Probabilistic Recursion Theory and Implicit Computational Complexity

In this thesis we provide a characterization of probabilistic computation in itself, from a recursion-theoretical perspective, without reducing it to deterministic computation. More specifically, we show that probabilistic computable functions, i.e., those functions which are computed by Probabilistic Turing Machines (PTM), can be characterized by a natural generalization of Kleene's partial recursive functions which includes, among initial functions, one that returns identity or successor with probability 1/2. We then prove the equi-expressivity of the obtained algebra and the class of functions computed by PTMs. In the the second part of the thesis we investigate the relations existing between our recursion-theoretical framework and sub-recursive classes, in the spirit of Implicit Computational Complexity. More precisely, endowing predicative recurrence with a random base function is proved to lead to a characterization of polynomial-time computable probabilistic functions.

Caveat Fractal: Dissecting the Body of Indexing Theory, Uncovering Complexity, and Moving Toward Performativity

Research poster about indexing theory

How environmental and organizational complexity affects opportunity recognition in development projects

New product development projects are experiencing increasing internal and external project complexity. Complexity leadership theory proposes that external complexity requires adaptive and enabling leadership, which facilitates opportunity recognition (OR). We ask whether internal complexity also requires OR for increased adaptability. We extend a model of EO and OR to conclude that internal complexity may require more careful OR. This means that leaders of technically or structurally complex projects need to evaluate opportunities more carefully than those in projects with external or technological complexity.

A model of project complexity : distinguishing dimensions of complexity from severity

There is increasing agreement that understanding complexity is important for project management because of difficulties associated with decision-making and goal attainment which appear to stem from complexity. However the current operational definitions of complex projects, based upon size and budget, have been challenged and questions have been raised about how complexity can be measured in a robust manner that takes account of structural, dynamic and interaction elements. Thematic analysis of data from 25 in-depth interviews of project managers involved with complex projects, together with an exploration of the literature reveals a wide range of factors that may contribute to project complexity. We argue that these factors contributing to project complexity may define in terms of dimensions, or source characteristics, which are in turn subject to a range of severity factors. In addition to investigating definitions and models of complexity from the literature and in the field, this study also explores the problematic issues of ‘measuring’ or assessing complexity. A research agenda is proposed to further the investigation of phenomena reported in this initial study.

How environmental and organizational complexity affects opportunity recognition and exploitation in development projects

