Language interpretation involves mapping from a string of words to a representation of an interpretation of those words. The problem is to be able to combine evidence I'rom the lexicon, syntax, semantics, ,'rod pragmatics to arrive at the best of the many possible interpretations. Given the well-worn sentence "The box is in the pen," ~;yntax may say that "pen '~ is a noun, while lexical knowled...

We discuss branch points of a ne coverings and their e ects on Veech groups. In particular, this allows us to show that even if one polygon tiles another, the respective Veech groups are not necessarily commensurable. We also show that there is no universal bound on the number of Teichm uller disks passing through the same point of Teichm uller space and having incommensurable lattice Veech g...

If X and Y are orthogonal hyperdefinable sets such that X is simple, then any group G interpretable in X ∪ Y has a normal hyperdefinable X-internal subgroup N such that G/N is Y -internal; N is unique up to commensurability. In order to make sense of this statement, local simplicity theory for hyperdefinable sets is developed. Moreover, a version of Schlichting’s Theorem for hyperdefinable fami...

Droplets can bounce indefinitely on a liquid bath vertically vibrated in a sinusoidal fashion. We here present experimental results that extend this observation to forcing signals composed of a combination of two commensurable frequencies. The Faraday and Goodridge thresholds are characterized. Then a number of vertical bouncing modes are reported, including walkers. The vertical motion can bec...

The class of Fuchsian groups that we are (by far) most interested in are the arithmetic groups. The easiest way to describe arithmetic Fuchsian groups is that class of groups containing all groups commensurable with PSL2(Z) and also all groups which uniformize compact Shimura curves. This is however, not a very wellmotivated definition: structurally, what do classical modular curves and Shimura...

Fermionic atoms in two different hyperfine states confined in optical lattices show strong commensurability effects due to the interplay between the atomic density wave ordering and the lattice potential. We show that spatially separated regions of commensurable and incommensurable phases can coexist. The commensurability between the harmonic trap and the lattice sites can be used to control th...

Quantum diffusion in a biased kicked Harper system, modeling field-induced transport in superlattices, is studied for fully chaotic dynamics of the underlying classical system. Under these conditions, the classical transport is diffusive whereas the quantum diffusion can be either enhanced or suppressed for commensurable or incommensurable ratio of the Bloch period to the driving period, respec...

Abstract We calculate asymptotic estimates for the conjugacy growth function of finitely generated class 2 nilpotent groups whose derived subgroups are infinite cyclic, including so-called higher Heisenberg groups. prove that these asymptotics stable when passing to commensurable groups, by understanding their twisted growth. also use that, in certain cases, series cannot be a holonomic function.

In Section 4 of the main paper, we present results on two benchmarks in terms of average ranking, since classification datasets may not be commensurable in terms of raw validation error. For the sake of completeness, we present here results in terms of average meta-test error. Meta-test error is defined slightly differently in our two experiments. We also present a PCA of our data in the MLP ex...