Related papers: Algebraic Approach to Directed Rough Sets
Traditional relation extraction predicts relations within some fixed and finite target schema. Machine learning approaches to this task require either manual annotation or, in the case of distant supervision, existing structured sources of…
Distributionally robust optimization tackles out-of-sample issues like overfitting and distribution shifts by adopting an adversarial approach over a range of possible data distributions, known as the ambiguity set. To balance conservatism…
This paper examines the characterization and learning of grammars defined with enriched representational models. Model-theoretic approaches to formal language theory traditionally assume that each position in a string belongs to exactly one…
Many real-world domains can be expressed as graphs and, more generally, as multi-relational knowledge graphs. Though reasoning and learning with knowledge graphs has traditionally been addressed by symbolic approaches, recent methods in…
Let $X$ be an analytic subset of $U\times C^n$ of pure dimension $k$ such that the projection of $X$ onto $U$ is a proper mapping, where $U$ is a Runge domain in $C^k$. We show that $X$ can be approximated by algebraic sets.
The identification of semantic relations between terms within texts is a fundamental task in Natural Language Processing which can support applications requiring a lightweight semantic interpretation model. Currently, semantic relation…
The aim of the present paper is to generalize the concept of residuated poset, by replacing the usual partial ordering by a generic binary relation, giving rise to relational systems which are residuated. In particular, we modify the…
One of the traditional applications of relation algebras is to provide a setting for infinite-domain constraint satisfaction problems. Complexity classification for these computational problems has been one of the major open research…
The goal of this note is to provide a geometric setting in which generalized arithmetic means are best predictors in an appropriate metric. This characterization provides a geometric interpretation to the concept of certainty equivalent.…
Fix a prime number $p$. We report on some recent developments in algebraic geometry (broadly construed) over $p$-adically complete commutative rings. These developments include foundational advances within the subject as well as external…
To any directed graph we associate an algebra with edges of the graph as generators and with relations defined by all pairs of directed paths with the same origin and terminus. Such algebras are related to factorizations of polynomials over…
High-dimensional representations for words, text, images, knowledge graphs and other structured data are commonly used in different paradigms of machine learning and data mining. These representations have different degrees of…
Process theories combine a graphical language for compositional reasoning with an underlying categorical semantics. They have been successfully applied to fields such as quantum computation, natural language processing, linear dynamical…
We are interested in shapes of real algebraic curves in the plane and regions surrounded by them: they are named refined algebraic domains by the author. As characteristic finite sets, we consider points contained in two curves and the sets…
General purpose relation extractors, which can model arbitrary relations, are a core aspiration in information extraction. Efforts have been made to build general purpose extractors that represent relations with their surface forms, or…
Covering-based rough set theory is an extension to classical rough set. The main purpose of this paper is to study covering rough sets from a topological point of view. The relationship among upper approximations based on topological spaces…
In the authors book, Associative Algebraic Geometry, 2023, and the following article Shemes of Associative Algebras,\\ https://doi.org/10.48550/arXiv.2410.17703,2024, we use an algebraization of the semi-local formal moduli of simple…
This paper pursues a twofold goal. First, we introduce and study in detail a new notion of variational analysis called generalized metric subregularity, which is a far-going extension of the conventional metric subregularity conditions. Our…
High-efficient direct numerical methods are currently in demand for optimization procedures in the fields of both conventional diffractive and metasurface optics. With a view of extending the scope of application of the previously proposed…
The main purpose of this paper is to lay the foundations of a general theory which encompasses the features of the classical Hough transform and extend them to general algebraic objects such as affine schemes. The main motivation comes from…