Weak coloring numbers generalize the notion of degeneracy a graph. They were introduced by Kierstead & Yang in context games on graphs. Recently, several connections have been uncovered between weak and various parameters studied graph minor theory its generalizations. In this note, we show that for every fixed $k\geq1$, maximum $r$-th number with simple treewidth $k$ is $\Theta(r^{k-1}\log...

In this research, the protonation constant value of tannic acid was determined at 25 °C and different ionic strengths (0.1 to 0.7 mol/dm3 NaCl) using potentiometric titration technique. The dependence of protonation constant on ionic strength was modeled and discussed by a Debye-Hückel type equation. Then, based on the obtained data from experiments, the minimizing Sum o...

In this paper we extend the Bayesian model fitting shape measurement method presented in Miller et al. (2007) and use the method to estimate the shear from the Shear TEsting Programme simulations (STEP). The method uses a fast model fitting algorithm which uses realistic galaxy profiles and analytically marginalises over the position and amplitude of the model by doing the model fitting in Four...

We study (weak) log abelian varieties with constant degeneration in the log flat topology. If the base is a log point, we further study the endomorphism algebras of log abelian varieties. In particular, we prove the dual short exact sequence for isogenies, Poincaré complete reducibility theorem for log abelian varieties, and the semisimplicity of the endomorphism algebras of log abelian varieti...

The stochastic block model for one community with parameters n,K, p, and q is considered: K out of n vertices are in the community; two vertices are connected by an edge with probability p if they are both in the community and with probability q otherwise, where p > q > 0 and p/q is assumed to be bounded. An estimator based on observation of the graph G = (V,E) is said to achieve weak recovery ...

With re nements to the WEAK-HEAPSORT algorithm we establish the general and practical relevant sequential sorting algorithm RELAXED-WEAK-HEAPSORT executing exactly ndlog ne 2 ne + 1 n log n 0:9n comparisons on any given input. The number of transpositions is bounded by n plus the number of comparisons. Experiments show that RELAXED-WEAK-HEAPSORT only requires O(n) extra bits. Even if this space...

The relationship between rat pharmacokinetics and physicochemical parameters [the partition coefficient between octanol and buffer at pH 7.4 (log D((7.4))) and pK(a)] was studied for a series of tetrahydropyran compounds. Sixteen compounds ranging in log D((7.4)) 0.1 to 1.8 were administered intravenously to rats, and the pharmacokinetic parameters were determined from blood concentration time ...