Let $G$ be a graph in which each vertex initially has weight 1. In step, the unit from $u$ to neighbouring $v$ can moved, provided that on is at least as large $u$. The acquisition number of $G$, denoted by $a_u(G)$, minimum cardinality set vertices with positive end process (over all protocols). this paper, we investigate Erdős-Rényi random $(\mathcal{G}(n,m))_{m =0}^{N}$, where $N = {n \choos...

Motor unit number estimation (MUNE) is an electrodiagnostic procedure used to evaluate the number of motor axons connected to a muscle. All MUNE techniques rely on assumptions that must be fulfilled to produce a valid estimate. As there is no gold standard to compare the MUNE techniques against, we have developed a model of the relevant neuromuscular physiology and have used this model to simul...

A sum graph is a graph for which there is a labeling of its vertices with positive integers so that two vertices are adjacent if and only if the sum of their labels is the label of another vertex. Integral sum graphs are defined similarly, except that the labels may be any integers. These concepts were first introduced by Harary, who provided examples of such graphs of all orders. The family of...

In this paper, we conjecture a formula for the value of the Pythagoras number for real multivariate sum of squares polynomials as a function of the (total or coordinate) degree and the number of variables. The conjecture is based on the comparison between the number of parameters and the number of conditions for a corresponding low-rank representation. This is then numerically verified for a nu...