Related papers: Yoneda lemma
We present a novel method of computing the beta-normal eta-long form of a simply-typed lambda-term by constructing traversals over a variant abstract syntax tree of the term. In contrast to beta-reduction, which changes the term by…
In this work we provide alternative formulations of the concepts of lambda theory and extensional theory without introducing the notion of substitution and the sets of all, free and bound variables occurring in a term. We also clarify the…
Szemer\'edi's regularity lemma is a basic tool in graph theory, and also plays an important role in additive combinatorics, most notably in proving Szemer\'edi's theorem on arithmetic progressions . In this note we revisit this lemma from…
This paper proposes a definition of recognizable transducers over monads and comonads, which bridges two important ongoing efforts in the current research on regularity. The first effort is the study of regular transductions, which extends…
The regularity of monotone transport maps plays an important role in several applications to PDE and geometry. Unfortunately, the classical statements on this subject are restricted to the case when the measures are compactly supported. In…
The Reynolds Transport Theorem, colloquially known as 'differentiation under the integral sign', is a central tool of applied mathematics, finding application in a variety of disciplines such as fluid dynamics, quantum mechanics, and…
We survey the construction and properties of the Yamada polynomial of spatial graphs and present the Yamada polynomial formulae for some classes of graphs. Then we construct an infinite family of spatial graphs for which roots of Yamada…
Session-based recommendation plays a central role in a wide spectrum of online applications, ranging from e-commerce to online advertising services. However, the majority of existing session-based recommendation techniques (e.g.,…
Given a graph, we associate each edge with the transposition which exchanges the endvertices. Fixing a linear order on the edge set, we obtain a permutation of the vertices. D\'enes proved that the permutation is a full cyclic permutation…
Inspired by distributed algorithms, we introduce a new class of finite graph automata that recognize precisely the graph languages definable in monadic second-order logic. For the cases of words and trees, it has been long known that the…
We decribe the correspondence between normalised $\omega$-operads and certain lax monoidal structures on the category of globular sets. As with ordinary monoidal categories, one has a notion of category enriched in a lax monoidal category.…
Using message-passing graph neural networks (MPNNs) for node and link prediction is crucial in various scientific and industrial domains, which has led to the development of diverse MPNN architectures. Besides working well in practical…
We will define new constructions similar to the graph systems of correspondences described by Deaconu et al. We will use these to prove a version of Ionescu's theorem for higher rank graphs. Afterwards we will examine the properties of…
For any graph G we define bigraded cohomology groups whose graded Euler characteristic is a multiple of the Yamada polynomial of G.
The literature on word-representable graphs is quite rich, and a number of variations of the original definition have been proposed over the years. We are initiating a systematic study of such variations based on formal languages. In our…
For a group $G$ and a subset $X$ of $G$, the commuting graph of $X$, denoted by $\Gamma(G,X)$ is the graph whose vertex set is $X$ and any two vertices $u$ and $v$ in $X$ are adjacent if and only if they commute in $G$. In this article,…
Graphs arise naturally in many real-world applications including social networks, recommender systems, ontologies, biology, and computational finance. Traditionally, machine learning models for graphs have been mostly designed for static…
Knowledge graphs such as DBpedia, Freebase or Wikidata always contain a taxonomic backbone that allows the arrangement and structuring of various concepts in accordance with the hypo-hypernym ("class-subclass") relationship. With the rapid…
Modern deep transfer learning approaches have mainly focused on learning generic feature vectors from one task that are transferable to other tasks, such as word embeddings in language and pretrained convolutional features in vision.…
Most Graph Neural Networks (GNNs) cannot distinguish some graphs or indeed some pairs of nodes within a graph. This makes it impossible to solve certain classification tasks. However, adding additional node features to these models can…