Principal Topic: Project structures are often created by entrepreneurs and large corporate organizations to develop new products. Since new product development projects (NPDP) are more often situated within a larger organization, intrapreneurship or corporate entrepreneurship plays an important role in bringing these projects to fruition. Since NPDP often involves the development of a new product using immature technology, we describe development of an immature technology. The Joint Strike Fighter (JSF) F-35 aircraft is being developed by the U.S. Department of Defense and eight allied nations. In 2001 Lockheed Martin won a $19 billion contract to develop an affordable, stealthy and supersonic all-weather strike fighter designed to replace a wide range of aging fighter aircraft. In this research we define a complex project as one that demonstrates a number of sources of uncertainty to a degree, or level of severity, that makes it extremely difficult to predict project outcomes, to control or manage project (Remington & Zolin, Forthcoming). Project complexity has been conceptualized by Remington and Pollock (2007) in terms of four major sources of complexity; temporal, directional, structural and technological complexity (See Figure 1). Temporal complexity exists when projects experience significant environmental change outside the direct influence or control of the project. The Global Economic Crisis of 2008 - 2009 is a good example of the type of environmental change that can make a project complex as, for example in the JSF project, where project managers attempt to respond to changes in interest rates, international currency exchange rates and commodity prices etc. Directional complexity exists in a project where stakeholders' goals are unclear or undefined, where progress is hindered by unknown political agendas, or where stakeholders disagree or misunderstand project goals. In the JSF project all the services and all non countries have to agree to the specifications of the three variants of the aircraft; Conventional Take Off and Landing (CTOL), Short Take Off/Vertical Landing (STOVL) and the Carrier Variant (CV). Because the Navy requires a plane that can take off and land on an aircraft carrier, that required a special variant of the aircraft design, adding complexity to the project. Technical complexity occurs in a project using technology that is immature or where design characteristics are unknown or untried. Developing a plane that can take off on a very short runway and land vertically created may highly interdependent technological challenges to correctly locate, direct and balance the lift fans, modulate the airflow and provide equivalent amount of thrust from the downward vectored rear exhaust to lift the aircraft and at the same time control engine temperatures. These technological challenges make costing and scheduling equally challenging. Structural complexity in a project comes from the sheer numbers of elements such as the number of people, teams or organizations involved, ambiguity regarding the elements, and the massive degree of interconnectedness between them. While Lockheed Martin is the prime contractor, they are assisted in major aspects of the JSF development by Northrop Grumman, BAE Systems, Pratt & Whitney and GE/Rolls-Royce Fighter Engineer Team and innumerable subcontractors. In addition to identifying opportunities to achieve project goals, complex projects also need to identify and exploit opportunities to increase agility in response to changing stakeholder demands or to reduce project risks. Complexity Leadership Theory contends that in complex environments adaptive and enabling leadership are needed (Uhl-Bien, Marion and McKelvey, 2007). Adaptive leadership facilitates creativity, learning and adaptability, while enabling leadership handles the conflicts that inevitably arise between adaptive leadership and traditional administrative leadership (Uhl-Bien and Marion, 2007). Hence, adaptive leadership involves the recognition and opportunities to adapt, while and enabling leadership involves the exploitation of these opportunities. Our research questions revolve around the type or source of complexity and its relationship to opportunity recognition and exploitation. For example, is it only external environmental complexity that creates the need for the entrepreneurial behaviours, such as opportunity recognition and opportunity exploitation? Do the internal dimensions of project complexity, such as technological and structural complexity, also create the need for opportunity recognition and opportunity exploitation? The Kropp, Zolin and Lindsay model (2009) describes a relationship between entrepreneurial orientation (EO), opportunity recognition (OR), and opportunity exploitation (OX) in complex projects, with environmental and organizational contextual variables as moderators. We extend their model by defining the affects of external complexity and internal complexity on OR and OX. ---------- Methodology/Key Propositions: When the environment complex EO is more likely to result in OR because project members will be actively looking for solutions to problems created by environmental change. But in projects that are technologically or structurally complex project leaders and members may try to make the minimum changes possible to reduce the risk of creating new problems due to delays or schedule changes. In projects with environmental or technological complexity project leaders who encourage the innovativeness dimension of EO will increase OR in complex projects. But projects with technical or structural complexity innovativeness will not necessarily result in the recognition and exploitation of opportunities due to the over-riding importance of maintaining stability in the highly intricate and interconnected project structure. We propose that in projects with environmental complexity creating the need for change and innovation project leaders, who are willing to accept and manage risk, are more likely to identify opportunities to increase project effectiveness and efficiency. In contrast in projects with internal complexity a much higher willingness to accept risk will be necessary to trigger opportunity recognition. In structurally complex projects we predict it will be less likely to find a relationship between risk taking and OP. When the environment is complex, and a project has autonomy, they will be motivated to execute opportunities to improve the project's performance. In contrast, when the project has high internal complexity, they will be more cautious in execution. When a project experiences high competitive aggressiveness and their environment is complex, project leaders will be motivated to execute opportunities to improve the project's performance. In contrast, when the project has high internal complexity, they will be more cautious in execution. This paper reports the first stage of a three year study into the behaviours of managers, leaders and team members of complex projects. We conduct a qualitative study involving a Group Discussion with experienced project leaders. The objective is to determine how leaders of large and potentially complex projects perceive that external and internal complexity will influence the affects of EO on OR. ---------- Results and Implications: These results will help identify and distinguish the impact of external and internal complexity on entrepreneurial behaviours in NPDP. Project managers will be better able to quickly decide how and when to respond to changes in the environment and internal project events.

