Utility functions on locally connected spaces

We investigate the role of local connectedness in utility theory and prove that any continuous total preorder on a locally connected separable space is continuously representable. This is a new simple criterion for the representability of continuous preferences, and is not a consequence of the standard theorems in utility theory that use conditions such as connectedness and separability, second countability, or path-connectedness. Finally we give applications to problems involving the existence of value functions in population ethics and to the problem of proving the existence of continuous utility functions in general equilibrium models with land as one of the commodities. (C) 2003 Elsevier B.V. All rights reserved.

Axial Anomaly for Eguchi-Hanson Metrics with Nonzero Total Mass

We compute the Dirac indexes for. the two spin structures kappa(0) and kappa(1) for Eguchi-Hanson metrics with nonzero total mass. It shows that the Dirac indexes do not vanish in general, and axial anomaly exists. When the metric has zero total mass, the Dirac index vanishes for the spin structure no, and no axial anomaly exists in this case.

Habitat selection and breeding success in a forest-nesting Alcid, the marbled murrelet, in two landscapes with different degrees of forest fragmentation

We studied habitat selection and breeding success in marked populations of a protected seabird (family Alcidae), the marbled murrelet (Brachyramphus marmoratus), in a relatively intact and a heavily logged old-growth forest landscape in south-western Canada. Murrelets used old-growth fragments either proportionately to their size frequency distribution (intact) or they tended to nest in disproportionately smaller fragments (logged). Multiple regression modelling showed that murrelet distribution could be explained by proximity of nests to landscape features producing biotic and abiotic edge effects. Streams, steeper slopes and lower elevations were selected in both landscapes, probably due to good nesting habitat conditions and easier access to nest sites. In the logged landscape, the murrelets nested closer to recent clearcuts than would be expected. Proximity to the ocean was favoured in the intact area. The models of habitat selection had satisfactory discriminatory ability in both landscapes. Breeding success (probability of nest survival to the middle of the chick rearing period), inferred from nest attendance patterns by radio-tagged parents, was modelled in the logged landscape. Survivorship was greater in areas with recent clearcuts and lower in areas with much regrowth, i.e. it was positively correlated with recent habitat fragmentation. We conclude that marbled murrelets can successfully breed in old-growth forests fragmented by logging.

Geodesics without differential equations: general relativistic calculations for introductory modern physics classes

Introductory courses covering modem physics sometimes introduce some elementary ideas from general relativity, though the idea of a geodesic is generally limited to shortest Euclidean length on a curved surface of two spatial dimensions rather than extremal aging in spacetime. It is shown that Epstein charts provide a simple geometric picture of geodesics in one space and one time dimension and that for a hypothetical uniform gravitational field, geodesics are straight lines on a planar diagram. This means that the properties of geodesics in a uniform field can be calculated with only a knowledge of elementary geometry and trigonometry, thus making the calculation of some basic results of general relativity accessible to students even in an algebra-based survey course on physics.

Resource partitioning in sympatric delphinids: Space use and habitat preferences of Australian snubfin and Indo-Pacific humpback dolphins

1. Many species of delphinids co-occur in space and time. However, little is known of their ecological interactions and the underlying mechanisms that mediate their coexistence. 2. Snubfin Orcaella heinsohni, and Indo-Pacific humpback dolphins Sousa chinensis, live in sympatry throughout most of their range in Australian waters. I conducted boat-based surveys in Cleveland Bay, north-east Queensland, to collect data on the space and habitat use of both species. Using Geographic Information Systems, kernel methods and Euclidean distances I investigated interspecific differences in their space use patterns, behaviour and habitat preferences. 3. Core areas of use (50% kernel range) for both species were located close to river mouths and modified habitat such as dredged channels and breakwaters close to the Port of Townsville. Foraging and travelling activities were the dominant behavioural activities of snubfin and humpback dolphins within and outside their core areas. 4. Their representative ranges (95% kernel range) overlapped considerably, with shared areas showing strong concordance in the space use by both species. Nevertheless, snubfin dolphins preferred slightly shallower (1-2 m) waters than humpback dolphins (2-5 m). Additionally, shallow areas with seagrass ranked high in the habitat preferences of snubfin dolphins, whereas humpback dolphins favoured dredged channels. 5. Slight differences in habitat preferences appear to be one of the principal factors maintaining the coexistence of snubfin and humpback dolphins. I suggest diet partitioning and interspecific aggression as the major forces determining habitat selection in these sympatric species.

3D information visualisation: An historical perspective

The use of 3D visualisation of digital information is a recent phenomenon. It relies on users understanding 3D perspectival spaces. Questions about the universal access of such spaces has been debated since its inception in the European Renaissance. Perspective has since become a strong cultural influence in Western visual communication. Perspective imaging assists the process of experimenting by the sketching or modelling of ideas. In particular, the recent 3D modelling of an essentially non-dimensional Cyber-space raises questions of how we think about information in general. While alternate methods clearly exist they are rarely explored within the 3D paradigm (such as Chinese isometry). This paper seeks to generate further discussion on the historical background of perspective and its role in underpinning this emergent field. © 2005 IEEE.