Related papers: A note on complementary knowledge spaces
The deductive closure of an ideal knowledge base (KB) contains exactly the logical queries that the KB can answer. However, in practice KBs are both incomplete and over-specified, failing to answer some queries that have real-world answers.…
We prove a new impossibility for quantum information (the no-splitting theorem): an unknown quantum bit (qubit) cannot be split into two complementary qubits. This impossibility, together with the no-cloning theorem, demonstrates that an…
We derive complementarity relations for arbitrary quantum states of multiparty systems, of arbitrary number of parties and dimensions, between the purity of a part of the system and several correlation quantities, including entanglement and…
This paper is concerned with a covering problem of Euclidean space by a particular arrangement of cones that are not necessarily full and are allowed to overlap. The problem provides an equivalent geometric reformulation of the solvability…
The work is devoted to study of quantum mutual information and coherent information -- the two important characteristics of quantum communication channel. Appropriate definitions of these quantities in the infinite-dimensional case are…
This paper addresses and expands on the contents of the recent Letter [Phys. Rev. Lett. 111, 030502 (2013)] discussing private quantum subsystems. Here we prove several previously presented results, including a condition for a given random…
Quantum capacities are fundamental quantities that are notoriously hard to compute and can exhibit surprising properties such as superadditivity. Thus, a vast amount of literature is devoted to finding tight and computable bounds on these…
Knowledge Graph Completion is a task of expanding the knowledge graph/base through estimating possible entities, or proper nouns, that can be connected using a set of predefined relations, or verb/predicates describing interconnections of…
We give a new completion for the quasi-uniform spaces. We call the whole procedure {\it $\tau$-completion} and the new space {\it $\tau$-complement of the given}. The basic result is that every $T_{_0}$ quasi-uniform space has a…
Quantum resources lie at the core of quantum computation as they are responsible for the computational advantage in many tasks. The complementary relations are a pathway to understanding how the physical quantities are related. Here it was…
We prove a conjecture that arose in the context of a subspace enumeration problem over finite fields. We prove, more generally, a bibasic, double-sum identity, which extends a $q$-analogue of the (terminating) binomial theorem.
Let $\mathcal{P}_{K} (^{n}E; F)$ (resp. $\mathcal{P}_{w} (^{n}E; F)$) the subspace of all $P\in \mathcal{P}(^{n}E; F)$ which are compact (resp. weakly continuous on bounded sets). We show that if $\mathcal{P}_{K} (^{n}E; F)$ contains an…
Complemented lattices and uniquely complemented lattices are very important, not only in mathematics, but also in physics, biology, and even in social sciences. They have been investigated for a long time, especially by Huntington,…
A real square matrix $A$ is called a $Q$-matrix if the linear complementarity problem $LCP(A,q)$ has a solution for all $q \in \mathbb{R}^n$. This means that for every vector $q$ there exists a vector $x$ such that $x \geq 0, y=Ax+q\geq 0$…
Knowledge graph completion (KGC), the task of predicting missing information based on the existing relational data inside a knowledge graph (KG), has drawn significant attention in recent years. However, the predictive power of KGC methods…
Knowledge Bases (KBs) play a key role in various applications. As two representative KB-related tasks, knowledge base completion (KBC) and knowledge base question answering (KBQA) are closely related and inherently complementary with each…
Given two $G$-Galois extensions of $\mathbb Q$, is there an extension of $\mathbb Q(t)$ that specializes to both? The equivalence relation on $G$-Galois extension of $\mathbb Q$, induced by the above question, is called $R$-equivalence. The…
Finite unions of convex sets are a central object of study in discrete and computational geometry. In this paper we initiate a systematic study of complements of such unions -- i.e., sets of the form $S=\mathbb{R}^d \setminus (\cup_{i=1}^n…
Motivated by the theory of locally definable groups, we study the theory of $K$-vector spaces with a predicate for the union $X$ of an infinite family of independent subspaces. We show that if $K$ is infinite then the theory is complete and…
Let K be a number field. A finite group G is called K-admissible if there exists a G-crossed product K-division algebra. K-admissibility has a necessary condition called K-preadmissibility that is known to be sufficient in many cases. It is…