相关论文: Toy operads
This is a survey on Drinfeld associators and their generalizations, where we focus on operadic aspects.
Machine reading comprehension (MRC) that requires discrete reasoning involving symbolic operations, e.g., addition, sorting, and counting, is a challenging task. According to this nature, semantic parsing-based methods predict interpretable…
A discrete model of pedestrian motion is presented that is implemented in the Floor field- and Agentbased Simulation Tool (F.A.S.T.) which has already been applicated to a variety of real life scenarios.
In this paper we develop the theory of presentations for globular operads and construct presentations for the globular operads corresponding to several key theories of $n$-category for $n \leqslant 4$.
Algebraic operations are understood as topologiztion of algebra. They become an example of simplest convergence space. In our article the convergence is a arbitrary multivalued appointment. The continuity of some mapping between two…
Diassociative algebras form a categoy of algebras recently introduced by Loday. A diassociative algebra is a vector space endowed with two associative binary operations satisfying some very natural relations. Any diassociative algebra is an…
An order-theoretic forest is a countable partial order such that the set of elements larger than any element is linearly ordered. It is an order-theoretic tree if any two elements have an upper-bound. The order type of a branch can be any…
We study cobordisms of a class of topological operads called ``manifold operads''. These operads are generalizations of the Fulton-MacPherson operad: an operad built from configurations of points in Euclidean space. Cobordism of manifold…
We study different algebraic structures associated to an operad and their relations: to any operad $\mathbf{P}$ is attached a bialgebra,the monoid of characters of this bialgebra, the underlying pre-Lie algebra and its enveloping algebra;…
We introduce two topological non-$\Sigma$ operad structures on planar line arrangements subject to a certain geometric order condition, ensuring a well-defined notion of particle ordering on a distinguished line. This is interpreted in…
Based on symmetry consideration, quasi-one-dimensional (1D) objects, relevant to numerous observables or phenomena, can be classified into eight different types. We provide various examples of each 1D type, and discuss their Symmetry…
We develop deformation theory of algebras over quadratic operads where the parameter space is a commutative local algebra. We also give a construction of a distinguised deformation of an algebra over a quadratic operad with a complete local…
Tree-like tableaux are objects in bijection with alternative or permutation tableaux. They have been the subject of a fruitful combinatorial study for the past few years. In the present work, we define and study a new subclass of tree-like…
We give a general account of family algebras over a finitely presented linear operad, this operad together with its presentation naturally defining an algebraic structure on the set of parameters.
We introduce unary operadic 2-categories as a framework for operadic Grothendieck construction for categorical $\mathbb{O}$-operads, $\mathbb{O}$ being a unary operadic category. The construction is a fully faithful functor…
We examine a variety of numerical methods that arise when considering dynamical systems in the context of physics-based simulations of deformable objects. Such problems arise in various applications, including animation, robotics, control…
Trying to enumerate all of the walks in a 2D lattice is a fun combinatorial problem and there are numerous applications, from polymers to sports. Computers provide a wonderful tool for analyzing these walks; we provide a Maple package for…
In this paper, we use the language of operads to study open dynamical systems. More specifically, we study the algebraic nature of assembling complex dynamical systems from an interconnection of simpler ones. The syntactic architecture of…
We determine a class of rearrangements that admit a supporting tree. This condition implies that the associated rearrangement operator has a bounded vector valued extension. We show that there exists a large subspace of $L^p$ on which a…
Many concepts of physical optics can be visually illustrated on a relatively simple optical setup in a table-top format, not requiring any very specific equipment. Diffraction, interferences, speckle, image formation, Fourier optics,…