Regular homomorphisms of minimal sets

The classification of minimal sets is a central theme in abstract topological dynamics. Recently this work has been strengthened and extended by consideration of homomorphisms. Background material is presented in Chapter I. Given a flow on a compact Hausdorff space, the action extends naturally to the space of closed subsets, taken with the Hausdorff topology. These hyperspaces are discussed and used to give a new characterization of almost periodic homomorphisms. Regular minimal sets may be described as minimal subsets of enveloping semigroups. Regular homomorphisms are defined in Chapter II by extending this notion to homomorphisms with minimal range. Several characterizations are obtained. In Chapter III, some additional results on homomorphisms are obtained by relativizing enveloping semigroup notions. In Veech's paper on point distal flows, hyperspaces are used to associate an almost one-to-one homomorphism with a given homomorphism of metric minimal sets. In Chapter IV, a non-metric generalization of this construction is studied in detail using the new notion of a highly proximal homomorphism. An abstract characterization is obtained, involving only the abstract properties of homomorphisms. A strengthened version of the Veech Structure Theorem for point distal flows is proved. In Chapter V, the work in the earlier chapters is applied to the study of homomorphisms for which the almost periodic elements of the associated hyperspace are all finite. In the metric case, this is equivalent to having at least one fiber finite. Strong results are obtained by first assuming regularity, and then assuming that the relative proximal relation is closed as well.

Almost Disjoint Families of Representing Sets

The thesis is concerned with a number of problems in Combinatorial Set Theory. The Generalized Continuum Hypothesis is assumed. Suppose X and K are non-zero cardinals. By successively identifying K with airwise disjoint sets of power K, a function/: X-*•K can be viewed as a transversal of a pairwise disjoint (X, K)family A . Questions about families of functions in K can thus bethought of as referring to families of transversals of A. We wish to consider generalizations of such questions to almost disjoint families; in particular we are interested in extensions of the following two problems: (i) What is the 'maximum' cardinality of an almost disjoint family of functions each mapping X into K? (ii) Describe the cardinalities of maximal almost disjoint families of functions each mapping X into K. Article in Bulletin of the Australian Mathematical Society 27(03):477 - 479 · June 1983  

On Ordinal VC-Dimension and Some Notions of Complexity

We generalize the classical notion of Vapnik–Chernovenkis (VC) dimension to ordinal VC-dimension, in the context of logical learning paradigms. Logical learning paradigms encompass the numerical learning paradigms commonly studied in Inductive Inference. A logical learning paradigm is defined as a set W of structures over some vocabulary, and a set D of first-order formulas that represent data. The sets of models of ϕ in W, where ϕ varies over D, generate a natural topology W over W. We show that if D is closed under boolean operators, then the notion of ordinal VC-dimension offers a perfect characterization for the problem of predicting the truth of the members of D in a member of W, with an ordinal bound on the number of mistakes. This shows that the notion of VC-dimension has a natural interpretation in Inductive Inference, when cast into a logical setting. We also study the relationships between predictive complexity, selective complexity—a variation on predictive complexity—and mind change complexity. The assumptions that D is closed under boolean operators and that W is compact often play a crucial role to establish connections between these concepts. We then consider a computable setting with effective versions of the complexity measures, and show that the equivalence between ordinal VC-dimension and predictive complexity fails. More precisely, we prove that the effective ordinal VC-dimension of a paradigm can be defined when all other effective notions of complexity are undefined. On a better note, when W is compact, all effective notions of complexity are defined, though they are not related as in the noncomputable version of the framework.

A new measure to quantify chest wall deformity in scoliosis patients : does rib hump measurement correlate with anterior chest wall deformity post surgery?

The primary aims of scoliosis surgery are to halt the progression of the deformity, and to reduce its severity (cosmesis). Currently, deformity correction is measured in terms of posterior parameters (Cobb angles and rib hump), even though the cosmetic concern for most patients is anterior chest wall deformity. In this study, we propose a new measure for assessing anterior chest wall deformity and examine the correlation between rib hump and the new measure. 22 sets of CT scans were retrieved from the QUT/Mater Paediatric Spinal Research Database. The Image J software (NIH) was used to manipulate formatted CT scans into 3-dimensional anterior chest wall reconstructions. A ‘chest wall angle’ was then measured in relation to the first sacral vertebral body. The chest wall angle was found to be a reliable tool in the analysis of chest wall deformity. No correlation was found between the new measure and rib hump angle. Since rib hump has been shown to correlate with vertebral rotation on CT, this suggests that there maybe no correlation between anterior and posterior deformity measures. While most surgical procedures will adequately address the coronal imbalance & posterior rib hump elements of scoliosis, they do not reliably alter the anterior chest wall shape. This implies that anterior chest wall deformity is to a large degree an intrinsic deformity, not directly related to vertebral rotation.

