Related papers: Linking systems of difference sets
Linking systems are crucial for studying the homotopy theory of fusion systems, but are also of interest from an algebraic point of view. We propose a definition of a linking system associated to a saturated fusion system which is more…
Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of…
The major challenge in designing a discriminative learning algorithm for predicting structured data is to address the computational issues arising from the exponential size of the output space. Existing algorithms make different assumptions…
A typical complex system should be described by a supernetwork or a network of networks, in which the networks are coupled to some other networks. As the first step to understanding the complex systems on such more systematic level,…
In principle, the rules of links formation of a network model can be considered as a kind of link prediction algorithm. By revisiting the preferential attachment mechanism for generating a scale-free network, here we propose a class of…
A theory of matchings for finite subsets of an abelian group, introduced in connection with a conjecture of Wakeford on canonical forms for homogeneous polynomials, has since been extended to the setting of field extensions and to that of…
Collaboration networks are studied as an example of growing bipartite networks. These have been previously observed to have structure such as positive correlations between nearest-neighbour degrees. However, a detailed understanding of the…
The complexity of many biological, social and technological systems stems from the richness of the interactions among their units. Over the past decades, a great variety of complex systems has been successfully described as networks whose…
Difference families are traditionally built using groups as their basis. This paper looks at what sort of generalised difference family constructions could be made, using the standard basis of translation and difference. The main result is…
In statistical relational learning, the link prediction problem is key to automatically understand the structure of large knowledge bases. As in previous studies, we propose to solve this problem through latent factorization. However, here…
Patterns of avoidance, adjacency, and association in complex systems design emerge from the system's underlying logical architecture (functional relationships among components) and physical architecture (component physical properties and…
Networks describe a range of social, biological and technical phenomena. An important property of a network is its degree correlation or assortativity, describing how nodes in the network associate based on their number of connections.…
Clustering is a fundamental problem in network analysis that finds closely connected groups of nodes and separates them from other nodes in the graph, while link prediction is to predict whether two nodes in a network are likely to have a…
Linking systems were introduced to provide algebraic models for $p$-completed classifying spaces of fusion systems. Every linking system over a saturated fusion system $\mathcal{F}$ corresponds to a group-like structure called a locality.…
Many systems of interest in science and engineering are made up of interacting subsystems. These subsystems, in turn, could be made up of collections of smaller interacting subsystems and so on. In a series of papers David Spivak with…
Effectively showing the relationships between objects in a dataset is one of the main tasks in information visualization. Typically there is a well-defined notion of distance between pairs of objects, and traditional approaches such as…
Applications of tangles of connectivity systems suggest a duality between these, in which for two sets $X$ and $Y\!$ the elements $x$ of $X$ map to subsets $Y_x$ of $Y\!$, and the elements $y$ of $Y\!$ map to subsets $X_y$ of $X$, so that…
We study the problem of group linkage: linking records that refer to entities in the same group. Applications for group linkage include finding businesses in the same chain, finding conference attendees from the same affiliation, finding…
In this paper, we study the machine learning elements which we are interested in together as a machine learning system, consisting of a collection of machine learning elements and a collection of relations between the elements. The…
In this article we aim to develop from first principles a theory of sum sets and partial sum sets, which are defined analogously to difference sets and partial difference sets. We obtain non-existence results and characterisations. In…