This study sought to determine how five neighbourhood models (the Grid, Loop and Cul-de-Sac, Fused Grid, New Urbanist and Greenway) compare in terms of the characteristics known to affect active transportation rates, and which model is most likely to be able to facilitate active transportation as a result. In order to do so, model principles and design characteristics of case study neighbourhoods were described and used to create a range of design specifications for each model. These specifications were then used to develop a GIS-based representation of an example neighbourhood for each model, which included the transportation network, parcels of different land use types and densities, homes and destinations. GIS, statistical and graph-based techniques were then used to comprehensively assess and compare the models in terms of their potential to facilitate walking and biking through the built environment correlates identified in through a literature review. The models were ranked on each variable, and then an overall comparison was made on the basis diversity (land use mix), density and design - the three dimensions identified by Cervero and Kockelman (1997) as being the key ways through which the built environment can contribute to creating walkable (and potentially bikeable) neighbourhoods. Additional measures related to trip characteristics and issues of importance to developers (such as buildable area) were also included. The results illustrate how each model’s unique approach to facilitating walking and/or biking is reflected in the built environment characteristics assessed. While a model that was strong in one category was often weaker in another (a finding which echoes that of Filion and Hammond, 2003), the three alternative models (Fused Grid, New Urbanist and Greenway) consistently fared better than the more traditional Grid and Loop and Cul-de-Sac designs, with the New Urbanist scoring the highest on the overall evaluation of walkability and bikeability and the Greenway the best on network design for cyclists. In addition to these findings, the study also provided an opportunity to explore several challenges related to model assessment, such as issues arising from frame choice, off-set networks, and the use of roads as proxies for active transportation networks.

This study sought to determine how five neighbourhood models (the Grid, Loop and Cul-de-Sac, Fused Grid, New Urbanist and Greenway) compare in terms of the characteristics known to affect active transportation rates, and which model is most likely to be able to facilitate active transportation as a result. In order to do so, model principles and design characteristics of case study neighbourhoods were described and used to create a range of design specifications for each model. These specifications were then used to develop a GIS-based representation of an example neighbourhood for each model, which included the transportation network, parcels of different land use types and densities, homes and destinations. GIS, statistical and graph-based techniques were then used to comprehensively assess and compare the models in terms of their potential to facilitate walking and biking through the built environment correlates identified in through a literature review. The models were ranked on each variable, and then an overall comparison was made on the basis diversity (land use mix), density and design - the three dimensions identified by Cervero and Kockelman (1997) as being the key ways through which the built environment can contribute to creating walkable (and potentially bikeable) neighbourhoods. Additional measures related to trip characteristics and issues of importance to developers (such as buildable area) were also included. The results illustrate how each model’s unique approach to facilitating walking and/or biking is reflected in the built environment characteristics assessed. While a model that was strong in one category was often weaker in another (a finding which echoes that of Filion and Hammond, 2003), the three alternative models (Fused Grid, New Urbanist and Greenway) consistently fared better than the more traditional Grid and Loop and Cul-de-Sac designs, with the New Urbanist scoring the highest on the overall evaluation of walkability and bikeability and the Greenway the best on network design for cyclists. In addition to these findings, the study also provided an opportunity to explore several challenges related to model assessment, such as issues arising from frame choice, off-set networks, and the use of roads as proxies for active transportation networks.

