Computing with semi-algebraic sets: Relaxation techniques and effective boundaries
TLDR
This paper exhibits new results in the theory of border polynomials of parametric semi-algebraic systems and proposes a technique, that is called relaxation, which can simplify the decomposition process and reduce the number of components in the output.About:
This article is published in Journal of Symbolic Computation.The article was published on 2013-05-01 and is currently open access. It has received 12 citations till now. The article focuses on the topics: Triangular decomposition & Polynomial.read more
Citations
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Algebraic Systems Biology: A Case Study for the Wnt Pathway
TL;DR: This case study explores multistationarity, model comparison, dynamics within regions of the state space, identifiability, and parameter estimation, from a geometric point of view using current methods from computational algebraic geometry, polyhedral geometry, and combinatorics.
Journal ArticleDOI
Multistability of Small Reaction Networks
Xiaoxian Tang,Hao Xu +1 more
TL;DR: For three typical sets of small reaction networks (networks with two reactions, one irreversible and one reversible reaction, or two reversible-reaction pairs), this work completely answers the challenging question: what is the smallest subset of all multistable networks such that any multistability network outside of the subset contains either more species or more reactants than any network in this subset.
Proceedings ArticleDOI
Computing Limits of Real Multivariate Rational Functions
TL;DR: An algorithm is presented for determining the existence of the limit of a real multivariate rational function q at a given point which is an isolated zero of the denominator of q when the limit exists, without making any assumption on the number of variables.
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‘Quella era veramente è Little Italy, la nostra Little Italy’: Multiple centres, cultural presence and the articulation of spaces of speech from Tasmania
TL;DR: This article examined the intersections between migrant experiences, multilingual practices, and the creation of space by focusing on Italians who migrated to Tasmania, a group that has long been isolated from the rest of the Italian diaspora.
Proceedings ArticleDOI
On the Extended Hensel Construction and its Application to the Computation of Limit Points
TL;DR: It is shown that the EHC requires only linear algebra and univariate polynomial arithmetic, and can be seen as an effective variant of Jung-Abhyankar Theorem.
References
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BookDOI
Algorithms in real algebraic geometry
TL;DR: This chapter discusses computing roadmaps and Connected Components of Algebraic Sets, as well as the "complexity of Basic Algorithms" and "cylindrical Decomposition Algorithm".
Quantifier elimination for real closed fields by cylindrical algebraic decomposition
TL;DR: In this paper, a quantifier elimination method for the elementary theory of real closed fields is presented. But it does not provide a decision method, which enables one to decide whether any sentence of the theory is true or false, since many important and difficult mathematical problems can be expressed in this theory.
Journal ArticleDOI
Real quantifier elimination is doubly exponential
James H. Davenport,Joos Heintz +1 more
TL;DR: It is shown that quantifier elimination over real closed fields can require doubly exponential space (and hence time) and time, and is done by explicitly constructing a sequence of expressions whose length is linear in the number of quantifiers, but whose quantifier-free expression has length doubly exponentiable.