A description of all subsemigroups of M2(C) which are given by a countable intersection of constructible sets is obtained. Furthermore, it is shown that they are intersections of constructible ...semigroups.
We provide an explicit algorithm for computing intersection numbers between basis elements of complementary codimension in the Hilbert scheme of N points in the projective plane.
We generalize the results of Clemens, Ein, and Voisin regarding rational curves and zero cycles on generic projective complete intersections to the logarithmic setup.
•An analytical algorithm to find the exact solution to the simplified vehicle trajectory optimization problem.•Applications to signalized highways and non-stop intersections.•Analysis of queue ...propagation pattern caused by the trajectory smoothing.•A core module to a range of general trajectory optimization problems at various infrastructure settings.
This paper formulates a simplified traffic smoothing model for guiding movements of connected automated vehicles on a general one-lane highway segment. Adapted from the shooting heuristic proposed by Zhou et al. (2017) and Ma et al. (2017), this model confines each vehicle’s trajectory as a piecewise quadratic function with no more than five pieces and lets all trajectories in the same platoon share identical acceleration and deceleration rates. Similar to the shooting heuristic, the proposed simplified model is able to control the overall smoothness of a platoon of connected automated vehicles and approximately optimize traffic performance in terms of fuel efficiency and driving comfort. While the shooting heuristic relies on numerical meta-heuristic algorithms that cannot ensure solution optimality, we discover a set of elegant theoretical properties for the general objective function and the associated constraints in the proposed simplified model, and consequentially propose an efficient analytical algorithm for solving this problem to the exact optimum. Interestingly, this exact algorithm has intuitive physical interpretations, i.e., stretching the transitional parts of the trajectories (i.e., parts with acceleration and deceleration adjustments) as far as they reach the upstream end of the investigated segment, and then balancing the acceleration and deceleration magnitudes as close as possible. This analytical exact model can be considered as a core module to a range of general trajectory optimization problems at various infrastructure settings. Numerical examples reveal that this exact algorithm has much more efficient computational performance and the same or better solution quality compared with the previously proposed shooting heuristic. These examples also illustrate how to apply this model to CAV control problems on signalized segments and at non-stop intersections. Further, we study a homogeneous special case of this model and analytically formulate the relationship between queue propagation and trajectory smoothing. One counter-intuitive finding is that trajectory smoothing may not always cause longer queue propagation but instead may mitigate queue propagation with appropriate settings. This theoretical finding has valuable implications to joint optimization of queuing management and traffic smoothing in complex transportation networks.
•This paper presents a mixed integer linear programming (MILP) model to optimize vehicle trajectories and traffic signals in a unified framework at isolated signalized intersections in a CAV ...environment.•Phase sequences, green start and duration of each phase, and cycle lengths are optimized together with vehicle lane-changing behaviors and vehicle arrival times for delay minimization.•Vehicle trajectories are determined by optimal control models and car-following models on the basis of optimized arrival times with the objective to minimize fuel consumption and emission.•Simulation results validate the advantages of the proposed control method over vehicle actuated control in terms of intersection capacity, vehicle delays, and CO2 emissions.
Existing traffic signal control systems only allocate green time to different phases to avoid conflicting vehicle movements. With advances in connected and automated vehicle (CAV) technologies, CAV trajectories not only provide more information than existing infrastructure-based detection systems, but also can be controlled to further improve mobility and sustainability. This paper presents a mixed integer linear programming (MILP) model to optimize vehicle trajectories and traffic signals in a unified framework at isolated signalized intersections in a CAV environment. A new planning horizon strategy is applied to conduct the optimization. All vehicle movements such as left-turning, right-turning and through are considered. Phase sequences, green start and duration of each phase, and cycle lengths are optimized together with vehicle lane-changing behaviors and vehicle arrival times for delay minimization. Vehicles are split into platoons and are guaranteed to pass through the intersection at desired speeds and avoid stops at stop bars. Exact vehicle trajectories are determined based on optimized vehicle arrival times. For the trajectory planning of platoon leading vehicles, an optimal control model is implemented to minimize fuel consumption/emission. For following vehicles in a platoon, Newell's car-following model is applied. Simulation results validate the advantages of the proposed control method over vehicle-actuated control in terms of intersection capacity, vehicle delays, and CO2 emissions. A sensitivity analysis is conducted to show the potential benefits of a short minimum green duration as well as the impacts of no-changing zones on the optimality of the proposed model.
A search for configuration space with well‐defined topological (Berry) phases corresponding to Jahn‐Teller (JT) conical intersection (CI) and Renner‐Teller (RT) parabolic intersection (PI) in the ...linear tetra‐atomic molecular system on introduction of bending demonstrates the interesting aspect that these potential intersections may appear in the molecular plane as well as out of the molecular plane. While understanding this aspect is important for following the class of phenomena led by potential intersections, till date, studies on molecular systems, including pairs such as (C2H2+, HCNH) and (N2H2+, HBNH+), have not been able to clarify the issue. The present article includes calculation of nonadiabatic coupling terms involving four low‐lying states of slightly bent HCNO+, a motivated choice of tetra‐atomic with all four different atoms, to study this aspect associated with JT‐CI and RT‐PI in a slightly bent linear system. The plane of appearance of these effects has been advocated to be related to the electronic configuration of the concerned states of the molecular system.
Potential intersections with well‐defined topological (Berry) phases corresponding to Jahn‐Teller conical intersection and Renner‐Teller parabolic intersection in the linear tetra‐atomic molecular system on introduction of bending may appear in the molecular plane as well as out of the molecular plane. For HCNO+, this aspect has been studied, leading to a generalization that the plane of appearance of these effects may be advocated to be related to the nature of Π‐orbital associated with the original linear state.
Abstract
Singularities of non-Hermitian systems typified by exceptional points (EPs) are critical for understanding non-Hermitian topological phases and trigger many intriguing phenomena. However, it ...remains unexplored what happens when EPs meet one another. Here, in a typical four-level model with both touching and crossing intersections of EP hypersurfaces, we report the interconversion mechanisms between EPs of different orders. By examining both the eigenvalues and eigenvectors, we show analytically that all EPs of higher orders are formed at the touching intersections of two different types of EP hypersurfaces of lower orders. Contrarily, the crossing intersection of EP structures lowers the order of EPs. The mechanisms of the increase and decrease in defectiveness discovered here are expected to hold for EPs of any order in various non-Hermitian systems, providing a comprehensive understanding of EPs and inspiration toward advanced applications such as biosensing and information processing.
•Sample intersection travel times can categorize a cycle into seven (7) cases.•Bayesian Network models are constructed for each case to infer queue length distribution.•Queued vehicles contribute ...directly to the estimation of queue lengths.•Free flow vehicles are essential to the selection of proper model structure.•Methods work better for congested intersections than non-congested ones.
We propose Bayesian Network based methods for estimating the cycle by cycle queue length distribution of a signalized intersection. Queue length here is defined as the number of vehicles in a cycle which have experienced significant delays. The data input to the methods are sample travel times from mobile traffic sensors collected between an upstream location and a downstream location of the intersection. The proposed methods first classify traffic conditions and sample scenarios to seven cases. BN models are then developed for each case. The methods are tested using data from NGSIM, a field experiment, and microscopic traffic simulation. The results are satisfactory compared with two specific queue length estimation methods previously developed in the literature.
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