9,080 research outputs found
Involutive Division Technique: Some Generalizations and Optimizations
In this paper, in addition to the earlier introduced involutive divisions, we
consider a new class of divisions induced by admissible monomial orderings. We
prove that these divisions are noetherian and constructive. Thereby each of
them allows one to compute an involutive Groebner basis of a polynomial ideal
by sequentially examining multiplicative reductions of nonmultiplicative
prolongations. We study dependence of involutive algorithms on the completion
ordering. Based on properties of particular involutive divisions two
computational optimizations are suggested. One of them consists in a special
choice of the completion ordering. Another optimization is related to
recomputing multiplicative and nonmultiplicative variables in the course of the
algorithm.Comment: 19 page
Generalized constructive tree weights
The Loop Vertex Expansion (LVE) is a quantum field theory (QFT) method which
explicitly computes the Borel sum of Feynman perturbation series. This LVE
relies in a crucial way on symmetric tree weights which define a measure on the
set of spanning trees of any connected graph. In this paper we generalize this
method by defining new tree weights. They depend on the choice of a partition
of a set of vertices of the graph, and when the partition is non-trivial, they
are no longer symmetric under permutation of vertices. Nevertheless we prove
they have the required positivity property to lead to a convergent LVE; in
fact, we formulate this positivity property precisely for the first time. Our
generalized tree weights are inspired by the Brydges-Battle-Federbush work on
cluster expansions and could be particularly suited to the computation of
connected functions in QFT. Several concrete examples are explicitly given.Comment: 22 pages, 2 figure
Understanding Algorithm Performance on an Oversubscribed Scheduling Application
The best performing algorithms for a particular oversubscribed scheduling
application, Air Force Satellite Control Network (AFSCN) scheduling, appear to
have little in common. Yet, through careful experimentation and modeling of
performance in real problem instances, we can relate characteristics of the
best algorithms to characteristics of the application. In particular, we find
that plateaus dominate the search spaces (thus favoring algorithms that make
larger changes to solutions) and that some randomization in exploration is
critical to good performance (due to the lack of gradient information on the
plateaus). Based on our explanations of algorithm performance, we develop a new
algorithm that combines characteristics of the best performers; the new
algorithms performance is better than the previous best. We show how hypothesis
driven experimentation and search modeling can both explain algorithm
performance and motivate the design of a new algorithm
Sunspots do matter: a simple disproof of Mas-Colell
Mas-Colell conjectured that, for economies admitting a unique deterministic equilibrium, sunspot equilibria that 'matter'' would not exist. I prove an abundance of such equilibria using simple linear algebra.Animal Spirits
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