An Overview of Schema Theory

The purpose of this paper is to give an introduction to the field of Schema Theory written by a mathematician and for mathematicians. In particular, we endeavor to to highlight areas of the field which might be of interest to a mathematician, to point out some related open problems, and to suggest some large-scale projects. Schema theory seeks to give a theoretical justification for the efficacy of the field of genetic algorithms, so readers who have studied genetic algorithms stand to gain the most from this paper. However, nothing beyond basic probability theory is assumed of the reader, and for this reason we write in a fairly informal style. Because the mathematics behind the theorems in schema theory is relatively elementary, we focus more on the motivation and philosophy. Many of these results have been proven elsewhere, so this paper is designed to serve a primarily expository role. We attempt to cast known results in a new light, which makes the suggested future directions natural. This involves devoting a substantial amount of time to the history of the field. We hope that this exposition will entice some mathematicians to do research in this area, that it will serve as a road map for researchers new to the field, and that it will help explain how schema theory developed. Furthermore, we hope that the results collected in this document will serve as a useful reference. Finally, as far as the author knows, the questions raised in the final section are new.Comment: 27 pages. Originally written in 2009 and hosted on my website, I've decided to put it on the arXiv as a more permanent home. The paper is primarily expository, so I don't really know where to submit it, but perhaps one day I will find an appropriate journa

The structure of problem-solving knowledge and the structure of organisations

This work presents a model of organisational problem solving able to account for the relationships between problem complexity, tasks decentralilzation and problem solving efficiency. Whenever problem solving requires the coordination of a multiplicity of interdependent elements, the varying degrees of decentralization of cognitive and operational tasks shape the solution which can be generated, tested and selected. Suboptimality and path-dependence are shown to be ubiquitous features of organisational problem solving. At the same time, the model allows a precise exploration of the possible trade-offs between decompostion patterns and search efficiency involved in different organisational architectures.-

Beyond statistical testing: individual differences and the contentand accuracy of mental representations of space

The article uses data from two experiments on the content and accuracy of mentalrepresentations of space by the blind and visually impaired in order expose some of theshortcomings of typical statistical testing and propose an individual differences approach to theanalysis of data. It begins with a discussion of some of the problems associated with the strictclassification and eventual comparison of individuals between groups. The individual differencesapproach is then presented and the concepts of ability and present competence are explored alongwith the importance of detailed participant description. Examples from the two experiments areused to demonstrate how null hypothesis significance testing can be complemented with effect sizeestimates, box-plots and ranking techniques. Throughout the article we are reminded of the need toadopt mutually supportive techniques to account for the heterogeneity of experience and skillsbetween participants. The article uses data from two experiments on the content and accuracy of mentalrepresentations of space by the blind and visually impaired in order expose some of theshortcomings of typical statistical testing and propose an individual differences approach to theanalysis of data. It begins with a discussion of some of the problems associated with the strictclassification and eventual comparison of individuals between groups. The individual differencesapproach is then presented and the concepts of ability and present competence are explored alongwith the importance of detailed participant description. Examples from the two experiments areused to demonstrate how null hypothesis significance testing can be complemented with effect sizeestimates, box-plots and ranking techniques. Throughout the article we are reminded of the need toadopt mutually supportive techniques to account for the heterogeneity of experience and skillsbetween participants

Creating Low-carbon Communities: Evaluating the Role of Individual Agency and Systemic Inequality in San Jose, CA

Following a scholarly need to test compelling community level sociodemographic representations of environmental behaviors and outcomes, a sequential mixed method approach was used to evaluate the connections of human agency and systemic inequalities with carbon footprints. Statistical analyses of the 2016 SDG San Jose Dashboard data of city blocks and 2009 - 2013 ACS survey data were supplemented with interviews with eight climate action-oriented community engagement professionals in the South Bay. Boundary limiting socioeconomic conditions for systemic inequalities and human agency, dimensions of Gidden’s Structuration model, were specified. Partially supporting structural inequality theories, socioeconomic resources, primarily, and to a lesser extent dominant race concentration, were associated with larger carbon footprints, particularly when wealth was concentrated. Both human (time driven alone) and demographic (senior and mid-aged blocks) agencies were also in part at play in shrinking or even enlarging carbon footprints, in wealthier communities. These findings not only contributed to the literature on climate action, but also highlighted the need for targeted interventions in communities of different socioeconomic standing