Related papers: Biracks: a notational proposal and applications
In this paper, we postulate that combining the domains of information visualization and music studies paves the ground for a more structured analysis of the design space of music notation, enabling the creation of alternative music…
In this note, we offer a palatable introduction to the field of arithmetic dynamics. That is, we study the patterns that arise when iterating a polynomial map. This note is accessible to those who have taken an introductory proof based…
The aim of this paper is to define certain algebraic structures coming from generalized Reidemeister moves of singular knot theory. We give examples, show that the set of colorings by these algebraic structures is an invariant of singular…
We introduce the notion of implicative algebra, a simple algebraic structure intended to factorize the model constructions underlying forcing and realizability (both in intuitionistic and classical logic). The salient feature of this…
The author advocates two specific mathematical notations from his popular course and joint textbook, "Concrete Mathematics". The first of these, extending an idea of Iverson, is the notation "[P]" for the function which is 1 when the…
A Hopf algebra object in Loday and Pirashvili's category of linear maps entails an ordinary Hopf algebra and a Yetter-Drinfel'd module. We equip the latter with a structure of a braided Leibniz algebra. This provides a unified framework for…
Using only the combinatorics of its defining ribbon graph, we classify the two-term tilting complexes, as well as their indecomposable summands, of a Brauer graph algebra. As an application, we determine precisely the class of Brauer graph…
In this paper we continue with the algebraic study of Krivine's realizability, refining some of the authors' previous constructions by introducing two categories, with objects the abstract Krivine structures and the implicative algebras…
Let R be a ring. A construction method for flexible quadratic algebras with scalar involution over R is presented which unifies various classical constructions in the literature, in particular those to construct composition algebras.
We study higher-order analogues of Dirac structures, extending the multisymplectic structures that arise in field theory. We define higher Dirac structures as involutive subbundles of $TM+\wedge^k TM^*$ satisfying a weak version of the…
Predicate-argument structure analysis is a central component in meaning representations of text. The fact that some arguments are not explicitly mentioned in a sentence gives rise to ambiguity in language understanding, and renders it…
We define the notion of circular words, then consider on such words a constraint derived from the Fibonacci condition. We give several results on the structure of these circular words, then mention possible applications to various…
The classical work of Feferman Vaught gives a powerful, constructive analysis of definability in (generalized) product structures, and certain associated enriched Boolean structures. %structures in terms of definability in the component…
Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…
This paper outlines a general formal framework for reasoning systems, intended to support future analysis of inference architectures across domains. We model reasoning systems as structured tuples comprising phenomena, explanation space,…
We present an algebraic approach to the internal structure of baryons in terms of three constituents. We investigate a collective model in which the nucleon is regarded as a rotating and vibrating oblate top with a prescribed distribution…
We try to bring to light some combinatorial structure underlying formal proofs in logic. We do this through the study of the Craig Interpolation Theorem which is properly a statement about the structure of formal derivations. We show that…
We introduce and investigate here a formalisation for conditionals that allows the definition of a broad class of reasoning systems. This framework covers the most popular kinds of conditional reasoning in logic-based KR: the semantics we…
Extending the lambda-calculus with a construct for sharing, such as let expressions, enables a special representation of terms: iterated applications are decomposed by introducing sharing points in between any two of them, reducing to the…
The increasing availability of corpora annotated for linguistic structure prompts the question: if we have the same texts, annotated for phrase structure under two different schemes, to what extent do the annotations agree on structuring…