Transition Operator Research Articles

Self-consistent M1 radiative transitions of excited Bc and heavy quarkonia with different polarizations in the light-front quark model

In this study, we investigate the properties of pseudoscalar and vector charmonia, bottomonia, and Bc mesons using the light-front quark model, focusing on the M1 radiative transition. For that purpose, we conduct a variational analysis with a quantum chromodynamics (QCD)-motivated effective Hamiltonian, employing a trial wave function expanded in the harmonic oscillator basis functions up to the 3S state. We fit the model parameters to mass spectra and decay constants, obtaining reasonable agreement with experimental data and correctly reflecting the hierarchy of mass spectra and decay constants. In analyzing the M1 radiative transition, we consider both good (μ=+) and transverse (μ=⊥) current components with both longitudinal (h=0) and transverse (h=±1) polarizations, demonstrating that the results from both components of currents and polarizations are identical. Self-consistency is achieved by substituting M with M0 when computing the operators for decay constants and radiative transitions. We also find that the difference between longitudinal and transverse polarizations of the observables may quantify the anisotropy of the model wave function. Our results on radiative transitions align reasonably well with experimental data, lattice QCD, and theoretical predictions. Furthermore, we also provide predictions for Bc mesons that can be tested in experiments. Published by the American Physical Society 2025

Stop plan optimisation for three-pattern skip-stop schemes for urban rail transit systems

Mass rapid transit systems around the world are typically designed for all-stop operation schemes, in which train overtaking is not possible. To accelerate transit operation, the conventional A/B skip-stop scheme may be planned. This research explores alternative skip-stop schemes with three stop patterns, aiming to better match transit services with the spatial distribution of travel demand. The proposed generalised skip-stop operation model considers both the total cost of passengers and operator. A genetic algorithm is employed to solve the stop-plan optimisation problem, and a heuristic is tailored to determine an optimal dispatch headway for the respective stop plan. Based on computational experiments using synthetic data, the results suggest that skip-stop schemes have the potential to reduce total time costs by about 10%, particularly when there are structured demand concentrations, transit systems can operate safely with low time headway and short-distance demand is low. Although the total-cost saving of the best A/B skip-stop plan found is generally superior to those of other three-pattern skip-stop schemes, a three-pattern skip-stop scheme was found to offer a better total-cost saving in a scenario without short-distance travel demands. Overall, this research offers valuable insights into the potential benefits and limitations of different skip-stop schemes, contributing to a better understanding of their impact on passengers and operators.

Rewriting History in Integrable Stochastic Particle Systems

Many integrable stochastic particle systems in one space dimension (such as TASEP—Totally Asymmetric Simple Exclusion Process—and its q-deformation, the q-TASEP) remain integrable if we equip each particle with its own speed parameter. In this work, we present intertwining relations between Markov transition operators of particle systems which differ by a permutation of the speed parameters. These relations generalize our previous works (Petrov and Saenz in Probab Theory Relat Fields 182:481–530, 2022), (Petrov in SIGMA 17(021):34, 2021), but here we employ a novel approach based on the Yang-Baxter equation for the higher spin stochastic six vertex model. Our intertwiners are Markov transition operators, which leads to interesting probabilistic consequences. First, we obtain a new Lax-type differential equation for the Markov transition semigroups of homogeneous, continuous-time versions of our particle systems. Our Lax equation encodes the time evolution of multipoint observables of the q-TASEP and TASEP in a unified way, which may be of interest for the asymptotic analysis of multipoint observables of these systems. Second, we show that our intertwining relations lead to couplings between probability measures on trajectories of particle systems which differ by a permutation of the speed parameters. The conditional distribution for such a coupling is realized as a “rewriting history” random walk which randomly resamples the trajectory of a particle in a chamber determined by the trajectories of the neighboring particles. As a byproduct, we construct a new coupling for standard Poisson processes on the positive real half-line with different rates.

