2,016 research outputs found
A Projection Argument for Differential Inclusions, with Applications to Persistence of Mass-Action Kinetics
Motivated by questions in mass-action kinetics, we introduce the notion of
vertexical family of differential inclusions. Defined on open hypercubes, these
families are characterized by particular good behavior under projection maps.
The motivating examples are certain families of reaction networks -- including
reversible, weakly reversible, endotactic, and strongly endotactic reaction
networks -- that give rise to vertexical families of mass-action differential
inclusions. We prove that vertexical families are amenable to structural
induction. Consequently, a trajectory of a vertexical family approaches the
boundary if and only if either the trajectory approaches a vertex of the
hypercube, or a trajectory in a lower-dimensional member of the family
approaches the boundary. With this technology, we make progress on the global
attractor conjecture, a central open problem concerning mass-action kinetics
systems. Additionally, we phrase mass-action kinetics as a functor on reaction
networks with variable rates.Comment: v5: published version; v3 and v4: minor additional edits; v2:
contains more general version of main theorem on vertexical families,
including its accompanying corollaries -- some of them new; final section
contains new results relating to prior and future research on persistence of
mass-action systems; improved exposition throughou
Benchmarking hypercube hardware and software
It was long a truism in computer systems design that balanced systems achieve the best performance. Message passing parallel processors are no different. To quantify the balance of a hypercube design, an experimental methodology was developed and the associated suite of benchmarks was applied to several existing hypercubes. The benchmark suite includes tests of both processor speed in the absence of internode communication and message transmission speed as a function of communication patterns
An ETH-Tight Exact Algorithm for Euclidean TSP
We study exact algorithms for {\sc Euclidean TSP} in . In the
early 1990s algorithms with running time were presented for
the planar case, and some years later an algorithm with
running time was presented for any . Despite significant interest in
subexponential exact algorithms over the past decade, there has been no
progress on {\sc Euclidean TSP}, except for a lower bound stating that the
problem admits no algorithm unless ETH fails. Up to
constant factors in the exponent, we settle the complexity of {\sc Euclidean
TSP} by giving a algorithm and by showing that a
algorithm does not exist unless ETH fails.Comment: To appear in FOCS 201
- …