title: On D-inverse constellations: An alternative view of ordered groupoids

authors: Hughes, Kaden

abstract: A groupoid is a category in which every arrow has an inverse. The ESN (Ehresmann-Schein-Nambooripad) theorem states that the category of inverse semigroups is isomorphic to the category of inductive groupoids, which are groupoids with additional order-theoretic structure. Inductive groupoids are special types of ordered groupoids; the latter shares most of the properties of inductive groupoids but do not correspond to any type of semigroup. Despite this, many of the main facts about inverse semigroups carry over to ordered groupoids, and ordered groupoids have been shown to be an important tool in the study of inverse semigroups. Since then, it has been found that a particular type of partial algebra we call D-inverse constellations are equivalent to ordered groupoids, but have an arguably simpler, purely algebraic definition. This thesis will explore and illustrate the value of working with D-inverse constellations rather than ordered groupoids, presenting an alternative formulation and proof of the ESN Theorem using D-inverse constellations.

text: On D-inverse constellations: An alternative view of ordered groupoids A groupoid is a category in which every arrow has an inverse. The ESN (Ehresmann-Schein-Nambooripad) theorem states that the category of inverse semigroups is isomorphic to the category of inductive groupoids, which are groupoids with additional order-theoretic structure. Inductive groupoids are special types of ordered groupoids; the latter shares most of the properties of inductive groupoids but do not correspond to any type of semigroup. Despite this, many of the main facts about inverse semigroups carry over to ordered groupoids, and ordered groupoids have been shown to be an important tool in the study of inverse semigroups. Since then, it has been found that a particular type of partial algebra we call D-inverse constellations are equivalent to ordered groupoids, but have an arguably simpler, purely algebraic definition. This thesis will explore and illustrate the value of working with D-inverse constellations rather than ordered groupoids, presenting an alternative formulation and proof of the ESN Theorem using D-inverse constellations.

year: 2024-04-13

title: A hydrothermally precipitated catalytic iron sulphide membrane as a first step toward life

authors: Russell, Michael J.

subjects: botryoid

abstract: We propose that life emerged from growing aggregates of iron sulphide bubbles containing alkaline and highly reduced hydrothermal solution. These bubbles were inflated hydrostatically at sulphidic submarine hot springs sited some distance from oceanic spreading centers four billion years ago. The membrane enclosing the bubbles was precipitated in response to contact between the spring waters and the mildly oxidized, acidic and iron-bearing Hadean ocean water. As the gelatinous sulphide bubbles aged and were inflated beyond their strength they budded, producing contiguous daughter bubbles by the precipitation of new membrane. [Fe2S2]+/0 or [Fe4S4]2+/+ clusters, possibly bonded by hydrothermal thiolate ligands as proferredoxins, could have catalyzed oxidation of thiolates to disulphides, thereby modifying membrane properties. 
We envisage the earliest iron sulphide bubbles (pro botryoids) first growing by hydrostatic inflation with hydrothermal fluid, but evolving to grow mainly by osmosis (the protocellular stage), driven by (1) catabolism of hydrothermal abiogenic organics trapped on the inner walls of the membrane, catalyzed by the iron sulphide clusters; and (2) cleavage of hydrophobic compounds dissolved in the membrane to hydrophilic moieties which were translocated, by the proton motive force inherent in the acidic Hadean ocean, to the alkaline interior of the protocell. The organics were generated first within the hydrothermal convective system feeding the hot springs operating in the oceanic crust and later in the pyritizing mound developing on the sea floor, as a consequence of the reduction of CO, CO2, and formaldehyde by Fe2+- and S2–-bearing minerals.
We imagine the physicochemical interactions in and on the membrane to have been sufficiently complex to have engendered auto- and cross-catalytic replication. The membrane may have been constructed in such a way that a  successful  parent could have  informed  the daughters of membrane characteristics functional for the then-current level of evolution.

text: A hydrothermally precipitated catalytic iron sulphide membrane as a first step toward life We propose that life emerged from growing aggregates of iron sulphide bubbles containing alkaline and highly reduced hydrothermal solution. These bubbles were inflated hydrostatically at sulphidic submarine hot springs sited some distance from oceanic spreading centers four billion years ago. The membrane enclosing the bubbles was precipitated in response to contact between the spring waters and the mildly oxidized, acidic and iron-bearing Hadean ocean water. As the gelatinous sulphide bubbles aged and were inflated beyond their strength they budded, producing contiguous daughter bubbles by the precipitation of new membrane. [Fe2S2]+/0 or [Fe4S4]2+/+ clusters, possibly bonded by hydrothermal thiolate ligands as proferredoxins, could have catalyzed oxidation of thiolates to disulphides, thereby modifying membrane properties. 
We envisage the earliest iron sulphide bubbles (pro botryoids) first growing by hydrostatic inflation with hydrothermal fluid, but evolving to grow mainly by osmosis (the protocellular stage), driven by (1) catabolism of hydrothermal abiogenic organics trapped on the inner walls of the membrane, catalyzed by the iron sulphide clusters; and (2) cleavage of hydrophobic compounds dissolved in the membrane to hydrophilic moieties which were translocated, by the proton motive force inherent in the acidic Hadean ocean, to the alkaline interior of the protocell. The organics were generated first within the hydrothermal convective system feeding the hot springs operating in the oceanic crust and later in the pyritizing mound developing on the sea floor, as a consequence of the reduction of CO, CO2, and formaldehyde by Fe2+- and S2–-bearing minerals.
We imagine the physicochemical interactions in and on the membrane to have been sufficiently complex to have engendered auto- and cross-catalytic replication. The membrane may have been constructed in such a way that a  successful  parent could have  informed  the daughters of membrane characteristics functional for the then-current level of evolution.

year: 1994

title: New Zealand’s indigenous forests – their status and drivers of change

authors: Allen, Robert

abstract: New Zealand’s remaining indigenous forests and shrublands are of immense cultural, environmental, and economic significance. A representative plot-based sample of these forests and shrublands has recently allowed an unbiased depiction of their composition
and structure. This is necessary for international reporting, performance assessment and management prioritisation. Their composition, structure, and function are driven by a diverse array of factors, many of which are complexly interrelated. The imprint of disturbances is pervasive and it is necessary to understand disturbances to interpret human-related impacts. For example, understanding impacts of exotic browsing mammals is only possible within a context of forest ecosystem development and tree demographic processes. There are now extensive areas of shrublands successional to forest, often composed of mixtures of indigenous and exotic species. These shrublands expand the pportunities for ecosystem services from, for example, carbon sequestration to water quality. An increasing area of indigenous forests and shrublands are managed for distinctive Māori aspirations that include sustainable use.

text: New Zealand’s indigenous forests – their status and drivers of change New Zealand’s remaining indigenous forests and shrublands are of immense cultural, environmental, and economic significance. A representative plot-based sample of these forests and shrublands has recently allowed an unbiased depiction of their composition
and structure. This is necessary for international reporting, performance assessment and management prioritisation. Their composition, structure, and function are driven by a diverse array of factors, many of which are complexly interrelated. The imprint of disturbances is pervasive and it is necessary to understand disturbances to interpret human-related impacts. For example, understanding impacts of exotic browsing mammals is only possible within a context of forest ecosystem development and tree demographic processes. There are now extensive areas of shrublands successional to forest, often composed of mixtures of indigenous and exotic species. These shrublands expand the pportunities for ecosystem services from, for example, carbon sequestration to water quality. An increasing area of indigenous forests and shrublands are managed for distinctive Māori aspirations that include sustainable use.

year: 2015