Overgroups of the Automorphism Group of the Rado Graph

We are interested in overgroups of the automorphism group of the Rado graph. One class of such overgroups is completely understood; this is the class of reducts. In this article we tie recent work on various other natural overgroups, in particular establishing group connections between them and the reducts.Comment: 11 pages, 2 figure

Convex sublattices of a lattice and a fixed point property

The collection CL(T) of nonempty convex sublattices of a lattice T ordered by bi-domination is a lattice. We say that T has the fixed point property for convex sublattices (CLFPP for short) if every order preserving map f from T to CL(T) has a fixed point, that is x > f(x) for some x > T. We examine which lattices may have CLFPP. We introduce the selection property for convex sublattices (CLSP); we observe that a complete lattice with CLSP must have CLFPP, and that this property implies that CL(T) is complete. We show that for a lattice T, the fact that CL(T) is complete is equivalent to the fact that T is complete and the lattice of all subsets of a countable set, ordered by containment, is not order embeddable into T. We show that for the lattice T = I(P) of initial segments of a poset P, the implications above are equivalences and that these properties are equivalent to the fact that P has no infinite antichain. A crucial part of this proof is a straightforward application of a wonderful Hausdor type result due to Abraham, Bonnet, Cummings, Dzamondja and Thompson [2010]

Siblings of an ℵ0-categorical relational structure

A sibling of a relational structure $R$ is any structure $S$ which can be embedded into $R$ and, vice versa, such that $R$ can be embedded into $S$. Let $\operatorname{sib}(R)$ be the number of siblings of $R$, these siblings being counted up to isomorphism. Thomassé conjectured that for countable relational structures made of at most countably many relations, $\operatorname{sib}(R)$ is either one, countably infinite, or the size of the continuum; but even showing the special case $\operatorname{sib}(R)1$ is one or infinite is unsettled when $R$ is a countable tree. We prove that if $R$ is countable and $\aleph_{0}$-categorical, then indeed $\operatorname{sib}(R)$ is one or infinite. Furthermore, $\operatorname{sib}(R)$ is one if and only if $R$ is finitely partitionable in the sense of Hodkinson and Macpherson [14]. The key tools in our proof are the notion of monomorphic decomposition of a relational structure introduced in [35] and studied further in [23], [24], and a result of Frasnay [11]

Symbiotic modeling: Linguistic Anthropology and the promise of chiasmus

Reflexive observations and observations of reflexivity: such agendas are by now standard practice in anthropology. Dynamic feedback loops between self and other, cause and effect, represented and representamen may no longer seem surprising; but, in spite of our enhanced awareness, little deliberate attention is devoted to modeling or grounding such phenomena. Attending to both linguistic and extra-linguistic modalities of chiasmus (the X figure), a group of anthropologists has recently embraced this challenge. Applied to contemporary problems in linguistic anthropology, chiasmus functions to highlight and enhance relationships of interdependence or symbiosis between contraries, including anthropology’s four fields, the nature of human being and facets of being human

A 36 ka environmental record in the southern tropics : Lake Tritrivakely (Madgascar) (Un enregistrement de l'environnement depuis 36 ka en zone tropicale sud : le lac Tritrivakely (Madagascar)).

The upper 13 m of a 40 m-long sedimentary profile core taken in a crater lake on the Malagasy Plateau reveals 36,000 yrs of hydroclimatic evolution. A shallow lake occupies the core site from ≃35 to ≃19 ka BP under climatic conditions cooler than today. The water table is very low and biological productivity extremely reduced during the Last Glacial Maximum. A large warming was initiated at ≃14.5 ka BP. The modern bog establishes about 4 ka ag

A pooled testing strategy for identifying SARS-CoV-2 at low prevalence

Suppressing infections of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) will probably require the rapid identification and isolation of individuals infected with the virus on an ongoing basis. Reverse-transcription polymerase chain reaction (RT-PCR) tests are accurate but costly, which makes the regular testing of every individual expensive. These costs are a challenge for all countries around the world, but particularly for low-to-middle-income countries. Cost reductions can be achieved by pooling (or combining) subsamples and testing them in groups1-7. A balance must be struck between increasing the group size and retaining test sensitivity, as sample dilution increases the likelihood of false-negative test results for individuals with a low viral load in the sampled region at the time of the test8. Similarly, minimizing the number of tests to reduce costs must be balanced against minimizing the time that testing takes, to reduce the spread of the infection. Here we propose an algorithm for pooling subsamples based on the geometry of a hypercube that, at low prevalence, accurately identifies individuals infected with SARS-CoV-2 in a small number of tests and few rounds of testing. We discuss the optimal group size and explain why, given the highly infectious nature of the disease, largely parallel searches are preferred. We report proof-of-concept experiments in which a positive subsample was detected even when diluted 100-fold with negative subsamples (compared with 30-48-fold dilutions described in previous studies9-11). We quantify the loss of sensitivity due to dilution and discuss how it may be mitigated by the frequent re-testing of groups, for example. With the use of these methods, the cost of mass testing could be reduced by a large factor. At low prevalence, the costs decrease in rough proportion to the prevalence. Field trials of our approach are under way in Rwanda and South Africa. The use of group testing on a massive scale to monitor infection rates closely and continually in a population, along with the rapid and effective isolation of people with SARS-CoV-2 infections, provides a promising pathway towards the long-term control of coronavirus disease 2019 (COVID-19).info:eu-repo/semantics/publishe