Existence of a semicontinuous or continuous utility function: a unified approach and an elementary proof

In this paper, we present a new unified approach and an elementary proof of a very general theorem on the existence of a semicontinuous or continuous utility function representing a preference relation. A simple and interesting new proof of the famous Debreu Gap Lemma is given. In addition, we prove a new Gap Lemma for the rational numbers and derive some consequences. We also prove a theorem which characterizes the existence of upper semicontinuous utility functions on a preordered topological space which need not be second countable. This is a generalization of the classical theorem of Rader which only gives sufficient conditions for the existence of an upper semicontinuous utility function for second countable topological spaces. (C) 2002 Elsevier Science B.V. All rights reserved.

The number of rational points of a class of Artin-Schreier curves

We determine the number of F-q-rational points of a class of Artin-Schreier curves by using recent results concerning evaluations of some exponential sums. In particular, we determine infinitely many new examples of maximal and minimal plane curves in the context of the Hasse-Weil bound. (C) 2002 Elsevier Science (USA).

Complex language functions and subcortical mechanisms: evidence from Huntington's disease and patients with non-thalamic subcortical lesions

The neuropathological changes associated with Huntington's disease (HD) are most marked in the head of the caudate nucleus and, to a lesser extent, in the putamen and globus pallidus, suggesting that at least part of the language impairments found in patients with HD may result from non-thalamic subcortical (NTS) pathology. The present study aimed to test the hypothesis that a signature profile of impaired language functions is found in patients who have sustained damage to the non-thalamic subcortex, either focally induced or resulting from neurodegenerative pathology. The language abilities of a group of patients with Huntington's disease (n=13) were compared with those of an age- and education-matched group of patients with chronic NTS lesions following stroke (n=13) and a non-neurologically impaired control group (n=13). The three groups were compared on language tasks that assessed both primary and more complex language abilities. The primary language battery consisted of The Western Aphasia Battery and The Boston Naming Test, whilst the more complex cognitive-linguistic battery employed selected subtests from The Test of Language Competence-Expanded, The Test of Word Knowledge and The Word Test-Revised. On many of the tests of primary language function from the Western Aphasia Battery, both the HD and NTS participants performed in a similar manner to the control participants. The language performances of the HD participants were significantly more impaired (p<0.05 using modified Bonferroni adjustments) than the control group, however, on various lexico-semantic tasks (e. g. the Boston Naming Test and providing definitions), on both single-word and sentence-level generative tasks (e. g. category fluency and formulating sentences), and on tasks which required interpretation of ambiguous, figurative and inferential meaning. The difficulties that patients with HD experienced with tasks assessing complex language abilities were strikingly similar, both qualitatively and quantitatively, to the language profile produced by NTS participants. The results provide evidence to suggest that a signature language profile is associated with damage to the non-thalamic subcortex resulting from either focal neurological insult or a degenerative disease.

Rational combinatorial chemistry-based selection, synthesis and evaluation of an affinity adsorbent for recombinant human clotting factor VII

The selection, synthesis and chromatographic evaluation of a synthetic affinity adsorbent for human recombinant factor VIIa is described. The requirement for a metal ion-dependent immunoadsorbent step in the purification of the recombinant human clotting factor, FVIIa, has been obviated by using the X-ray crystallographic structure of the complex of tissue factor (TF) and Factor VIIa and has directed our combinatorial approach to select, synthesise and evaluate a rationally-selected affinity adsorbent from a limited library of putative ligands. The selected and optimised ligand comprises a triazine scaffold bis-substituted with 3-aminobenzoic acid and has been shown to bind selectively to FVIIa in a Ca2+-dependent manner. The adsorbent purifies FVIIa to almost identical purity (>99%), yield (99%), activation/degradation profile and impurity content (∼1000 ppm) as the current immunoadsorption process, while displaying a 10-fold higher static capacity and substantially higher reusability and durability. © 2002 Elsevier Science B.V. All rights reserved.

