"A matrix representation of places of residence and places of commuting destination in a metropolis, is coupled with evidence regarding spatio-temporal change in average household size. This approach allows the average number of persons per household who commute to be hierarchically ordered in a square matrix which shows attributes associated with a well-known class of matrices. Based on these attributes it is shown that any given spatial distribution of households implies a bounded range of vectors representing the spatial distribution of commuters.... The proposed methodology is applied to thirty four subareas throughout the city of Saskatoon, Saskatchewan."
"Distinction made between household-persons and household-markers [the person who identifies the family or household as a unit] is formalized in the notion of nested populations. This leads to an extension of the Leslie model into a formulation of growth for both population and households. The extended model involves the matrix presentation of household composition where ratios of household-persons who are age 0, per household-marker, function as surrogate values for fertility rates. The extended model describes change over time in the distribution of population by age, and in the distribution of households by age of household-marker, or household-head. The model involves the inversion of a nonnegative matrix, and is feasible only if it yields, projected over time, nonnegative entries in vectors representing distribution of population by age, and distribution of household-heads by age. Conditions for the feasibility of the extended model are discussed, and a sufficient condition for feasibility over a single interval is identified." (SUMMARY IN FRE)
Mutual feedback between human-made environments and facets of thought throughout history has yielded two myths: the Garden and the Citadel. Both myths correspond to Jung's feminine and masculine collective subconscious, as well as to Nietzsche's premise of Apollonian and Dionysian impulses in art. Nietzsche's premise suggests, furthermore, that the feminine myth of the Garden is time-bound whereas the masculine myth of the Citadel, or the Ideal City, constitutes a spatial deportment. Throughout history the two myths have continually molded the built environment and thought, but the myth of the Ideal City -from Plato to Descartes to modernity -came to dominate city-form and ensuing aspects of contemplation. This relationship seems to have shifted during the twentieth century. Intellectual dispositions have begun to be largely nurtured by an incongruous city-form emerging from the gap between the incessant promise for an automated, well-functioning city, on the one hand, and looming alienation, coupled with the factual, malfunctioning city, on the other hand. Urban decay, a persisting and time-bound urban event that is a byproduct of this configuration, suggests the ascent of the Garden myth in post-modern city-form.
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