Related papers: An Invitation to Higher Arity Science
Large knowledge graphs combine human knowledge garnered from projects ranging from academia and institutions to enterprises and crowdsourcing. Within such graphs, each relationship between two nodes represents a basic fact involving these…
Many of the essential features of the evolution of scientific research are imprinted in the structure of citation networks. Connections in these networks imply information about the transfer of knowledge among papers, or in other words,…
This paper quantitatively explores the social and socio-semantic patterns of constitution of academic collaboration teams. To this end, we broadly underline two critical features of social networks of knowledge-based collaboration: first,…
Purpose: Science is subject to a normative structure that includes how the contributions and interactions between scientists are rewarded. Authorship and citations have been the key elements within the reward system of science, whereas…
A new prior is proposed for learning representations of high-level concepts of the kind we manipulate with language. This prior can be combined with other priors in order to help disentangling abstract factors from each other. It is…
Complex systems and their underlying convoluted networks are ubiquitous, all we need is an eye for them. They pose problems of organized complexity which cannot be approached with a reductionist method. Complexity science and its emergent…
Complex systems are characterized by specific time-dependent interactions among their many constituents. As a consequence they often manifest rich, non-trivial and unexpected behavior. Examples arise both in the physical and non-physical…
We clarify the mathematical structure underlying unitary $t$-designs. These are sets of unitary matrices, evenly distributed in the sense that the average of any $t$-th order polynomial over the design equals the average over the entire…
We propose an approach to extending the concept of a Lie algebra to ternary structures based on $\omega$-symmetry, where $\omega$ is a primitive cube root of unity. We give a definition of a corresponding structure, called a ternary Lie…
Cooperative behaviors are deeply embedded in structured biological and social systems. Networks are often employed to portray pairwise interactions among individuals, where network nodes represent individuals and links indicate who…
Traditional graph analysis focuses on nodes and edges, that is, pairwise relationships. Yet many real-world networks, including biological, social, and communication networks, involve higher-order relationships in which multiple nodes…
Higher-order quantum theory is an extension of quantum theory where one introduces transformations whose input and output are transformations, thus generalizing the notion of channels and quantum operations. The generalization then goes…
Turing theory of pattern formation is among the most popular theoretical means to account for the variety of spatio-temporal structures observed in Nature and, for this reason, finds applications in many different fields. While Turing…
Certain operator-valued functions and new generating structures (instead of generating functionals) are proposed for the analysis of equations for n-point information (n-pi). Some remarks are made concerning the intertwining of linearity…
We propound the thesis that there is a limitation to the number of possible structures which are axiomatically endowed with identities involving operations. In the case of algebras with a binary operation satisfying a formally reducible (to…
Networks can describe the structure of a wide variety of complex systems by specifying which pairs of entities in the system are connected. While such pairwise representations are flexible, they are not necessarily appropriate when the…
Potential heuristics for state-space search are defined as weighted sums over simple state features. Atomic features consider the value of a single state variable in a factored state representation, while binary features consider joint…
The results here presented are a continuation of the algebraic research line which attempts to find properties of multiple-valued systems based on a poset of two agents. The aim of this paper is to exhibit two relationships between some…
This paper argues that mathematical objects are constructions and that constructions introduce a flexibility in the ways that mathematical objects are represented (as sets of binary sequences for example) and presented (in a particular…
Induction is the process by which we obtain predictive laws or theories or models of the world. We consider the structural aspect of induction. We answer the question as to whether we can find a finite and minmalistic set of operations on…