title: A study of knot-graphs

authors: Turner, John Christopher

abstract: This thesis is an account of studies made of knot projections, the tools used being graph-theoretic methods and extensions of them. The basic tool is the adjacency matrix. In fact several kinds of adjacency matrix are defined, for knot diagrams which are either nonoriented or are given orientations which reflect certain topological properties of the knots concerned.
First the properties of knot-graph adjacency matrices are studied. In particular, a matrix equation is derived which is shown to be satisfied by the α- and β-adjacency matrices of all knot-graphs; other matrices appearing in the equation are studied.
Examination of types of walk that can be made on a knot-graph leads to a definition of walk-groups and groupoids on knot-graphs. Relations between the Cayley diagrams of walk-groups and certain other knots which are derived from the diagrams lead to interesting correspondences between knots, both finite and infinite.
An extensive study of the spectra of knot-graph adjacency matrices is presented. Methods for obtaining spectra are given, both for general cases and for certain classes of knots.
The concept of balanced orientations of knot-graphs is introduced; and numbers of rooted directed spanning trees of oriented knot-graphs are studied. It is shown that one type of tree number is a knot invariant, and evidence for the invariance of another one is given. A general inequality relating the two types of number is conjectured. The first tree number has several topological interpretations, and these are discussed. Tables of the numbers are given for knots of orders n = 3, ... ,10; and methods for calculating them for various knot classes are developed.
A vertex deletion theorem relating tree numbers of three knot-graphs is proved. Families of twins which arise from vertex deletions in knot-graphs are defined and studied. It is shown that by repeatedly applying the deletion operation on a given alternating knot-graph, one is led to a certain distribution of ‘twists’, which is given the name ‘twist spectrum’. Twist spectra have many interesting topological properties: they are topological invariants, and their moments are powerful knot discriminants; they distinguish between a knot-graph and its mirror image and hence can be used to investigate amphicheirality. 
The twist spectra for prime alternating 1-links up to order n = 9 and for 2- links up to order n = 8 are tabulated. A general algorithm for computing a twist spectrum is given, and formulae are obtained for twist spectra of members of certain knot-classes.

text: A study of knot-graphs This thesis is an account of studies made of knot projections, the tools used being graph-theoretic methods and extensions of them. The basic tool is the adjacency matrix. In fact several kinds of adjacency matrix are defined, for knot diagrams which are either nonoriented or are given orientations which reflect certain topological properties of the knots concerned.
First the properties of knot-graph adjacency matrices are studied. In particular, a matrix equation is derived which is shown to be satisfied by the α- and β-adjacency matrices of all knot-graphs; other matrices appearing in the equation are studied.
Examination of types of walk that can be made on a knot-graph leads to a definition of walk-groups and groupoids on knot-graphs. Relations between the Cayley diagrams of walk-groups and certain other knots which are derived from the diagrams lead to interesting correspondences between knots, both finite and infinite.
An extensive study of the spectra of knot-graph adjacency matrices is presented. Methods for obtaining spectra are given, both for general cases and for certain classes of knots.
The concept of balanced orientations of knot-graphs is introduced; and numbers of rooted directed spanning trees of oriented knot-graphs are studied. It is shown that one type of tree number is a knot invariant, and evidence for the invariance of another one is given. A general inequality relating the two types of number is conjectured. The first tree number has several topological interpretations, and these are discussed. Tables of the numbers are given for knots of orders n = 3, ... ,10; and methods for calculating them for various knot classes are developed.
A vertex deletion theorem relating tree numbers of three knot-graphs is proved. Families of twins which arise from vertex deletions in knot-graphs are defined and studied. It is shown that by repeatedly applying the deletion operation on a given alternating knot-graph, one is led to a certain distribution of ‘twists’, which is given the name ‘twist spectrum’. Twist spectra have many interesting topological properties: they are topological invariants, and their moments are powerful knot discriminants; they distinguish between a knot-graph and its mirror image and hence can be used to investigate amphicheirality. 
The twist spectra for prime alternating 1-links up to order n = 9 and for 2- links up to order n = 8 are tabulated. A general algorithm for computing a twist spectrum is given, and formulae are obtained for twist spectra of members of certain knot-classes.

