Theory of mind and relational complexity

Cognitive complexity and control theory and relational complexity theory attribute developmental changes in theory of mind (TOM) to complexity. In 3 studies, 3-, 4-, and 5-year-olds performed TOM tasks (false belief, appearance-reality), less complex connections (Level 1 perspective-taking) tasks, and transformations tasks (understanding the effects of location changes and colored filters) with content similar to TOM. There were also predictor tasks at binary-relational and ternary-relational complexity levels, with different content. Consistent with complexity theories: (a) connections and transformations were easier and mastered earlier than TOM; (b) predictor tasks accounted for more than 80% of age-related variance in TOM; and (c) ternary-relational items accounted for TOM variance, before and after controlling for age and binary-relational items. Prediction did not require hierarchically structured predictor tasks.

Young children's performance on the balance scale: The influence of relational complexity

Three experiments investigated the effect of complexity on children's understanding of a beam balance. In nonconflict problems, weights or distances varied, while the other was held constant. In conflict items, both weight and distance varied, and items were of three kinds: weight dominant, distance dominant, or balance (in which neither was dominant). In Experiment 1, 2-year-old children succeeded on nonconflict-weight and nonconflict-distance problems. This result was replicated in Experiment 2, but performance on conflict items did not exceed chance. In Experiment 3, 3- and 4-year-olds succeeded on all except conflict balance problems, while 5- and 6-year-olds succeeded on all problem types. The results were interpreted in terms of relational complexity theory. Children aged 2 to 4 years succeeded on problems that entailed binary relations, but 5- and 6-year-olds also succeeded on problems that entailed ternary relations. Ternary relations tasks from other domains-transitivity and class inclusion-accounted for 93% of the age-related variance in balance scale scores. (C) 2002 Elsevier Science (USA).

The future role of government in knowledge-based economies

In this article, we draw together aspects of contemporary theories of knowledge (particularly organisational knowledge) and complexity theory to demonstrate how appropriate conceptual rigor enables both the role of government and the directions of policy development in knowledge-based economies to be identified. Specifically we ask, what is the role of government in helping shape the knowledge society of the future? We argue that knowledge policy regimes must go beyond the modes of policy analysis currently used in innovation, information and technology policy because they are based in an industrial rather than post-industrial analytical framework. We also argue that if we are to develop knowledge-based economies, more encompassing images of the future than currently obtain in policy discourse are required. We therefore seek to stimulate and provoke an array of lines of thought about government and policy for such economies. Our objective is to focus on ideas more than argument and persuasion.

Phenomenological turbulence and innovation in knowledge systems

Most considerations of knowledge management focus on corporations and, until recently, considered knowledge to be objective, stable, and asocial. In this paper we wish to move the focus away from corporations, and examine knowledge and national innovation systems. We argue that the knowledge systems in which innovation takes place are phenomenologically turbulent, a state not made explicit in the change, innovation and socio-economic studies of knowledge literature, and that this omission poses a serious limitation to the successful analysis of innovation and knowledge systems. To address this lack we suggest that three evolutionary processes must be considered: self-referencing, self-transformation and self-organisation. These processes, acting simultaneously, enable system cohesion, radical innovation and adaptation. More specifically, we argue that in knowledge-based economies the high levels of phenomenological turbulence drives these processes. Finally, we spell out important policy principles that derive from these processes.

Theory of modulational instability in Bragg gratings with quadratic nonlinearity

Modulational instability in optical Bragg gratings with a quadratic nonlinearity is studied. The electric field in such structures consists of forward and backward propagating components at the fundamental frequency and its second harmonic. Analytic continuous wave (CW) solutions are obtained, and the intricate complexity of their stability, due to the large number of equations and number of free parameters, is revealed. The stability boundaries are rich in structures and often cannot be described by a simple relationship. In most cases, the CW solutions are unstable. However, stable regions are found in the nonlinear Schrodinger equation limit, and also when the grating strength for the second harmonic is stronger than that of the first harmonic. Stable CW solutions usually require a low intensity. The analysis is confirmed by directly simulating the governing equations. The stable regions found have possible applications in second-harmonic generation and dark solitons, while the unstable regions maybe useful in the generation of ultrafast pulse trains at relatively low intensities. [S1063-651X(99)03005-6].

