Related papers: Internal parametricity, without an interval

Integrable two-dimensional models which possess an integral of motion cubic or quartic in velocities are governed by a single prepotential, which obeys a nonlinear partial differential equation. Taking into account the latter's invariance…

We introduce a rigorous approach to the study of the symmetry breaking and pattern formation phenomenon for isotropic functionals with local/nonlocal interactions in competition. We consider a general class of nonlocal variational problems…

The paper studies coincidence points of parameterized set-valued mappings (multifunctions), which provide an extended framework to cover several important topics in variational analysis and optimization that include the existence of…

Deep neural networks often contain far more parameters than training examples, yet they still manage to generalize well in practice. Classical complexity measures such as VC-dimension or PAC-Bayes bounds usually become vacuous in this…

Probabilistic models often have parameters that can be translated, scaled, permuted, or otherwise transformed without changing the model. These symmetries can lead to strong correlation and multimodality in the posterior distribution over…

We investigate completeness and parametricity for a general class of realizability semantics for System F defined in terms of closure operators over sets of $\lambda$-terms. This class includes most semantics used for normalization…

A parametric manifold can be viewed as the manifold of orbits of a (regular) foliation of a manifold by means of a family of curves. If the foliation is hypersurface orthogonal, the parametric manifold is equivalent to the 1-parameter…

In this short note, we introduce a generalization of the canonical base property, called transfer of internality on quotients. A structural study of groups definable in theories with this property yields as a consequence infinitely many new…

In resolving instances of a computational problem, if multiple instances of interest share a feature in common, it may be fruitful to compile this feature into a format that allows for more efficient resolution, even if the compilation is…

Designing and implementing typed programming languages is hard. Every new type system feature requires extending the metatheory and implementation, which are often complicated and fragile. To ease this process, we would like to provide…

Within a category $\mathtt{C}$, having objects $\mathtt{C}_0$, it may be instructive to know not only that two objects are non-isomorphic, but also how far from being isomorphic they are. We introduce pseudo-metrics $d:\mathtt{C}_0 \times…

Volumetric parameterization problem refers to parameterization of both the interior and boundary of a 3D model. It is a much harder problem compared to surface parameterization where a parametric representation is worked out only for the…

For two-dimensional lattice equations one definition of integrability is that the model can be naturally and consistently extended to three dimensions, i.e., that it is "consistent around a cube" (CAC). As a consequence of CAC one can…

We propose a series-based nonparametric specification test for a regression function when data are spatially dependent, the `space' being of a general economic or social nature. Dependence can be parametric, parametric with increasing…

We prove normalization for MTT, a general multimodal dependent type theory capable of expressing modal type theories for guarded recursion, internalized parametricity, and various other prototypical modal situations. We prove that deciding…

We propose a new way of thinking about one parameter persistence. We believe topological persistence is fundamentally not about decomposition theorems but a central role is played by a choice of metrics. Choosing a pseudometric between…

Statistical inference in high dimensional settings has recently attracted enormous attention within the literature. However, most published work focuses on the parametric linear regression problem. This paper considers an important…

Parametric models abstract part of the specification of dynamical models by integral parameters. They are for example used in computational systems biology, notably with parametric regulatory networks, which specify the global architecture…

We prove that the existence of best coapproximation to any element of the normed linear space out of any one dimensional subspace and its coincidence with the best approximation to that element out of that subspace characterizes a real…

One often sees a sharp distinction in mathematics between descriptions from the outside and from the inside. Think of defining a set in the plane through an algebraic equation, or dynamically as the closure of the orbit of some point under…