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

Hypernetworks: Multidimensional relationships in multilevel systems

Networks provide a powerful way of modelling the dynamics of complex systems. Going beyond binary relations, embracing n-ary relations in network science can generalise many structures. This starts with hypergraphs and their Galois structures. Simplicial complexes generalise hypergraphs by adding orientation. Their multidimensional q-connectivity structure generalises connectivity in networks. Hypersimplices generalise simplices by making the relational structure explicit in the notation. This gives a new way of representing multilevel systems and their dynamics, leading to a new fragment-recombine operator to model the complex dynamics of interacting multilevel systems

Design and Analysis of Optical Interconnection Networks for Parallel Computation.

In this doctoral research, we propose several novel protocols and topologies for the interconnection of massively parallel processors. These new technologies achieve considerable improvements in system performance and structure simplicity. Currently, synchronous protocols are used in optical TDM buses. The major disadvantage of a synchronous protocol is the waste of packet slots. To offset this inherent drawback of synchronous TDM, a pipelined asynchronous TDM optical bus is proposed. The simulation results show that the performance of the proposed bus is significantly better than that of known pipelined synchronous TDM optical buses. Practically, the computation power of the plain TDM protocol is limited. Various extensions must be added to the system. In this research, a new pipelined optical TDM bus for implementing a linear array parallel computer architecture is proposed. The switches on the receiving segment of the bus can be dynamically controlled, which make the system highly reconfigurable. To build large and scalable systems, we need new network architectures that are suitable for optical interconnections. A new kind of reconfigurable bus called segmented bus is introduced to achieve reduced structure simplicity and increased concurrency. We show that parallel architectures based on segmented buses are versatile by showing that it can simulate parallel communication patterns supported by a wide variety of networks with small slowdown factors. New kinds of interconnection networks, the hypernetworks, have been proposed recently. Compared with point-to-point networks, they allow for increased resource-sharing and communication bandwidth utilization, and they are especially suitable for optical interconnects. One way to derive a hypernetwork is by finding the dual of a point-to-point network. Hypercube Q\sb{n}, where n is the dimension, is a very popular point-to-point network. It is interesting to construct hypernetworks from the dual Q\sbsp{n}{*} of hypercube of Q\sb{n}. In this research, the properties of Q\sbsp{n}{*} are investigated and a set of fundamental data communication algorithms for Q\sbsp{n}{*} are presented. The results indicate that the Q\sbsp{n}{*} hypernetwork is a useful and promising interconnection structure for high-performance parallel and distributed computing systems

Hypergraph-Based Recognition Memory Model for Lifelong Experience

Cognitive agents are expected to interact with and adapt to a nonstationary dynamic environment. As an initial process of decision making in a real-world agent interaction, familiarity judgment leads the following processes for intelligence. Familiarity judgment includes knowing previously encoded data as well as completing original patterns from partial information, which are fundamental functions of recognition memory. Although previous computational memory models have attempted to reflect human behavioral properties on the recognition memory, they have been focused on static conditions without considering temporal changes in terms of lifelong learning. To provide temporal adaptability to an agent, in this paper, we suggest a computational model for recognition memory that enables lifelong learning. The proposed model is based on a hypergraph structure, and thus it allows a high-order relationship between contextual nodes and enables incremental learning. Through a simulated experiment, we investigate the optimal conditions of the memory model and validate the consistency of memory performance for lifelong learning

Derivable Single Valued Neutrosophic Graphs Based on KM-Fuzzy Metric

In this paper we consider the concept of KM-fuzzy metric spaces and we introduce a novel concept of KM-single valued neutrosophic metric graphs based on KM-fuzzy metric spaces. Then we investigate the finite KM-fuzzy metric spaces with respect to KM-fuzzy metrics and we construct the KMfuzzy metric spaces on any given non-empty sets. We try to extend the concept of KM-fuzzy metric spaces to a larger class of KM-fuzzy metric spaces such as union and product of KM-fuzzy metric spaces and in this regard we investigate the class of products of KM-single valued neutrosophic metric graphs. In the final, we define some operations such as tensor product, Cartesian product, semi-strong product, strong product, union, semi-ring sum, suspension, and complement of KM-single valued neutrosophic metric graphs