Error, Bias, and Long-Branch Attraction in Data for Two Chloroplast Photosystem Genes in Seed Plants

Sequences of two chloroplast photosystem genes, psaA and psbB, together comprising about 3,500 bp, were obtained for all five major groups of extant seed plants and several outgroups among other vascular plants. Strongly supported, but significantly conflicting, phylogenetic signals were obtained in parsimony analyses from partitions of the data into first and second codon positions versus third positions. In the former, both genes agreed on a monophyletic gymnosperms, with Gnetales closely related to certain conifers. In the latter, Gnetales are inferred to be the sister group of all other seed plants, with gymnosperms paraphyletic. None of the data supported the modern ‘‘anthophyte hypothesis,’’ which places Gnetales as the sister group of flowering plants. A series of simulation studies were undertaken to examine the error rate for parsimony inference. Three kinds of errors were examined: random error, systematic bias (both properties of finite data sets), and statistical inconsistency owing to long-branch attraction (an asymptotic property). Parsimony reconstructions were extremely biased for third-position data for psbB. Regardless of the true underlying tree, a tree in which Gnetales are sister to all other seed plants was likely to be reconstructed for these data. None of the combinations of genes or partitions permits the anthophyte tree to be reconstructed with high probability. Simulations of progressively larger data sets indicate the existence of long-branch attraction (statistical inconsistency) for third-position psbB data if either the anthophyte tree or the gymnosperm tree is correct. This is also true for the anthophyte tree using either psaA third positions or psbB first and second positions. A factor contributing to bias and inconsistency is extremely short branches at the base of the seed plant radiation, coupled with extremely high rates in Gnetales and nonseed plant outgroups. M. J. Sanderson,* M. F. Wojciechowski,*† J.-M. Hu,* T. Sher Khan,* and S. G. Brady

What shapes attitudes toward paying taxes? Evidence from multicultural European countries

Objectives. Considerable evidence suggests that enforcement efforts cannot fully explain the high degree of tax compliance. To resolve this puzzle of tax compliance, several researchers have argued that citizens' attitudes toward paying taxes, defined as tax morale, helps to explain the high degree of tax compliance. However, most studies have treated tax morale as a black box, without discussing which factors shape it. Additionally, the tax compliance literature provides little empirical research that investigates attitudes toward paying taxes in Europe. Methods. Thus, this article is unique in its examination of citizen tax morale within three multicultural European countries, Switzerland, Belgium, and Spain, a choice that allows far more detailed examination of the impact of culture and institutions using data sets from the World Values Survey and the European Values Survey. Results. The results indicate the tendency that cultural and regional differences affect tax morale. Conclusion. The findings suggest that higher legitimacy for political institutions leads to higher tax morale.

On medium specificity and discipline crossovers in modern art : An interview with Jacques Ranciére on Medium-Specificity and Discipline Crossovers in Modern Art

Jacques Ranciere's work on aesthetics has received a great deal of attention recently. Given his work has enormous range – taking in art and literature, political theory, historiography, pedagogy and worker's history – Andrew McNamara and Toni Ross (UNSW) seek to explore his wider project in this interview, while showing how it leads to his alternative insights into aesthetics. Rancière sets aside the core suppositions linking the medium to aesthetic judgment, which has informed many definitions of modernism. Rancière is emphatic in freeing aesthetic judgment from issues of medium-specificity. He argues that the idea of autonomy associated with medium-specificity – or 'truth to the medium' – was 'a very late one' in modernism, and that post-medium trends were already evident in early modernism. While not stressing a simple continuity between early modernism and contemporary art, Ranciere nonetheless emphasizes the ethical and political ramifications of maintaining an a-disciplinary stance.

Effectuation & newness : an intertwined relationship?

