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 mitogen-activated protein kinases (MAPK) network has consumed considerable effort using special insights into the structure of corresponding models. Here we apply combinations of symbolic computation methods for mixed equality/inequality systems, specifically virtual substitution, lazy real triangularization and cylindrical algebraic decomposition. We determine multistationarity of an 11-dimensional MAPK network when numeric values are known for all but potentially one parameter. More precisely, our considered model has 11 equations in 11 variables and 19 parameters, 3 of which are of interest for symbolic treatment, and furthermore positivity conditions on all variables and parameters.

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 importance but rather the truth values of certain quantifier free formulae involving them. This observation motivates our article and definition of a Truth Table Invariant CAD (TTICAD). In ISSAC 2013 the current authors presented an algorithm that can efficiently and directly construct a TTICAD for a list of formulae in which each has an equational constraint. This was achieved by generalising McCallum's theory of reduced projection operators. In this paper we present an extended version of our theory which can be applied to an arbitrary list of formulae, achieving savings if at least one has an equational constraint. We also explain how the theory of reduced projection operators can allow for further improvements to the lifting phase of CAD algorithms, even in the context of a single equational constraint. The algorithm is implemented fully in Maple and we present both promising results from experimentation and a complexity analysis showing the benefits of our contributions.

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.

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 of those polynomials that are of paramount importance but rather the truth values of certain quantifier free formulae involving them. This motivates our definition of a Truth Table Invariant CAD (TTICAD). We generalise the theory of equational constraints to design an algorithm which will efficiently construct a TTICAD for a wide class of problems, producing stronger results than when using equational constraints alone. The algorithm is implemented fully in Maple and we present promising results from experimentation.

Given an elementary function with algebraic branch cuts, we show how to decide which sheet of the associated Riemann surface we are on at any given point. We do this by establishing a correspondence between the Cylindrical Algebraic Decomposition (CAD) of the complex plane defined by the branch cuts and a finite subset of sheets of the Riemann surface. The key advantage is that we no longer have to deal with the difficult 'constant problem'.

Simplification has been long recognised to be a fundamental problem within computer algebra [17]. However, even for the class of elementary functions, it has not been resolved in a satisfactory way.Algorithms were presented in [4, 2] to solve this problem, and it was seen that both methods had their own strengths and weaknesses. Also, not all functions could be handled by either of the methods alone. The current paper continues this line of development by combining the two methods, and reporting on progress made with the various sub-algorithms involved.

In [5], we introduced an algorithm for deciding whether a proposed simplification of elementary functions was correct in the presence of branch cuts. This algorithm used multivalued function simplification followed by verification that the branches were consistent.In [14] an algorithm was presented for zero-testing functions defined by ordinary differential equations, in terms of their power series.The purpose of the current paper is to investigate merging the two techniques. In particular, we will show an explicit reduction to the constant problem [16].

We present an algorithm for simplifying a large class of elementary functions in the presence of branch cuts. This algorithm works by:(a) verifying that the proposed simplification is correct as a simplification of multi-valued functions;(b) decomposing C (or Cn in the case of multivariate simplifications) according to the branch cuts of the relevant functions;(c) checking that the proposed identity is valid on each component of that decomposition.This process can be interfaced to an assume facility, and, if required, can verify that simplifications are valid "almost everywhere".

This paper discusses the use of a parallel discrete-event network emulator called the Internet Protocol Traffic and Network Emulator (IP-TNE) for Web server benchmarking. The experiments in this paper demonstrate the feasibility of high-performance WAN emulation using parallel discrete-event simulation techniques on shared-memory multiprocessors. Our experiments with the Apache Web server achieve 3400 HTTP transactions per second for simple Web workloads, and 1000 HTTP transactions per second for realistic Web workloads, for static document retrieval across emulated WAN topologies of up to 4096 concurrent Web/TCP clients. The results show that WAN characteristics, including round-trip delays, link speeds, packet losses, packet sizes, and bandwidth asymmetry, all have significant impacts on Web server performance. WAN emulation enables stress testing and benchmarking of Web server performance in ways that may not be possible in simple LAN test scenarios.

Testing distributed applications over the Internet is fraught with problems: due to the inability to control a wide area network consistent, reproducible performance experiments are not possible. A system is described that uses a parallel discrete event simulator that can act as a real-time network emulator. Real Internet Protocol (IP) traffic generated by application programs running on user workstations can interact with modelled traffic in the emulator; thus providing a controlled test environment for distributed applications. Parallel execution enables the emulator to simulate large virtual networks and to model traffic interactions that could not be done in real-time sequentially. This paper gives an overview of the emulator and explores the various external data routing methods that the emulator supports. These routing methods allow the emulator to be operated in shared environments with certain constraints, as well as in dedicated test environments. Preliminary performance results are included.

We describe the approach to the concurrent execution of object-oriented programs that is being research at the University of Bath. The aim of this project is the concurrent execution of both new Lisp programs and existing Lisp applications. We are pursuing this goal by addressing the problems of concurrent execution at several levels: static analysis of Lisp programs as a basis for semi-automatic transformation, modification of medium-sized Lisp programs to use concurrent primitives to gain experience in their use and behaviour and the implementation of various concurrency primitives in a compiled distributed heterogeneous Lisp environment. Each of these topics is described in turn and its relationship to the long term aim defined above is examined.

We have experimented with a little elementary parallelism applied to Buchberger's algorithm. This is in contrast to [Ponder] and [Vidal], as gains can be achieved by using the method even on a single processor.

The defect of an algebraic number field (or, more correctly, of a presentation of the field) is the largest rational integer that divides the denominator of any algebraic integer in the field when written using that presentation. Knowing the defect, or estimating it accurately is extremely valuable in many algorithms, the factorization of polynomials over algebraic number fields being a prime example. We present a few results that are a move in the right direction.