Model free data assimilation with Takens embedding

In many practical scenarios, the dynamical system is not available and standard data assimilation methods are not applicable. Our objective is to construct a data-driven model for state estimation without the underlying dynamics. Instead of directly modeling the observation operator with noisy observation, we establish the state space model of the denoised observation. Through data assimilation techniques, the denoised observation information could be used to recover the original model state. Takens’ theorem shows that an embedding of the partial and denoised observation is diffeomorphic to the attractor. This gives a theoretical base for estimating the model state using the reconstruction map. To realize the idea, the procedure consists of offline stage and online stage. In the offline stage, we construct the surrogate dynamics using dynamic mode decomposition with noisy snapshots to learn the transition operator for the denoised observation. The filtering distribution of the denoised observation can be estimated using adaptive ensemble Kalman filter, without knowledge of the model error and observation noise covariances. Then the reconstruction map can be established using the posterior mean of the embedding and its corresponding state. In the online stage, the observation is filtered with the surrogate dynamics. Then the online state estimation can be performed utilizing the reconstruction map and the filtered observation. Furthermore, the idea can be generalized to the nonparametric framework with nonparametric time series prediction methods for chaotic problems. The numerical results show the proposed method can estimate the state distribution without the physical dynamical system.

Research on the Optimization of Urban–Rural Passenger and Postal Integration Operation Scheduling Based on Uncertainty Theory

The integration of postal and passenger transport is an effective measure to enhance the utilization efficiency of passenger and freight transportation resources and to promote the sustainable development of urban–rural transit and logistics. This paper considers the uncertainty in passenger and freight demand as well as transit operation times, constructing an optimization model for integrated urban–rural transit and postal services based on uncertainty theory. Passenger and freight demand, along with the inverse uncertain distribution of events, serve as constraints, while minimizing passenger travel time and the cost for passenger transport companies are the optimization objectives. Taking into account the uncertainty of urban–rural bus travel time, the scheduling model is transformed into a robust form for scenarios involving single and multiple origin stations. The model is solved using an improved NSGA-II (Nondominated Sorting Genetic Algorithm II) to achieve effective coordinated scheduling of both passenger and freight services. Through a case study in Lotus County, Jiangxi Province, vehicle routing plans with varying levels of conservativeness were obtained. Comparing the results from different scenarios, it was found that when the total vehicle operating mileage increased from 1.96% to 62.26%, passenger transport costs rose from 2.95% to 62.66%, while the total passenger travel time decreased from 55.99% to 172.31%. In terms of optimizing costs and improving passenger travel efficiency, operations involving multiple starting stations for a single vehicle demonstrated greater advantages. Meanwhile, at a moderate level of robustness, it was easier to achieve a balance between operational costs and passenger travel time. The research findings provide theoretical support for improving travel conditions and resource utilization in rural areas, which not only helps enhance the operational efficiency of urban–rural transit but also contributes positively to promoting balanced urban–rural sustainable development and narrowing the urban–rural gap.

Quantum Representation for Deterministic Push-Down Automata

There are many papers presenting quantum computing models. The definitions parallel the classical definitions of finite state automata, push-down automata, context-free grammars, etc. Classical computing model definitions define languages precisely. We can state that a string belongs to a language or does not belong to it with no room for error. Quantum definitions do not possess this certainty. Sacrificing the certainty and adopting a quantum definition of a computing model does not appear to provide any concrete power to the model. Therefore, the path of this paper is to begin from the classical definition and end in a quantum circuit. In this paper, we start from a deterministic push-down automaton (DPDA). We present circuits for state transition and stack operations. The circuits presented can be viewed as independent algorithms. As an example, the approach used to construct the circuit for state transition can be utilized to build the circuit for a function presented as a Boolean matrix.

Vibration vulnerability assessment of heritage structures in Lahore: a step towards sustainable conservation

Lahore is among the most important historical cities in Pakistan, and many cultural heritage structures, such as Shalamar Gardens and Lahore Fort, which are recognised as World Heritage Sites by UNESCO, are located there. The rapid increase in transit operations and infrastructure development in Lahore can increase the vulnerability of nearby heritage structures to ground-borne vibrations. In this study, a vibration vulnerability assessment of the heritage structures present in Lahore was performed with the help of the framework provided by the Federal Transit Administration (FTA), USA. A remote survey was carried out to gather valuable information regarding the distance between the heritage structures and potential vibrational sources, as well as the latitude and longitude of the heritage structures, via the web-based mapping tool Google Earth. A vibration vulnerability map of heritage structures was developed on the basis of a vibration vulnerability assessment to make it convenient for policymakers to visualise the present state of heritage structures with respect to vibration vulnerability. The performed vibration vulnerability assessment was validated by experimentally measuring vibrations at the Buddha’s Tomb (Buddha Ka Awa) heritage structure. The study revealed that 17% of the heritage structures present in Lahore are vulnerable to vibrations at present, with potential vibrational sources such as road traffic, metro trains, and rail traffic. The vibration vulnerability assessment revealed that 72% of the vibrationally vulnerable heritage structures in Lahore are most influenced by vibrations from road traffic. The results of this study can aid policymakers in creating intervention packages for vibrationally vulnerable heritage structures in Lahore in relation to their respective needs, which will make it possible to achieve the sustainable conservation of heritage structures.

