A Graphical Language for Proof Strategies

Complex automated proof strategies are often difficult to extract, visualise, modify, and debug. Traditional tactic languages, often based on stack-based goal propagation, make it easy to write proofs that obscure the flow of goals between tactics and are fragile to minor changes in input, proof structure or changes to tactics themselves. Here, we address this by introducing a graphical language called PSGraph for writing proof strategies. Strategies are constructed visually by "wiring together" collections of tactics and evaluated by propagating goal nodes through the diagram via graph rewriting. Tactic nodes can have many output wires, and use a filtering procedure based on goal-types (predicates describing the features of a goal) to decide where best to send newly-generated sub-goals. In addition to making the flow of goal information explicit, the graphical language can fulfil the role of many tacticals using visual idioms like branching, merging, and feedback loops. We argue that this language enables development of more robust proof strategies and provide several examples, along with a prototype implementation in Isabelle

Flutter at Mach 3 of thermally stressed panels and comparison with theory for panels with edge rotational restraint

Flutter at Mach 3 of thermally stressed flat isotropic panel

Radiation-induced nucleic acid synthesis in L cells under energy deprivation

Radiation induced nucleic acid synthesis in energy deprived L cell

Feminist Geopolitics: Material States

No abstract available

The orbifold transform and its applications

We discuss the notion of the orbifold transform, and illustrate it on simple examples. The basic properties of the transform are presented, including transitivity and the exponential formula for symmetric products. The connection with the theory of permutation orbifolds is addressed, and the general results illustrated on the example of torus partition functions

On the Relationship between the Uniqueness of the Moonshine Module and Monstrous Moonshine

We consider the relationship between the conjectured uniqueness of the Moonshine Module, ${\cal V}^\natural$, and Monstrous Moonshine, the genus zero property of the modular invariance group for each Monster group Thompson series. We first discuss a family of possible $Z_n$ meromorphic orbifold constructions of ${\cal V}^\natural$ based on automorphisms of the Leech lattice compactified bosonic string. We reproduce the Thompson series for all 51 non-Fricke classes of the Monster group $M$ together with a new relationship between the centralisers of these classes and 51 corresponding Conway group centralisers (generalising a well-known relationship for 5 such classes). Assuming that ${\cal V}^\natural$ is unique, we then consider meromorphic orbifoldings of ${\cal V}^\natural$ and show that Monstrous Moonshine holds if and only if the only meromorphic orbifoldings of ${\cal V}^\natural$ give ${\cal V}^\natural$ itself or the Leech theory. This constraint on the meromorphic orbifoldings of ${\cal V}^\natural$ therefore relates Monstrous Moonshine to the uniqueness of ${\cal V}^\natural$ in a new way.Comment: 53 pages, PlainTex, DIAS-STP-93-0

Note on graviton MHV amplitudes

Two new formulas which express n-graviton MHV tree amplitudes in terms of sums of squares of n-gluon amplitudes are discussed. The first formula is derived from recursion relations. The second formula, simpler because it involves fewer permutations, is obtained from the variant of the Berends, Giele, Kuijf formula given in Arxiv:0707.1035.Comment: 10 page

Associating object names with descriptions of shape that distinguish possible from impossible objects.

Five experiments examine the proposal that object names are closely linked torepresentations of global, 3D shape by comparing memory for simple line drawings of structurally possible and impossible novel objects.Objects were rendered impossible through local edge violations to global coherence (cf. Schacter, Cooper, & Delaney, 1990) and supplementary observations confirmed that the sets of possible and impossible objects were matched for their distinctiveness. Employing a test of explicit recognition memory, Experiment 1 confirmed that the possible and impossible objects were equally memorable. Experiments 2–4 demonstrated that adults learn names (single-syllable non-words presented as count nouns, e.g., “This is a dax”) for possible objectsmore easily than for impossible objects, and an item-based analysis showed that this effect was unrelated to either the memorability or the distinctiveness of the individual objects. Experiment 3 indicated that the effects of object possibility on name learning were long term (spanning at least 2months), implying that the cognitive processes being revealed can support the learning of object names in everyday life. Experiment 5 demonstrated that hearing someone else name an object at presentation improves recognition memory for possible objects, but not for impossible objects. Taken together, the results indicate that object names are closely linked to the descriptions of global, 3D shape that can be derived for structurally possible objects but not for structurally impossible objects. In addition, the results challenge the view that object decision and explicit recognition necessarily draw on separate memory systems,with only the former being supported by these descriptions of global object shape. It seems that recognition also can be supported by these descriptions, provided the original encoding conditions encourage their derivation. Hearing an object named at encoding appears to be just such a condition. These observations are discussed in relation to the effects of naming in other visual tasks, and to the role of visual attention in object identification