On the Topology of the Cambrian Semilattices

For an arbitrary Coxeter group $W$, David Speyer and Nathan Reading defined Cambrian semilattices $C_{\gamma}$ as semilattice quotients of the weak order on $W$ induced by certain semilattice homomorphisms. In this article, we define an edge-labeling using the realization of Cambrian semilattices in terms of $\gamma$-sortable elements, and show that this is an EL-labeling for every closed interval of $C_{\gamma}$. In addition, we use our labeling to show that every finite open interval in a Cambrian semilattice is either contractible or spherical, and we characterize the spherical intervals, generalizing a result by Nathan Reading.Comment: 20 pages, 5 figure

The C-value enigma and timing of the Cambrian explosion

The Cambrian explosion is a grand challenge to science today and involves multidisciplinary study. This event is generally believed as a result of genetic innovations, environmental factors and ecological interactions, even though there are many conflicts on nature and timing of metazoan origins. The crux of the matter is that an entire roadmap of the evolution is missing to discern the biological complexity transition and to evaluate the critical role of the Cambrian explosion in the overall evolutionary context. Here we calculate the time of the Cambrian explosion by an innovative and accurate "C-value clock"; our result (560 million years ago) quite fits the fossil records. We clarify that the intrinsic reason of genome evolution determined the Cambrian explosion. A general formula for evaluating genome size of different species has been found, by which major questions of the C-value enigma can be solved and the genome size evolution can be illustrated. The Cambrian explosion is essentially a major transition of biological complexity, which corresponds to a turning point in genome size evolution. The observed maximum prokaryotic complexity is just a relic of the Cambrian explosion and it is supervised by the maximum information storage capability in the observed universe. Our results open a new prospect of studying metazoan origins and molecular evolution.Comment: 46 pages, 10 figure

Aspects of the taphonomy of the Cambrian Explosion in North Greenland

This thesis describes and elucidates the taphonomic pathways responsible for the exceptional preservation of some of the most common elements of the Sirius Passet Lagerstätte (early Cambrian), North Greenland. Investigative techniques including cathodoluminescence, are tested first on silicified molluscs from the Oligocene of Antigua, associated with a volcanic source; described in chapter 2. By describing the depositional environment of the Sirius Passet biota in detail and using a combination of analytical techniques such as SEM, EDAX, SEM-CL and elemental mapping two published papers address a number of the key research questions surrounding the unique taphonomic pathways in the Sirius Passet biota and their broader significance in understanding Cambrian ecosystems. The papers are included in the form of chapters 3 and 4 and the published versions included in the appendices. A unique, mat-dominated, tissue specific taphonomic pathway is proposed, more akin to the Proterozoic than the typical Burgess Shale Type (BST) preservation seen elsewhere in the Cambrian. This together with mouldic preservation indicates a range of taphonomic styles concomitant with the range of new biotas at the dawn of the Cambrian Explosion

Welsh Basin

The Cambrian rocks of Wales mostly lie within the Avalon composite terrane, apart from a small area of Cambrian rocks of the Monian composite terrane that is discussed in Chapter 9. The Cambrian rocks of the Welsh basin form the greater part of the Dyfed Supergroup of Woodcock (1990), the base of which overlies a widespread early Cambrian unconformity and the top of which extends to the late Tremadocian (Ordovician). The Dyfed Supergroup extends onto the Midland microcraton in attenuated form, with substantial gaps in the successions locally. The correlation of the basal parts of the Dyfed Supergroup is uncertain because of the lack of suitable evidence, but Woodcock was able to interpret the supergroup as a megasequence composed of five sequences, labelled in ascending order Ia to Ie, each separated by eustatic, tectonic or volcanic events, or a combination of these (Woodcock 1990, fig. 6). Sequence Ib includes strata assigned to the later Terreneuvian and all of Series 2; the strata of Sequence Ic are those of Stage 5 and the Drumian. The bases of sequences Id and Ie are particularly strongly marked, mainly by eustatic regressions, the former in the Guzhangian and the latter near the top of the Furongian, so that Ie is essentially composed of Tremadocian strata. Based principally on his extensive work in the eastern North American sector of Avalonia, Landing (1996) divided the Cambrian to Tremadocian successions in Avalonia into ten epeirogenic sequences (Landing 1996, figs. 2, 5). He recognized equivalents of some of these sequences in selected Welsh and English successions (Landing 1996, p. 51, fig. 7), for example the base of his Sequence 6 (which corresponds to Woodcock’s Ic) and Sequence 9 (part of Woodcock’s Id). Although some correlations are doubtful, the presence in Britain of a hiatus at the level of his Sequence 5, as suggested by Landing’s analysis (1996, fig. 7), is a possibility that merits further investigation. On the other hand, the downward extension of the Arvon ‘Slate Belt’ succession to the base of the Terreneuvian appears speculative