Rearrangement and breakup amplitudes from the solution of Faddeev-AGS equations by pseudo-state discretization of the two-particle continuum

The AGS equations for rearrangement transition operators in the three-particle problem are turned into a set of effective multi-channel two-body equations using the pseudo-state discretization of the two-particle resolvent. The resulting effective equations are LS-type integral equations in the spectator degrees of freedom, much like the LS equations of multichannel inelastic scattering. In particular, the effective potential matrix is real, energy-independent and non-singular, while the propagator matrix has only simple poles. Difficulties associated with the moving singularities of the effective potential matrix in the usual separable-T approach to AGS equations are avoided. After regularization of the kernel via subtraction procedures well known from two-particle scattering, the set of coupled LS-type equations in the spectator momenta are solved rather straightforwardly by the Nyström method. Solutions of effective two-body equations are then used to calculate the breakup amplitudes using the well-known relationship between rearrangement and breakup amplitudes. Calculations using a local momentum-space basis on a benchmark model of the n+d collision show that rather accurate results for elastic and breakup amplitudes can be obtained with rather small bases.

Plan Your System and Price for Free: Fast Algorithms for Multimodal Transit Operations

We study the problem of jointly pricing and designing a smart transit system, where a transit agency (the platform) controls a fleet of demand-responsive vehicles (cars) and a fixed line service (buses). The platform offers commuters a menu of options (modes) to travel between origin and destination (e.g., direct car trip, a bus ride, or a combination of the two), and commuters make a utility-maximizing choice within this menu, given the price of each mode. The goal of the platform is to determine an optimal set of modes to display to commuters, prices for these modes, and the design of the transit network in order to maximize the social welfare of the system. In this work, we tackle the commuter choice aspect of this problem, traditionally approached via computationally intensive bilevel programming techniques. In particular, we develop a framework that efficiently decouples the pricing and network design problem: Given an efficient (approximation) algorithm for centralized network design without prices, there exists an efficient (approximation) algorithm for decentralized network design with prices and commuter choice. We demonstrate the practicality of our framework via extensive numerical experiments on a real-world data set. We moreover explore the dependence of metrics such as welfare, revenue, and mode usage on (i) transfer costs and (ii) cost of contracting with on-demand service providers and exhibit the welfare gains of a fully integrated mobility system. Funding: This work was supported by the National Science Foundation [Awards CMMI-2308750, CNS-1952011, and CMMI-2144127]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0452 .

Identification of Risk Factors for Bus Operation Based on Bayesian Network

Public transit has been continuously developing because of advocacy for low-carbon living, and concerns about its safety have gained prominence. The various factors that constitute the bus operating environment are extremely complex. Although existing research on operational security is crucial, previous studies often fail to fully represent this complexity. In this study, a novel method was proposed to identify the risk factors for bus operations based on a Bayesian network. Our research was based on monitoring data from the public transit system. First, the Tabu Search algorithm was applied to identify the optimal structure of the Bayesian network with the Bayesian Information Criterion. Second, the network parameters were calculated using bus monitoring data based on Bayesian Parameter Estimation. Finally, reasoning was conducted through prediction and diagnosis in the network. Additionally, the most probable explanation of bus operation spatial risk was identified. The results indicated that factors such as speed, traffic volume, isolation measures, intersections, bus stops, and lanes had a significant effect on the spatial risk of bus operation. In conclusion, the study findings can help avert dangers and support decision-making for the operation and management of public transit in metropolitan areas to enhance daily public transit safety.

