Related papers: Relational Connectors and Heterogeneous Bisimulati…
The notion of a duality between two derived functors as well as an extension theorem for derived functors to larger categories in which they need not be defined is introduced. These ideas are then applied to extend and study the coext…
Category theory offers a mathematical foundation for knowledge representation and database systems. Popular existing approaches model a database instance as a functor into the category of sets and functions, or as a 2-functor into the…
Behavioural distances provide a quantitative approach to comparing the states of transition systems, moving beyond traditional Boolean notions of equivalence. In this paper, we develop a sound and complete axiomatisation of behavioural…
We revisit the behavioral approach to systems theory and make explicit the abstract pattern that governs it. Our end goal is to use that pattern to understand interaction-related phenomena that emerge when systems interact. Rather than…
We prove a general congruence result for bisimilarity in higher-order languages, which generalises previous work to languages specified by a labelled transition system in which programs may occur as labels, and which may rely on operations…
In previous work, Abramsky, Dawar and Wang (LiCS 2017) and Abramsky and Shah (CSL 2018) have shown how a range of model comparison games which play a central role in finite model theory, including Ehrenfeucht-Fraisse, pebbling, and…
We provide a rigorous construction of I.M. Singer's universal connection, a natural connection on a bundle of paths associated to any manifold, using the theory of diffeology. Furthermore, we generalize the universal connection to the…
Coalgebras for analytic functors uniformly model graph-like systems where the successors of a state may admit certain symmetries. Examples of successor structure include ordered tuples, cyclic lists and multisets. Motivated by goals in…
By considering labeled configurations of ``bounded multiplicity'', one can construct a functor that fits between homology and stable homotopy. Based on previous work, we are able to give an equivalent description of this labeled…
We interpret ontological models for finite-dimensional quantum theory as functors from the category of finite-dimensional Hilbert spaces and bounded linear maps to the category of measurable spaces and Markov kernels. This uniformises…
In the first half of the paper, some recent advances in coupled dynamical systems, in particular, a globally coupled map are surveyed. First, dominance of Milnor attractors in partially ordered phase is demonstrated. Second, chaotic…
Attractor-repeller decompositions of isolated invariant sets give rise to so-called connecting homomorphisms. These homomorphisms reveal information on the existence and structure of connecting trajectories of the underlying dynamical…
Several notions of bisimulation relations for probabilistic non-deterministic transition systems have been considered in the literature. We consider a novel testing-based behavioral equivalence called upper-expectation bisimilarity and…
Universal schema jointly embeds knowledge bases and textual patterns to reason about entities and relations for automatic knowledge base construction and information extraction. In the past, entity pairs and relations were represented as…
In classical set theory, there are many equivalent ways to introduce ordinals. In a constructive setting, however, the different notions split apart, with different advantages and disadvantages for each. We consider three different notions…
A construction of the bi-Hamiltonian structures for integrable systems on regular time scales is presented. The trace functional on an algebra of $\delta$-pseudo-differential operators, valid on an arbitrary regular time scale, is…
We study Abramsky's applicative bisimilarity abstractly, in the context of call-by-value $\lambda$-calculi with algebraic effects. We first of all endow a computational $\lambda$-calculus with a monadic operational semantics. We then show…
Motivated by a recent conjecture concerning the expressiveness of declarative networking, we propose a formal computation model for "eventually consistent" distributed querying, based on relational transducers. A tight link has been…
Every exchangeable Feller process taking values in a suitably nice combinatorial state space can be constructed by a system of iterated random Lipschitz functions. In discrete time, the construction proceeds by iterated application of…
This paper is divided into two parts. The first is a review, through categorical lenses, of the classical theory of regular-singular differential systems over $C((x))$ and $\mathbb P^1_C\smallsetminus\{0,\infty\}$, where $C$ is…