61 citations · 359 across the 17 of their papers we have counts for
17 papers
The DEWCAD Project: Pushing Back the Doubly Exponential Wall of Cylindrical Algebraic Decomposition
R. Bradford, J. H. Davenport, M. England +2
This abstract seeks to introduce the ISSAC community to the DEWCAD project, which is based at Coventry University and the University of Bath, in the United Kingdom. The project see…
Cylindrical Algebraic Decomposition with Equational Constraints
Matthew England, Russell Bradford, James H. Davenport
Cylindrical Algebraic Decomposition (CAD) has long been one of the most important algorithms within Symbolic Computation, as a tool to perform quantifier elimination in first order…
Identifying the Parametric Occurrence of Multiple Steady States for some Biological Networks
R. Bradford, J. H. Davenport, M. England +8
We consider a problem from biological network analysis of determining regions in a parameter space over which there are multiple steady states for positive real values of variables…
Does the "Artificial Intelligence Clinician" learn optimal treatment strategies for sepsis in intensive care?
Russell Jeter, Christopher Josef, Supreeth Shashikumar +1
From 2017 to 2018 the number of scientific publications found via PubMed search using the keyword "Machine Learning" increased by 46% (4,317 to 6,307). The results of studies invol…
Non-linear Real Arithmetic Benchmarks derived from Automated Reasoning in Economics
C. Mulligan, R. Bradford, J. H. Davenport +2
We consider problems originating in economics that may be solved automatically using mathematical software. We present and make freely available a new benchmark set of such problem…
Quantifier Elimination for Reasoning in Economics
Casey B. Mulligan, Russell Bradford, James H. Davenport +2
We consider the use of Quantifier Elimination (QE) technology for automated reasoning in economics. QE dates back to Tarski's work in the 1940s with software to perform it dating t…
Efficient characterisation of large deviations using population dynamics
Tobias Brewer, Stephen R. Clark, Russell Bradford +1
We consider population dynamics as implemented by the cloning algorithm for analysis of large deviations of time-averaged quantities. Using the simple symmetric exclusion process a…
A Case Study on the Parametric Occurrence of Multiple Steady States
Russell Bradford, James H. Davenport, Matthew England +8
We consider the problem of determining multiple steady states for positive real values in models of biological networks. Investigating the potential for these in models of the mito…
Improving the use of equational constraints in cylindrical algebraic decomposition
Matthew England, Russell Bradford, James H. Davenport
When building a cylindrical algebraic decomposition (CAD) savings can be made in the presence of an equational constraint (EC): an equation logically implied by a formula. The pres…
Using the distribution of cells by dimension in a cylindrical algebraic decomposition
David Wilson, Matthew England, Russell Bradford +1
We investigate the distribution of cells by dimension in cylindrical algebraic decompositions (CADs). We find that they follow a standard distribution which seems largely independe…
Using the Regular Chains Library to build cylindrical algebraic decompositions by projecting and lifting
Matthew England, David Wilson, Russell Bradford +1
Cylindrical algebraic decomposition (CAD) is an important tool, both for quantifier elimination over the reals and a range of other applications. Traditionally, a CAD is built thro…
Truth Table Invariant Cylindrical Algebraic Decomposition by Regular Chains
R. Bradford, C. Chen, J. H. Davenport +3
A new algorithm to compute cylindrical algebraic decompositions (CADs) is presented, building on two recent advances. Firstly, the output is truth table invariant (a TTICAD) meanin…
Cylindrical Algebraic Sub-Decompositions
D. J. Wilson, R. J. Bradford, J. H. Davenport +1
Cylindrical algebraic decompositions (CADs) are a key tool in real algebraic geometry, used primarily for eliminating quantifiers over the reals and studying semi-algebraic sets. I…
Truth Table Invariant Cylindrical Algebraic Decomposition
Russell Bradford, James H. Davenport, Matthew England +2
When using cylindrical algebraic decomposition (CAD) to solve a problem with respect to a set of polynomials, it is likely not the signs of those polynomials that are of paramount…
Branch Cuts in Maple 17
M. England, E. Cheb-Terrab, R. Bradford +2
Accurate and comprehensible knowledge about the position of branch cuts is essential for correctly working with multi-valued functions, such as the square root and logarithm. We di…
Cylindrical Algebraic Decompositions for Boolean Combinations
Russell Bradford, James H. Davenport, Matthew England +2
This article makes the key observation that when using cylindrical algebraic decomposition (CAD) to solve a problem with respect to a set of polynomials, it is not always the signs…
Speeding up Cylindrical Algebraic Decomposition by Gröbner Bases
David J. Wilson, Russell J. Bradford, James H. Davenport
Gröbner Bases and Cylindrical Algebraic Decomposition are generally thought of as two, rather different, methods of looking at systems of equations and, in the case of Cylindrical…