title: Algebraic Properties of Chromatic Polynomials and Their Roots

authors: Gilmore, Hamish Julian

subjects: chromatic

abstract: In this thesis we examine chromatic polynomials from the viewpoint of algebraic number theory. We relate algebraic properties of chromatic polynomials of graphs to structural properties of those graphs for some simple families of graphs. We then compute the Galois groups of chromatic polynomials of some sub-families of an infinite family of graphs (denoted {Gp,q }) and prove a conjecture posed in [15] concerning the Galois groups of one specific sub-family. Finally we investigate a conjecture due to Peter Cameron [8] that says that for any algebraic integer α there is some n ∈ ℕ such that α + n is the root of some chromatic polynomial. We prove the conjecture for quadratic and cubic integers and provide strong computational evidence that it is true for quartic
and quintic integers.

text: Algebraic Properties of Chromatic Polynomials and Their Roots In this thesis we examine chromatic polynomials from the viewpoint of algebraic number theory. We relate algebraic properties of chromatic polynomials of graphs to structural properties of those graphs for some simple families of graphs. We then compute the Galois groups of chromatic polynomials of some sub-families of an infinite family of graphs (denoted {Gp,q }) and prove a conjecture posed in [15] concerning the Galois groups of one specific sub-family. Finally we investigate a conjecture due to Peter Cameron [8] that says that for any algebraic integer α there is some n ∈ ℕ such that α + n is the root of some chromatic polynomial. We prove the conjecture for quadratic and cubic integers and provide strong computational evidence that it is true for quartic
and quintic integers.

year: 2015

title: Efficient three-dimensional reconstruction of aquatic vegetation geometry: Estimating morphological parameters influencing hydrodynamic drag

authors: Liénard, Jean

subjects: drag coefficient

abstract: Aquatic vegetation can shelter coastlines from energetic waves and tidal currents, sometimes enabling accretion of fine sediments. Simulation of flow and sediment transport within submerged canopies requires quantification of vegetation geometry. However, field surveys used to determine vegetation geometry can be limited by the time required to obtain conventional caliper and ruler measurements. Building on recent progress in photogrammetry and computer vision, we present a method for reconstructing three-dimensional canopy geometry. The method was used to survey a dense canopy of aerial mangrove roots, called pneumatophores, in Vietnam’s Mekong River Delta. Photogrammetric estimation of geometry required 1) taking numerous photographs at low tide from multiple viewpoints around 1 m2 quadrats, 2) computing relative camera locations and orientations by triangulation of key features present in multiple images and reconstructing a dense 3D point cloud, and 3) extracting pneumatophore locations and diameters from the point cloud data. Step 3) was accomplished by a new ‘sector-slice’ algorithm, yielding geometric parameters every 5 mm along a vertical profile. Photogrammetric analysis was compared with manual caliper measurements. In all 5 quadrats considered, agreement was found between manual and photogrammetric estimates of stem number, and of number × mean diameter, which is a key parameter appearing in hydrodynamic models. In two quadrats, pneumatophores were encrusted with numerous barnacles, generating a complex geometry not resolved by hand measurements. In remaining cases, moderate agreement between manual and photogrammetric estimates of stem diameter and solid volume fraction was found. By substantially reducing measurement time in the field while capturing in greater detail the 3D structure, photogrammetry has potential to improve input to hydrodynamic models, particularly for simulations of flow through large-scale, heterogenous canopies.

text: Efficient three-dimensional reconstruction of aquatic vegetation geometry: Estimating morphological parameters influencing hydrodynamic drag Aquatic vegetation can shelter coastlines from energetic waves and tidal currents, sometimes enabling accretion of fine sediments. Simulation of flow and sediment transport within submerged canopies requires quantification of vegetation geometry. However, field surveys used to determine vegetation geometry can be limited by the time required to obtain conventional caliper and ruler measurements. Building on recent progress in photogrammetry and computer vision, we present a method for reconstructing three-dimensional canopy geometry. The method was used to survey a dense canopy of aerial mangrove roots, called pneumatophores, in Vietnam’s Mekong River Delta. Photogrammetric estimation of geometry required 1) taking numerous photographs at low tide from multiple viewpoints around 1 m2 quadrats, 2) computing relative camera locations and orientations by triangulation of key features present in multiple images and reconstructing a dense 3D point cloud, and 3) extracting pneumatophore locations and diameters from the point cloud data. Step 3) was accomplished by a new ‘sector-slice’ algorithm, yielding geometric parameters every 5 mm along a vertical profile. Photogrammetric analysis was compared with manual caliper measurements. In all 5 quadrats considered, agreement was found between manual and photogrammetric estimates of stem number, and of number × mean diameter, which is a key parameter appearing in hydrodynamic models. In two quadrats, pneumatophores were encrusted with numerous barnacles, generating a complex geometry not resolved by hand measurements. In remaining cases, moderate agreement between manual and photogrammetric estimates of stem diameter and solid volume fraction was found. By substantially reducing measurement time in the field while capturing in greater detail the 3D structure, photogrammetry has potential to improve input to hydrodynamic models, particularly for simulations of flow through large-scale, heterogenous canopies.

year: 2016

title: “Literacy is not a Māori thing": Debunking the deficit discourse

authors: Derby, Melissa

abstract: Literacy has been entrenched in Māori society for more than 200 years, meeting needs that range from serving a political purpose to reading purely for pleasure. Literacy is not solely a Western competency, and Māoristriving for excellence in literacy is not an act of modern-day colonisation. Instead, what the evidence shows is that literacy is a skill at which Māori have excelled, and can excel, without compromising their identity asMāori. I challenge us to be conscious of the discourses underpinning statements related to Māori learners, however well-meaning those statements might be, and reiterate that literacy is indeed “a Māori thing” – both historically and in contemporary times.

text: “Literacy is not a Māori thing": Debunking the deficit discourse Literacy has been entrenched in Māori society for more than 200 years, meeting needs that range from serving a political purpose to reading purely for pleasure. Literacy is not solely a Western competency, and Māoristriving for excellence in literacy is not an act of modern-day colonisation. Instead, what the evidence shows is that literacy is a skill at which Māori have excelled, and can excel, without compromising their identity asMāori. I challenge us to be conscious of the discourses underpinning statements related to Māori learners, however well-meaning those statements might be, and reiterate that literacy is indeed “a Māori thing” – both historically and in contemporary times.

year: 2022-03-22