Specialising finite domain programs with polyhedra

A procedure is described for tightening domain constraints of finite domain logic programs by applying a static analysis based on convex polyhedra. Individual finite domain constraints are over-approximated by polyhedra to describe the solution space over ninteger variables as an n dimensional polyhedron. This polyhedron is then approximated, using projection, as an n dimensional bounding box that can be used to specialise and improve the domain constraints. The analysis can be implemented straightforwardly and an empirical evaluation of the specialisation technique is given

Incremental closure for systems of two variables per inequality

Subclasses of linear inequalities where each inequality has at most two vari- ables are popular in abstract interpretation and model checking, because they strike a balance between what can be described and what can be efficiently computed. This paper focuses on the TVPI class of inequalities, for which each coefficient of each two variable inequality is unrestricted. An implied TVPI in- equality can be generated from a pair of TVPI inequalities by eliminating a given common variable (echoing resolution on clauses). This operation, called result , can be applied to derive TVPI inequalities which are entailed (implied) by a given TVPI system. The key operation on TVPI is calculating closure: satisfiability can be observed from a closed system and a closed system also simplifies the calculation of other operations. A closed system can be derived by repeatedly applying the result operator. The process of adding a single TVPI inequality to an already closed input TVPI system and then finding the closure of this augmented system is called incremental closure. This too can be calcu- lated by the repeated application of the result operator. This paper studies the calculus defined by result , the structure of result derivations, and how deriva- tions can be combined and controlled. A series of lemmata on derivations are presented that, collectively, provide a pathway for synthesising an algorithm for incremental closure. The complexity of the incremental closure algorithm is analysed and found to be O (( n 2 + m 2 )lg( m )), where n is the number of variables and m the number of inequalities of the input TVPI system

Free resolutions of algebras

Given an algebra A, presented by generators and relations, i.e. as a quotient of a tensor algebra by an ideal, we construct a free algebra resolution of A, i.e. a differential graded algebra which is quasi-isomorphic to A and which is itself a tensor algebra. The construction rests combinatorially on the set of bracketings that arise naturally in the description of a free contractible differential graded algebra with given generators

Fuelling Active Galactic Nuclei

We suggest that most nearby active galactic nuclei are fed by a series of small--scale, randomly--oriented accretion events. Outside a certain radius these events promote rapid star formation, while within it they fuel the supermassive black hole. We show that the events have a characteristic time evolution. This picture agrees with several observational facts. The expected luminosity function is broadly in agreement with that observed for moderate--mass black holes. The spin of the black hole is low, and aligns with the inner disc in each individual feeding event. This implies radio jets aligned with the axis of the obscuring torus, and uncorrelated with the large--scale structure of the host galaxy. The ring of young stars observed about the Galactic Centre are close to where our picture predicts that star formation should occur.Comment: MNRAS, in pres

The computation of the cohomology rings of all groups of order 128

We describe the computation of the mod-2 cohomology rings of all 2328 groups of order 128. One consequence is that all groups of order less than 256 satisfy the strong form of Benson's Regularity Conjecture.Comment: 15 pages; revised versio

Blunting the Spike: the CV Minimum Period

The standard picture of CV secular evolution predicts a spike in the CV distribution near the observed short-period cutoff P_0 ~ 78 min, which is not observed. We show that an intrinsic spread in minimum (`bounce') periods P_b resulting from a genuine difference in some parameter controlling the evolution can remove the spike without smearing the sharpness of the cutoff. The most probable second parameter is different admixtures of magnetic stellar wind braking (at up to 5 times the GR rate) in a small tail of systems, perhaps implying that the donor magnetic field strength at formation is a second parameter specifying CV evolution. We suggest that magnetic braking resumes below the gap with a wide range, being well below the GR rate in most CVs, but significantly above it in a small tail.Comment: 5 pages, 4 figures; accepted for publication in MNRA

The Virtual Runner Learning Game

A learning game has been developed which allows learners to study and learn about the significance of three important variables in human physiology (lactate, glycogen, and hydration) and their influence on sports performance during running. The player can control the speed of the runner, and as a consequence the resulting physiological processes are simulated in real-time. The performance degradation of the runner due to these processes requires that different strategies for pacing the running speed are applied by the player, depending on the total length of the run. The game has been positively evaluated in a real learning context of academic physiology teaching

Verifying termination and error-freedom of logic programs with block declarations

We present verification methods for logic programs with delay declarations. The verified properties are termination and freedom from errors related to built-ins. Concerning termination, we present two approaches. The first approach tries to eliminate the well-known problem of speculative output bindings. The second approach is based on identifying the predicates for which the textual position of an atom using this predicate is irrelevant with respect to termination. Three features are distinctive of this work: it allows for predicates to be used in several modes; it shows that block declarations, which are a very simple delay construct, are sufficient to ensure the desired properties; it takes the selection rule into account, assuming it to be as in most Prolog implementations. The methods can be used to verify existing programs and assist in writing new programs

Ray methods for free boundary problems

We discuss the use of the WKB ansatz in a variety of parabolic problems involving a small parameter. We analyse the Stefan problem for small latent heat, the Black–Scholes problem for an American put option, and some nonlinear diffusion equations, in each case constructing an asymptotic solution by the use of ray methods