Related papers: Definability via the tilting correspondence

Seiberg-Witten theory leads to a delicate interplay between Riemannian geometry and smooth topology in dimension four. In particular, the scalar curvature of any metric must satisfy certain non-trivial estimates if the manifold in question…

We consider one dimensional deformed Heisenberg algebra leading to existence of minimal length for coordinate operator and minimal and maximal uncertainty of momentum operator. For this algebra an exactly solvable Hamiltonian is…

The almost purity theorem is central to the geometry of perfectoid spaces and has numerous applications in algebra and geometry. This result is known to have several different proofs in the case that the base ring is a perfectoid valuation…

We analyse a new notion of total anisotropic higher-order variation which, differently from the Total Generalized Variation by Bredies et al., quantifies for possibly non-symmetric tensor fields their variations at arbitrary order weighted…

We introduce a new consistency-based approach for defining and solving nonnegative/positive matrix and tensor completion problems. The novelty of the framework is that instead of artificially making the problem well-posed in the form of an…

We show that a gentle algebra over a field is $\tau$-tilting finite if and only if it is representation-finite. The proof relies on the "brick-$\tau$-tilting correspondence" of Demonet-Iyama-Jasso and on a combinatorial analysis.

This is a survey of results on definability and undefinability in models of arithmetic. The goal is to present a stark difference between undefinability results in the standard model and much stronger versions about expansions of…

An N-dimensional position-dependent mass Hamiltonian (depending on a parameter \lambda) formed by a curved kinetic term and an intrinsic oscillator potential is considered. It is shown that such a Hamiltonian is exactly solvable for any…

The geometric formulation of fiducial probability employed in this paper is an improvement over the usual pivotal quantity formulation. For a single parameter and single observation, the new formulation is based on the geometric properties…

We investigate the equational theory of Kleene algebra terms with variable complements -- (language) complement where it applies only to variables -- w.r.t. languages. While the equational theory w.r.t. languages coincides with the language…

Calibration is a frequently invoked concept when useful label probability estimates are required on top of classification accuracy. A calibrated model is a function whose values correctly reflect underlying label probabilities. Calibration…

We study the implications of model completeness of a theory for the effectiveness of presentations of models of that theory. It is immediate that for a computable model $\mathcal A$ of a computably enumerable, model complete theory, the…

We contribute to the knowledge of the quantifier completions and their applications by using the language of doctrines. This algebraic presentation allows us to properly analyse the behaviour of the existential and universal quantifiers. We…

In this note we prove that the class of valuation functions representable via integral assignment messages is a proper subset of strong substitutes valuations. Thus, there are strong substitutes valuations not expressible via assignment…

We study here slopes of periodicity of tilings. A tiling is of slope if it is periodic along direction but has no other direction of periodicity. We characterize in this paper the set of slopes we can achieve with tilings, and prove they…

Learning the parameters of a (potentially partially observable) random field model is intractable in general. Instead of focussing on a single optimal parameter value we propose to treat parameters as dynamical quantities. We introduce an…

The nonlinear equations describing all the nonsingular pencils of metrics of constant Riemannian curvature are derived and the integrability of these nonlinear equations by the method of inverse scattering problem is proved. It is proved…

In this paper, we show that a partitioned formula \phi is dependent if and only if \phi has uniform definability of types over finite partial order indiscernibles. This generalizes our result from a previous paper [1]. We show this by…

We are concerned with topology of Hensel minimal structures on non-trivially valued fields $K$, whose axiomatic theory was introduced in a recent paper by Cluckers-Halupczok-Rideau. We additionally require that every definable subset in the…

A new characterization of harmonic functions is obtained. It is based on quadrature identities involving mean values over annular domains and over concentric spheres lying within these domains or on their boundaries. The analogous result…