Managing process model complexity via abstract syntax modifications

As a result of the growing adoption of Business Process Management (BPM) technology different stakeholders need to understand and agree upon the process models that are used to configure BPM systems. However, BPM users have problems dealing with the complexity of such models. Therefore, the challenge is to improve the comprehension of process models. While a substantial amount of literature is devoted to this topic, there is no overview of the various mechanisms that exist to deal with managing complexity in (large) process models. It is thus hard to obtain comparative insight into the degree of support offered for various complexity reducing mechanisms by state-of-the-art languages and tools. This paper focuses on complexity reduction mechanisms that affect the abstract syntax of a process model, i.e. the structure of a process model. These mechanisms are captured as patterns, so that they can be described in their most general form and in a language- and tool-independent manner. The paper concludes with a comparative overview of the degree of support for these patterns offered by state-of-the-art languages and language implementations.

Mind change complexity of learning logic programs

The present paper motivates the study of mind change complexity for learning minimal models of length-bounded logic programs. It establishes ordinal mind change complexity bounds for learnability of these classes both from positive facts and from positive and negative facts. Building on Angluin’s notion of finite thickness and Wright’s work on finite elasticity, Shinohara defined the property of bounded finite thickness to give a sufficient condition for learnability of indexed families of computable languages from positive data. This paper shows that an effective version of Shinohara’s notion of bounded finite thickness gives sufficient conditions for learnability with ordinal mind change bound, both in the context of learnability from positive data and for learnability from complete (both positive and negative) data. Let Omega be a notation for the first limit ordinal. Then, it is shown that if a language defining framework yields a uniformly decidable family of languages and has effective bounded finite thickness, then for each natural number m >0, the class of languages defined by formal systems of length <= m: • is identifiable in the limit from positive data with a mind change bound of Omega (power)m; • is identifiable in the limit from both positive and negative data with an ordinal mind change bound of Omega × m. The above sufficient conditions are employed to give an ordinal mind change bound for learnability of minimal models of various classes of length-bounded Prolog programs, including Shapiro’s linear programs, Arimura and Shinohara’s depth-bounded linearly covering programs, and Krishna Rao’s depth-bounded linearly moded programs. It is also noted that the bound for learning from positive data is tight for the example classes considered.

The sample complexity of pattern classification with neural networks: the size of the weights is more important than the size of the network

Sample complexity results from computational learning theory, when applied to neural network learning for pattern classification problems, suggest that for good generalization performance the number of training examples should grow at least linearly with the number of adjustable parameters in the network. Results in this paper show that if a large neural network is used for a pattern classification problem and the learning algorithm finds a network with small weights that has small squared error on the training patterns, then the generalization performance depends on the size of the weights rather than the number of weights. For example, consider a two-layer feedforward network of sigmoid units, in which the sum of the magnitudes of the weights associated with each unit is bounded by A and the input dimension is n. We show that the misclassification probability is no more than a certain error estimate (that is related to squared error on the training set) plus A3 √((log n)/m) (ignoring log A and log m factors), where m is the number of training patterns. This may explain the generalization performance of neural networks, particularly when the number of training examples is considerably smaller than the number of weights. It also supports heuristics (such as weight decay and early stopping) that attempt to keep the weights small during training. The proof techniques appear to be useful for the analysis of other pattern classifiers: when the input domain is a totally bounded metric space, we use the same approach to give upper bounds on misclassification probability for classifiers with decision boundaries that are far from the training examples.

Complexity, evolution, and the structure of demand

This chapter argues that evolutionary economics should be founded upon complex systems theory rather than neo-Darwinian analogies concerning natural selection, which focus on supply side considerations and competition amongst firms and technologies. It suggests that conceptions such as production and consumption functions should be replaced by network representations, in which the preferences or, more correctly, the aspirations of consumers are fundamental and, as such, the primary drivers of economic growth. Technological innovation is viewed as a process that is intermediate between these aspirational networks, and the organizational networks in which goods and services are produced. Consumer knowledge becomes at least as important as producer knowledge in determining how economic value is generated. It becomes clear that the stability afforded by connective systems of rules is essential for economic flexibility to exist, but that too many rules result in inert and structurally unstable states. In contrast, too few rules result in a more stable state, but at a low level of ordered complexity. Economic evolution from this perspective is explored using random and scale free network representations of complex systems.

