With the expansion of cities over time, Urban Rail Transit (URT) networks have also grown significantly. Accurate demand prediction plays a crucial role in supporting planning, scheduling, fleet management, and other operational decisions. This study proposes an Origin-Destination (OD) demand prediction model called Multi-Graph Inductive Representation Learning (mGraphSAGE) for large-scale URT networks under operational uncertainties. The proposed model represents each OD pair as a node in multiple graphs that capture distinct spatial and temporal correlations, thereby enhancing the spatial learning capability of graph-based methods while maintaining scalability. Moreover, operational uncertainties such as train delays and cancellations are explicitly incorporated as model inputs to improve robustness under real-world disruptions. The model is validated on three network scales of the Copenhagen URT system. Experimental results show that mGraphSAGE outperforms both conventional graph-based and machine learning baselines, achieving up to a 5% reduction in RMSE across network scales. The consistent improvement demonstrates the model’s enhanced spatial representation and robustness under operational uncertainties, confirming its suitability for large-scale and disrupted URT environments. • We propose mGraphSAGE, a novel multi-graph inductive representation learning model for OD demand prediction in Urban Rail Transit (URT) networks. • The model represents each OD pair as a node and simultaneously learns from multiple graphs capturing spatial and temporal correlations. • Operational disruptions such as train delays and cancellations are incorporated as input features to improve prediction performance. • The approach is validated on three different scales of the Copenhagen URT network, demonstrating scalability and adaptability.

Enhancing the urban rail transit network (URT) resilience under disruptions is crucial for improving its ability to respond to such events. However, prior studies have rarely enhanced the URT network resilience by jointly optimizing the restoration sequences of failed components and bus bridging services (BBSs). To address this gap, a URT network resilience enhancement strategy combining a restoration sequence and extended BBS optimization (ESCRB strategy) is developed herein to improve the URT network resilience under disruptions. The real-world Chengdu subway network is utilized as an example to validate the effectiveness of the proposed ESCRB strategy. Results imply that the travel weight between stations is critical in assessing the network resilience. The proposed ESCRB strategy can effectively enhance the URT network resilience by simultaneously optimizing restoration sequences and extended BBSs. After employing the ESCRB strategy, the network resilience metrics under random and deliberate disruptions are decreased by 83.96% and 81.80%, respectively. Finally, a sensitivity analysis is conducted to discuss the impact of parameters on the effectiveness of the formulated ESCRB strategy, and some practical implications are provided to improve the URT network resilience.

Improving the integration of rail and long-distance bus services is essential for enhancing regional connectivity and sustainable transport accessibility. Existing node-place models mainly focus on station surroundings and do not consider how buses extend access explicitly to support the transit network. Therefore, this study develops a multimodal network-based approach applied to a case of sub-rural Scotland. Three new integration metrics are designed — travel time-weighted population (demand coverage), feeder bus service availability (supply), and network centrality (regional connectivity). These indicators are then incorporated into a three-dimensional node-place framework, which evaluates the integration performance of 102 railway stations across the study area. Results reveal spatial differences in integration performance, identifying well-connected hubs such as Inverness and Stirling, alongside stations like Rosyth and Dunfermline City where demand is not matched by service provision. The analysis also shows opportunities to strengthen east–west regional links and improve multimodal access through targeted interventions, such as co-locating bus termini. By extending the node–place model to include multimodal catchments and network-level connectivity, the framework captures aspects of integration that are overlooked in rail-only assessments and offers a unified diagnostic tool for identifying where rail-bus integration improvements may have the greatest effect. The method is built on publicly available data, enabling its application in other regions and adaptation to support future demand modelling. • An integrated bus-rail network is constructed for multimodal node-place analysis. • Feeder bus services to stations are evaluated with time-weighted population coverage. • Impact of both interurban and feeder bus services on rail accessibility is evaluated. • Centrality analysis of rail-only and rail-bus networks reveals structural differences. • Generation of spatial options to help identify gaps for integration improvements.

