Related papers: PRINC domains and comaximal factorization domains

In this paper we propose a new definition of prime ends for domains in metric spaces under rather general assumptions. We compare our prime ends to those of Carath\'eodory and N\"akki. Modulus ends and prime ends, defined by means of the…

Existing domain adaptation focuses on transferring knowledge between domains with categorical indices (e.g., between datasets A and B). However, many tasks involve continuously indexed domains. For example, in medical applications, one…

Let $D$ be the ring of integers of a quadratic number field $\mathbb{Q}[\sqrt{d}]$. We study the factorizations of $2 \times 2$ matrices over $D$ into idempotent factors. When $d < 0$ there exist singular matrices that do not admit…

The appeal of metric evaluation of research impact has attracted considerable interest in recent times. Although the public at large and administrative bodies are much interested in the idea, scientists and other researchers are much more…

We investigate a special class of Pr\"ufer domains, firstly introduced by Dress in 1965. The {\it minimal Dress ring} $D_K$, of a field $K$, is the smallest subring of $K$ that contains every element of the form $1/(1+x^2)$, with $x\in K$.…

Behavioral software models play a key role in many software engineering tasks; unfortunately, these models either are not available during software development or, if available, quickly become outdated as implementations evolve. Model…

Let R be a Dedekind domain with global quotient field K. The purpose of this note is to provide a characterization of when a strongly graded R-order with semiprime 1-component is hereditary. This generalizes earlier work by the first author…

Protection domains are one of the most enduring concepts in Access Control. Entities with identical access control characteristics are grouped under the same protection domain, and domain-based policies assign access privileges to the…

Let $S(D)$ represent a set of proper nonzero ideals $I(D)$ (resp., $t$ -ideals $I_{t}(D)$) of an integral domain $D\neq qf(D)$ and let $P$ be a valid property of ideals of $D.$ We say $S(D)$ meets $P$ (denoted $ S(D)\vartriangleleft P)$ if…

For rings R with identity, we define a class of nonlinear higher order recurrences on unitary left R-modules that include linear recurrences as special cases. We obtain conditions under which a recurrence of order k+1 in this class is…

Given a causal graph representing the data-generating process shared across different domains/distributions, enforcing sufficient graph-implied conditional independencies can identify domain-general (non-spurious) feature representations.…

In recent work, we proved that the domain recursion inference rule makes domain-lifted inference possible on several relational probability models (RPMs) for which the best known time complexity used to be exponential. We also identified…

Given data from diverse sets of distinct distributions, domain generalization aims to learn models that generalize to unseen distributions. A common approach is designing a data-driven surrogate penalty to capture generalization and…

In this paper we give the first explicit enumeration of all maximal Condorcet domains on $n\leq 7$ alternatives. This has been accomplished by developing a new algorithm for constructing Condorcet domains, and an implementation of that…

We develop the theory of continuous and algebraic domains in constructive and predicative univalent foundations, building upon our earlier work on basic domain theory in this setting. That we work predicatively means that we do not assume…

This article investigates the properties of Dedekind superrings, invertible supermodules and projective supermodules within the $\mathbb{Z}_2$-graded framework. Rather than treating these entities as specialized instances of general…

Let $D$ be an integral domain and $\star$ a semistar operation on $D$. As a generalization of the notion of Noetherian domains to the semistar setting, we say that $D$ is a $\star$--Noetherian domain if it has the ascending chain condition…

Motivated by the classical theory of spin structures, we develop a theory for lifting free C$^*$-dynamical systems, a.k.a. noncommutative principal bundles, along central extensions. This theory extends the bundle-theoretic notion of spin…

Continuous Domain Adaptation (CDA) effectively bridges significant domain shifts by progressively adapting from the source domain through intermediate domains to the target domain. However, selecting intermediate domains without explicit…

Solomonoff unified Occam's razor and Epicurus' principle of multiple explanations to one elegant, formal, universal theory of inductive inference, which initiated the field of algorithmic information theory. His central result is that the…