Zero forcing is an iterative graph coloring process whereby a colored vertex with a single uncolored neighbor forces that neighbor to be colored. It is NP-hard to find a minimum zero forcing set – a smallest set of initially colored vertices which forces the entire graph to be colored. We show that the problem remains NP-hard when the initially colored set induces a connected subgraph. We also ...

Abstract. The zero forcing number Z(G), which is the minimum number of vertices in a zero forcing set of a 1 graph G, is used to study the maximum nullity/minimum rank of the family of symmetric matrices described by 2 G. It is shown that for a connected graph of order at least two, no vertex is in every zero forcing set. The positive 3 semidefinite zero forcing number Z+(G) is introduced, and ...

An edge geodetic set of a connected graph G of order p ≥ 2 is a set S ⊆ V (G) such that every edge of G is contained in a geodesic joining some pair of vertices in S. The edge geodetic number g1(G) of G is the minimum cardinality of its edge geodetic sets and any edge geodetic set of cardinality g1(G) is a minimum edge geodetic set of G or an edge geodetic basis of G. An edge geodetic set S in ...

If κ < λ are such that κ is a strong cardinal whose strongness is indestructible under κ-strategically closed forcing and λ is weakly compact, then we show that A = {δ < κ | δ is a non-weakly compact Mahlo cardinal which reflects stationary sets} must be unbounded in κ. This phenomenon, however, need not occur in a universe with relatively few large cardinals. In particular, we show how to cons...

[1] The main uncertainty in anthropogenic forcing of the Earth’s climate stems from pollution aerosols, particularly their ‘‘indirect effect’’ whereby aerosols modify cloud properties. We develop a new methodology to derive a measurement-based estimate using almost exclusively information from an Earth radiation budget instrument (CERES) and a radiometer (MODIS). We derive a statistical relatio...

[1] Trends in global oceanic heat content (OHC) over the late 20th century as simulated by climate models that incorporate all radiative forcing factors are smaller than the observed, but the causes are not clear. Given the cooling effect associated with increasing anthropogenic aerosols and natural forcing (i.e., volcanic aerosols), we examine their respective roles in the simulated global OHC...

A new axiom is proposed, the Ground Axiom, asserting that the universe is not a nontrivial set forcing extension of any inner model. The Ground Axiom is first-order expressible, and any model of zfc has a class forcing extension which satisfies it. The Ground Axiom is independent of many well-known set-theoretic assertions including the Generalized Continuum Hypothesis, the assertion v=hod that...

We use a statistical metric of multi-dimensional climate change to quantify the emergence of global climate change hotspots in the CMIP5 climate model ensemble. Our hotspot metric extends previous work through the inclusion of extreme seasonal temperature and precipitation, which exert critical influence on climate change impacts. The results identify areas of the Amazon, the Sahel and tropical...

We posit that feasible reversal of the growth of atmospheric CH(4) and other trace gases would provide a vital contribution toward averting dangerous anthropogenic interference with global climate. Such trace gas reductions may allow stabilization of atmospheric CO(2) at an achievable level of anthropogenic CO(2) emissions, even if the added global warming constituting dangerous anthropogenic i...