Related papers: Capturing the Future by Replaying the Past
Game comonads have brought forth a new approach to studying finite model theory categorically. By representing model comparison games semantically as comonads, they allow important logical and combinatorial properties to be exressed in…
We study a model of side-effecting processes obtained by starting from a monad modelling base effects and adjoining free operations using a cofree coalgebra construction; one thus arrives at what one may think of as types of non-wellfounded…
In this note we give a simple unifying proof of the undecidability of several diagrammatic properties of term rewriting systems that include: local confluence, strong confluence, diamond property, subcommutative property, and the existence…
We present an abstract machine and a reduction semantics for the lambda-calculus extended with control operators that give access to delimited continuations in the CPS hierarchy. The abstract machine is derived from an evaluator in…
This short note contains random thoughts about a factorization theorem for closure/interior operators on a powerset which is reminiscent to the notion of resolution for a monad/comonad. The question originated from formal topology but is…
While any infimum in a poset can also be computed as a supremum, and vice versa, categorical limits and colimits do not always approximate each other. If I approach a point from below, and you approach it from above, then we will surely…
In graph theory, the Szemer\'edi regularity lemma gives a decomposition of the indicator function for any graph $G$ into a structured component, a uniform part, and a small error. This result, in conjunction with a counting lemma that…
We prove automatic continuity theorems for "decomposable" or "local" linear transformations between certain natural subspaces of operator algebras. The transformations involved are not algebra homomorphisms but often are module…
Computational effects are commonly modelled by monads, but often a monad can be presented by an algebraic theory of operations and equations. This talk is about monads and algebraic theories for languages for inference, and their…
Flow Language Models (FLMs) are a recently introduced class of language models which adapt continuous flow matching for one-hot encoded token sequences. Their denoisers have a special structure absent from generic continuous diffusion…
Compositional minimisation can be an effective technique to reduce the state space explosion problem. This technique considers a parallel composition of several processes. In its simplest form, each sequential process is replaced by an…
Even a functor without an adjoint induces a monad, namely, its codensity monad; this is subject only to the existence of certain limits. We clarify the sense in which codensity monads act as substitutes for monads induced by adjunctions. We…
In this paper, we consider topological featurizations of data defined over simplicial complexes, like images and labeled graphs, obtained by convolving this data with various filters before computing persistence. Viewing a convolution…
Equational reasoning is among the most important tools that functional programming provides us. Curiously, relatively less attention has been paid to reasoning about monadic programs. In this report we derive a backtracking algorithm for…
We introduce an algorithm for the uniform generation of infinite runs in concurrent systems under a partial order probabilistic semantics. We work with trace monoids as concurrency models. The algorithm outputs on-the-fly approximations of…
In this paper we develop in detail the geometric constructions that lead to many uniqueness results for the determination of polyhedral sets, typically scatterers, by a finite minimal number of measurements. We highlight how unique…
Parameterizing mathematical models of biological systems often requires fitting to stable periodic data. In cardiac electrophysiology this typically requires converging to a stable action potential through long simulations. We explore this…
Topological degeneracy is the degeneracy of the ground states in a many-body system in the large-system-size limit. Topological degeneracy cannot be lifted by any local perturbation of the Hamiltonian. The topological degeneracies on closed…
It has been recently shown that probabilistic protocols based on postselection boost the performances of phase estimation and the replication of quantum clocks. Here we demonstrate that the improvements in these two tasks have to match…
We compare the expressive power of three programming abstractions for user-defined computational effects: Bauer and Pretnar's effect handlers, Filinski's monadic reflection, and delimited control without answer-type-modification. This…