Although Turing pattern is one of the most universal mechanisms for pattern formation, in its standard model the number of stripes changes with the system size, since the wavelength of the pattern is invariant. It fails to preserve the proportionality of the pattern, i.e. the ratio of the wavelength to the size, that is often required in biological morphogenesis. To get over this problem, we sh...

Here, we show that the most basic features of tree and forest architecture can be put on a unifying theoretical basis, which is provided by the constructal law. Key is the integrative approach to understanding the emergence of "designedness" in nature. Trees and forests are viewed as integral components (along with dendritic river basins, aerodynamic raindrops, and atmospheric and oceanic circu...

A test for proportionality of two covariance matrices with large dimension, possibly larger than the sample size, is proposed. The statistic simple, computationally efficient, and can be used a class multivariate distributions including normality. properties statistic, asymptotic distribution, are given under high-dimensional set up. Through simulations, shown to perform accurately, outperform ...

In MESA (Multi-Ethnic Study of Atherosclerosis), it is of interest to model the development and progression of CAC (coronary artery calcium). With about half of the CAC scores equal to zero and the rest continuously distributed, semiparametric two-part models are needed. Our main interest lies in determining the (partial) proportionality between the two covariate effects in two-part models. Suc...

Rosmarinic acid (RA), one of the main bioactive compounds of Rosmarinus officinalis L., exhibits diverse pharmacological effects. However, its oral absolute bioavailability and dose proportionality in vivo have not been comprehensively studied. In the present study, a validated LC-MS/MS method was developed for the determination of RA in rat plasma. Pharmacokinetic parameters were obtained foll...

Accurate measurement of ground reaction forces under discrete areas of the foot is important in the development of more advanced foot models, which can improve our understanding of foot and ankle function. To overcome current equipment limitations, a few investigators have proposed combining a pressure mat with a single force platform and using a proportionality assumption to estimate subarea s...

Constraints on changes in expression levels across all cell components imposed by the steady growth of cells have recently been discussed both experimentally and theoretically. By assuming a small environmental perturbation and considering a linear response to it, a common proportionality in such expression changes was derived and partially verified by experimental data. Here, we examined globa...

In the classic apportionment problem, goal is to decide how many seats of a parliament should be allocated each party as result an election. The divisor methods solve this problem by defining notion proportionality guided some rounding rule. Motivated recent challenges in context electoral apportionment, we consider question allocate under parity constraints between candidate types (e.g., equal...