Spatial heterogeneity is believed to play an important role in the persistence and dynamics of epidemics of childhood diseases because asynchrony between populations within different regions allows global persistence, even if the disease dies out locally. A simple multi-patch (metapopulation) model for spatial heterogeneity in epidemics is analysed and we examine conditions under which patches ...

Papers published in Hydrology and Earth System Sciences Discussions are under open-access review for the journal Hydrology and Earth System Sciences Abstract An integrated global water resources model was developed consisting of six modules: land surface hydrology, river routing, crop growth, reservoir operation, environmental flow requirement estimation, and anthropogenic water withdrawal. It ...

The controllability for complex network system is to find the minimum number of leaders achieve effective control global networks. In this paper, problem directed a family matrices carrying structure under hypercube considered. relationship between and signed zero forcing set established. networks obtained by computing graph.

The minimum rank of a simple graph G is the smallest possible rank over all symmetric real matrices A whose nonzero off-diagonal entries correspond to the edges of G. Using the zero forcing number, we prove that the minimum rank of the r-th butterfly network is 1 9 [ (3r + 1)2r+1 − 2(−1)r ] and that this is equal to the rank of its adjacency matrix.

The positive zero forcing number of a graph is a graph parameter that arises from a non-traditional type of graph colouring, and is related to a more conventional version of zero forcing. We establish a relation between the zero forcing and the fast-mixed searching, which implies some NP-completeness results for the zero forcing problem. For chordal graphs much is understood regarding the relat...

MARCH 2003 AMERICAN METEOROLOGICAL SOCIETY | T his commentary describes how an examination of the global heat budget allows a straightforward explanation for understanding one of the consequences of human changes in the composition of the earth’s atmosphere. Data and analysis provided in Levitus et al. (2000, 2001) on increases in heat stored within the world’s oceans provide a unique opportuni...

[1] This paper diagnoses the spatial mean and the spatial gradient of the aerosol radiative forcing in comparison with those of well-mixed green-house gases (GHG). Unlike GHG, aerosols have much greater spatial heterogeneity in their radiative forcing. The heterogeneous diabatic heating can modulate the gradient in horizontal pressure field and atmospheric circulations, thus altering the region...

Portions of western NorthAmerica have experienced prolonged drought over the last decade. This drought has occurred at the same time as the global warming hiatus—a decadal period with little increase in global mean surface temperature. Climate models and observational analyses are used to clarify the dual role of recent tropical Pacific changes in driving both the global warming hiatus and Nort...

Given a simple undirected graph G and a positive integer k, the k-forcing number of G, denoted Fk(G), is the minimum number of vertices that need to be initially colored so that all vertices eventually become colored during the discrete dynamical process described by the following rule. Starting from an initial set of colored vertices and stopping when all vertices are colored: if a colored ver...

[1] Biomass burning is one of the largest sources of trace gases and aerosols to the atmosphere and has profound influence on tropospheric oxidants and radiative forcing. Using a fully coupled chemistry-climate model (GFDL AM3), we find that co-emission of trace gases and aerosol from present-day biomass burning increases the global tropospheric ozone burden by 5.1% and decreases global mean OH...