On Turing dynamical systems and the Atiyah problem

Main theorems of the article concern the problem of M. Atiyah on possible values of l^2-Betti numbers. It is shown that all non-negative real numbers are l^2-Betti numbers, and that "many" (for example all non-negative algebraic) real numbers are l^2-Betti numbers of simply connected manifolds with respect to a free cocompact action. Also an explicit example is constructed which leads to a simply connected manifold with a transcendental l^2-Betti number with respect to an action of the threefold direct product of the lamplighter group Z/2 wr Z. The main new idea is embedding Turing machines into integral group rings. The main tool developed generalizes known techniques of spectral computations for certain random walk operators to arbitrary operators in groupoid rings of discrete measured groupoids.Comment: 35 pages; essentially identical to the published versio

A Census Of Highly Symmetric Combinatorial Designs

As a consequence of the classification of the finite simple groups, it has been possible in recent years to characterize Steiner t-designs, that is t-(v,k,1) designs, mainly for t = 2, admitting groups of automorphisms with sufficiently strong symmetry properties. However, despite the finite simple group classification, for Steiner t-designs with t > 2 most of these characterizations have remained longstanding challenging problems. Especially, the determination of all flag-transitive Steiner t-designs with 2 < t < 7 is of particular interest and has been open for about 40 years (cf. [11, p. 147] and [12, p. 273], but presumably dating back to 1965). The present paper continues the author's work [20, 21, 22] of classifying all flag-transitive Steiner 3-designs and 4-designs. We give a complete classification of all flag-transitive Steiner 5-designs and prove furthermore that there are no non-trivial flag-transitive Steiner 6-designs. Both results rely on the classification of the finite 3-homogeneous permutation groups. Moreover, we survey some of the most general results on highly symmetric Steiner t-designs.Comment: 26 pages; to appear in: "Journal of Algebraic Combinatorics

Well-quasi-ordering versus clique-width : new results on bigenic classes.

Daligault, Rao and Thomassé conjectured that if a hereditary class of graphs is well-quasi-ordered by the induced subgraph relation then it has bounded clique-width. Lozin, Razgon and Zamaraev recently showed that this conjecture is not true for infinitely defined classes. For finitely defined classes the conjecture is still open. It is known to hold for classes of graphs defined by a single forbidden induced subgraph H, as such graphs are well-quasi-ordered and are of bounded clique-width if and only if H is an induced subgraph of P4P4. For bigenic classes of graphs i.e. ones defined by two forbidden induced subgraphs there are several open cases in both classifications. We reduce the number of open cases for well-quasi-orderability of such classes from 12 to 9. Our results agree with the conjecture and imply that there are only two remaining cases to verify for bigenic classes

"The Great Event of the Fortnight”: Steamship Rhythms and Colonial Communication

This paper engages with Tim Cresswell’s ‘contellations of mobility’ in order to contribute some understanding of historical maritime rhythms. The empirical focus is upon a steamship mail service in the post-emancipation Caribbean. In examining this communications network, it is stressed that while those managing the network valorised predictable efficiency, ‘friction’ was prized by mercantile groups at the steamers’ ports of call. Thus, the different aspects of mobility signified differently across the network, and this historical case study reinforces the resonance of slowness and stoppage time. The synchronisation of steamship arrivals with sociocultural norms in the Caribbean colonies also necessitated the adaptation of mail service rhythms. Through a focus on shipping operations, this paper proposes to temper our understanding of the role of steamship technology in empire. The influence of colonies on the metropole encompassed an alteration of the rhythms of imperial circulation, and it is within the maritime arena that these realities came into sharp focus

Homeomorphic Embedding for Online Termination of Symbolic Methods

Well-quasi orders in general, and homeomorphic embedding in particular, have gained popularity to ensure the termination of techniques for program analysis, specialisation, transformation, and verification. In this paper we survey and discuss this use of homeomorphic embedding and clarify the advantages of such an approach over one using well-founded orders. We also discuss various extensions of the homeomorphic embedding relation. We conclude with a study of homeomorphic embedding in the context of metaprogramming, presenting some new (positive and negative) results and open problems

A method for finding new sets of axioms for classes of semigroups

We introduce a general technique for finding sets of axioms for a given class of semigroups. To illustrate the technique, we provide new sets of defining axioms for groups of exponent n, bands, and semilattices

The 28 November 2020 Landslide, Tsunami, and Outburst Flood – A Hazard Cascade Associated With Rapid Deglaciation at Elliot Creek, British Columbia, Canada

We describe and model the evolution of a recent landslide, tsunami, outburst flood, and sediment plume in the southern Coast Mountains, British Columbia, Canada. On November 28, 2020, about 18 million m3 of rock descended 1,000&nbsp;m from a steep valley wall and traveled across the toe of a glacier before entering a 0.6&nbsp;km2 glacier lake and producing &gt;100-m high run-up. Water overtopped the lake outlet and scoured a 10-km long channel before depositing debris on a 2-km2 fan below the lake outlet. Floodwater, organic debris, and fine sediment entered a fjord where it produced a 60+km long sediment plume and altered turbidity, water temperature, and water chemistry for weeks. The outburst flood destroyed forest and salmon spawning habitat. Physically based models of the landslide, tsunami, and flood provide real-time simulations of the event and can improve understanding of similar hazard cascades and the risk they pose

MolProbity: all-atom structure validation for macromolecular crystallography

MolProbity structure validation will diagnose most local errors in macromolecular crystal structures and help to guide their correction

Toxic marine microalgae and shellfish poisoning in the British isles: history, review of epidemiology, and future implications

The relationship between toxic marine microalgae species and climate change has become a high profile and well discussed topic in recent years, with research focusing on the possible future impacts of changing hydrological conditions on Harmful Algal Bloom (HAB) species around the world. However, there is very little literature concerning the epidemiology of these species on marine organisms and human health. Here, we examine the current state of toxic microalgae species around the UK, in two ways: first we describe the key toxic syndromes and gather together the disparate reported data on their epidemiology from UK records and monitoring procedures. Secondly, using NHS hospital admissions and GP records from Wales, we attempt to quantify the incidence of shellfish poisoning from an independent source. We show that within the UK, outbreaks of shellfish poisoning are rare but occurring on a yearly basis in different regions and affecting a diverse range of molluscan shellfish and other marine organisms. We also show that the abundance of a species does not necessarily correlate to the rate of toxic events. Based on routine hospital records, the numbers of shellfish poisonings in the UK are very low, but the identification of the toxin involved, or even a confirmation of a poisoning event is extremely difficult to diagnose. An effective shellfish monitoring system, which shuts down aquaculture sites when toxins exceed regularity limits, has clearly prevented serious impact to human health, and remains the only viable means of monitoring the potential threat to human health. However, the closure of these sites has an adverse economic impact, and the monitoring system does not include all toxic plankton. The possible geographic spreading of toxic microalgae species is therefore a concern, as warmer waters in the Atlantic could suit several species with southern biogeographical affinities enabling them to occupy the coastal regions of the UK, but which are not yet monitored or considered to be detrimental