Equivalence between spectral properties of graphs with and without loops

In this paper we introduce a spectra preserving relation between graphs with loops and graphs without loops. This relation is achieved in two steps. First, by generalizing spectra results got on (m, k)-stars to a wider class of graphs, the (m, k, s)-stars with or without loops. Second, by defining a covering space of graphs with loops that allows to remove the presence of loops by increasing the graph dimension. The equivalence of the two class of graphs allows to study graph with loops as simple graph without loosing information

On the multiplicity of Laplacian eigenvalues and Fiedler partitions

In this paper we study two classes of graphs, the (m,k)-stars and l-dependent graphs, investigating the relation between spectrum characteristics and graph structure: conditions on the topology and edge weights are given in order to get values and multiplicities of Laplacian matrix eigenvalues. We prove that a vertex set reduction on graphs with (m,k)-star subgraphs is feasible, keeping the same eigenvalues with reduced multiplicity. Moreover, some useful eigenvectors properties are derived up to a product with a suitable matrix. Finally, we relate these results with Fiedler spectral partitioning of the graph. The physical relevance of the results is shortly discussed

Signless normalized Laplacian for hypergraphs

The spectral theory of the normalized Laplacian for chemical hypergraphs is further investigated. The signless normalized Laplacian is introduced and it is shown that its spectrum for classical hypergraphs coincides with the spectrum of the normalized Laplacian for bipartite chemical hypergraphs. Furthermore, the spectra of special families of hypergraphs are established

Cooperative merging strategy between connected autonomous vehicles in mixed traffic

In this work we propose a new cooperation strategy between connected autonomous vehicles in on-ramps merging scenarios and we implement the cut-in risk indicator (CRI) to investigate the safety effect of the proposed strategy. The new cooperation strategy considers a pair of vehicles approaching an on-ramp. The strategy then makes decisions on the target speeds/accelerations of both vehicles, possible lane changing, and a dynamic decision-making approach in order to reduce the risk during the cut-in manoeuvre. In this work, the CRI was first used to assess the risk during the merging manoeuvre. For this purpose, scenarios with penetration rates of autonomous vehicles from 20% to 100%, with step of 10%, both connected and non-connected autonomous vehicles were evaluated. As a result, on average a 35% reduction of the cut-in risk manoeuvres in connected autonomous vehicles compared to non-connected autonomous vehicles is obtained. It is shown through the analysis of probability density functions characterising the CRI distribution that the reduction is not homogeneous across all indicator values, but depends on the penetration rate and the severity of the manoeuvre

Cooperative merging strategy between connected autonomous vehicles in mixed traffic

In this work we propose a new cooperation strategy between connected autonomous vehicles in on-ramps merging scenarios and we implement the cut-in risk indicator (CRI) to investigate the safety effect of the proposed strategy. The new cooperation strategy considers a pair of vehicles approaching an on-ramp. The strategy then makes decisions on the target speeds/accelerations of both vehicles, possible lane changing, and a dynamic decision-making approach in order to reduce the risk during the cut-in manoeuvre. In this work, the CRI was first used to assess the risk during the merging manoeuvre. For this purpose, scenarios with penetration rates of autonomous vehicles from 20% to 100%, with step of 10%, both connected and non-connected autonomous vehicles were evaluated. As a result, on average a 35% reduction of the cut-in risk manoeuvres in connected autonomous vehicles compared to non-connected autonomous vehicles is obtained. It is shown through the analysis of probability density functions characterising the CRI distribution that the reduction is not homogeneous across all indicator values, but depends on the penetration rate and the severity of the manoeuvre

Mathematical Definitions of Scene and Scenario for Analysis of Automated Driving Systems in Mixed-Traffic Simulations

This paper introduces a unified mathematical definition for describing commonly used terms encountered in systematical analysis of automated driving systems in mixed-traffic simulations. The most significant contribution of this work is in translating the terms that are clarified previously in literature into a mathematical set and function based format. Our work can be seen as an incremental step towards further formalisation of Domain-Specific-Language (DSL) for scenario representation. We also extended the previous work in the literature to allow more complex scenarios by expanding the model-incompliant information using set-theory to represent the perception capacity of the road-user agents. With this dynamic perception definition, we also support interactive scenarios and are not limited to reactive and pre-defined agent behavior. Our main focus is to give a framework to represent realistic road-user behavior to be used in simulation or computational tool to examine interaction patterns in mixed-traffic conditions. We believe that, by formalising the verbose definitions and extending the previous work in DSL, we can support automatic scenario generation and dynamic/evolving agent behavior models for simulating mixed traffic situations and scenarios. In addition, we can obtain scenarios that are realistic but also can represent rare-conditions that are difficult to extract from field-tests and real driving data repositories

Simulation-based impact projection of autonomous vehicle deployment using real traffic flow

In this work we focus on future projected impacts of the autonomous vehicles in a realistic condition representing mixed traffic. By using real flow and speed data collected in 2002 and 2019 in the city of Gothenburg, we replicated and simulated the daily flow variation in SUMO. The expansion of the city in recent years was reflected in an increase in road users, and it is reasonable to expect it will increase further. Through simulations, it was possible to project this increase and to predict how this will impact the traffic in future. Furthermore, the composition of vehicle types in the future traffic can be expected to change through the introduction of autonomous vehicles. In order to predict the most likely drawbacks during the transition from a traffic consisting only manually driven vehicles to a traffic consisting only fully-autonomous vehicles, we focus on mixed traffic with different percentages of autonomous and manually driven vehicles. To realize this aim, several parameters of the car following and lane change models of autonomous vehicles are investigated in this paper. Along with the fundamental diagram, the number of lane changes and the number of conflicts are analyzed and studied as measures for improving road safety and efficiency