We derive an explicit generating function of correlation functions of an arbitrary tau-function of the KdV hierarchy. In particular applications, our formulation gives closed formulæ of a new type ...for the generating series of intersection numbers of ψ-classes as well as of mixed ψ- and κ-classes in full genera.
Twenty years ago, the concept of aggregation‐induced emission (AIE) was proposed, and this unique luminescent property has attracted scientific interest ever since. However, AIE denominates only the ...phenomenon, while the details of its underlying guiding principles remain to be elucidated. This minireview discusses the basic principles of AIE based on our previous mechanistic study of the photophysical behavior of 9,10‐bis(N,N‐dialkylamino)anthracene (BDAA) and the corresponding mechanistic analysis by quantum chemical calculations. BDAA comprises an anthracene core and small electron donors, which allows the quantum chemical aspects of AIE to be discussed. The key factor for AIE is the control over the non‐radiative decay (deactivation) pathway, which can be visualized by considering the conical intersection (CI) on a potential energy surface. Controlling the conical intersection (CI) on the potential energy surface enables the separate formation of fluorescent (CI:high) and non‐fluorescent (CI:low) molecules control of conical intersection accessibility (CCIA). The novelty and originality of AIE in the field of photochemistry lies in the creation of functionality by design and in the active control over deactivation pathways. Moreover, we provide a new design strategy for AIE luminogens (AIEgens) and discuss selected examples.
What is essential in the aggregation‐induced emission (AIE) mechanism? This question is addressed by using the photophysical processes associated with 9,10‐bis(N,N‐dialkylamino)anthracene as a case study. The AIE phenomenon requires control of the non‐radiative decay (deactivation) pathway, that is, controlling the conical intersection (CI) on the potential energy surface enables the formation of fluorescent molecules (CI high) and non‐fluorescent (CI low) molecules separately.
•Introduce a phase-time-traffic hypernetwork model to model intersection automation.•Develop scheduling-oriented formulations to define the intersection automation problem.•Develop a sequential ...branch-and-bound algorithm to search the optimal solution.•Enhance solution search with efficient dominance rule and phase-time prism.
It is a common vision that connected and automated vehicles (CAVs) will increasingly appear on the road in the near future and share roads with traditional vehicles. Through sharing real-time locations and receiving guidance from infrastructure, a CAV's arrival and request for green light at intersections can be approximately predicted along their routes. When many CAVs from multiple approaches at intersections place such requests, a central challenge is how to develop an intersection automation policy (IAP) to capture complex traffic dynamics and schedule resources (green lights) to serve both CAV requests (interpreted as request for green lights on a particular signal phase at time t) and traditional vehicles. To represent heterogeneous vehicle movements and dynamic signal timing plans, we first formulate the IAP optimization as a special case of machine scheduling problem using a mixed integer linear programming formulation. Then we develop a novel phase-time-traffic (PTR) hypernetwork model to represent heterogeneous traffic propagation under traffic signal operations. Since the IAP optimization, by nature, is a special sequential decision process, we also develop sequential branch-and-bound search algorithms over time to IAP optimization considering both CAVs and traditional vehicles in the PTR hypernetwork. As the critical part of the branch-and-bound search, special dominance and bounding rules are also developed to reduce the search space and find the exact optimum efficiently. Multiple numerical experiments are conducted to examine the performance of the proposed IAP optimization approach.
Busemann's intersection inequality gives an upper bound for the volume of the intersection body of a star body in terms of the volume of the body itself. Koldobsky, Paouris, and Zymonopoulou asked if ...there is a similar result for k-intersection bodies. We solve this problem for star bodies that are close to the Euclidean ball in the Banach-Mazur distance. We also improve a bound obtained by Koldobsky, Paouris, and Zymonopoulou for general star bodies in the case when k is proportional to the dimension.
•A simplified continuous flow intersection called CFI-Lite is proposed.•CFI-Lite does not need sub-intersections, thus is ideal for arterials with short links.•CFI-Lite performs superiorly to the ...conventional and CFI designs.•Pareto capacity improvement can be achieved in CFI-Lite under effortless conditions.
