Conjugacy classes in maximal parabolic subgroups of general linear groups

We compute conjugacy classes in maximal parabolic subgroups of the general linear group. This computation proceeds by reducing to a ``matrix problem''. Such problems involve finding normal forms for matrices under a specified set of row and column operations. We solve the relevant matrix problem in small dimensional cases. This gives us all conjugacy classes in maximal parabolic subgroups over a perfect field when one of the two blocks has dimension less than 6. In particular, this includes every maximal parabolic subgroup of GL_n(k) for n < 12 and k a perfect field. If our field is finite of size q, we also show that the number of conjugacy classes, and so the number of characters, of these groups is a polynomial in $q$ with integral coefficients.Comment: 23 pages, 6 figures. See also http://zaphod.uchicago.edu/~murray/research/index.html . Submitted to Journal of Algebr

The Evolution of E-Inclusion: Technology in Education for the Vision-Impaired

The 1970s and 1980s saw a rapid take-up in the use of personal computers. During the same time period, society began to move towards providing equity for people with disabilities. As legislators around the world created new disability and Information Technology policies, more people with disabilities were given access to education and the evolving computing tools provided unprecedented educational opportunities. These opportunities were due to the use of new technologies such as outputting of electronic text to voice synthesizers. The provision of assistive technology was not only helpful; it also provided education through a medium that was previously unavailable, particular to the blind and vision impaired. For much of the 1980s the development of text-processing sensory technologies, connected to personal computers, led to a closer equality between the educational services of the able-bodied and people with disabilities. Unfortunately this evolution as not without notable difficulties: issues surrounding the cost of products, the lack of support from large corporations and choice of platform resulted in substantial difficulties for educators in the assessment of appropriate technology. In addition, many of these products became largely redundant in the late-1980s as corporations began to place more emphasis on the Graphical User Interface (GUI). Although the GUI was remarkably successful in allowing the general public to gain better access to personal computing, it’s non-text nature once again caused a digital divide for people with disabilities. Although it is clear that the evolution of the personal computer has had a significant impact on the provision of education for people with disabilities, this paper highlights the historical repetition where innovation is prioritized above e-inclusion

An overview of link-level measurement techniques for wide-area wireless networks

By building wireless link-level measurement tools we hope to improvement the design, deployment and management of wide-area wireless community networks. This paper identifies existing link-level measurement techniques and discusses the advantages and disadvantages of each in the context of measuring and monitoring such networks. Finally, we make a case for the need for more sophisticated techniques and tools which will assist both day-to-day network operations as well as wireless network research

Rail Track Maintenance Planning: An Assessment Model

In Australia, railway track maintenance costs comprise between 25-35 percent of total freight train operating costs. Track maintenance planning models have been shown to reduce maintenance costs by 5 to 10 percent though improved planning. This paper describes a model which has been developed to deal with the track maintenance planning function at the medium to long-term levels. This model simulates the impacts of degrading railway track conditions and related maintenance work, in contrast to tradition models that mainly use expert systems. The model simulates the degrading track condition using an existing track degradation model. Track condition data from that model is used to determine if safety related speed restrictions are needed and what immediate maintenance work may be required for safe train operations. The model outputs the net present value of the benefits of undertaking a given maintenance strategy, when compared with a base-case scenario. The model approach has advantages over current models in investigating what if scenarios. The track engineer can assess the possible benefits in reduced operating costs from upgrading track infrastructure or from the use of improved maintenance equipment. After describing the model inputs and the assumptions used, the paper deals with the simulation of track maintenance and of train operating costs over time. The results of applying the model to a test track section using a number of different maintenance strategies are also given

Constructive homomorphisms for classical groups

Let Omega be a quasisimple classical group in its natural representation over a finite vector space V, and let Delta be its normaliser in the general linear group. We construct the projection from Delta to Delta/Omega and provide fast, polynomial-time algorithms for computing the image of an element. Given a discrete logarithm oracle, we also represent Delta/Omega as a group with at most 3 generators and 6 relations. We then compute canonical representatives for the cosets of Omega. A key ingredient of our algorithms is a new, asymptotically fast method for constructing isometries between spaces with forms. Our results are useful for the matrix group recognition project, can be used to solve element conjugacy problems, and can improve algorithms to construct maximal subgroups

Fundamental domains for congruence subgroups of SL2 in positive characteristic

In this work, we construct fundamental domains for congruence subgroups of $SL_2(F_q[t])$ and $PGL_2(F_q[t])$. Our method uses Gekeler's description of the fundamental domains on the Bruhat- Tits tree $X = X_{q+1}$ in terms of cosets of subgroups. We compute the fundamental domains for a number of congruence subgroups explicitly as graphs of groups using the computer algebra system Magma

More effective social services

In June 2014, the Productivity Commission was asked to look at ways to improve how government agencies commission and purchase social services. The final report was released in mid-September 2015. It makes several recommendations about how to make social services more responsive, client-focused, accountable and innovative. The final inquiry report has two key messages. First, system-wide improvement can be achieved and should be pursued. Second, New Zealand needs better ways to join up services for those with multiple, complex needs. Capable clients should be empowered with more control over the services they receive. Those less capable need close support and a response tailored to their needs, without arbitrary distinctions between services and funds divided into “health”, “education”, etc. These are significant, but extremely worthwhile, changes for New Zealand

Computing in unipotent and reductive algebraic groups

The unipotent groups are an important class of algebraic groups. We show that techniques used to compute with finitely generated nilpotent groups carry over to unipotent groups. We concentrate particularly on the maximal unipotent subgroup of a split reductive group and show how this improves computation in the reductive group itself.Comment: 22 page