相关论文: Scope ambiguities, monads and strengths

A strongly polynomial algorithm is given for the generalized flow maximization problem. It uses a new variant of the scaling technique, called continuous scaling. The main measure of progress is that within a strongly polynomial number of…

We abstract and generalize homotopical monadicity statements, placing in a single conceptual framework a range of old and recent recognition and characterization principles in iterated loop space theory in classical, equivariant, and…

These are notes from a multi-year learning seminar on the algebraic approach to Constraint Satisfaction Problems (CSPs). The main topics covered are the theory of algebraic structures with few subpowers, the theory of absorbing subalgebras…

3D point cloud segmentation has made tremendous progress in recent years. Most current methods focus on aggregating local features, but fail to directly model long-range dependencies. In this paper, we propose Stratified Transformer that is…

Embodied AI has made significant progress acting in unexplored environments. However, tasks such as object search have largely focused on efficient policy learning. In this work, we identify several gaps in current search methods: They…

The theory of regular cost functions is a quantitative extension to the classical notion of regularity. A cost function associates to each input a non-negative integer value (or infinity), as opposed to languages which only associate to…

The coalgebraic modelling of alternating automata and of probabilistic automata has long been obstructed by the absence of distributive laws of the powerset monad over itself, respectively of the powerset monad over the finite distribution…

We introduce contextads and the Ctx construction, unifying various structures and constructions in category theory dealing with context and contextful arrows -- comonads and their Kleisli construction, actegories and their Para…

This paper deals with three traditional ways of defining contextuality: (C1) in terms of (non)existence of certain joint distributions involving measurements made in several mutually exclusive contexts; (C2) in terms of relationship between…

In this work, we investigate the problem of learning distance functions within the query-based learning framework, where a learner is able to pose triplet queries of the form: ``Is $x_i$ closer to $x_j$ or $x_k$?'' We establish formal…

The free algebra adjunction, between the category of algebras of a monad and the underlying category, induces a comonad on the category of algebras. The coalgebras of this comonad are the topic of study in this paper (following earlier…

We study the complexity of reasoning in abstracts argumentation frameworks close to graph classes that allow for efficient reasoning methods, i.e.\ to one of the classes of acyclic, noeven, biparite and symmetric AFs. In this work we show…

Computationally tractable methods are developed for centralized goal assignment and planning of collision-free polynomial-in-time trajectories for systems of multiple aerial robots. The method first assigns robots to goals to minimize total…

We describe a MOND-related approach to natural scales of distance and mass, viewing it as a logical step following Planck's modification of the Stoney system of units. The MOND-induced scales are not based on the strength of any physical…

We describe a generic construction of non-wellfounded syntax involving variable binding and its monadic substitution operation. Our construction of the syntax and its substitution takes place in category theory, notably by using monoidal…

Statisticians have recently developed propensity score methods to improve generalizations from randomized experiments that do not employ random sampling. However, these methods typically rely on assumptions whose plausibility may be…

I consider configuration spaces for $N$-body problems, gauge theories and for GR in both geometrodynamical and Ashtekar variables forms, including minisuperspace and inhomogeneous perturbations thereabout in the former case. These examples…

Given topological spaces X and Y, a fundamental problem of algebraic topology is understanding the structure of all continuous maps X -> Y . We consider a computational version, where X, Y are given as finite simplicial complexes, and the…

Using the braided version of Lawvere's algebraic theories and Mac Lane's PROPs, we introduce polynomial identities for arbitrary algebraic structures in a braided monoidal category C as well as their codimensions in the case when C is…

A general notion of operad is given, which includes as instances, the operads originally conceived to study loop spaces, as well as the higher operads that arise in the globular approach to higher dimensional algebra. In the framework of…