Chemostratigraphy of Neoproterozoic carbonates: implications for 'blind dating'

The delta C-13(carb) and Sr-87/Sr-86 secular variations in Neoproteozoic seawater have been used for the purpose of 'isotope stratigraphy' but there are a number of problems that can preclude its routine use. In particular, it cannot be used with confidence for 'blind dating'. The compilation of isotopic data on carbonate rocks reveals a high level of inconsistency between various carbon isotope age curves constructed for Neoproteozoic seawater, caused by a relatively high frequency of both global and local delta C-13(carb) fluctuations combined with few reliable age determinations. Further complication is caused by the unresolved problem as to whether two or four glaciations, and associated negative delta C-13(carb) excursions, can be reliably documented. Carbon isotope stratigraphy cannot be used alone for geological correlation and 'blind dating'. Strontium isotope stratigraphy is a more reliable and precise tool for stratigraphic correlations and indirect age determinations. Combining strontium and carbon isotope stratigraphy, several discrete ages within the 590-544 Myr interval, and two age-groups at 660-610 and 740-690 Myr can be resolved

Structural Properties of the Cambrian Semilattices -- Consequences of Semidistributivity

The $\gamma$-Cambrian semilattices $\mathcal{C}_{\gamma}$ defined by Reading and Speyer are a family of meet-semilattices associated with a Coxeter group $W$ and a Coxeter element $\gamma\in W$, and they are lattices if and only if $W$ is finite. In the case where $W$ is the symmetric group $\mathfrak{S}_{n}$ and $\gamma$ is the long cycle $(1\;2\;\ldots\;n)$ the corresponding $\gamma$-Cambrian lattice is isomorphic to the well-known Tamari lattice $\mathcal{T}_{n}$. Recently, Kallipoliti and the author have investigated $\mathcal{C}_{\gamma}$ from a topological viewpoint, and showed that many properties of the Tamari lattices can be generalized nicely. In the present article this investigation is continued on a structural level using the observation of Reading and Speyer that $\mathcal{C}_{\gamma}$ is semidistributive. First we prove that every closed interval of $\mathcal{C}_{\gamma}$ is a bounded-homomorphic image of a free lattice (in fact it is a so-called $\mathcal{H\!H}$-lattice). Subsequently we prove that each closed interval of $\mathcal{C}_{\gamma}$ is trim, we determine its breadth, and we characterize the closed intervals that are dismantlable.Comment: This paper has been withdrawn by the author due to a gap in the proof of Theorem 1.1(i). The results in Theorems 1.1(ii)-(iv) and 1.2, and those needed for their proofs remain true, and will be addressed in separate articles. I suspect that the claim of Theorem 1.1(i) is still true. In fact, I suspect that quotients of HH-lattices are HH-lattices again. Comments are very welcom

The Geologic Features of the Occurrence of Copper in North America

Copper is of such widespread natural occurrence in North America and there are so few metal-mining districts that have not contributed to its production that it is obviously necessary in any brief general treatment of the geology of the copper deposits of the continent to restrict the discussion to the districts in which copper is the dominant metallic product. Otherwise the summary would be unreasonably long. The copper deposits of North America may be classified in various ways--with respect to form, genesis, geologic age, distribution, and distinctive features of character or occurrence. On the whole, an areal grouping will probably be most satisfactory. To some extent this will coincide with a classification based on the form or character of the deposits, but there will be notable exceptions. Classification, after all, is merely a human-expedient for systematizing description and for facilitating studies of origin. It is essentially artificial and sets up class distinctions, the legality of which, at least so far as ore deposits are concerned, Nature does not recognize