Node Importance Evaluation of Urban Rail Transit Based on Signaling System Failure: A Case Study of the Nanjing Metro

Assessing the importance of nodes in urban rail transit systems helps enhance their ability to respond to emergencies and improve reliability in view of the fact that most of the existing methods for evaluating the importance of rail transit nodes ignore the disturbance effect of signaling system failures and are unable to objectively identify critical stations in specific disturbance scenarios. Therefore, this paper proposed a method for evaluating the importance of urban rail transit nodes in signaling system failure scenarios. The method was based on the research background of the signaling system failure that occurs most frequently and analyzed the network failure mechanism after the occurrence of a disturbance. The node importance evaluation indices were selected from the network topology and network operation performance in two aspects. The variation coefficient–VIKOR method was employed to comprehensively assess the significance of urban rail transit stations during signaling system failures. The Nanjing Metro network was also used as an example to evaluate the importance of network stations. The results showed that under the attack method of signaling system failure, most ECC and interlocking stations experienced significantly higher network performance losses compared to the original attack method, and a few interchange stations showed smaller performance losses. The critical stations identified based on the proposed method are mainly distributed in the passenger flow backbone of the Nanjing Metro and were constructed in the early stage; of these, 85% are ECC stations or interlocking stations, which are easily neglected in daily management, in contrast to interchange stations with heavy passenger flow. The results of this study can provide an important reference for the stable operation and sustainable construction of urban rail transit.

How does the built environment affect intermodal transit demand across different spatiotemporal contexts?

Bus and metro are the two primary modes of public transportation in many megacities worldwide. Understanding their cooperation is crucial for the integration of the public transportation system. Despite extensive research on public transportation demand, studies focusing on bus-metro cooperation remain limited. Intermodal transit demand directly reflects the level of cooperation between the two modes in travel behavior. In this study, intermodal transit demand is extracted from smart card data in Beijing, China. The extreme gradient boosting algorithm is employed to investigate the determinants of intermodal transit demand considering spatiotemporal variation. The SHapley Additive exPlanations method further interprets these models. Findings reveal that (1) the relative spatial relationship between bus and metro service facilities significantly influences their cooperation; however, these influences gradually weaken as urban space expands from the core to the peripheral area; (2) in peripheral area, the characteristics of the bus network hold the highest average importance ranking; (3) extensive nonlinear relationships and threshold effects exist between the built environment and intermodal transit demand, with the magnitude, pattern, and direction of these impacts varying significantly across different spatiotemporal contexts; and (4) changes in the spatial layout of transportation service supplies impact their competition and cooperation, such as adequate bus service supplies potentially reducing the cooperation between bus and metro to some extent. These findings will assist planners and public transit operators in developing regulations that encourage cooperation between bus and metro, thereby increasing the attraction and competitiveness of the public transit system.

Capacity of infinite graphs over non-Archimedean ordered fields

In this article we study the notion of capacity of a vertex for infinite graphs over non-Archimedean fields. In contrast to graphs over the real field monotone limits do not need to exist. Thus, in our situation next to positive and null capacity there is a third case of divergent capacity. However, we show that either of these cases is independent of the choice of the vertex and is therefore a global property for connected graphs. The capacity is shown to connect the minimization of the energy, solutions of the Dirichlet problem and existence of a Green's function. We furthermore give sufficient criteria in form of a Nash-Williams test, study the relation to Hardy inequalities and discuss the existence of positive superharmonic functions. Finally, we investigate the analytic features of the transition operator in relation to the inverse of the Laplace operator.

Resilience of socio-technical transportation systems: A demand-driven community detection in human mobility structures

Existing scholarship on transportation resilience analysis has primarily focused on engineering resilience, often overlooking the intricate socio-technical dimensions. This oversight underscores the necessity for a more comprehensive understanding of the dynamic interplay between social, including travel behaviors, and technical infrastructure components within transportation systems. This article delves into the impact of “social shocks” on transportation systems, which are defined as disturbances affecting the social subsystem without yet affecting the technical subsystem. Drawing inspiration from C.S. Holling’s ecological resilience, which signifies a system’s ability to cope with change by adapting its structure and functionality, we propose a multi-level resilience assessment framework. It encompasses four mobility-related indicators: entropy (measuring network-level complexity), stationarity (assessing community compositional changes at the cluster level), and two node-level metrics — within-module degree and weighted participation coefficient — capturing location connectivity. These indicators proxy for evaluating the mobility structure and node functionality within the social subsystem. In a case study, we analyze historical smart card data to examine the mobility pattern’s structural changes within Hong Kong, a rail-oriented metropolis, during a prolonged and city-wide protest. The framework and associated indicators provide an alternative perspective for transit planners and operators, allowing them to assess both the overall system and individual stations, moving beyond traditional assessments of service supply and patronage changes.

