Perturbative sigma models, elliptic cohomology and the Witten genus

We provide a differential cocycle model for elliptic cohomology with complex coefficients and use analytic methods to construct a cocycle representative for the Witten class in this language. Our motivation stems from the conjectural connection between 2-dimensional field theories and elliptic cohomology originally due to G. Segal and E. Witten. The specifics of our constructions are informed by the work of S. Stolz and P. Teichner on super Euclidean field theories and K. Costello's construction of the Witten genus using perturbative quantization. As a warm-up, we prove analogous results for supersymmetric quantum mechanics and K-theory with complex coefficients.Comment: Changes made from referees suggestions: statements of main theorems were sharpened, physical motivations were separated from the main mathematical discussion, and the relation to Witten's original construction was clarifie

Smooth one-dimensional topological field theories are vector bundles with connection

We prove that smooth 1-dimensional topological field theories over a manifold are the same as vector bundles with connection. The main novelty is our definition of the smooth 1-dimensional bordism category, which encodes cutting laws rather than gluing laws. We make this idea precise through a smooth generalization of Rezk's complete Segal spaces. With such a definition in hand, we analyze the category of field theories using a combination of descent, a smooth version of the 1-dimensional cobordism hypothesis, and standard differential geometric arguments.Comment: 20 pages. Comments and questions are very welcom

A Note on Zipf's Law, Natural Languages, and Noncoding DNA regions

In Phys. Rev. Letters (73:2, 5 Dec. 94), Mantegna et al. conclude on the basis of Zipf rank frequency data that noncoding DNA sequence regions are more like natural languages than coding regions. We argue on the contrary that an empirical fit to Zipf's ``law'' cannot be used as a criterion for similarity to natural languages. Although DNA is a presumably an ``organized system of signs'' in Mandelbrot's (1961) sense, an observation of statistical features of the sort presented in the Mantegna et al. paper does not shed light on the similarity between DNA's ``grammar'' and natural language grammars, just as the observation of exact Zipf-like behavior cannot distinguish between the underlying processes of tossing an $M$ sided die or a finite-state branching process.Comment: compressed uuencoded postscript file: 14 page

A workbook of exercises to stimulate interest in reading, to enrich the concepts, and to provide practice in the reading skills--grade five interest level--grade two vocabulary level

Thesis (Ed.M.)--Boston University, 1950. N.B.:Pages missing : 171, 178, 179. Only one copy was available

How do we increase public understanding of the benefits provided by SUDS?

Background to researchRecent Scottish Government policy is to develop Scotland as the world’s first Hydro Nation which places more emphasis on water as central to our national identity. This agenda isincreasing the international profile of Scotland’s skills and experience in supporting the good stewardship of water resources. There is a need to increase awareness among thepublic of the benefits that water provides and how our actions can help protect and improve them. Successful legislative and policy reform have been responsible for sustainable urbandrainage systems (SUDS) becoming commonplace in Scotland. There is a deficit of understanding surrounding the multiple benefits which SUDS can offer communities such as pollutioncontrol, flood prevention, enhancement of biodiversity and wildlife habitats. Conveying an understanding of benefits to those who live within close proximity to SUDS can help lendacceptance to these innovative green technologies that are replacing traditional forms of drainage.Objectives of researchKey CREW objectives are to develop a hydro literacy programme that:(a) increases public understanding of the benefits water provides and issues involved in its management(b) increase science engagement through community outreach/public education(c) support Scottish water policy.This project was a public outreach activity that targeted primary and secondary school children located to the north of Dundee where there are excellent examples of SUDS. The key objective was to raise awareness of the Hydro Nation agenda with a scope that was twofold: explain the urban water cycle; and promote awareness and understanding of the local SUDS and related benefits. To realise these objectives we had to ensure alignment of the science, environmental, engineering and social aspects related to SUDS with the curriculum forexcellence and which contributed to general science experiences and outcomes.Key findings and recommendationsDissemination of the Hydro Nation Agenda and the benefits of SUDS were delivered to a total of 106 children (ages 3-10) and 14 adults. Based on feedback, the outreach programmeto schools was deemed an unquestionable success by the Local Authority, teachers and school children alike. This was due to a strategic approach taken for the development anddelivery of a ‘water and SUDS’ learning package that included a variety of mechanisms and activities to fit the time available and suit the knowledge level of the target audiences. Thisfacilitated engagement, enthusiasm, knowledge retention and empowerment – learning whilst also having fun. Evaluation of feedback, and with hindsight, recommendations for improvingfuture outreach initiatives to school children and local community groups include:• Timing is crucial to ensure alignment with the curriculum, particularly secondary schools.• Hands on sessions including experiments and digital technology related to local real world issues combined with local walks were powerful strategies that provided a direct and personal connection that engaged, promoted and embedded learning concepts and new terminology.• Future roll out of the initiative would be beneficial to integrate the SUDS learning package materials with current lesson plans; specifically delivery of a practical legacy teaching asset that could be up scaled/rolled out across Scotland.• The Community Group session was put together quickly with limited time. This was beneficial for the Group regarding imminent dialogue with Dundee City Council planners however a more organised session and discussion would have enhanced understanding of current best practice SUDS.<br/