The GraphBLAS standard (GraphBlas.org) is being developed to bring the potential of matrix based graph algorithms to the broadest possible audience. Mathematically the Graph- BLAS defines a core set ...of matrix-based graph operations that can be used to implement a wide class of graph algorithms in a wide range of programming environments. This paper provides an introduction to the mathematics of the GraphBLAS. Graphs represent connections between vertices with edges. Matrices can represent a wide range of graphs using adjacency matrices or incidence matrices. Adjacency matrices are often easier to analyze while incidence matrices are often better for representing data. Fortunately, the two are easily connected by matrix mul- tiplication. A key feature of matrix mathematics is that a very small number of matrix operations can be used to manipulate a very wide range of graphs. This composability of small number of operations is the foundation of the GraphBLAS. A standard such as the GraphBLAS can only be effective if it has low performance overhead. Performance measurements of prototype GraphBLAS implementations indicate that the overhead is low.
These studies examined the in vivo pharmacokinetics and efficacy of five anti-methamphetamine monoclonal antibodies (mAbs, KD values from 11 to 250 nM) in rats. While no substantive differences in ...mAb systemic clearance (t1/2 = 6.1-6.9 days) were found, in vivo function was significantly reduced within 1-3 days for four of the five mAbs. Only mAb4G9 was capable of prolonged efficacy, as judged by prolonged high methamphetamine serum concentrations. MAb4G9 also maintained high amphetamine serum concentrations, along with reductions in methamphetamine and amphetamine brain concentrations, indicating neuroprotection. The combination of broad specificity for methamphetamine-like drugs, high affinity, and prolonged action in vivo suggests mAb4G9 is a potentially efficacious medication for treating human methamphetamine-related medical diseases.
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