Node importance identification method for urban rail transit networks based on improved mutual information considering inter-station cross-dependencies

The computation of optimal routes considering multiple factors is a key challenge in operations research, with significant impact on practical decision-making and real-world efficiency. Optimal bus transit routes require efficiency across multiple factors in order to achieve savings in time, cost, fuel consumption, and vehicle amortization. In such constrained urban routing settings, the impact of genetic algorithm (GA) crossover operators remains insufficiently explored, particularly for Path-TSP formulations derived from existing bus transit networks. In this paper, we present a comparative analysis of a genetic algorithm employing different crossover methods. The proposed approach is applied to optimize bus transit routes for key destinations within urban areas. For users with limited time and resources, our framework provides a practical and versatile solution, demonstrating its applicability through experiments on real-world datasets from Astana and Shymkent, Kazakhstan. Our experiments show a good match with existing results reported in the literature. The effectiveness of this approach is validated on real-world datasets, and the results demonstrate strong performance in terms of runtime efficiency, the number of feasible solutions generated, and the frequency of recovering optimal routes.

Faced with the increasing contradiction between the elderly transportation and the traffic system in most rural areas, the road infrastructure enhancement, the bus service improvement, and the traffic safety management should be given full consideration. An investigation on current rural transportation infrastructures is first performed in the studied area, including the road network configuration, the traffic facility, the surface pavement, and the bus services. Meanwhile, to better grasp the trip behavior and characteristics, in-depth discussions on the elderly travel demands and experiences are performed based on field observation and public data, where the K-means clustering method is applied to identify different trip groups, and the natural language processing technology is adopted to extract specialized needs from public textual data. Based on the foregoing investigation and analysis, a hierarchical improvement framework for elderly-oriented rural traffic is then proposed, including network planning, transportation management, and facility configuration, where quantification models of evaluation indicators are established considering transit network topology and spatial demand distribution. Through a combined evaluation of qualitative analysis and quantitative analysis, the recommended strategies will greatly enhance the global network accessibility by upgrading the road network and reconstructing the bus network, and improve the trip safety and convenience by optimizing the maintenance works and bus services. Specially, under a three-layer rural bus network architecture, the enhancement rates of service coverage and average accessible distance are expected to be 26.2% and 54.6% respectively, at the expense of a 30.8% increase in the daily operation cost.

• Integrated electric dial-a-ride problem with capacitated charging stations studied • A MILP formulation based on a novel departure-expanded network is developed • Departure-expanded network significantly reduces computational time • Arc-based charging station model achieves up to two two-digit time reduction This study addresses the integrated dial-a-ride problem using a fleet of electric vehicles. We propose a mixed-integer-linear programming modelling approach considering multiple depots, customer rejection, partial recharge policy and capacitated charging stations. State-of-the-art mixed-integer-linear programming approaches can solve the problem exactly for only less than 10 requests. This is due to the cumbersome modeling of partial routes in a mass transit network, where the number of arcs expands rapidly with the network size. We developed an efficient departure-expanded transit graph to model the problem efficiently by trimming off unnecessary arcs, and we include a preprocessing step based on time-window tightening on the timetabled transit network. We test the proposed method on a set of test instances with up to 50 requests and different initial battery levels of vehicles within a four-hour computational time limit. The results show that the problem can be solved optimally up to 20 customers and about 95% faster compared to the state-of-the-art. We developed a novel compact arc-based formulation for optimizing electric vehicle routing problems with capacitated charging stations. Our computational results provide a reduction in computational time by up to two digits compared to the state-of-the-art replication-based method.

