On the variations of the Betti numbers of regular levels of Morse flows

We generalize results in Cruz and de Rezende (1999) [7] by completely describing how the Beth numbers of the boundary of an orientable manifold vary after attaching a handle, when the homology coefficients are in Z, Q, R or Z/pZ with p prime. First we apply this result to the Conley index theory of Lyapunov graphs. Next we consider the Ogasa invariant associated with handle decompositions of manifolds. We make use of the above results in order to obtain upper bounds for the Ogasa invariant of product manifolds. (C) 2011 Elsevier B.V. All rights reserved.

Geodesics and Almost Geodesic Cycles in Random Regular Graphs

A geodesic in a graph G is a shortest path between two vertices of G. For a specific function e(n) of n, we define an almost geodesic cycle C in G to be a cycle in which for every two vertices u and v in C, the distance d(G)(u, v) is at least d(C)(u, v) - e(n). Let omega(n) be any function tending to infinity with n. We consider a random d-regular graph on n vertices. We show that almost all pairs of vertices belong to an almost geodesic cycle C with e(n)= log(d-1)log(d-1) n+omega(n) and vertical bar C vertical bar =2 log(d-1) n+O(omega(n)). Along the way, we obtain results on near-geodesic paths. We also give the limiting distribution of the number of geodesics between two random vertices in this random graph. (C) 2010 Wiley Periodicals, Inc. J Graph Theory 66: 115-136, 2011

Regular Derivations in Basic Superposition-Based Calculi

We prove the completeness of the regular strategy of derivations for superposition-based calculi. The regular strategy was pioneered by Kanger in [Kan63], who proposed that all equality inferences take place before all other steps in the proof. We show that the strategy is complete with the elimination of tautologies. The implication of our result is the completeness of non-standard selection functions by which in non-relational clauses only equality literals (and all of them) are selected.

Modelling regular and estimable inverse demand systems : a distance function approach

To be useful for policy simulation in the current climate of rapid structural change, inverse demand systems must remain regular over substanstial variations in quantities. The distance function is a convenient vehicle for generating such systems. It also allows convenient imposition of prior ideas about the structure of preferences required for realistic policy work. While the distance function directly yields Hicksian inverse demand functions via the Shepard-Hanoch lemma, they are usually explicit in the unobservable level of utility (u), but lack a closed-form representation in terms of the observable variables. Note however that the unobservability of u need not hinder estimation. A simple one-dimensional numerical inversion allows the estimation of the distance function via the parameters of the implied Marshallian inverse demand functions. This paper develops the formal theory for using distance functions in this context, and reports on initial trials on the operational feasibility of the method.

The influence of leisure preference, life priority and making time on regular participation in leisure time physical activity

Using an attitude-behaviour theory approach this study examined the direct and indirect influence of preference, life priority and time allocation on regular participation in leisure-time physical activity (LTPA). The crosssectional study used self-report questionnaires to collect data from a random sample of 250 people aged 19 to 87 years living in an Australian city. The findings suggest that people’s regular participation in LTPA is not directly influenced by their preference for it. Rather, making LTPA a high life priority and allocating time for LTPA are intervening factors that explain the relationship. The outcomes emphasise the importance of encouraging the formation of a preference for physical activity in young children. They suggest all levels of government and the leisure profession emphasise work/life balance by prioritising LTPA, educating people about time management and helping them to develop time management skills.

Regular exercise participation mediates the affective response to acute bouts of vigorous exercise

Physical inactivity is a leading factor associated with cardiovascular disease and a major contributor to the global burden of disease in developed countries. Subjective mood states associated with acute exercise are likely to influence future exercise adherence and warrant further investigation. The present study examined the effects of a single bout of vigorous exercise on mood and anxiety between individuals with substantially different exercise participation histories. Mood and anxiety were assessed one day before an exercise test (baseline), 5 minutes before (pre-test) and again 10 and 25 minutes post-exercise. Participants were 31 university students (16 males, 15 females; Age M = 20), with 16 participants reporting a history of regular exercise with the remaining 15 reporting to not exercise regularly. Each participant completed an incremental exercise test on a Monark cycle ergometer to volitional exhaustion. Regular exercisers reported significant post-exercise improvements in mood and reductions in state anxiety. By contrast, non-regular exercisers reported an initial decline in post-exercise mood and increased anxiety, followed by an improvement in mood and reduction in anxiety back to pre-exercise levels. Our findings suggest that previous exercise participation mediates affective responses to acute bouts of vigorous exercise. We suggest that to maximise positive mood changes following exercise, practitioners should carefully consider the individual's exercise participation history before prescribing new regimes.

Graph matching with subdivision surfaces for texture synthesis on surfaces

Existing texture synthesis-from-example strategies for polygon meshes typically make use of three components: a multi-resolution mesh hierarchy that allows the overall nature of the pattern to be reproduced before filling in detail; a matching strategy that extends the synthesized texture using the best fit from a texture sample; and a transfer mechanism that copies the selected portion of the texture sample to the target surface. We introduce novel alternatives for each of these components. Use of p2-subdivision surfaces provides the mesh hierarchy and allows fine control over the surface complexity. Adaptive subdivision is used to create an even vertex distribution over the surface. Use of the graph defined by a surface region for matching, rather than a regular texture neighbourhood, provides for flexible control over the scale of the texture and allows simultaneous matching against multiple levels of an image pyramid created from the texture sample. We use graph cuts for texture transfer, adapting this scheme to the context of surface synthesis. The resulting surface textures are realistic, tolerant of local mesh detail and are comparable to results produced by texture neighbourhood sampling approaches.