5,319 research outputs found
Special Algorithm for Stability Analysis of Multistable Biological Regulatory Systems
We consider the problem of counting (stable) equilibriums of an important
family of algebraic differential equations modeling multistable biological
regulatory systems. The problem can be solved, in principle, using real
quantifier elimination algorithms, in particular real root classification
algorithms. However, it is well known that they can handle only very small
cases due to the enormous computing time requirements. In this paper, we
present a special algorithm which is much more efficient than the general
methods. Its efficiency comes from the exploitation of certain interesting
structures of the family of differential equations.Comment: 24 pages, 5 algorithms, 10 figure
An Elementary Proof of Sylvester's Double Sums for Subresultants
In 1853 Sylvester stated and proved an elegant formula that expresses the
polynomial subresultants in terms of the roots of the input polynomials.
Sylvester's formula was also recently proved by Lascoux and Pragacz by using
multi-Schur functions and divided differences. In this paper, we provide an
elementary proof that uses only basic properties of matrix multiplication and
Vandermonde determinants.Comment: 9 pages, no figures, simpler proof of the main results thanks to
useful comments made by the referees. To appear in Journal of Symbolic
Computatio
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