In this thesis, we describe linear codes over prime fields obtained from incidence designs of iterated line graphs of complete graphs Li(Kn) where i = 1, 2. In the binary case, results are extended to codes from neighbourhood designs of the line graphs Li+1(Kn) using certain elementary relations. Codes from incidence designs of complete graphs, Kn, and neighbourhood designs of their line graphs, L1(Kn) (the so-called triangular graphs), have been considered elsewhere by others. We consider codes from incidence designs of L1(Kn) and L2(Kn), and neighbourhood designs of L2(Kn) and L3(Kn). In each case, basic parameters of the codes are determined. Further, we introduce a family of vertex-transitive graphs 􀀀n that are embeddable into the strong product L1(Kn) ⊠ K2, of triangular graphs and K2, a class which at first sight may seem unnatural but, on closer look, is a repository of graphs rich with combinatorial structures. For instance, unlike most regular graphs considered here and elsewhere that only come with incidence and neighbourhood designs, 􀀀n also has what we have termed as 6-cycle designs. These are designs in which the point set contains vertices of the graph and every block contains vertices of a 6-cycle in the graph. Also, binary codes from incidence matrices of these graphs have other minimum words in addition to incidence vectors of the blocks. In addition, these graphs have induced subgraphs isomorphic to the family Hn of complete porcupines (see Definition 4.11). We describe codes from incidence matrices of 􀀀n and Hn and determine their parameters.

In this thesis, we describe linear codes over prime fields obtained from incidence designs of iterated line graphs of complete graphs Li(Kn) where i = 1, 2. In the binary case, results are extended to codes from neighbourhood designs of the line graphs Li+1(Kn) using certain elementary relations. Codes from incidence designs of complete graphs, Kn, and neighbourhood designs of their line graphs, L1(Kn) (the so-called triangular graphs), have been considered elsewhere by others. We consider codes from incidence designs of L1(Kn) and L2(Kn), and neighbourhood designs of L2(Kn) and L3(Kn). In each case, basic parameters of the codes are determined. Further, we introduce a family of vertex-transitive graphs 􀀀n that are embeddable into the strong product L1(Kn) ⊠ K2, of triangular graphs and K2, a class which at first sight may seem unnatural but, on closer look, is a repository of graphs rich with combinatorial structures. For instance, unlike most regular graphs considered here and elsewhere that only come with incidence and neighbourhood designs, 􀀀n also has what we have termed as 6-cycle designs. These are designs in which the point set contains vertices of the graph and every block contains vertices of a 6-cycle in the graph. Also, binary codes from incidence matrices of these graphs have other minimum words in addition to incidence vectors of the blocks. In addition, these graphs have induced subgraphs isomorphic to the family Hn of complete porcupines (see Definition 4.11). We describe codes from incidence matrices of 􀀀n and Hn and determine their parameters.

Over the last decade, there has been rapid growth in research into the influence of the physical environment on physical activity. Previously, individual and social factors dominated research into the influences of physical activity. This new area of study has been built on the understanding that the physical environment may create an opportunity or a barrier to engagement in physical activity behaviours (Sallis & Owen, 1997). This research develops objectively measured features of the physical environment in order to investigate relationships with walking behaviour. Public health research of this nature is still at a preliminary stage, although research expertise outside of public health including transportation, urban planning and geographic information science has much to contribute to this emerging field. This study investigated walking in the neighbourhood in a sample of adults residing in Perth, Western Australia. Objective measurement of the physical environment using Geographic Information Systems (GIS) was conducted including measurement of street connectivity, residential density, land use mix and retail floor area ratio at three different geographic scales (suburb, census collection district, 15 minute walk from a survey participants home). These measures were then combined into an index known as a walkability index and validated against survey participant reported data on walking within the neighbourhood using binary logistic regression. Among other findings, the evidence presented shows that depending on which geographic scale the physical environment is measured at and what type of walking in the neighbourhood is reported, the strength of relationship varies between an objectively measured walkability index and walking behaviour in the neighbourhood. These findings highlight the need to differentiate between walking for transport and walking for recreation, health and exercise when investigating the relationship between physical activity and the environment. These findings also show the importance of geographic scale of measurement in the relationship between physical activity and the physical environment, and the need for current high quality geographic data in this type of research.

Philosophiae Doctor - PhD (Mathematics) / The main theme of this thesis is the construction of linear codes from adjacency matrices or sub-matrices of adjacency matrices of regular graphs. We first examine the binary codes from the row span of biadjacency matrices and their transposes for some classes of bipartite graphs. In this case we consider a sub-matrix of an adjacency matrix of a graph as the generator of the code. We then shift our attention to uniform subset graphs by exploring the automorphism groups of graph covers and some classes of uniform subset graphs. In the sequel, we explore equal codes from adjacency matrices of non-isomorphic uniform subset graphs and finally consider codes generated by an adjacency matrix formed by adding adjacency matrices of two classes of uniform subset graphs.

