On Large-Scale Graph Generation with Validation of Diverse Triangle Statistics at Edges and Vertices

Researchers developing implementations of distributed graph analytic algorithms require graph generators that yield graphs sharing the challenging characteristics of real-world graphs (small-world, scale-free, heavy-tailed degree distribution) with efficiently calculable ground-truth solutions to the desired output. Reproducibility for current generators used in benchmarking are somewhat lacking in this respect due to their randomness: the output of a desired graph analytic can only be compared to expected values and not exact ground truth. Nonstochastic Kronecker product graphs meet these design criteria for several graph analytics. Here we show that many flavors of triangle participation can be cheaply calculated while generating a Kronecker product graph. Given two medium-sized scale-free graphs with adjacency matrices $A$ and $B$, their Kronecker product graph has adjacency matrix $C = A \otimes B$. Such graphs are highly compressible: $|{\cal E}|$ edges are represented in ${\cal O}(|{\cal E}|^{1/2})$ memory and can be built in a distributed setting from small data structures, making them easy to share in compressed form. Many interesting graph calculations have worst-case complexity bounds ${\cal O}(|{\cal E}|^p)$ and often these are reduced to ${\cal O}(|{\cal E}|^{p/2})$ for Kronecker product graphs, when a Kronecker formula can be derived yielding the sought calculation on $C$ in terms of related calculations on $A$ and $B$. We focus on deriving formulas for triangle participation at vertices, ${\bf t}_C$, a vector storing the number of triangles that every vertex is involved in, and triangle participation at edges, $\Delta_C$, a sparse matrix storing the number of triangles at every edge.Comment: 10 pages, 7 figures, IEEE IPDPS Graph Algorithms Building Block

The Fossil Record of Angiosperm Families in Relation to Baraminology

To help estimate the number and boundaries of created kinds (i.e., baramins) of flowering plants, the fossil record has been analyzed. To designate the status of baramin, a criterion is applied that tests whether some but not all of a group’s hierarchically immediate subgroups have a fossil record back to the Flood (accepted here as near the Cretaceous-Paleogene boundary). Because of the lag time in population size and dispersal immediately after the Flood, this record is considered established if the group has fossils in Lower Eocene or lower strata. The quality of the flowering plant fossil record was found to decrease significantly below a family size of 600 species. Therefore the criterion was modified to account for small families and groups that lack a fossil record but are sister groups of so designated baramins. Depending on the classification used, the method identified between 212 and 222 flowering plant baramins, mostly families and suborders but some orders. This corroborates other baraminological criteria and significantly lowers the taxonomic level designated in studies using the unmodified criterion. Different baramins appear to contain significantly different degrees of originally designed diversity versus post-Flood diversification

Elm Farm Organic Research Centre December 2006

The Organic Research Centre. Elm Farm Research Centre Bulletin with Technical Updates from The Organic Advisory Service is a regular publication from The Organic Research Centre. The current issue covers: Report from 2006 Cirencester Conference; Quest for more home produced organic food; in a world where bread matters; Improving wheat with plenty of parents; Unlocking the secrets of the ancient (cereal varieties); Brain food- a good read; Not to late to protect the future: The organic role; Bumper Oat yields- Tradis trials top ten tonnes; Multiage flocks- a viable solution to wheigh variability; Letters

EFRC Bulletin 81 December 2005

EFRC's regular Bulletin with updates from the Organic Advisory Servic

The Cognitum: A Perception-Dependent Concept Needed in Baraminology

The taxonomic concept of cognitum (pl., cognita) is introduced to study design among baramins and to relieve other taxonomic concepts (e.g. holobaramin, baramin, basic type) concepts from considerations that may hinder their development. The cognitum is defined as a group of organisms recognized through the human cognitive senses as belonging together and sharing an underlying, unifying gestalt. This concept recognizes the importance of human neuro-cognitive processes in classification. It also implies that, at creation, organisms were endued with characteristics that elicit a unique, divinely-created psychological response in humans and that, after the Flood, the descendant species of the surviving representatives of the baramins retained these specially created characteristics. The cognitum affords research into the relative contribution by objective biosystematic techniques and neuro-cognitive phenomena to the study of biological design and classification. It also promises to clarify current problems in singly nested hierarchies, conflicting characters (homoplasy), fuzzy boundaries of groups, and unplaced taxa. Through its use in the study of biological phenomena, criteria that have been or might be proposed for baramins can be evaluated independently

Elm Farm Research Centre Bulletin 82 February 2006

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Paleobotany Supports the Floating Mat Model for the Origin of Carboniferous Coal Beds

A review of the history of the debate on origin of Carboniferous coal shows the priority that autochthonists have placed on paleobotanical data and interpretation. New data and methodology are offered here for interpreting the paleobotany and paleoecology of dominant Carboniferous coal plants: tree lycopsids and the tree-fern Psaronius. Lycopsid and tree-fern anatomies are characterized by air-filled chambers for buoyancy with rooting structures that are not suited for growth into and through terrestrial soil. Lycopsid development included boat-like dispersing spores, establishment of abundant buoyant, photosynthetic, branching and radiating rhizomorphs prior to upright stem growth, and prolonged life of the unbranched trunk prior to abrupt terminating growth of reproductive branches. The tree fern Psaronius is now understood better than previously to have had a much thicker, more flaring, and further spreading outer root mantle that formed a buoyant raft. Its increasingly heavy leaf crown was counterbalanced by forcing the basally rotting cane-like trunk and attached inner portion of the root mantle continually deeper underwater. Lycopsids and tree-ferns formed living floating mats capable of supporting the trunks. Paleobotany of coal plants should now be best understood as supporting a floating raft that deposited the detritus that now forms Carboniferous coal beds

Historical Survey of the Floating Mat Model for the Origin of Carboniferous Coal Beds

For three hundred years geologists and paleobotanists have been attempting to describe the process that deposited plant material that formed Carboniferous coal beds. Autochthonous and allochthonous explanations in the early Nineteenth Century showed how scientific methodology becomes involved in coal interpretation. Autochthonous modelers used the paleobotany-strata-petrology-environment method to argue that coal is a terrestrial swamp deposit. Allochthonous modelers used the petrology-strata-paleobotany-environment method to describe coal as a subaqueous deposit. The two methodologies are best displayed at the end of the Nineteenth Century in the consensus autochthonists versus the French School allochthonists. Three depositional models have been offered for the origin of coal: (1) peat swamp model, (2) drift model, and (3) floating mat model. Many paleobotany questions about lycopods and tree ferns had not been solved at the end of the Nineteenth Century, but the “floating mat model” offered a very robust path to direct research. Unfortunately, at the beginning of the Twentieth Century when the uniformitarian paradigm prevailed, the floating mat model was intentionally suppressed. Now new data from coal petrology indicate that Carboniferous coal is detrital having accumulated underwater, not as a terrestrial swamp deposit. New data and methodology from paleobotany (Sanders and Austin, 2018) show lycopsids and tree ferns were capable of forming living floating mats able to support the trunks. Paleobotany of coal plants should now be best understood as supporting a floating raft that deposited the detritus that now forms Carboniferous coal beds. We present here for the first time a three-hundred-year historical survey of the notion that coal accumulated from floating vegetation mats