Transmission of packets on a hierarchical network: statistics and explosive percolation

The transition to synchronization on branching hierarchical lattices

We study the transition to synchronization on hierarchical lattices using the evolution of Chaté-Manneville maps placed on a triangular lattice. Connections are generated between the levels of the triangular lattice, assuming that each site is connected to its neighbors on the level below with probability half. The maps are diffusively coupled, and the map parameters increase hierarchically, depending on the map parameters at the sites they are coupled to in the previous level. The system shows a transition to synchronization, which is second order in nature, with associated critical exponents. However, the V-lattice, which is a special realization of this lattice, shows a transition to synchronization that is discontinuous with accompanying hysteretic behavior. This transition can thus be said to belong to the class of explosive synchronization with the explosive nature depending on the nature of the substrate. We carry out finite-size-finite-time scaling for the continuous transition and analyze the scaling of the jump size for the discontinuous case. We discuss the implications of our results and draw parallels with avalanche statistics on branching hierarchical lattices.

A Graph Representation Learning Algorithm for Low-Order Proximity Feature Extraction to Enhance Unsupervised IDS Preprocessing

Most existing studies on an unsupervised intrusion detection system (IDS) preprocessing ignore the relationship among packets. According to the homophily hypothesis, the local proximity structure in the similarity relational graph has similar embedding after preprocessing. To improve the performance of IDS by building a relationship among packets, we propose a packet2vec learning algorithm that extracts accurate local proximity features based on graph representation by adding penalty to node2vec. In this algorithm, we construct a relational graph G’ by using each packet as a node, calculate the cosine similarity between packets as edges, and then explore the low-order proximity of each packet via the penalty-based random walk in G’. We use the above algorithm as a preprocessing method to enhance the accuracy of unsupervised IDS by retaining the local proximity features of packets maximally. The original features of the packet are combined with the local proximity features as the input of a deep auto-encoder for IDS. Experiments based on ISCX2012 show that the proposal outperforms the state-of-the-art algorithms by 11.6% with respect to the accuracy of unsupervised IDS. It is the first time to introduce graph representation learning for packet-embedded preprocessing in the field of IDS.

Hidden geometry of traffic jamming

We introduce an approach based on algebraic topological methods that allow an accurate characterization of jamming in dynamical systems with queues. As a prototype system, we analyze the traffic of information packets with navigation and queuing at nodes on a network substrate in distinct dynamical regimes. A temporal sequence of traffic density fluctuations is mapped onto a mathematical graph in which each vertex denotes one dynamical state of the system. The coupling complexity between these states is revealed by classifying agglomerates of high-dimensional cliques that are intermingled at different topological levels and quantified by a set of geometrical and entropy measures. The free-flow, jamming, and congested traffic regimes result in graphs of different structure, while the largest geometrical complexity and minimum entropy mark the edge of the jamming region.