT, and (R(2) = 0.34; r = 0.59; p < 0.001) for SUT vs. ST in female. CONCLUSIONS/INTERPRETATION: The SUT showed low inter-relation with the other proposed tests indicating that the adoption of a single test for the global evaluation of muscle endurance is not the optimal approach. Moreover, the SUT was found to be inexpensive, safe, and appropriate for core muscle endurance measurement for both male and female.

A stochastic model of cancer growth subject to an intermittent treatment with combined effects: reduction in tumor size and rise in growth rate.

A model of cancer growth based on the Gompertz stochastic process with jumps is proposed to analyze the effect of a therapeutic program that provides intermittent suppression of cancer cells. In this context, a jump represents an application of the therapy that shifts the cancer mass to a return state and it produces an increase in the growth rate of the cancer cells. For the resulting process, consisting in a combination of different Gompertz processes characterized by different growth parameters, the first passage time problem is considered. A strategy to select the inter-jump intervals is given so that the first passage time of the process through a constant boundary is as large as possible and the cancer size remains under this control threshold during the treatment. A computational analysis is performed for different choices of involved parameters. Finally, an estimation of parameters based on the maximum likelihood method is provided and some simulations are performed to illustrate the validity of the proposed procedure.

On the return process with refractoriness for a non-homogeneous Ornstein-Uhlenbeck neuronal model.

An Ornstein-Uhlenbeck diffusion process is considered as a model for the membrane potential activity of a single neuron. We assume that the neuron is subject to a sequence of inhibitory and excitatory post-synaptic potentials that occur with time-dependent rates. The resulting process is characterized by time-dependent drift. For this model, we construct the return process describing the membrane potential. It is a non homogeneous Ornstein-Uhlenbeck process with jumps on which the effect of random refractoriness is introduced. An asymptotic analysis of the process modeling the number of firings and the distribution of interspike intervals is performed under the assumption of exponential distribution for the firing time. Some numerical evaluations are performed to provide quantitative information on the role of the parameters.