There exist two conjectures for constraint satisfaction problems (CSPs) of reducts of finitely bounded homogeneous structures: the first one states that tractability of the CSP of such a structure is, when the structure is a model-complete core, equivalent to its polymorphism clone satisfying a certain non-trivial linear identity modulo outer embeddings. The second conjecture, challenging the approach via model-complete cores by reflections, states that tractability is equivalent to the linear identities (without outer embeddings) satisfied by its polymorphisms clone, together with the natural uniformity on it, being non-trivial.We prove that the identities satisfied in the polymorphism clone of a structure allow for conclusions about the orbit growth of its automorphism group, and apply this to show that the two conjectures are equivalent. We contrast this with a counterexample showing that ω-categoricity alone is insufficient to imply the equivalence of the two conditions above in a model-complete core.Taking a different approach, we then show how the Ramsey property of a homogeneous structure can be utilized for obtaining a similar equivalence under different conditions.We then prove that any polymorphism of sufficiently large arity which is totally symmetric modulo outer embeddings of a finitely bounded structure can be turned into a non-trivial system of linear identities, and obtain non-trivial linear identities for all tractable cases of reducts of the rational order, the random graph, and the random poset.Finally, we provide a new and short proof, in the language of monoids, of the theorem stating that every ω-categorical structure is homomorphically equivalent to a model-complete core.

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We discuss the Ramsey property, the existence of a stationary independence relation and the coherent extension property for partial isometries (coherent EPPA) for all classes of metrically homogeneous graphs from Cherlin's catalogue, which is conjectured to include all such structures. We show that, with the exception of tree-like graphs, all metric spaces in the catalogue have precompact Ramsey expansions (or lifts) with the expansion property. With two exceptions we can also characterise the existence of a stationary independence relation and the coherent EPPA.Our results can be seen as a new contribution to Nešetřil's classification programme of Ramsey classes and as empirical evidence of the recent convergence in techniques employed to establish the Ramsey property, the expansion (or lift or ordering) property, EPPA and the existence of a stationary independence relation. At the heart of our proof is a canonical way of completing edge-labelled graphs to metric spaces in Cherlin's classes. The existence of such a "completion algorithm" then allows us to apply several strong results in the areas that imply EPPA and respectively the Ramsey property.The main results have numerous corollaries on the automorphism groups of the Fraïssé limits of the classes, such as amenability, unique ergodicity, existence of universal minimal flows, ample generics, small index property, 21-Bergman property and Serre's property (FA).

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The diffuse x-ray scattering and small-angle neutron scattering of a Pt-47 at. % Rh single crystal aged at 923 K were measured to determine the local atomic arrangement. The separated short-range order scattering including the small-angle scattering range showed weak intensity modulations, with the maximum at 1 1 2 0 positions, thus indicating the presence of local order. In contrast to short-range order scattering, size-effect scattering is already well visible in the raw data, in spite of the small difference of 3% in the atomic sizes. Size-effect scattering is mainly due to Rh-Rh displacements.