First Published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.

We study connections between classical asymptotic density, computability and computable enumerability. In an earlier paper, the second two authors proved that there is a computably enumerable set A of density 1 with no computable subset of density 1. In the current paper, we extend this result in three different ways: The degrees of such sets A are precisely the nonlow c.e. degrees. There is a c.e. set A of density 1 with no computable subset of nonzero density. There is a (...) c.e. set A of density 1 such that every subset of A of density 1 is of high degree. We also study the extent to which c.e. sets A can be approximated by their computable subsets B in the sense that A\B has small density. There is a very close connection between the computational complexity of a set and the arithmetical complexity of its density and we characterize the lower densities, upper densities and densities of both computable and computably enumerable sets. We also study the notion of "computable at density r" where r is a real in the unit interval. Finally, we study connections between density and classical smallness notions such as immunity, hyperimmunity, and cohesiveness. (shrink)

We characterize the class of c.e. degrees that bound a critical triple as those degrees that compute a function that has no ω-c.e. approximation.

We prove that there exists a noncomputable c.e. real which is low for weak 2-randomness, a definition of randomness due to Kurtz, and that all reals which are low for weak 2-randomness are low for Martin-Löf randomness.

Schnorr randomness is a notion of algorithmic randomness for real numbers closely related to Martin-Löf randomness. After its initial development in the 1970s the notion received considerably less attention than Martin-Löf randomness, but recently interest has increased in a range of randomness concepts. In this article, we explore the properties of Schnorr random reals, and in particular the c.e. Schnorr random reals. We show that there are c.e. reals that are Schnorr random but not Martin-Löf random, and provide a new (...) characterization of Schnorr random real numbers in terms of prefix-free machines. We prove that unlike Martin-Löf random c.e. reals, not all Schnorr random c.e. reals are Turing complete, though all are in high Turing degrees. We use the machine characterization to define a notion of "Schnorr reducibility" which allows us to calibrate the Schnorr complexity of reals. We define the class of "Schnorr trivial" reals, which are ones whose initial segment complexity is identical with the computable reals, and demonstrate that this class has non-computable members. (shrink)

Late in 1990, the Center for the Study of Ethics in the Professions at Illinois Institute of Technology (lIT) received a grant of more than $200,000 from the National Science Foundation to try a campus-wide approach to integrating professional ethics into its technical curriculum.! Enough has now been accomplished to draw some tentative conclusions. I am the grant's principal investigator. In this paper, I shall describe what we at lIT did, what we learned, and what others, especially philosophers, can learn (...) from us. We set out to develop an approach that others could profitably adopt. I believe that we succeeded. (shrink)

Government-sponsored school lunch programs have garnered attention from activists and policymakers for their potential to promote public health, sustainable diets, and food sovereignty. However, across country contexts, these programs often fall far short of their transformative potential. It is vital, then, to identify policies and organizing strategies that enable school lunch programs to be redesigned at the national scale. In this article, we use document analysis of historical newspapers and government data to examine the motivating factors and underlying conditions that (...) allowed South Korea’s universal free, eco-friendly school lunch program to become a tool for advancing social justice and ecological goals at the national scale. We analyze the socio-historical evolution and current status of the Korean school lunch program, combining the multi-level perspective with insights from environmental sociology and critical food studies, in order to shed light on the factors that enabled the program to become an innovative niche and articulate the opportunities and challenges it now faces. We identify the state-sponsored creation of what we call “precautionary infrastructure” as a key anchoring mechanism between the school food niche and agri-food regime. Precautionary infrastructure includes new supply chains, certification standards, and sourcing policies that provide a stable market for eco-friendly farms and small-scale producers, while minimizing the environmental health risks of school lunch by delivering organic and pesticide-free ingredients to on-site kitchens that serve free lunches to all students. This analysis offers insight into how public school-lunch programs can become protected niches that help drive sustainability transitions within agri-food systems. (shrink)

During the past few years significant progress has been made in our understanding of the structure and function of the proteins involved in eukaryotic DNA replication. Data from several laboratories suggest that, in contrast to prokaryotic DNA replication, two distinct DNA polymerases are required for eukaryotic DNA replication, i.e. DNA polymerase delta for the synthesis of the leading strand and DNA polymerase alpha for the lagging strand. Several accessory proteins analogous to prokaryotic replication factors have been identified and some of (...) these are specific for pol delta whereas others affect both DNA replicases. The replicases and their accessory proteins appear to be highly conserved in eukaryotes, as homologous proteins have been found in species ranging from humans to yeast. (shrink)