Related papers: A note on complementary knowledge spaces
We prove structural theorems for computing the completion of a G-spectrum at the augmentation ideal of the Burnside ring of a finite group G. First we show that a G-spectrum can be replaced by a spectrum obtained by allowing only isotropy…
In this paper, we present a constructive generalization of metric and uniform spaces by introducing a new class of spaces, called cover spaces. These spaces form a topological concrete category with a full reflective subcategory of complete…
We address the fundamental question of whether epistemic models can reproduce the empirical predictions of general quantum preparations. This involves comparing the common quantum overlap determined by the anti-distinguishability of a set…
Two infinite sequences A and B of non-negative integers are called additive complements, if their sum contains all sufficiently large integers. Let $A(x)$ and $B(x)$ be the counting functions of A and B. In this paper, we extend the results…
A $t\text{-}(n,K,\lambda;q)$ design, also called the $q$-analog of a $t$-wise balanced design, is a set ${\mathcal B}$ of subspaces with dimensions contained in $K$ of the $n$-dimensional vector space ${\mathbb F}_q^n$ over the finite field…
For infinite cardinals $\kappa,\lambda$ let $C(\kappa,\lambda)$ denote the class of all compact Hausdorff spaces of weight $\kappa$ and size $\lambda$. So $C(\kappa,\lambda)=\emptyset$ if $\kappa>\lambda$ or $\lambda>2^\kappa$. If F is a…
A specialization semilattice is a join semilattice together with a coarser preorder $ \sqsubseteq $ satisfying an appropriate compatibility condition. If $X$ is a topological space, then $(\mathcal P(X), \cup, \sqsubseteq )$ is a…
Knowledge base (KB) completion adds new facts to a KB by making inferences from existing facts, for example by inferring with high likelihood nationality(X,Y) from bornIn(X,Y). Most previous methods infer simple one-hop relational synonyms…
Learning product representations that reflect complementary relationship plays a central role in e-commerce recommender system. In the absence of the product relationships graph, which existing methods rely on, there is a need to detect the…
We prove that, for every compact spaces $K_1,K_2$ and compact group $G$, if both $K_1$ and $K_2$ map continuously onto $G$, then the Banach space $C(K_1 \times K_2)$ contains a complemented subspace isometric to the Banach space $C(G)$.…
The restrictions that nature places on the distribution of correlations in a multipartite quantum system play fundamental roles in the evolution of such systems, and yield vital insights into the design of protocols for the quantum control…
In this paper, we study the properties of coverings of locally conformally K\"ahler (LCK) spaces with singularities. We begin by proving that a space is LCK if any only if its universal cover is K\"ahler, thereby generalizing a result from…
Any subset Q' of the domain Q of a learning space defines a projection of that learning space on Q' which is itself a learning space consistent with the original one. Moreover, such a construction defines a partition of Q having each of its…
Knowledge graphs (KGs) consisting of triples are always incomplete, so it's important to do Knowledge Graph Completion (KGC) by predicting missing triples. Multi-Source KG is a common situation in real KG applications which can be viewed as…
Let X,Y be two Banach spaces ; in the first part of this work, we show that K(X,Y) contains a complemented copy of c0 if Y contains a copy of c0 and each bounded sequence in Y has a subsequece which is w* convergente. Afterward we obtain…
In this paper we discuss a couple of observations related to polynomial convexity. More precisely, (i) We observe that the union of finitely many disjoint closed balls with centres in $\cup_{\theta\in[0,\pi/2]}e^{i\theta}V$ is polynomially…
We show that any quantum family of maps from a non commutative space to a compact quantum metric space has a canonical quantum semi metric structure.
Graph Neural Networks (GNNs) have demonstrated great success in Knowledge Graph Completion (KGC) by modeling how entities and relations interact in recent years. However, most of them are designed to learn from the observed graph structure,…
Mutually unbiased bases encapsulate the concept of complementarity - the impossibility of simultaneous knowledge of certain observables - in the formalism of quantum theory. Although this concept is at the heart of quantum mechanics, the…
Knowledge graphs (KGs) contain rich information about world knowledge, entities and relations. Thus, they can be great supplements to existing pre-trained language models. However, it remains a challenge to efficiently integrate information…