Related papers: Linking systems of difference sets
This article provides a link diagram to visualize relations between two ordered sets representing precedences on decision-making options or solutions to strategic form games. The diagram consists of floating loops whose any two loops cross…
Traditionally introduced in terms of advanced topological constructions, many link invariants may also be defined in much simpler terms given their values on a few initial links and a recursive formula on a skein triangle. Then the crucial…
Relation linking is essential to enable question answering over knowledge bases. Although there are various efforts to improve relation linking performance, the current state-of-the-art methods do not achieve optimal results, therefore,…
This article presents an overview of the theory of integrable systems with symmetries, focusing on toric systems, semitoric systems, and their classifications via decorated polygons. We discuss certain one-parameter families of integrable…
Clustering is a fundamental analysis tool aiming at classifying data points into groups based on their similarity or distance. It has found successful applications in all natural and social sciences, including biology, physics, economics,…
Complex systems are usually represented as an intricate set of relations between their components forming a complex graph or network. The understanding of their functioning and emergent properties are strongly related to their structural…
This paper addresses the task of set prediction using deep feed-forward neural networks. A set is a collection of elements which is invariant under permutation and the size of a set is not fixed in advance. Many real-world problems, such as…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
Complex applications such as big data analytics involve different forms of coupling relationships that reflect interactions between factors related to technical, business (domain-specific) and environmental (including socio-cultural and…
Complex systems are often driven by higher-order interactions among multiple units, naturally represented as hypergraphs. Understanding dependency structures within these hypergraphs is crucial for understanding and predicting the behavior…
We define a bi-directional embedding between hypersequent calculi and a subclass of systems of rules (2-systems). In addition to showing that the two proof frameworks have the same expressive power, the embedding allows for the recovery of…
Knowledge is a network of interconnected concepts. Yet, precisely how the topological structure of knowledge constrains its acquisition remains unknown, hampering the development of learning enhancement strategies. Here we study the…
Many groups possess highly symmetric generating sets that are naturally endowed with an underlying combinatorial structure. Such generating sets can prove to be extremely useful both theoretically in providing new existence proofs for…
The concept of coreflexive set is introduced to study the structure of digraphs. New characterizations of line digraphs and nth-order line digraphs are given. Coreflexive sets also lead to another natural way of forming an intersection…
A previous article was devoted to an analysis of the symmetry properties of a class of first-order delay ordinary differential systems (DODSs). Here we concentrate on linear DODSs. They have infinite-dimensional Lie point symmetry groups…
Delayed interactions are a common property of coupled natural systems and therefore arise in a variety of different applications. For instance, signals in neural or laser networks propagate at finite speed giving rise to delayed…
In many real world problems, features do not act alone but in combination with each other. For example, in genomics, diseases might not be caused by any single mutation but require the presence of multiple mutations. Prior work on feature…
Learning from unordered sets is a fundamental learning setup, recently attracting increasing attention. Research in this area has focused on the case where elements of the set are represented by feature vectors, and far less emphasis has…
Link prediction is a paradigmatic problem in network science with a variety of applications. In latent space network models this problem boils down to ranking pairs of nodes in the order of increasing latent distances between them. The…
It is shown the construction of a module structure [2] with universe over a set of a particular kind of mathematical proofs, the base ring of this module will be built on a maximal consistent extension of a set of propositions, this…