The Limits of Rational Choice: New Institutionalism in the Test Bed of Central Banking Politics in Australia

This paper tests the explanatory capacities of different versions of new institutionalism by examining the Australian case of a general transition in central banking practice and monetary politics: namely, the increased emphasis on low inflation and central bank independence. Standard versions of rational choice institutionalism largely dominate the literature on the politics of central banking, but this approach (here termed RC1) fails to account for Australian empirics. RC1 has a tendency to establish actor preferences exogenously to the analysis; actors' motives are also assumed a priori; actor's preferences are depicted in relatively static, ahistorical terms. And there is the tendency, even a methodological requirement, to assume relatively simple motives and preference sets among actors, in part because of the game theoretic nature of RC1 reasoning. It is possible to build a more accurate rational choice model by re-specifying and essentially updating the context, incentives and choice sets that have driven rational choice in this case. Enter RC2. However, this move subtly introduces methodological shifts and new theoretical challenges. By contrast, historical institutionalism uses an inductive methodology. Compared with deduction, it is arguably better able to deal with complexity and nuance. It also utilises a dynamic, historical approach, and specifies (dynamically) endogenous preference formation by interpretive actors. Historical institutionalism is also able to more easily incorporate a wider set of key explanatory variables and incorporate wider social aggregates. Hence, it is argued that historical institutionalism is the preferred explanatory theory and methodology in this case.

Is maximizing resilience compatible with established ecological goal functions?

Cropp and Gabric [Ecosystem adaptation: do ecosystems maximise resilience? Ecology. In press] used a simple phytoplanktonzooplankton-nutrient model and a genetic algorithm to determine the parameter values that would maximize the value of certain goal functions. These goal functions were to maximize biomass, maximize flux, maximize flux to biomass ratio, and maximize resilience. It was found that maximizing goal functions maximized resilience. The objective of this study was to investigate whether the Cropp and Gabric [Ecosystem adaptation: do ecosystems maximise resilience? Ecology. In press] result was indicative of a general ecosystem principle, or peculiar to the model and parameter ranges used. This study successfully replicated the Cropp and Gabric [Ecosystem adaptation: do ecosystems maximise resilience? Ecology. In press] experiment for a number of different model types, however, a different interpretation of the results is made. A new metric, concordance, was devised to describe the agreement between goal functions. It was found that resilience has the highest concordance of all goal functions trialled. for most model types. This implies that resilience offers a compromise between the established ecological goal functions. The parameter value range used is found to affect the parameter versus goal function relationships. Local maxima and minima affected the relationship between parameters and goal functions, and between goal functions. (C) 2003 Elsevier B.V. All rights reserved.

Unsaturated diffusivity functions for concrete derived from NMR images

Deterioration of concrete or reinforcing steel through excessive contaminant concentration is often the result of repeated wetting and drying cycles. At each cycle, the absorption of water carries new contaminants into the unsaturated concrete. Nuclear Magnetic Resonance (NMR) is used with large concrete samples to observe the shape of the wetting profile during a simple one-dimensional wetting process. The absorption of water by dry concrete is modelled by a nonlinear diffusion equation with the unsaturated hydraulic diffusivity being a strongly nonlinear function of the moisture content. Exponential and power functions are used for the hydraulic diffusivity and corresponding solutions of the diffusion equation adequately predict the shape of the experimental wetting profile. The shape parameters, describing the wetting profile, vary little between different blends and are relatively insensitive to subsequent re-wetting experiments allowing universal parameters to be suggested for these concretes.

Mapping the royal road and other hierarchical functions

In this paper we present a technique for visualising hierarchical and symmetric, multimodal fitness functions that have been investigated in the evolutionary computation literature. The focus of this technique is on landscapes in moderate-dimensional, binary spaces (i.e., fitness functions defined over {0, 1}(n), for n less than or equal to 16). The visualisation approach involves an unfolding of the hyperspace into a two-dimensional graph, whose layout represents the topology of the space using a recursive relationship, and whose shading defines the shape of the cost surface defined on the space. Using this technique we present case-study explorations of three fitness functions: royal road, hierarchical-if-and-only-if (H-IFF), and hierarchically decomposable functions (HDF). The visualisation approach provides an insight into the properties of these functions, particularly with respect to the size and shape of the basins of attraction around each of the local optima.