Related papers: An Invitation to Higher Arity Science
The division of a social group into subgroups with opposing opinions, which we refer to as opinion disparity, is a prevalent phenomenon in society. This phenomenon has been modeled by including mechanisms such as opinion homophily, bounded…
The AHP/ANP are multicriteria decision-making theories that deal with both hierarchic structures when the criteria are independent of the alternatives and with networks when there is any dependence within and between elements of the…
The practice of scientific research is often thought of as individuals and small teams striving for disciplinary advances. Yet as a whole, this endeavor more closely resembles a complex system of natural computation, in which information is…
Real-world knowledge can take various forms, including structured, semi-structured, and unstructured data. Among these, knowledge graphs are a form of structured human knowledge that integrate heterogeneous data sources into structured…
We propose the concept of a system algebra with a parallel composition operation and an interface connection operation, and formalize composition-order invariance, which postulates that the order of composing and connecting systems is…
Recently there has been an increasing interest in studying dynamical processes on networks exhibiting higher-order structures, such as simplicial complexes, where the dynamics acts above and beyond dyadic interactions. Using simulations or…
We specialise a recently introduced notion of generalised dinaturality for functors $T : (\mathcal{C}^\text{op})^p \times \mathcal{C}^q \to \mathcal{D}$ to the case where the domain (resp., codomain) is constant, obtaining notions of ends…
Recent years have witnessed the rise of compositional semantics as a foundation for formal verification of complex systems. In particular, interaction trees have emerged as a popular denotational semantics. Interaction trees achieve…
We discuss multiplicative properties of the binary quadratic form $a x^2 + b x y + c y^2$ by considering a ring of matrices which is closed under a triple product. We prove that the ring forms a ternary algebra in the sense of Hestenes, and…
Association schemes on triples (ASTs) are ternary analogues of classical association schemes, whose relations and adjacency algebras are ternary instead of binary. We provide a survey of the current progress in the study of ASTs,…
To construct ternary "quaternions" following Hamilton we must introduce two "imaginary "units, $q_1$ and $q_2$ with propeties $q_1^n=1$ and $q_2^m=1$. The general is enough difficult, and we consider the $m=n=3$. This case gives us the…
One of the possible representations of three-valued instantaneous noise-based logic is proposed. The third value is an uncertain bit value, which can be useful in artificial intelligence applications. There is a forth value, too, that can…
The research on the brain mechanism of creativity mainly has two aspects, one is the creative thinking process, and the other is the brain structure and functional connection characteristics of highly creative people. The billions of nerve…
Relational reasoning is the ability to infer relations that jointly bind multiple entities, attributes, or variables. This ability is central to scientific reasoning, but existing evaluations of relational reasoning in large language models…
Complexity is an interdisciplinary concept which, first of all, addresses the question of how order emerges out of randomness. For many reasons matrices provide a very practical and powerful tool in approaching and quantifying the related…
As Christopher Alexander discovered, all space or matter - either organic or inorganic - has some degree of order in it according to its structure and arrangement. The order refers to a kind of structural character, called living structure,…
Art can be a powerful tool in science engagement efforts to help facilitate learning and public discourse around space and space exploration. The Art of Planetary Science is an annual exhibition combining science and art which aims to help…
Systems of cooperation and interaction are usually studied in the context of real or complex vector spaces. Additional insight, however, is gained when such systems are represented in vector spaces with multiplicative structures, i.e., in…
Battiston et al. (arXiv:2110.06023) provide a comprehensive overview of how investigations of complex systems should take into account interactions between more than two elements, which can be modelled by hypergraphs and studied via…
Convolution is a ubiquitous operation in mathematics and computing. The Kripke semantics for substructural and interval logics motivates its study for quantale-valued functions relative to ternary relations. The resulting notion of…