Hypernetworks for reconstructing the dynamics of multilevel systems

Networks are fundamental for reconstructing the dynamics of many systems, but have the drawback that they are restricted to binary relations. Hypergraphs extend relational structure to multi-vertex edges, but are essentially set-theoretic and unable to represent essential structural properties. Hypernetworks are a natural multidimensional generalisation of networks, representing n-ary relations by simplices with n vertices. The assembly of vertices to make simplices is key for moving between levels in multilevel systems, and integrating dynamics between levels. It is argued that hypernetworks are necessary, if not sufficient, for reconstructing the dynamics of multilevel complex systems

Embracing <i>n</i>-ary Relations in Network Science

Most network scientists restrict their attention to relations between pairs of things, even though most complex systems have structures and dynamics determined by n-ary relation where n is greater than two. Various examples are given to illustrate this. The basic mathematical structures allowing more than two vertices have existed for more than half a century, including hypergraphs and simplicial complexes. To these can be added hypernetworks which, like multiplex networks, allow many relations to be defined on the vertices. Furthermore, hypersimplices provide an essential formalism for representing multilevel part-whole and taxonomic structures for integrating the dynamics of systems between levels. Graphs, hypergraphs, networks, simplicial complex, multiplex network and hypernetworks form a coherent whole from which, for any particular application, the scientist can select the most suitable

Affiliative Subgroups in Preschool Classrooms: Integrating Constructs and Methods from Social Ethology and Sociometric Traditions

Recent studies of school-age children and adolescents have used social network analyses to characterize selection and socialization aspects of peer groups. Fewer network studies have been reported for preschool classrooms and many of those have focused on structural descriptions of peer networks, and/or, on selection processes rather than on social functions of subgroup membership. In this study we started by identifying and describing different types of affiliative subgroups (HMP- high mutual proximity, LMP- low mutual proximity, and ungrouped children) in a sample of 240 Portuguese preschool children using nearest neighbor observations. Next, we used additional behavioral observations and sociometric data to show that HMP and LMP subgroups are functionally distinct: HMP subgroups appear to reflect friendship relations, whereas LMP subgroups appear to reflect common social goals, but without strong, within-subgroup dyadic ties. Finally, we examined the longitudinal implications of subgroup membership and show that children classified as HMP in consecutive years had more reciprocated friendships than did children whose subgroup classification changed from LMP or ungrouped to HMP. These results extend previous findings reported for North American peer groups

Affiliative Subgroups in Preschool Classrooms: Integrating Constructs and Methods from Social Ethology and Sociometric Traditions

Recent studies of school-age children and adolescents have used social network analyses to characterize selection and socialization aspects of peer groups. Fewer network studies have been reported for preschool classrooms and many of those have focused on structural descriptions of peer networks, and/or, on selection processes rather than on social functions of subgroup membership. In this study we started by identifying and describing different types of affiliative subgroups (HMP- high mutual proximity, LMP- low mutual proximity, and ungrouped children) in a sample of 240 Portuguese preschool children using nearest neighbor observations. Next, we used additional behavioral observations and sociometric data to show that HMP and LMP subgroups are functionally distinct: HMP subgroups appear to reflect friendship relations, whereas LMP subgroups appear to reflect common social goals, but without strong, within-subgroup dyadic ties. Finally, we examined the longitudinal implications of subgroup membership and show that children classified as HMP in consecutive years had more reciprocated friendships than did children whose subgroup classification changed from LMP or ungrouped to HMP. These results extend previous findings reported for North American peer groups

An object-oriented approach to security policies and their access controls for database management

The constructs of the object-oriented data model seem to be good candidates for the specifications of the need-to-know and multilevel security policies and their respective access control requirements. This report demonstrates such specifications. The implication of this demonstration may be profound, since for the first time multiple security policies and their respective access controls may be realized and supported in a single object- oriented database management systemhttp://archive.org/details/objectorientedap00hsiaN

Multilayer Networks

In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is important to take such "multilayer" features into account to try to improve our understanding of complex systems. Consequently, it is necessary to generalize "traditional" network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion. The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science. In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks. To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other, and provide a thorough discussion that compares, contrasts, and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks, and many others. We also survey and discuss existing data sets that can be represented as multilayer networks. We review attempts to generalize single-layer-network diagnostics to multilayer networks. We also discuss the rapidly expanding research on multilayer-network models and notions like community structure, connected components, tensor decompositions, and various types of dynamical processes on multilayer networks. We conclude with a summary and an outlook.Comment: Working paper; 59 pages, 8 figure