ETCE-Net: Emotion transition and causal emotion entailment network for dialogue emotion recognition

Study on the synergistic development efficiency of Guangzhou under the rail transit Networks: A dual-dimensional perspective of inter-district and inter-industry

Real-time bus control of urban transit networks with overtaking and passenger transfers: A decomposition solution method combined with spatial branch-and-bound

Resilience assessment of interdependent transit networks: an indifference perception threshold-based approach

• Covid-19 interrupted patterns of social encounters on transit networks. • Non-obligatory, social encounters important to prevent loneliness. • Social encounters on transit networks did not regenerate within 2 yrs. • Transport policies must adapt to enduring changes in mobility to restore social connections. Familiar strangers, also known as invisible social ties, emerge from shared schedules and socially institutionalised routines that repeatedly bring individuals together in time–space. While unplanned and non-obligatory, these social encounters of repeated propinquity are vital sources of belonging, connection and ontological security. Drawing on four years of disaggregate smart card travel data we employ time series analyses to examine changes in familiar stranger within a public transit environment relations pre-post the onset of covid. We find a sudden and dramatic decline in the volume of repeated social encounters following the onset of the pandemic. Familiar stranger encounters did not return to pre-pandemic levels within the two-year post-pandemic onset captured in our study. Social context is an integral part of the transit experience and plays a significant role in modal choice. Our findings suggest that transport policies that aim to increase public transit ridership should consider how increased temporal and spatial flexibility in everyday obligatory activities (such as tele-commuting) has shifted shared transit routines and, in turn, uncoupled people from their familiar strangers. To support the re-generation of familiar strangers, as a vital source of belonging in the transit community and as an incentive for public transit ridership, we may need to contemplate new ways to encourage time–space co-presence through vehicle and station design, virtual transit chat-groups and/or adjustments to service scheduling.

A novel complex network framework: Multi-span transition network with Riemann similarity measure

A novel transit accessibility measure is proposed following a utility framework to account for the stochasticity in transit services, the effect of real-time information, traffic congestion, and structural features of the transit network, which are disregarded in prior literature. The quantification of accessibility is formulated as a network optimization problem. Through a case study using real-world transit data, the impact of the above features on accessibility was investigated. The results indicate that accessibility is a random quantity exhibiting considerable within-day, day-to-day, and spatial variation across stops, and the disutility from travel time components should be weighted differently for an unbiased estimate. Traffic congestion, represented by the average pace on alternate paths, decreases accessibility linearly. The transit network structure was found to strongly affect accessibility, where the number of available alternative paths had a positive cubic effect, and the degree of overlap among paths had a negative influence on the percentage of improvement in accessibility. Moreover, besides making supply changes, accessibility can be enhanced by providing accurate real-time information on bus arrivals, and the benefit increases quadratically as a function of the out-of-vehicle travel time reduction. The proposed measure, visualization, and analysis methods used, and recommendations made will help transit agencies and planners identify critical locations for interventions to improve transit service accessibility across space and time.

Understanding moment-to-moment therapeutic change is critical for advancing psychological interventions, yet existing tools rarely capture these dynamics. Dynamical systems theory offers a transtheoretical framework for modeling how therapeutic microprocesses shift and stabilize, but few methods can quantitatively link features such as stable states (“attractors”) and shifts (“transitions”) with empirical data, especially for high-dimensional systems when governing equations are unknown or unresolvable. We introduce Temporal Mapper, a topological data analysis (TDA) method that detects these features and represents their organization as attractor transition networks. As a proof-of-concept, we apply Temporal Mapper to psychotherapy microprocess data examining interpersonal behaviors and alliance ruptures. Our analyses revealed that therapist warmth stabilized dyadic interpersonal states within and between sessions, whereas confrontation ruptures stabilized dyadic interpersonal states within sessions but diversified and destabilized them across sessions. Beyond this example, Temporal Mapper offers a generalizable approach for uncovering fine-grained dynamic patterns, analyzing multimodal data of psychotherapy process, and identifying mechanisms of change at the system level to inform more effective interventions.

