Multivalued Functions in Digital Topology

We study several types of multivalued functions in digital topology

Evaluating platform architectures within ecosystems: modeling the relation to indirect value

This thesis establishes a framework for understanding the role of a supplier within the context of a business ecosystem. Suppliers typically define their business in terms of capturing value by meeting the demands of direct customers. However, the framework recognises the importance of understanding how a supplier captures indirect value by meeting the demands of indirect customers. These indirect customers increasingly use a supplier’s products and services over time in combination with those of other suppliers. This type of indirect demand is difficult for the supplier to anticipate because it is asymmetric to their own definition of demand. Customers pay the costs of aligning products and services to their particular needs by expending time and effort, for example, to link disparate social technologies or to coordinate healthcare services to address their particular condition. The accelerating tempo of variation in individual needs increases the costs of aligning products and services for customers. A supplier’s ability to reduce its indirect customers’ costs of alignment represents an opportunity to capture indirect value. The hypothesis is that modelling the supplier's relationship to indirect demands improves the supplier’s ability to identify opportunities for capturing indirect value. The framework supports the construction and analysis of such models. It enables the description of the distinct forms of competitive advantage that satisfy a given variety of indirect demands, and of the agility of business platforms supporting that variety of indirect demands. Models constructed using this framework are ‘triply-articulated’ in that they articulate the relationships among three sub-models: (i) the technical behaviours generating products and services, (ii) the social entities managing their supply, and (iii) the organisation of value defined by indirect customers’ demands. The framework enables the derivation from such a model of a layered analysis of the risks to which the capture of indirect value exposes the supplier, and provides the basis for an economic valuation of the agility of the supporting platform architectures. The interdisciplinary research underlying the thesis is based on the use of tools and methods developed by the author in support of his consulting practice within large and complex organisations. The hypothesis is tested by an implementation of the modeling approach applied to suppliers within their ecosystems in three cases: (a) UK Unmanned Airborne Systems, (b) NATO Airborne Warning and Control Systems, both within their respective theatres of operation, and (c) Orthotics Services within the UK's National Health Service. These cases use this implementation of the modeling approach to analyse the value of platforms, their architectural design choices, and the risks suppliers face in their use. The thesis has implications for the forms of leadership involved in managing such platform-based strategies, and for the economic impact such strategies can have on their larger ecosystem. It informs the design of suppliers’ platforms as system-of-system infrastructures supporting collaborations within larger ecosystems. And the ‘triple-articulation’ of the modelling approach makes new demands on the mathematics of systems modeling

Alternate product adjacencies in digital topology

[EN] We study properties of Cartesian products of digital images, using a variety of adjacencies that have appeared in the literature.Boxer, L. (2018). Alternate product adjacencies in digital topology. Applied General Topology. 19(1):21-53. doi:10.4995/agt.2018.7146SWORD215319

Abelian Surfaces over totally real fields are Potentially Modular

We show that abelian surfaces (and consequently curves of genus 2) over totally real fields are potentially modular. As a consequence, we obtain the expected meromorphic continuation and functional equations of their Hasse--Weil zeta functions. We furthermore show the modularity of infinitely many abelian surfaces A over Q with End_C(A)=Z. We also deduce modularity and potential modularity results for genus one curves over (not necessarily CM) quadratic extensions of totally real fields.Comment: 285 page

Discourses of change ownership in higher education

PURPOSE - This paper demonstrates how the positioning of self and others affects change in higher education. DESIGN/METHODOLOGY/APPROACH - The discourse of various educators was collected during various interviews and discussion groups. A positioning theory framework was used to analyse the data and derive conclusions. FINDINGS - It is shown that if individuals are understood in terms of their agendas in relation to the organisational context that they can be better led. RESEARCH LIMITATIONS/IMPLICATIONS - The quantity and quality of data available has limited the integrity of conclusions drawn from this paper. Further research is proposed that will provide a more robust understanding. PRACTICAL IMPLICATIONS - An approach to understand how to deal with various stakeholders is presented for leaders. There is a need to deal with each person as an individual depending on how their personal agendas influence their priorities. ORIGINALITY/VALUE - This paper introduces a social constructionist perspective to leading academics

Using positioning theory to understand how senior managers deal with sustainability

Social pressure for sustainability has become a significant factor in Australian business. Made popular by a variety of diverse social movements that employ various tactics, sustainability is increasingly being debated in boardrooms and work areas of both large and small businesses. In this research, sustainability issues are treated as a set of a wider range of obligatory and externally imposed (OEI) issues that are increasingly confronting contemporary business. Of interest to this research is how senior managers deal with sustainability issues. While some businesses excel in dealing with OEI issues, others prevaricate. This research focuses on those businesses that appear to excel in resolving sustainability issues to explore how senior managers deal with sustainability issues. Such understanding is essential for contemporary practising senior managers, as it provides guidance for management behaviour that will enable sustainability and other OEI issues to be dealt with. The author's effort to understand how senior managers deal with sustainability issues has led to the first business context application of Harré's positioning theory. A social constructionist approach, positioning theory is concerned with ordinary conversations, and presumes that these are the building blocks of all other discursive phenomena. The resulting theory builds on positioning theory and provides a point of departure to conduct related research on other organizations that excel in dealing with OEI issues and those that prevaricate. With positioning theory it has been shown that, in dealing with sustainability issues, senior managers engage in a range of positioning of themselves and others. In doing so, power and knowledge have been considered in the light of Foucault's unique and penetrating concepts. This has led to the proposed augmentation of positioning theory to include a concept of social flux, which is put forward as an indication of social order or culture. Through this development, it has shown how senior managers confront opposition and reinforce support to enable them to achieve and preserve sustainability objectives. In practical terms, senior managers alter four components of the social order to align the culture with the issues that need to be dealt with. These components - rights, duties, morals and actions - are parameters that senior managers tune or level when they deal with sustainability issues. When the social order is appropriately tuned or levelled, it is aligned with the issues that need to be dealt with. That alignment enables issues to be resolved in a way appropriate for the organization