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One of the most fundamental rules in metabolic ecology is the allometric equation, which is a power-law scaling that describes the connection between body measurements and body size. The biological dynamics of this essentially empirical allometric equation, however, have yet to be properly addressed in cell level. In order to fill the gap between biological process in cell level and allometric scaling in metabolic ecology, we simply assumed a cell bipartition without limitation, and then exponential cells increased during their lifetime. Two synchronous exponential increasing could generate a power-law scaling between body mass and an organ's weight. And the power-law scaling between body mass and metabolic rate may also be obtained by substituting an organ's weight with the weight of erythrocytes. Based on the same assumption, the dynamic of cell proliferation reveal a complex exponential scaling between body mass and longevity rather than the previously reported power-law scaling. In other words, there is a quadratic relationship between longevity and logarithmic form of body mass. In these relationships, all parameters can be explained by indices in cell division and embryo.

Natural selection imply that any organisms including human being will evolve to improve its fitness advantage and the selected genotype or phenotype in equilibrium state will not vary over the time. However, evolutionary process of biological organisms in reality is greatly affected by the environmental change and historical accidents. In this research, we construct a co-evolutionary system to investigate the impact of species-environment feedback. When we talk about an invasion species or mutation, positive feedback is detrimental to the success of the invasion because positive feedback benefits a large number of individuals, whereas negative feedback benefits the invasion because negative feedback disadvantages a large number of individuals. In the case of a competition between two species with initially equal numbers of individuals, both positive and negative feedback will favor the species with low fitness, increasing its chances of taking over the whole population. The reason for this is that feedback allows initially inferior species to have greater fitness than initially dominating species in the early stages, emphasizing the importance of early random accident. Our findings emphasize the significance of the evolutionary path driven by species-environment feedback.

We predict that the $a_0^0(980)$-$f_0(980)$ mixing would lead to large CP violation. We calculate the localized direct CP asymmetry in the decays $B^\pm \to f_0(980) [a_0^0(980)] \pi^\pm \to \pi^+ \pi^- \pi^\pm $ via the $a_0^0(980)$-$f_0(980)$ mixing mechanism based on the hypothetical $q\bar q$ structures of $a^0_0(980)$ and $f_0(980)$ in the QCD factorization. It is shown that there is a peak for CP violation, which could be as large as 58%, when the invariance mass of $\pi\pi$ is near the masses of $a^0_0(980)$ and $f_0(980)$. Since the CP asymmetry is sensitive to the $a_0^0(980)$-$f_0(980)$ mixing, measuring the CP violating parameter in the aforementioned decays could provide a new way to verify the existence of the $a_0^0(980)$-$f_0(980)$ mixing and be helpful in clarifying the configuration nature of the light scalar mesons., Comment: 12 pages, 2 figures; accepted by Phys. Rev. D

We study the $S$-wave $D\Xi$ bound state in the Bethe-Salpeter formalism in the ladder and instantaneous approximations. With the kernel generated by the hadronic effective Lagrangian, two open-charmed bound states, which quantum numbers are $I=0$, $J^P=(\frac{1}{2})^-$ and $I=1$, $J^P=(\frac{1}{2})^-$, respectively, are predicted as new candidates of hadronic pentaquark molecules in our formalism. If existing, they could contribute to the broad 3188 eV structure near the five new narrow $\Omega_c$ states observed recently by the LHCb Collaboration., Comment: 8 pages, 4 figures, accepted by Eur. Phys. J. C