The simple measure of complexity Γα,β of Shiner, Davison and Landsberg (SDL) and the statistical one C, according to López-Ruiz, Mancini and Calbet (LMC), are compared in atoms as functions of the atomic number Z. Shell effects i.e. local minima at the closed shells atoms are observed, as well as certain qualitative trends of Γα,β(Z) and C(Z). If we impose the condition that Γ and C behave simi...

For all $a,b>0$, the following two optimal inequalities are presented: $H^{alpha}(a,b)L^{1-alpha}(a,b)geq M_{frac{1-4alpha}{3}}(a,b)$ for $alphain[frac{1}{4},1)$, and $ H^{alpha}(a,b)L^{1-alpha}(a,b)leq M_{frac{1-4alpha}{3}}(a,b)$ for $alphain(0,frac{3sqrt{5}-5}{40}]$. Here, $H(a,b)$, $L(a,b)$, and $M_p(a,b)$ denote the harmonic, logarithmic, and power means of order $p$ of two positive numbers...

Protochlorophyllide (Pchlide) accumulation and xantophyll composition were studied in 5-day old etiolated seedlings of three ecotypes of Arabidopsis thaliana: Columbia (Col-0), Landsberg erecta (Ler) and Wassiliewska (Ws). The total Pchlide level as measured by fluorescence spectroscopy varied significantly between ecotypes. A rapid HPLC method revealed quantitative differences in carotenoid co...

The simple measure of complexity Γα,β of Shiner, Davison and Landsberg (SDL) and the statistical one C, according to López-Ruiz, Mancini, and Calbet (LMC) are compared in atoms as functions of the atomic number Z. Shell effects i.e. local minima at the closed shells atoms are observed as well as similar qualitative trends of Γα,β(Z) and C(Z). It is conjectured that the above conclusion does not...

We critique the measure of complexity introduced by Shiner, Davison, and Landsberg [Phys. Rev. E 59, 1459 (1999)]. In particular, we point out that it is over universal, in the sense that it has the same dependence on disorder for structurally distinct systems. We then give counterexamples to the claim that complexity is synonymous with being out of equilibrium: equilibrium systems can be struc...

We find the greatest values $alpha_{1} $ and $alpha_{2} $, and the least values $beta_{1} $ and $beta_{2} $ such that the inequalities $alpha_{1} C(a,b)+(1-alpha_{1} )H(a,b)

During a recent investigation of parasites infecting fishes from the Okavango River and Delta, Botswana (southern Africa) fourteen sharptooth catfish, Clarias gariepinus (Burchell, 1822) (Siluriformes: Clariidae) were examined for the presence of myxozoan infections. Results revealed the presence of two species of the genus Henneguya Thélohan, 1895 and one species of the genus Myxobolus Bütschl...

This is a report on a workshop held August 1 to August 5, 2011 at the Institute for Computational and Experimental Research in Mathematics (ICERM) at Brown University, Providence, Rhode Island, organized by Saugata Basu, Joseph M. Landsberg, and J. Maurice Rojas. We provide overviews of the more recent results presented at the workshop, including some works-in-progress as well as tentative and ...

We revisit a geometric lower bound for Waring rank of polynomials (symmetric rank of symmetric tensors) of [LT10] and generalize it to a lower bound for rank with respect to arbitrary varieties, improving the bound given by the “non-Abelian” catalecticants recently introduced by Landsberg and Ottaviani. This is applied to give lower bounds for ranks of multihomogeneous polynomials (partially sy...