Stability threshold approach for complex dynamical systems

Acknowledgments This paper was developed within the scope of the IRTG 1740/TRP 2011/50151-0, funded by the DFG/FAPESP, and supported by the Government of the Russian Federation (Agreement No. 14.Z50.31.0033 with the Institute of Applied Physics RAS). The first author thanks Dr Roman Ovsyannikov for valuable discussions regarding estimation of the mistake probability.

Topological structures of complex belief systems

The concepts of substantive beliefs and derived beliefs are defined, a set of substantive beliefs S like open set and the neighborhood of an element substantive belief. A semantic operation of conjunction is defined with a structure of an Abelian group. Mathematical structures exist such as poset beliefs and join-semilattttice beliefs. A metric space of beliefs and the distance of belief depending on the believer are defined. The concepts of closed and opened ball are defined. S′ is defined as subgroup of the metric space of beliefs Σ and S′ is a totally limited set. The term s is defined (substantive belief) in terms of closing of S′. It is deduced that Σ is paracompact due to Stone's Theorem. The pseudometric space of beliefs is defined to show how the metric of the nonbelieving subject has a topological space like a nonmaterial abstract ideal space formed in the mind of the believing subject, fulfilling the conditions of Kuratowski axioms of closure. To establish patterns of materialization of beliefs we are going to consider that these have defined mathematical structures. This will allow us to understand better cultural processes of text, architecture, norms, and education that are forms or the materialization of an ideology. This materialization is the conversion by means of certain mathematical correspondences, of an abstract set whose elements are beliefs or ideas, in an impure set whose elements are material or energetic. Text is a materialization of ideology.

Topological structures of complex belief systems (II): Textual materialization

Mythical and religious belief systems in a social context can be regarded as a conglomeration of sacrosanct rites, which revolve around substantive values that involve an element of faith. Moreover, we can conclude that ideologies, myths and beliefs can all be analyzed in terms of systems within a cultural context. The significance of being able to define ideologies, myths and beliefs as systems is that they can figure in cultural explanations. This, in turn, means that such systems can figure in logic-mathematical analyses.

The prediction and representation of phase equilibria and physicochemical properties in complex slag systems

The development of new experimental techniques for the determination of phase equilibria in complex slag systems, chemical thermodynamic, and viscosity models is reported. The new experimental data, and new thermodynamic and viscosity models, have been combined in a custom-designed computer software package to produce limiting operability diagrams for slag systems. These diagrams are used to describe phase equilibria and physicochemical properties in complex slag systems. The approach is illustrated with calculations on the system FeO-Fe2O3-CaO-SiO-Al2O3 at metallic iron saturation, slags produced in coal slagging gasifiers, and in the reprocessing of nonferrous smelting slags. This article was presented at the Mills Symposium Molten Metals, Slags and Glasses-Characterisation of Properties and Phenomena held in London in August 2000.

Examining the strategy development process through the lens of complex adaptive systems theory

The development of strategy remains a debate for academics and a concern for practitioners. Published research has focused on producing models for strategy development and on studying how strategy is developed in organisations. The Operational Research literature has highlighted the importance of considering complexity within strategic decision making; but little has been done to link strategy development with complexity theories, despite organisations and organisational environments becoming increasingly more complex. We review the dominant streams of strategy development and complexity theories. Our theoretical investigation results in the first conceptual framework which links an established Strategic Operational Research model, the Strategy Development Process model, with complexity via Complex Adaptive Systems theory. We present preliminary findings from the use of this conceptual framework applied to a longitudinal, in-depth case study, to demonstrate the advantages of using this integrated conceptual model. Our research shows that the conceptual model proposed provides rich data and allows for a more holistic examination of the strategy development process. © 2012 Operational Research Society Ltd. All rights reserved.

Strategic development process and complex adaptive systems

The two areas of theory upon which this research was based were „strategy development process?(SDP) and „complex adaptive systems? (CAS), as part of complexity theory, focused on human social organisations. The literature reviewed showed that there is a paucity of empirical work and theory in the overlap of the two areas, providing an opportunity for contributions to knowledge in each area of theory, and for practitioners. An inductive approach was adopted for this research, in an effort to discover new insights to the focus area of study. It was undertaken from within an interpretivist paradigm, and based on a novel conceptual framework. The organisationally intimate nature of the research topic, and the researcher?s circumstances required a research design that was both in-depth and long term. The result was a single, exploratory, case study, which included use of data from 44 in-depth, semi-structured interviews, from 36 people, involving all the top management team members and significant other staff members; observations, rumour and grapevine (ORG) data; and archive data, over a 5½ year period (2005 – 2010). Findings confirm the validity of the conceptual framework, and that complex adaptive systems theory has potential to extend strategy development process theory. It has shown how and why the strategy process developed in the case study organisation by providing deeper insights to the behaviour of the people, their backgrounds, and interactions. Broad predictions of the „latent strategy development? process and some elements of the strategy content are also possible. Based on this research, it is possible to extend the utility of the SDP model by including peoples? behavioural characteristics within the organisation, via complex adaptive systems theory. Further research is recommended to test limits of the application of the conceptual framework and improve its efficacy with more organisations across a variety of sectors.

Classrooms as complex adaptive systems:a relational model

In this article, we describe and model the language classroom as a complex adaptive system (see Logan & Schumann, 2005). We argue that linear, categorical descriptions of classroom processes and interactions do not sufficiently explain the complex nature of classrooms, and cannot account for how classroom change occurs (or does not occur), over time. A relational model of classrooms is proposed which focuses on the relations between different elements (physical, environmental, cognitive, social) in the classroom and on how their interaction is crucial in understanding and describing classroom action.

Large-scale complex IT systems

Society depends on complex IT systems created by integrating and orchestrating independently managed systems. The incredible increase in scale and complexity in them over the past decade means new software-engineering techniques are needed to help us cope with their inherent complexity. The key characteristic of these systems is that they are assembled from other systems that are independently controlled and managed. While there is increasing awareness in the software engineering community of related issues, the most relevant background work comes from systems engineering. The interacting algos that led to the Flash Crash represent an example of a coalition of systems, serving the purposes of their owners and cooperating only because they have to. The owners of the individual systems were competing finance companies that were often mutually hostile. Each system jealously guarded its own information and could change without consulting any other system.