Interactive Simplifier Tracing and Debugging in Isabelle

The Isabelle proof assistant comes equipped with a very powerful tactic for term simplification. While tremendously useful, the results of simplifying a term do not always match the user's expectation: sometimes, the resulting term is not in the form the user expected, or the simplifier fails to apply a rule. We describe a new, interactive tracing facility which offers insight into the hierarchical structure of the simplification with user-defined filtering, memoization and search. The new simplifier trace is integrated into the Isabelle/jEdit Prover IDE.Comment: Conferences on Intelligent Computer Mathematics, 201

Experimental investigation of the effects of pulse pressure distortions imposed on the inlet of a turbofan engine

Pulse pressure distortion effects imposed on inlet of turbofan engin

Isabelle/PIDE as Platform for Educational Tools

The Isabelle/PIDE platform addresses the question whether proof assistants of the LCF family are suitable as technological basis for educational tools. The traditionally strong logical foundations of systems like HOL, Coq, or Isabelle have so far been counter-balanced by somewhat inaccessible interaction via the TTY (or minor variations like the well-known Proof General / Emacs interface). Thus the fundamental question of math education tools with fully-formal background theories has often been answered negatively due to accidental weaknesses of existing proof engines. The idea of "PIDE" (which means "Prover IDE") is to integrate existing provers like Isabelle into a larger environment, that facilitates access by end-users and other tools. We use Scala to expose the proof engine in ML to the JVM world, where many user-interfaces, editor frameworks, and educational tools already exist. This shall ultimately lead to combined mathematical assistants, where the logical engine is in the background, without obstructing the view on applications of formal methods, formalized mathematics, and math education in particular.Comment: In Proceedings THedu'11, arXiv:1202.453

Impressions of convexity - An illustration for commutator bounds

We determine the sharpest constant $C_{p,q,r}$ such that for all complex matrices $X$ and $Y$, and for Schatten $p$-, $q$- and $r$-norms the inequality $$\|XY-YX\|_p\leq C_{p,q,r}\|X\|_q\|Y\|_r$$ is valid. The main theoretical tool in our investigations is complex interpolation theory.Comment: 32 pages, 88 picture

Digging for gold nuggets : uncovering novel candidate genes for variation in gastrointestinal nematode burden in a wild bird species

Acknowledgements This study was funded by a BBSRC studentship (MAWenzel) and NERC grants NE/H00775X/1 and NE/D000602/1 (SB Piertney). The authors are grateful to Marianne James, Mario Roder and Keliya Bai for field-work assistance, Lucy M.I. Webster and Steve Paterson for help during prior development of genetic markers,Heather Ritchie for helpful comments on manuscript drafts and all estate owners, factors and keepers for access to field sites, most particularly MJ Taylor and Mike Nisbet (Airlie), Neil Brown (Allargue), RR Gledson and David Scrimgeour (Delnadamph), Andrew Salvesen and John Hay (Dinnet), Stuart Young and Derek Calder (Edinglassie), Kirsty Donald and DavidBusfield (Glen Dye), Neil Hogbin and Ab Taylor (Glen Muick), Alistair Mitchell (Glenlivet), Simon Blackett, Jim Davidson and Liam Donald (Invercauld), Richard Cooke and Fred Taylor (Invermark), Shaila Rao and Christopher Murphy (Mar Lodge), and Ralph Peters and Philip Astor (Tillypronie)Peer reviewedPostprin

Analytical investigation of nonrecoverable stall

A lumped parameter model of the TF34 engine is formulated to study nonrecoverable stall. Features of the model include forward and reverse flow, radial flow in the fan, and variable corrected speed. The purpose of the study is to point out those parameters to which recoverability is highly sensitive but are not well known. Experimental research may then be directed toward identification of the parameters in that category. Compressor performance in the positive flow region and radial flow in the fan are shown to be important but unknown parameters determining recoverability. Other parameters such as compressor performance during reverse flow and in-stall efficiency have relatively small impact on recoverability

Re-examining the directional-ordering transition in the compass model with screw-periodic boundary conditions

We study the directional-ordering transition in the two-dimensional classical and quantum compass models on the square lattice by means of Monte Carlo simulations. An improved algorithm is presented which builds on the Wolff cluster algorithm in one-dimensional subspaces of the configuration space. This improvement allows us to study classical systems up to $L=512$. Based on the new algorithm we give evidence for the presence of strongly anomalous scaling for periodic boundary conditions which is much worse than anticipated before. We propose and study alternative boundary conditions for the compass model which do not make use of extended configuration spaces and show that they completely remove the problem with finite-size scaling. In the last part, we apply these boundary conditions to the quantum problem and present a considerably improved estimate for the critical temperature which should be of interest for future studies on the compass model. Our investigation identifies a strong one-dimensional magnetic ordering tendency with a large correlation length as the cause of the unusual scaling and moreover allows for a precise quantification of the anomalous length scale involved.Comment: 10 pages, 8 figures; version as publishe

Analysis of dynamic inlet distortion applied to a parallel compressor model

An investigation of surge was conducted by using a parallel compressor model of the J85-13 compressor implement on an analog computer. Surges were initiated by various types of dynamic disturbances in inlet pressure. The compressor model was less sensitive to disturbances of short duration, high frequency, and long duration where the compressor discharge pressure could react. Adding steady distortion to dynamic disturbances reduced the amount of dynamic disturbance required to effect surge. Steady and unsteady distortions combined linearly to reduce surge margin

A method to account for variation of average compressor inlet pressure during instantaneous distortion analyses

A method is presented to calculate the available surge margin as a function of time and incorporate it into an instantaneous distortion analysis. Results show that inlet pressure variations which cause only a small change at the compressor exit can cause a significant variation in the available surge margin

Deflection of a Viscoelastic Cantilever under a Uniform Surface Stress: Applications to Static-mode Microcantilever Sensors Undergoing Adsorption

The equation governing the curvature of a viscoelastic microcantilever beam loaded with a uniform surface stress is derived. The present model is applicable to static-mode microcantilever sensors made with a rigid polymer, such as SU-8. An analytical solution to the differential equation governing the curvature is given for a specific surface stress representing adsorption of analyte onto the viscoelastic beam’s surface. The solution for the bending of the microcantilever shows that, in many cases, the use of Stoney’s equation to analyze stress-induced deflection of viscoelastic microcantilevers (in the present case due to surface analyte adsorption) can lead to poor predictions of the beam’s response. It is shown that using a viscoelastic substrate can greatly increase sensitivity (due to a lower modulus), but at the cost of a longer response time due to viscoelasticcreep in the microcantilever. In addition, the effects of a coating on the cantilever are considered. By defining effective moduli for the coated-beam case, the analytical solution for the uncoated case can still be used. It is found that, unlike the case of a silicon microcantilever, the stress in the coating due to bending of a polymer cantilever can be significant, especially for metalcoatings. The theoretical results presented here can also be used to extract time-domain viscoelasticproperties of the polymermaterial from beam response data