A Hypergraph Model for Communication Patterns

The article deals with interaction in concurrent systems. A calculus able to express specific communication patterns is defined, together with its abstract control structures. A hypergraph model for these structures is presented. The hypergraphs are able to properly express the communication patterns, providing a fully abstract model for the pattern calculus. It is also proved that the hypergraph model preserves the operational reductions of processes from pattern calculus and of the actions from the control structures.

Spectrum Allocation and Device Association in Federated Learning-Enabled Industrial IoT via Hypergraph Matching

In this paper, a joint spectrum allocation and device association problem is investigated for a federated learning aided hierarchical Industrial Internet of Things (IIoT) system for smart factory. To achieve the optimization jointly, we design a weighted learning utility maximization problem, which is a 0-1 integer linear programming problem. To solve this problem, we convert it into a weighted 3D hypergraph model by capturing the 3D mapping relation for IIoT device, subchannel, and edge server. A local search algorithm is then presented to find a 3D hypergraph matching with maximum total weights as the suboptimal solution. Simulation results demonstrate the superior performance of the proposed algorithm compared with the greedy algorithm in the system learning utility.

Spectrum Allocation and Device Association in Federated Learning-Enabled Industrial IoT via Hypergraph Matching

In this paper, a joint spectrum allocation and device association problem is investigated for a federated learning aided hierarchical Industrial Internet of Things (IIoT) system for smart factory. To achieve the optimization jointly, we design a weighted learning utility maximization problem, which is a 0-1 integer linear programming problem. To solve this problem, we convert it into a weighted 3D hypergraph model by capturing the 3D mapping relation for IIoT device, subchannel, and edge server. A local search algorithm is then presented to find a 3D hypergraph matching with maximum total weights as the suboptimal solution. Simulation results demonstrate the superior performance of the proposed algorithm compared with the greedy algorithm in the system learning utility.

Epidemics on hypergraphs: spectral thresholds for extinction

Epidemic spreading is well understood when a disease propagates around a contact graph. In a stochastic susceptible–infected–susceptible setting, spectral conditions characterize whether the disease vanishes. However, modelling human interactions using a graph is a simplification which only considers pairwise relationships. This does not fully represent the more realistic case where people meet in groups. Hyperedges can be used to record higher order interactions, yielding more faithful and flexible models and allowing for the rate of infection of a node to depend on group size and also to vary as a nonlinear function of the number of infectious neighbours. We discuss different types of contagion models in this hypergraph setting and derive spectral conditions that characterize whether the disease vanishes. We study both the exact individual-level stochastic model and a deterministic mean field ODE approximation. Numerical simulations are provided to illustrate the analysis. We also interpret our results and show how the hypergraph model allows us to distinguish between contributions to infectiousness that (i) are inherent in the nature of the pathogen and (ii) arise from behavioural choices (such as social distancing, increased hygiene and use of masks). This raises the possibility of more accurately quantifying the effect of interventions that are designed to contain the spread of a virus.

Hesitant fuzzy graphs, hesitant fuzzy hypergraphs and fuzzy graph decisions1

Up to now, there have been a lot of research results about multi-attribute decision making problems by fuzzy graph theory. However, there are few investigations about multi-attribute decision making problems under the background of indecisiveness. The main reason is that the difference of cognition and the complexity of thinking by decision makers, for the same question have different opinions. In this paper, we proposed a hesitant fuzzy hypergraph model based on hesitant fuzzy sets and fuzzy hypergraphs. At the same time, some basic graph operations of hesitant fuzzy hypergraphs are investigated and several equivalence relationship between hesitant fuzzy hypergraphs, hesitant fuzzy formal concept analysis and hesitant fuzzy information systems are discussed. Since granular computing can deal with multi-attribute decision-making problems well, we considered the hesitant fuzzy hypergraph model of granular computing, and established an algorithm of multi-attribute decision-making problem based on hesitant fuzzy hypergraph model. Finally an example is given to illustrate the effectiveness of the algorithm.

A chaotic viewpoint-based approach to solve haplotype assembly using hypergraph model

Decreasing the cost of high-throughput DNA sequencing technologies, provides a huge amount of data that enables researchers to determine haplotypes for diploid and polyploid organisms. Although various methods have been developed to reconstruct haplotypes in diploid form, their accuracy is still a challenging task. Also, most of the current methods cannot be applied to polyploid form. In this paper, an iterative method is proposed, which employs hypergraph to reconstruct haplotype. The proposed method by utilizing chaotic viewpoint can enhance the obtained haplotypes. For this purpose, a haplotype set was randomly generated as an initial estimate, and its consistency with the input fragments was described by constructing a weighted hypergraph. Partitioning the hypergraph specifies those positions in the haplotype set that need to be corrected. This procedure is repeated until no further improvement could be achieved. Each element of the finalized haplotype set is mapped to a line by chaos game representation, and a coordinate series is defined based on the position of mapped points. Then, some positions with low qualities can be assessed by applying a local projection. Experimental results on both simulated and real datasets demonstrate that this method outperforms most other approaches, and is promising to perform the haplotype assembly.