Review : alternative splicing (AS) of genes as an approach for generating protein complexity

Prior to the completion of the human genome project, the human genome was thought to have a greater number of genes as it seemed structurally and functionally more complex than other simpler organisms. This along with the belief of “one gene, one protein”, were demonstrated to be incorrect. The inequality in the ratio of gene to protein formation gave rise to the theory of alternative splicing (AS). AS is a mechanism by which one gene gives rise to multiple protein products. Numerous databases and online bioinformatic tools are available for the detection and analysis of AS. Bioinformatics provides an important approach to study mRNA and protein diversity by various tools such as expressed sequence tag (EST) sequences obtained from completely processed mRNA. Microarrays and deep sequencing approaches also aid in the detection of splicing events. Initially it was postulated that AS occurred only in about 5%; of all genes but was later found to be more abundant. Using bioinformatic approaches, the level of AS in human genes was found to be fairly high with 35-59%; of genes having at least one AS form. Our ability to determine and predict AS is important as disorders in splicing patterns may lead to abnormal splice variants resulting in genetic diseases. In addition, the diversity of proteins produced by AS poses a challenge for successful drug discovery and therefore a greater understanding of AS would be beneficial.

Context-resonant systems perspectives in career theory

"The focus of this chapter is on context-resonant systems perspectives in career theory and their implications for practice in diverse cultural and contextual settings. For over two decades, the potential of systems theory to offer a context-resonant approach to career development has been acknowledged. Career development theory and practice, however, have been dominated for most of their history by more narrowly defined theories informed by a trait-and-factor tradition of matching the characteristics of individuals to occupations. In contrast, systems theory challenges this parts-in-isolation approach and offers a response that can accommodate the complexity of both the lives of individuals and the world of the 21st century by taking a more holistic approach that considers individuals in context. These differences in theory and practice may be attributed to the underlying philosophies that inform them. For example, the philosophy informing the trait-and-factor theoretical position, logical positivism, places value on: studying individuals in isolation from their environments; content over process; facts over feelings; objectivity over subjectivity; and views individual behavior as observable, measurable, and linear. In practice, this theory base manifests in expert-driven practices founded on the assessment of personal traits such as interests, personality, values, or beliefs which may be matched to particular occupations. The philosophy informing more recent theoretical positions, constructivism, places value on: studying individuals in their contexts; making meaning of experience through the use of subjective narrative accounts; and a belief in the capacity of individuals known as agency. In practice, this theory base manifests in practices founded on collaborative relationships with clients, narrative approaches, and a reduced emphasis on expert-driven linear processes. Thus, the tenets of constructivism which inform the systems perspectives in career theory are context-resonant. Systems theory stresses holism where the interconnectedness of all elements of a system is considered. Systems may be open or closed. Closed systems have no relationship with their external environment whereas open systems interact with their external environment and are open to external influence which is necessary for regeneration. Congruent with general systems theory, the systems perspectives emerging within career theory are based on open systems. Such systems are complex and dynamic and comprise many elements and subsystems which recursively interact with each other as well as with influences from the surrounding environment. As elements of a system should not be considered in isolation, a systems approach is holistic. Patterns of behavior are found in the relationships between the elements of dynamic systems. Because of the multiplicity of relationships within and between elements of subsystems, the possibility of linear causal explanations is reduced. Story is the mechanism through which the relationships and patterns within systems are recounted by individuals. Thus the career guidance practices emanating from theories informed by systems perspectives are inherently narrative in orientation. Narrative career counseling encourages career development to be understood from the subjective perspective of clients. The application of systemic thinking in practice takes greater account of context. In so doing, practices informed by systems theory may facilitate relevance to a diverse client group in diverse settings. In a world that has become increasingly global and diverse it seems that context-resonant systems perspectives in career theory are essential to ensure the future of career development. Translating context-resonant systems perspectives into practice offers important possibilities for methods and approaches that are respectful of diversity."--publisher website

A contextualised general systems theory

A system is something that can be separated from its surrounds, but this definition leaves much scope for refinement. Starting with the notion of measurement, we explore increasingly contextual system behaviour, and identify three major forms of contextuality that might be exhibited by a system: (a) between components; (b) between system and experimental method, and; (c) between a system and its environment. Quantum Theory is shown to provide a highly useful formalism from which all three forms of contextuality can be analysed, offering numerous tests for contextual behaviour, as well as modelling possibilities for systems that do indeed display it. I conclude with the introduction of a Contextualised General Systems Theory based upon an extension of this formalism.