Interim periods between peak and off-peak operations in urban rail transit networks often suffer from mismatched headways across lines, which increases passenger transfer waiting and operating costs. This paper proposes a passenger-oriented timetable synchronization method for network-wide interim period train service. In this study, based on the AFC data, passengers are assigned to the shortest travel time paths, and passenger transfer flows are linked to connecting train pairs by consideration of the maximum acceptable waiting time. As a result, the transfer waiting time is accurately calculated by matching passengers’ platform arrival times with the departures of feasible connecting trains. A mixed integer nonlinear programming model then jointly optimizes departure headways at each line’s first station, arrival and departure times at transfer stations, subject to safety headways and time bounds. The objective minimizes total cost, combining transfer waiting time cost and train operating cost (depreciation and distance-related cost). A simulated-annealing-based genetic algorithm (SA-GA) is designed to solve the NP-hard problem. A case study on the Nanjing rail transit network from 6:30 to 7:30 reduces total cost by 6.88%, including 3.77% lower transfer waiting time cost and 14.49% lower operating cost, and shows stable results under typical transfer demand fluctuations.

Economic complexity algorithms aim to uncover the hidden capabilities that drive economic systems. Here we present a fundamental reinterpretation of two of these algorithms, the economic complexity index (ECI) and the economic fitness and complexity (EFC), by reformulating them as optimization problems that minimize specific cost functions. We show that ECI computation is equivalent to finding eigenvectors of the network's transition matrix by minimizing the quadratic form associated with the network's Laplacian. For EFC, we derive a novel cost function that exploits the algorithm's intrinsic logarithmic structure and clarifies the role of the regularization parameter in its nonhomogeneous version. Additionally, we establish the existence and uniqueness of its solution, providing theoretical foundations for its application. This optimization-based reformulation bridges economic complexity and established frameworks in spectral theory, network science, and optimization. The theoretical insights translate into practical computational advantages: We introduce a conservative, gradient-based update rule that substantially accelerates algorithmic convergence, with potential implications for a broader class of algorithms, including the Sinkhorn-Knopp method. Finally, we apply the energetic framework to a real-world trade network, demonstrating how linkwise energy provides a direct way to identify structurally relevant and vulnerable regions of the export matrix, thus complementing and enriching standard economic complexity analyses. Beyond advancing our theoretical understanding of economic complexity indicators, this work opens new pathways for algorithmic improvements and extends applicability to general network structures beyond traditional bipartite economic networks.

Risk evaluation of urban rail transit emergencies using a multilayer hypernetwork approach

Abstract The growing demand for sustainable transport has led to increasing interest in developing rail transit networks for both intra-city and inter-city travel. However, train-induced vibrations may cause significant negative environmental impacts on nearby buildings, sensitive equipment, and residents, thereby garnering considerable attention from researchers and engineers. An efficient prediction model is essential for assessing train-induced vibrations and for designing appropriate vibration mitigation measures. The complex dynamics of the train, track, infrastructure, soils, and buildings, along with their interactions, make the modeling of train-induced environmental vibrations a challenging task. This paper provides a comprehensive review of the current state-of-the-art methods for modeling train-induced vibrations from surface and underground railway traffic. It begins by addressing wave propagation in natural soils, followed by an in-depth examination of analytical, numerical, and empirical approaches for predicting train-induced vibrations in the ground and buildings. Finally, this paper identifies unresolved issues in the field and outlines areas that require further investigation.

This paper quantifies the economic and operational impact of spatial accuracy in metropolitan public transport systems, proposing a standardized GIS-based method for measuring inter-stop distances. Addressing the geometric limitations of legacy GTFS data, this study introduces a replicable workflow that integrates open spatial data with infrastructure-specific maneuvering constraints. The method was validated in the Górnośląsko-Zagłębiowska Metropolis (GZM), achieving near-identical precision to manual field measurements (MAPE ≈ 0.02%) while offering superior scalability compared to traditional odometer or satellite-based techniques. The analysis reveals that even minor measurement errors (approx. 2.5%) in legacy datasets propagate into significant budget misallocations, estimated at tens of thousands of PLN per line annually. These findings demonstrate that precise distance computation is a fundamental driver of cost efficiency and schedule reliability in large-scale transit networks.