year: 1984

title: Stimulation of TNF-α release in monocytes by honey

authors: Tonks, A.

subjects: honey

abstract: Although evidence exists for the antibacterial effects of honey there is limited objective evidence for direct promotion of healing. We investigated the effect of manuka, pasture and an artificial honey on macrophage function. Reactive oxygen intermediate (ROI) production was assessed by luminol enhanced chemoluminescence and tumour necrosis factor-alpha (TNF-α) release was determined by immunoassay. ROI production was significantly (P<0.001) decreased by pasture honey and manuka honey. TNF-α release was significantly enhanced (P<0.001) in unprimed MM6 cells by manuka and pasture honey but was not altered in primed cells. These results could explain the suggested therapeutic properties of honey in promoting wound healing.

text: Stimulation of TNF-α release in monocytes by honey Although evidence exists for the antibacterial effects of honey there is limited objective evidence for direct promotion of healing. We investigated the effect of manuka, pasture and an artificial honey on macrophage function. Reactive oxygen intermediate (ROI) production was assessed by luminol enhanced chemoluminescence and tumour necrosis factor-alpha (TNF-α) release was determined by immunoassay. ROI production was significantly (P<0.001) decreased by pasture honey and manuka honey. TNF-α release was significantly enhanced (P<0.001) in unprimed MM6 cells by manuka and pasture honey but was not altered in primed cells. These results could explain the suggested therapeutic properties of honey in promoting wound healing.

year: 2001

title: Applying Kaupapa Māori Processes to Documentary Film.

authors: Waititi, Kahurangi Rora

subjects: Maori documentary

abstract: This thesis explores the application of Kaupapa Māori processes to documentary filmmaking through practiced-led research. The need for this research came to light through the experience of witnessing unacceptable behaviour shown by film crews towards kaumātua who were attending the 2006 28th Māori Battalion Reunion. In reflecting on this experience and considering my own filming experience as a person with a Te Ao Māori background, the basis for this argument was conceived. This thesis argues that there are alternative ways in which filming can be conducted by considering processes that already exist within Māori practices and philosophies.          

This Thesis, therefore, investigates alternative processes of filming that have developed from a Kaupapa Māori perspective through practical filming experience.  An historical overview of the relationship between Māori, media and filming practices have been provided to give context to this discussion.  The application of Kaupapa Māori processes to film was considered through the use of Marae protocol and philosophies. The application of these concepts was supported by the creative research which was utilised by referencing specific examples. The reader is, therefore, instructed to refer to the DVD in the front of the thesis as referenced in the written text.

text: Applying Kaupapa Māori Processes to Documentary Film. This thesis explores the application of Kaupapa Māori processes to documentary filmmaking through practiced-led research. The need for this research came to light through the experience of witnessing unacceptable behaviour shown by film crews towards kaumātua who were attending the 2006 28th Māori Battalion Reunion. In reflecting on this experience and considering my own filming experience as a person with a Te Ao Māori background, the basis for this argument was conceived. This thesis argues that there are alternative ways in which filming can be conducted by considering processes that already exist within Māori practices and philosophies.          

This Thesis, therefore, investigates alternative processes of filming that have developed from a Kaupapa Māori perspective through practical filming experience.  An historical overview of the relationship between Māori, media and filming practices have been provided to give context to this discussion.  The application of Kaupapa Māori processes to film was considered through the use of Marae protocol and philosophies. The application of these concepts was supported by the creative research which was utilised by referencing specific examples. The reader is, therefore, instructed to refer to the DVD in the front of the thesis as referenced in the written text.

year: 2007