An independent broadcast on a connected graph $G$is a function $f:V(G)to mathbb{N}_0$such that, for every vertex $x$ of $G$, the value $f(x)$ is at most the eccentricity of $x$ in $G$,and $f(x)>0$ implies that $f(y)=0$ for every vertex $y$ of $G$ within distance at most $f(x)$ from $x$.The broadcast independence number $alpha_b(G)$ of $G$is the largest weight $sumlimits_{xin V(G)}f(x)$of an ind...

We introduce a notion of emergence for macroscopic variables associated with highly multivariate microscopic dynamical processes. Dynamical independence instantiates the intuition an emergent process as one possessing characteristics system ``in its own right,'' laws distinct from those underlying dynamics. quantify (departure from) by transformation-invariant Shannon information-based measure ...

It is widely believed, at least among central bankers, that “independence” is a prerequisite for achieving the goals that traditionally have been assigned to central banks specifically for achieving price stability. “Independence” does not mean literally independence from government, because central banks here and abroad are almost always part of government. The relationship of central banks to...

The independence polynomial of a graph is the generating polynomial for the number of independent sets of each size and its roots are called independence roots. We investigate the stability of such polynomials, that is, conditions under which the independence roots lie in the left half-plane. We use results from complex analysis to determine graph operations that result in a stable or nonstable...