Measure Theory in Noncommutative Spaces

The integral in noncommutative geometry (NCG) involves a non-standard trace called a Dixmier trace. The geometric origins of this integral are well known. From a measure-theoretic view, however, the formulation contains several difficulties. We review results concerning the technical features of the integral in NCG and some outstanding problems in this area. The review is aimed for the general user of NCG

Annotated Type Systems for Program Analysis

In this Ph.D. thesis, we study four program analyses. Three of them are specified by annotated type systems and the last one by abstract interpretation.We present a combined strictness and totality analysis. We are specifying the analysis as an annotated type system. The type system allows conjunctions of annotated types, but only at the top-level. The analysis is somewhat more powerful than the strictness analysis by Kuo and Mishra due to the conjunctions and in that we also consider totality. The analysis is shown sound with respect to a natural-style operational semantics. The analysis is not immediately extendable to full conjunction.The second analysis is also a combined strictness and totality analysis, however with ``full´´ conjunction. Soundness of the analysis is shown with respect to a denotational semantics. The analysis is more powerful than the strictness analyses by Jensen and Benton in that it in addition to strictness considers totality. So far we have only specified the analyses, however in order for the analyses to be practically useful we need an algorithm for inferring the annotated types. We construct an algorithm for the second analysis using the lazy type approach by Hankin and Le Métayer. The reason for choosing the second analysis from the thesis is that the approach is not applicable to the first analysis.The third analysis we study is a binding time analysis. We take the analysis specified by Nielson and Nielson and we construct a more efficient algorithm than the one proposed by Nielson and Nielson. The algorithm collects constraints in a structural manner like the type inference algorithm by Damas. Afterwards the minimal solution to the set of constraints is found.The last analysis in the thesis is specified by abstract interpretation. Hunt shows that projection based analyses are subsumed by PER (partial equivalence relation) based analyses using abstract interpretation. The PERs used by Hunt are strict, i.e. bottom is related to bottom. Here we lift this restriction by requiring the PERs to be uniform, in the sense that they treat all the integers equally. By allowing non-strict PERs we get three properties on the integers, corresponding to the three annotations used in the first and second analysis in the thesis

Felony Disenfranchisement Legislation: A Test of the Group Threat Hypothesis

The group threat hypothesis is part of the conflict theoretical perspective, which has been one of the most dominant and useful theories in the fields of criminology and criminal justice for decades. The usefulness of this perspective relates to the understanding it provides of how the law can be used by those in power as a measure of control. The use of law as a method of control has a long history in the US society, and there are many examples from which to pull. This project examines the use of one set of laws, felony disenfranchisement legislation, to determine if these laws can be seen as a method for controlling a subgroup of the population. Historically, felony disenfranchisement legislation has been a part of the American legal system from the founding of this country. While the laws have changed many times, the constant has been an effort to disenfranchise a segment of the population deemed as dangerous and prevent such groups from participating in the political process through their votes. Using data on African American population, arrests, and incarceration, this study tests if the strictness of disenfranchisement legislation is associated with the size of African American population, as well as African American arrest and incarceration rates. Both qualitative and quantitative methods were used to understand the nature of felony disenfranchisement legislation and to determine if disenfranchisement legislation could be used as a tool to control African Americans. The qualitative analysis indicates that African Americans are more impacted by disenfranchisement laws in two regards: the criteria that leads to disenfranchisement and the requirements for vote restoration. However, the research hypotheses are partially supported by quantitative analysis. That is, while results indicate that the proportion of African Americans in a state is correlated to the strictness of a state’s disenfranchisement law, there is no relationship between the arrest and incarceration rates and either the strictness of disenfranchisement legislation or the difficulty of the vote restoration procedures. These results point to limitations of using the group threat hypothesis to understand the relationship between disenfranchisement law and criminal justice operation

On non-recursive trade-offs between finite-turn pushdown automata

It is shown that between one-turn pushdown automata (1-turn PDAs) and deterministic finite automata (DFAs) there will be savings concerning the size of description not bounded by any recursive function, so-called non-recursive tradeoffs. Considering the number of turns of the stack height as a consumable resource of PDAs, we can show the existence of non-recursive trade-offs between PDAs performing k+ 1 turns and k turns for k >= 1. Furthermore, non-recursive trade-offs are shown between arbitrary PDAs and PDAs which perform only a finite number of turns. Finally, several decidability questions are shown to be undecidable and not semidecidable