Three-Dimensional Ray Tracing and Geophysical Inversion in Layered Media

In this paper the problem of finding seismic rays in a three-dimensional layered medium is examined. The "layers" are separated by arbitrary smooth interfaces that can vary in three dimensions. The endpoints of each ray and the sequence of interfaces it encounters are specified. The problem is formulated as a nonlinear system of equations and efficient, accurate methods of solution are discussed. An important application of ray tracing methods, which is discussed, is the nonlinear least squares estimation of medium parameters from observed travel times. In addition the "type" of each ray is also determined by the least squares process—this is in effect a deconvolution procedure similar to that desired in seismic exploration. It enables more of the measured data to be used without filtering out the multiple reflections that are not pure P-waves

A Reflection on Community Research and Action as an Evolving Practice

Community research and action is an evolving field of practice with multiple influences. Its varied ways of knowing and doing reflect recombined elements from different disciplines, including behavioral science, community psychology, public health, and community development. This article offers a personal reflection based on my evolving practice over nearly 50 years. The focus is on three types of influence: (a) engaging with different communities, fields, and networks (e.g., discovering shared values, diverse methods); (b) building methods and capabilities for the work (e.g., methods for participatory research, tools for capacity building); and (c) partnering for collaborative research and action, locally and globally. This story highlights the nature of the field’s evolution as an increasing variation in methods. Our evolving practice of community research and action—individually and collectively—emerges from the recombination of ideas and methods discovered through engagement in a wide variety of contexts

The base size of a primitive diagonal group

A base B for a finite permutation group G acting on a set X is a subset of X with the property that only the identity of G can fix every point of B. We prove that a primitive diagonal group G has a base of size 2 unless the top group of G is the alternating or symmetric group acting naturally, in which case a tight bound for the minimal base size of G is given. This bound also satisfies a well-known conjecture of Pyber. Moreover, we prove that if the top group of G does not contain the alternating group, then the proportion of pairs of points that are bases for G tends to 1 as |G| tends to infinity. A similar result for the case when the degree of the top group is fixed is given.Comment: 24 page

The Liminality of Indigenous Urbanism in Saskatchewan

This dissertation explores conditions and possibilities for enhancing Indigenous urbanism in prairie cities, and it examines how mainstream spatial production impedes this objective through two examples of urban change: First Nations’ urban reserves in Saskatchewan cities, and inner-city ‘revitalization’ in Saskatoon. By centering Indigenous resurgence as an analytical frame of reference, as well as lived knowledge and perceptions of urban change among Indigenous individuals who experience or contribute to processes of spatial restructuring, the argument follows that urban Indigenous space, and practices of Indigenous urbanism, are liminal. That is, while settler governments and non-Indigenous society perpetually reinforce colonial boundaries around liberal property relations, Indigenous people adapt to and resist this apparatus, many of whom aspire and labour to regenerate land and kinship as territory beyond such imposed frontiers. Indigenous urban space is positioned as precarious in Saskatchewan cities, located ‘in between’ legal property regimes and traditional territoriality, and ‘in transition’ from settler-state jurisdiction to self-determined places flowing with distinctive rights and responsibilities. Findings reveal that urban reserve creation takes place amid broader political and economic geographies that severely constrain their uses, binding First Nations’ sovereignty to corporate participation in the market economy through municipalized forms of self-government regulated by and answerable to crown title and state authority. Yet, there exists a commonly held long-term goal among First Nations of transforming or transcending these systems, which points to a temporal dimension of urban reserves as expedient but provisional pathways to access urban space and markets for longer-term strategies to expand First Nations’ legally recognized land base, financial self-sufficiency, governing capacities, and sociocultural revitalization. The transformative potential of Indigenous urbanism is emphasized in relation to core neighbourhood ‘revitalization’, revealing fundamental limitations and contradictions of mainstream settler urbanism in Saskatoon, Saskatchewan, and across the prairies. The repatriation of Indigenous land and life akin to resurgence includes rights and responsibilities to regenerate urban space – not to simply adapt to it – among diverse, multinational Indigenous inhabitants. This dissertation concludes with an argument for the expansion of urban Indigenous land, or an urban ‘Indigenous commons’ in support of community resurgence, and a material basis from which Indigenous urbanism can flourish in prairie cities