<inline-formula> <tex-math notation="LaTeX">$H_2$</tex-math> </inline-formula> Analysis of LTI Systems via Conversion to Externally Positive Systems

Minimum Vertex Degree Threshold for <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"></math>tiling

We prove that the vertex degree threshold for tiling C3 4 (the 3-uniform hypergraph with four vertices and two triples) in a 3-uniform hypergraph on n ∈ 4N vertices is (n−1 2 ) − ( 4 n 2 ) + 8n + c, where c = 1 if n ∈ 8N and c = −2 otherwise. This result is best possible, and is one of the first results on vertex degree conditions for hypergraph tiling. C © 2014 Wiley Periodicals, Inc. J. Graph...

To Inline or Not to Inline? Enhanced Inlining Decisions

The decision to inline a procedure in the Open Research Compiler (ORC) was based on a temperature heuristics that takes into consideration the time spent in a procedure and the size of the procedure. In this paper we describe the trade-off that has to be worked out to make the correct inlining decisions. We introduce two new heuristics to enhance the ORC inlining heuristics: adaptation and cycl...

Biological System of Analysis of Systems Math

We present two examples of computational cellular biology that provide perspective on the complexity of creating predictive models of cell behaviors as they emerge from the interaction of molecular species. The first is a model of the diffusion and reaction of neurotransmitter in a neuromuscular junction using a continuum based finite element formulation [1]. Whereas this formulation accounts f...

Math 254a: the Analytic Class Number Formula, and Dirichlet Characters

Math 254a: the Analytic Class Number Formula I