Philosophiae Doctor - PhD / In this thesis, we describe linear codes over prime fields obtained from incidence designs of iterated line graphs of complete graphs Li(Kn) where i = 1, 2. In the binary case, results are extended to codes from neighbourhood designs of the line graphs Li+1(Kn) using certain elementary relations. Codes from incidence designs of complete graphs, Kn, and neighbourhood designs of their line graphs, L1(Kn) (the so-called triangular graphs), have been considered elsewhere by others. We consider codes from incidence designs of L1(Kn) and L2(Kn), and neighbourhood designs of L2(Kn) and L3(Kn). In each case, basic parameters of the codes are determined. Further, we introduce a family of vertex-transitive graphs Γn that are embeddable into the strong product L1(Kn)⊠  K2, of triangular graphs and K2, a class which at first sight may seem unnatural but, on closer look, is a repository of graphs rich with combinatorial structures. For instance, unlike most regular graphs considered here and elsewhere that only come with incidence and neighbourhood designs, Γn also has what we have termed as 6-cycle designs. These are designs in which the point set contains vertices of the graph and every block contains vertices of a 6-cycle in the graph. Also, binary codes from incidence matrices of these graphs have other minimum words in addition to incidence vectors of the blocks. In addition, these graphs have induced subgraphs isomorphic to the family Hn of complete porcupines (see Definition 4.11). We describe codes from incidence matrices of Γn and Hn and determine their parameters. / South Africa

Philosophiae Doctor - PhD / In this thesis, we describe linear codes over prime fields obtained from incidence designs of iterated line graphs of complete graphs Li(Kn) where i = 1,2. In the binary case, results are extended to codes from neighbourhood designs of the line graphs Li+l(Kn) using certain elementary relations. Codes from incidence designs of complete graphs, Kn' and neighbourhood designs of their line graphs, £1(Kn) (the so-called triangular graphs), have been considered elsewhere by others. We consider codes from incidence designs of Ll(Kn) and L2(Kn), and neighbourhood designs of L2(Kn) and L3(Kn). In each case, the basic parameters of the codes are determined. Further, we introduce a family of vertex-transitive graphs Rn that are embeddable into the strong product Ll(Kn) ~ K2' of triangular graphs and K2' a class that at first sight may seem unnatural but, on closer look, is a repository of graphs rich with combinatorial structures. For instance, unlike most regular graphs considered here and elsewhere that only come with incidence and neighbourhood designs, Rn also has what we have termed as 6-cycle designs. These are designs in which the point set contains vertices of the graph and every block contains vertices of a 6-cycle in the graph. Also, binary codes from incidence matrices of these graphs have other minimum words in addition to incidence vectors of the blocks. In addition, these graphs have induced subgraphs isomorphic to the family Hn of complete porcupines (see Definition 4.11). We describe codes from incidence matrices of Rn and Hn and determine their parameters. The discussion is concluded with a look at complements of Rn and Hn, respectively denoted by Rn and Hn. Among others, the complements rn are contained in the union of the categorical product Ll(Kn) x Kn' and the categorical product £1(Kn) x Kn (where £1(Kn) is the complement of the iii triangular graph £1(Kn)). As with the other graphs, we have also considered codes from the span of incidence matrices of Rn and Hn and determined some of their properties. In each case, automorphisms of the graphs, designs and codes have been determined. For the codes from incidence designs of triangular graphs, embeddings of Ll(Kn) x K2 and complements of complete porcupines, we have exhibited permutation decoding sets (PD-sets) for correcting up to terrors where t is the full error-correcting capacity of the codes. For the remaining codes, we have only been able to determine PD-sets for which it is possible to correct a fraction of t-errors (partial permutation decoding). For these codes, we have also determined the number of errors that can be corrected by permutation decoding in the worst-case.