Lower Bounds on the State Complexity of Geometric Goppa Codes

We reinterpret the state space dimension equations for geometric Goppa codes. An easy consequence is that if deg G less than or equal to n-2/2 or deg G greater than or equal to n-2/2 + 2g then the state complexity of C-L(D, G) is equal to the Wolf bound. For deg G is an element of [n-1/2, n-3/2 + 2g], we use Clifford's theorem to give a simple lower bound on the state complexity of C-L(D, G). We then derive two further lower bounds on the state space dimensions of C-L(D, G) in terms of the gonality sequence of F/F-q. (The gonality sequence is known for many of the function fields of interest for defining geometric Goppa codes.) One of the gonality bounds uses previous results on the generalised weight hierarchy of C-L(D, G) and one follows in a straightforward way from first principles; often they are equal. For Hermitian codes both gonality bounds are equal to the DLP lower bound on state space dimensions. We conclude by using these results to calculate the DLP lower bound on state complexity for Hermitian codes.

A cognitive complexity metric applied to cognitive development

Two experiments tested predictions from a theory in which processing load depends on relational complexity (RC), the number of variables related in a single decision. Tasks from six domains (transitivity, hierarchical classification, class inclusion, cardinality, relative-clause sentence comprehension, and hypothesis testing) were administered to children aged 3-8 years. Complexity analyses indicated that the domains entailed ternary relations (three variables). Simpler binary-relation (two variables) items were included for each domain. Thus RC was manipulated with other factors tightly controlled. Results indicated that (i) ternary-relation items were more difficult than comparable binary-relation items, (ii) the RC manipulation was sensitive to age-related changes, (iii) ternary relations were processed at a median age of 5 years, (iv) cross-task correlations were positive, with all tasks loading on a single factor (RC), (v) RC factor scores accounted for 80% (88%) of age-related variance in fluid intelligence (compositionality of sets), (vi) binary- and ternary-relation items formed separate complexity classes, and (vii) the RC approach to defining cognitive complexity is applicable to different content domains. (C) 2002 Elsevier Science (USA). All rights reserved.

Ex ante evaluations of alternate data structures for end user queries: Theory and experimental test

The data structure of an information system can significantly impact the ability of end users to efficiently and effectively retrieve the information they need. This research develops a methodology for evaluating, ex ante, the relative desirability of alternative data structures for end user queries. This research theorizes that the data structure that yields the lowest weighted average complexity for a representative sample of information requests is the most desirable data structure for end user queries. The theory was tested in an experiment that compared queries from two different relational database schemas. As theorized, end users querying the data structure associated with the less complex queries performed better Complexity was measured using three different Halstead metrics. Each of the three metrics provided excellent predictions of end user performance. This research supplies strong evidence that organizations can use complexity metrics to evaluate, ex ante, the desirability of alternate data structures. Organizations can use these evaluations to enhance the efficient and effective retrieval of information by creating data structures that minimize end user query complexity.

Selecting optimal instantiations of data models - Theory and validation of an ex ante approach

The schema of an information system can significantly impact the ability of end users to efficiently and effectively retrieve the information they need. Obtaining quickly the appropriate data increases the likelihood that an organization will make good decisions and respond adeptly to challenges. This research presents and validates a methodology for evaluating, ex ante, the relative desirability of alternative instantiations of a model of data. In contrast to prior research, each instantiation is based on a different formal theory. This research theorizes that the instantiation that yields the lowest weighted average query complexity for a representative sample of information requests is the most desirable instantiation for end-user queries. The theory was validated by an experiment that compared end-user performance using an instantiation of a data structure based on the relational model of data with performance using the corresponding instantiation of the data structure based on the object-relational model of data. Complexity was measured using three different Halstead metrics: program length, difficulty, and effort. For a representative sample of queries, the average complexity using each instantiation was calculated. As theorized, end users querying the instantiation with the lower average complexity made fewer semantic errors, i.e., were more effective at composing queries. (c) 2005 Elsevier B.V. All rights reserved.