Related papers: Finite Relation Algebras with Normal Representatio…
We introduce a finite-dimensional algebra that controls the possible boundary conditions of a conformal field theory. For theories that are obtained by modding out a Z_2 symmetry (corresponding to a so-called D_odd-type, or half-integer…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
Two extension problems are solved. First, the class of locally matricial algebras over an arbitrary field is closed under extensions. Second, the class of locally finite dimensional semisimple algebras over a fixed field is closed under…
For a first-order theory $T$, the Constraint Satisfaction Problem of $T$ is the computational problem of deciding whether a given conjunction of atomic formulas is satisfiable in some model of $T$. In this article we develop sufficient…
Let \Gamma be a structure with a finite relational signature and a first-order definition in (R;*,+) with parameters from R, that is, a relational structure over the real numbers where all relations are semi-algebraic sets. In this article,…
Lie conformal algebras appear in the theory of vertex algebras. Their relation is similar to that of Lie algebras and their universal enveloping algebras. Associative conformal algebras play a role in conformal representation theory. We…
The spreadsheet application is among the most widely used computing tools in modern society. It provides excellent usability and usefulness, and it easily enables a non-programmer to perform programming-like tasks in a visual tabular "pen…
Kinematic algebras can be realised on geometric spaces and constrain the physical models that can live on these spaces. Different types of kinematic algebras exist and we consider the interplay of these algebras for non-relativistic limits…
Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field $k$. We survey some results on algebras of finite global dimension and address some open problems.
Classical algebraic structures require exact satisfaction of their defining axioms. We propose similarity algebra, a framework extending algebraic and Lie structures to settings where operations satisfy quantitative bounds up to a tolerance…
A qualitative representation $\phi$ is like an ordinary representation of a relation algebra, but instead of requiring $(a; b)^\phi = a^\phi | b^\phi$, as we do for ordinary representations, we only require that $c^\phi\supseteq a^\phi |…
We exhibit an adjunction between a category of abstract algebras of partial functions that we call difference-restriction algebras and a category of Hausdorff \'etale spaces. Difference-restriction algebras are those algebras isomorphic to…
Increasing amounts of available data have led to a heightened need for representing large-scale probabilistic knowledge bases. One approach is to use a probabilistic database, a model with strong assumptions that allow for efficiently…
In this paper, we propose an abstract definition of dependent type theories as essentially algebraic theories. One of the main advantages of this definition is its composability: simple theories can be combined into more complex ones, and…
Conformal boundary conditions in two-dimensional conformal field theories are still mostly an uncharted territory. Even less is known about the relevant boundary deformations that connect them. A natural approach to the problem is via…
The universal-algebraic approach has proved a powerful tool in the study of the complexity of CSPs. This approach has previously been applied to the study of CSPs with finite or (infinite) omega-categorical templates, and relies on two…
These notes collect results about algebraic correspondences and adapt them to the setting of correspondences on projective lines. The focus lies on finite orbits of algebraic correspondences. The main result is a field theoretic…
From algebraic geometry perspective database relations are succinctly defined as Finite Varieties. After establishing basic framework, we give analytic proof of Heath theorem from Database Dependency theory. Next, we leverage…
Relation extraction is a fundamental problem in natural language processing. Most existing models are defined for relation extraction in the general domain. However, their performance on specific domains (e.g., biomedicine) is yet unclear.…
Abstract argumentation frameworks (AFs) provide a formal setting to analyze many forms of reasoning with conflicting information. While the expressiveness of general infinite AFs make them a tempting tool for modeling many kinds of…