Oversaturation has become a severe problem for urban intersections, especially the bottleneck intersections that cause queue spillover and network gridlock. Further improvement of oversaturated arterial traffic using traditional mitigation strategies, which aim to improve intersection capacity by merely adjusting signal control parameters, becomes challenging since exiting strategies may (or already) have reached their “theoretical” limits of optimum. Under such circumstance, several novel unconventional intersection designs, including the well-recognized continuous flow intersection (CFI) design, are originated to improve the capacity at bottleneck intersections. However, the requirement of installing extra sub-intersections in a CFI design would increase vehicular stops and, more critically, is unacceptable in tight urban areas with closed spaced intersections. To address these issues, this research proposes a simplified continuous flow intersection (called CFI-Lite) design that is ideal for arterials with short links. It benefits from the CFI concept to enable simultaneous move of left-turn and through traffic at bottleneck intersections, but does not need installation of sub-intersections. Instead, the upstream intersection is utilized to allocate left-turn traffic to the displaced left-turn lane. It is found that the CFI-Lite design performs superiorly to the conventional design and regular CFI design in terms of bottleneck capacity. Pareto capacity improvement for every traffic stream in an arterial system can be achieved under effortless conditions. Case study using data collected at Foothill Blvd in Los Angeles, CA, shows that the new design is beneficial in more than 90% of the 408 studied cycles. The testing also shows that the average improvements of green bandwidths for the synchronized phases are significant.
The aim of this paper is to compute all the Frenet apparatus of non-transversal intersection curves (hyper-curves) of three implicit hypersurfaces in Euclidean 4-space. The tangential direction at a ...transversal intersection point can be computed easily, but at a non-transversal intersection point, it is difficult to calculate even the tangent vector. If three normal vectors are parallel at a point, the intersection is “tangential intersection”; and if three normal vectors are not parallel but are linearly dependent at a point, we have “almost tangential” intersection at the intersection point. We give algorithms for each case to find the Frenet vectors (t,n,b1,b2) and the curvatures (k1,k2,k3) of the non-transversal intersection curve.
The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many ...important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students.
Geographically weighted regression (GWR) models have been employed in previous studies regarding vehicular travel demands, but few studies have locally modeled walking travel demands at intersections ...to address the issue of spatially varying relationships. Harnessing a comprehensive collection of walking and bicycling traffic counts over 10years in Chittenden County, Vermont, US, along with socioeconomic characteristics, transit accessibility indices, land use attributes and characteristics of intersections and roadway networks, this study utilizes GWR models to identify whether there are spatially varying relationships between active mode travel demands and ambient built-environment attributes. One Ordinary Least Square (OLS) model and two GWR models were parametrically calibrated: a full GWR model of all local variables and a mixed GWR model of both global and local variables. K-fold cross-validation method is used to select variables that significantly influence the volume of active travel modes in the OLS model. The uniform set of variables is investigated in two GWR models. Only residuals of the mixed GWR model exhibit spatial independence. The prediction accuracy of the three models is respectively compared by means of the k-fold cross-validation method. Results show that the mixed GWR model has higher prediction accuracy, while the other two models have roughly the same level of performance. We find that not all independent variables possess a spatially varying relationship with active mode volumes. The flexibility of the mixed GWR model that allows some independent variables to be global strengthens its prediction power. With these findings, transportation planners can dynamically estimate bicycle and pedestrian volumes at widespread intersections, and this geographical realism would facilitate local transportation planning, facility design, safety enhancement and operation analysis, as well as instilling new insights into interdisciplinary spatial research domain.
Connected and automated vehicles (CAVs) have the potential to improve safety by reducing and mitigating traffic accidents. They can also provide opportunities to reduce transportation energy ...consumption and emissions by improving traffic flow. Vehicle communication with traffic structures and traffic lights can allow individual vehicles to optimize their operation and account for unpredictable changes. This paper summarizes the developments and the research trends in coordination with the CAVs that have been reported in the literature to date. Remaining challenges and potential future research directions are also discussed.
Numerous efforts have been made to improve intersection operations under signal-free control enabled by connected autonomous vehicles (CAVs). However, vehicle crossing paths in existing literature ...primarily followed conventional geometric design. The performance of unconventional intersections with alternative conflict layouts under signal-free control remains a knowledge gap.To address this problem,we model the operations of three unconventional (signal-free) autonomous intersections and compare their operational performance with one conventional autonomous intersection. Results show that unconventional vehicle crossing paths at intersections are likely to reduce vehicle delay and fuel consumption compared with conventional intersections in most scenarios. Three crucial intersection layout factors, i.e. the number of conflicts, the distance between conflicting points, and the conflict angle, are investigated, which provides new insights into the mechanism of the performance change of unconventional intersections under the CAV environment. Our analysis suggests vehicle path design offers new space for operational performance enhancement of autonomous intersections.
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