Principal topic: Effectuation theory suggests that entrepreneurs develop their new ventures in an iterative way by selecting possibilities through flexibility and interactions with the market; a focus on affordability of loss rather than maximal return on the capital invested, and the development of pre-commitments and alliances from stakeholders (Sarasvathy, 2001, 2008; Sarasvathy et al., 2005, 2006). In contrast, causation may be described as a rationalistic reasoning method to create a company. After a comprehensive market analysis to discover opportunities, the entrepreneur will select the alternative with the higher expected return and implement it through the use of a business plan. However, little is known about the consequences of following either of these two processes. One aspect that remains unclear is the relationship between newness and effectuation. On one hand it can be argued that the combination of a means-centered, interactive (through pre-commitments and alliances with stakeholders from the early phases of the venture creation) and open-minded process (through flexibility of exploiting contingencies) should encourage and facilitate the development of innovative solutions. On the other hand, having a close relationship with their “future first customers” and focussing too much on the resources and knowledge already within the firm may be a constraint that is not conducive to innovation, or at least not to a radical innovation. While it has been suggested that effectuation strategy is more likely to be used by innovative entrepreneurs (Sarasvathy, 2001), this hypothesis has not been demonstrated yet (Sarasvathy, 2001). Method: In our attempt to capture newness in its different aspects we have considered the following four domains where newness may happen: new product/service; new method for promotion and sales; new production methods/sourcing; market creation. We identified how effectuation may be differently associated with these four domains of newness. To test our four sets of hypotheses a dataset of 1329 firms (702 nascent and 627 young firms) randomly selected in Australia was examined through ANOVA Tukey HSD Test. Results and Implications: Results indicate the existence of a curvilinear relationship between effectuation and newness where low and high levels of newness are associated with low level of effectuation while medium level of newness is associated with high level of effectuation. Implications for academia, practitioners and policy makers are also discussed.

"Get new lawyers!"

In James Rubin's account of the Kosovo war, he describes an exchange between Secretary Albright and Robin Cook (the British Foreign Secretary). Cook was explaining that it is difficult for Britain to commit to the war without UN Security Council approval because the legal advice he had received was that such action would be illegal under international law. Albright's response was, simply, "get new lawyers". Rubin "credits" Blair with a "push" that swung the British to "finally agree" that a UN Security Council resolution was "not legally required". Robin Cook later stated in Parliament and that the war was legal. Interestingly, Blair did not. This article does not look at whether or not such an exchange took place; rather look at the ethical issues that such a situation would generate. The article suggests what the ethical obligations of the key legal players in such institutional dramas should be—including governments seeking advice, the lawyers giving it, the ministers reporting it and the opposition in Parliament. The article sets out the particular responsibilities of the lawyers and officials of a Westminster system. It also sets out some of the institutional mechanisms for making it more likely that those obligations are fulfilled—as always through the interaction of obligations by different players that make it more risky for any player to breach his or her ethical obligations. Analogous duties would be faced by the relevant actors in other systems.

Cultural selection and its influence on perceptions of reputation within organisations

The capacity to identify, interpret, and prioritise environmental issues is critical in the management of corporate reputation. In spite of the significance of these abilities for corporate reputation management, there has been little effort to document and describe internal organizational influences on these capacities. Contrary to this state of affairs in the discipline of public relations, a long history of ethnographic research in cultural anthropology documents how sets of shared environmental perceptions can influence and moderate environmental factors in cultural populations (see for example, Durham, 1991 ). This study explores how cultural “frames of reference” derived from shared values and assumptions among organizational members influence organizational perceptions, and consequently, organizational actions. Specifically, this study explores how a central attribute of organizational culture--the property of cultural selection-- influences perceptions of organizational reputation held by organizational members. Perceptions of reputation among organizational members are obvious drivers to both the nature of and rationale for organizational communication strategies and responses. These perceptions are the result of collective processes that synthesise (with varying degrees of consensus) member conceptualisations, interpretations, and representations of the environmental realities in which their organization operate. To explore how cultural selection influences member perceptions of organizational reputation, this study employs ethnographic research including 20 depth interviews and six months of organizational observation in the focal organization. We argue that while external indicators of organizational reputation are acknowledged by members as significant, the internal action of cultural selection is a far stronger influence on organizational action.

Physical aspects

As teachers, we must know about the physical developmental processes our students are experiencing. These are reflected in behaviour, emotions and relationships. And for adolescents, who are trying hard to figure out how the world operates, the physical changes they experience have a potent impact on their world view. While the sequencing of much of our physical development is pretty well according to a grand template and rolls out in much the same way from one person to the next, not everything occurs in a set way (Richter, 2006). Some aspects of our physical development cause other things to occur and are tied together. For example, hormonal changes during puberty are tied to the development of secondary sexual characteristics. However, there is individual variation at multiple levels, and we will discuss these. To complicate things, adolescents’ feelings and ideas about themselves and the ways in which they interact with the world as they grow and change are coloured by our societies’ multifaceted sets of ideals, standards and expectations for physical development. Many other things also impact on our conceptions of self and these will be discussed when we turn our attention to the development of identity through adolescence. In this chapter we will present some basic information about the types of physical changes to expect during adolescence, and consider some challenges that confront adolescents during this time of development.