Related papers: Basis discrepancies for extensions of valued field…

An expansion of a definably complete field either defines a discrete subring, or the image of a definable discrete set under a definable map is nowhere dense. As an application we show a definable version of Lebesgue's differentiation…

An adjoint-based procedure to determine weaknesses, or, more generally the material properties of structures is developed and tested. Given a series of force and deformation/strain measurements, the material properties are obtained by…

We consider existentially closed fields with several orderings, valuations, and $p$-valuations. We show that these structures are NTP$_2$ of finite burden, but usually have the independence property. Moreover, forking agrees with dividing,…

A field is existentially t-henselian if it is has the same existential theory in the first-order language of rings as a field that admits a nontrivial henselian valuation. This property turns out to be equivalent to $\mathbb{Z}$-largeness,…

Differential algebraic geometry seeks to extend the results of its algebraic counterpart to objects defined by differential equations. Many notions, such as that of a projective algebraic variety, have close differential analogues but their…

Machine learning models achieve state-of-the-art performance across domains, yet their lack of interpretability limits safe deployment in high-stakes settings. Counterfactual explanations are widely used to provide actionable "what-if"…

The history of complementary observables and mutual unbiased bases is reviewed. A characterization is given in terms of conditional entropy of subalgebras. The concept of complementarity is extended to non-commutative subalgebras.…

We introduce and study a new class of differential fields in positive characteristic. We call them separably differentially closed fields and demonstrate that they are the differential analogue of separably closed fields. We prove several…

A variety of methods exist to explain image classification models. However, whether they provide any benefit to users over simply comparing various inputs and the model's respective predictions remains unclear. We conducted a user study…

We construct the base $2$ expansion of an absolutely normal real number $x$ so that, for every integer $b$ greater than or equal to $2$, the discrepancy modulo $1$ of the sequence $(b^0 x, b^1 x, b^2 x , \ldots)$ is essentially the same as…

We use a generalization of a construction by Ziegler to show that for any field $F$ and any countable collection of countable subsets $A_i \subseteq F, i \in \calI \subset \Z_{>0}$ there exist infinitely many fields $K$ of arbitrary…

Argumentation is a central subarea of Artificial Intelligence (AI) for modeling and reasoning about arguments. The semantics of abstract argumentation frameworks (AFs) is given by sets of arguments (extensions) and conditions on the…

Given a valuation $v$ on a field $K$, an extension $\bar{v}$ to an algebraic closure and an extension $w$ to $K(X)$. We want to study the common extensions of $\bar{v}$ and $w$ to $\bar{K}(X)$. First we give a detailed link between the…

An equivalence is established between the category of at most $a$-ramified finite separable extensions of a complete discrete valuation field $K$ and the category of at most $a$-ramified finite extensions of the "length-$a$ truncation"…

So far there exist just a few results about the uniqueness of maximal immediate valued differential field extensions and about the relationship between differential-algebraic maximality and differential-henselianity; see arXiv:1509.02588,…

Let K be a finite Galois extension of Q. The normal basis theorem provides an element of K whose conjugates form a Q-basis of K. Here we obtain such an element with controlled size. This improves a recent result by Fukshansky and Jeong. By…

Knowledge bases are widely used for information management, enabling high-impact applications such as web search, question answering, and natural language processing. They also serve as the backbone for automatic decision systems, e.g., for…

We study fragments of the existential theory of henselian valued fields with parameters. This includes the $\exists_n$-fragment in the equicharacteristic or unramified mixed characteristic case, the $\exists_n\exists_1$-fragment in the…

We consider estimation under model misspecification where there is a model mismatch between the underlying system, which generates the data, and the model used during estimation. We propose a model misspecification framework which enables a…

Suppose $F$ is a field with valuation $v$ and valuation ring $O_{v}$, $E$ is a finite field extension and $w$ is a quasi-valuation on $E$ extending $v$. We study quasi-valuations on $E$ that extend $v$; in particular, their corresponding…