Helicity evolution at small x: quark to gluon and gluon to quark transition operators

We include the quark to gluon and gluon to quark shock-wave transition operators into the small Bjorken-x evolution equations for helicity in the flavor-singlet channel derived earlier in [1, 2–3]. While such transitions do not affect the large-Nc version of the evolution equations for helicity, the large-Nc & Nf equations are affected. (Nc and Nf are the numbers of quark colors and flavors, respectively.) We derive the corresponding corrected large-Nc & Nf equations for the polarized dipole amplitudes contributing to the flavor-singlet quark and gluon helicity distributions in the double-logarithmic approximation (DLA), resumming powers of αs ln2(1/x) with αs the strong coupling constant. We solve these equations iteratively and extract the polarized splitting functions up to four loops. We show that our splitting functions agree with the fixed-order perturbative calculations up to and including the existing three-loops results [4, 5, 6–7]. Similar to the large-Nc helicity evolution in the shock-wave approach [8], our large-Nc & Nf small-x splitting functions agree with those obtained in the infrared evolution equations framework from [9, 10] up to three loops, but appear to slightly disagree at four loops.

On representations and topological aspects of positive maps on non-unital quasi *- algebras

In this paper we provide a representation of a certain class of C*-valued positive sesquilinear and linear maps on non-unital quasi *-algebras, thus extending the results from Bellomonte (GNS-construction for positive C∗-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^*-$$\\end{document}valued sesquilinear maps on a quasi ∗-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$*-$$\\end{document}algebra, Mediterr. J. Math., 21 166 (22 pp) (2024)) to the case of non-unital quasi *-algebras. Also, we illustrate our results on the concrete examples of non-unital Banach quasi *-algebras, such as the standard Hilbert module over a commutative C*-algebra, Schatten p-ideals and noncommutative L2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^2$$\\end{document}-spaces induced by a semifinite, nonfinite trace. As a consequence of our results, we obtain a representation of all bounded positive linear C*-valued maps on non-unital C*-algebras. We also deduce some norm inequalities for these maps. Finally, we consider a noncommutative L2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^2$$\\end{document}-space equipped with the topology generated by a positive sesquilinear form and we construct a topologically transitive operator on this space.

A sequential transit network design algorithm with optimal learning under correlated beliefs

Mobility service route design requires demand information to operate in a service region. Transit planners and operators can access various data sources including household travel survey data and mobile device location logs. However, when implementing a mobility system with emerging technologies, estimating demand becomes harder because of limited data resulting in uncertainty. This study proposes an artificial intelligence-driven algorithm that combines sequential transit network design with optimal learning to address the operation under limited data. An operator gradually expands its route system to avoid risks from inconsistency between designed routes and actual travel demand. At the same time, observed information is archived to update the knowledge that the operator currently uses. Three learning policies are compared within the algorithm: multi-armed bandit, knowledge gradient, and knowledge gradient with correlated beliefs. For validation, a new route system is designed on an artificial network based on public use microdata areas in New York City. Prior knowledge is reproduced from the regional household travel survey data. The results suggest that exploration considering correlations can achieve better performance compared to greedy choices and other independent belief-based techniques in general. In future work, the problem may incorporate more complexities such as demand elasticity to travel time, no limitations to the number of transfers, and costs for expansion.

Composite Accessibility Index: A Novel and Holistic Measure for Evaluating Transit Accessibility

The accessibility of public transport is a vital factor for the overall success of transit operations. It determines whether people choose to use and rely on public transport by assessing the ease of accessing opportunities. Accessibility, as a measure of the system’s performance, encompasses various travel segments and can be evaluated from different perspectives. Evaluating transit accessibility in data-constrained environments, particularly in developing countries, requires an optimal framework. The present study proposed a framework by modifying available accessibility measurement indices and trying to encompass all affecting variables in a single composite index. The integrated transit system comprising the bus rapid transit system and city bus in Surat city, India, is selected to demonstrate the proposed framework. The results of the ranked-based correlation coefficient test exhibit the comprehensive assessment capabilities of the proposed composite index in evaluating transit performance. Surat city’s transit network shows better coverage based on the gravity model theory, that is, moderate performance in local coverage offered capacity per population. However, it exhibits poor accessibility with respect to reaching destinations, resulting in below-average transit accessibility. Except for the city center and eastern part, 65% of the city area experiences inadequate accessibility of public transport. These findings align with the city’s low transit mode share of 2.5% and stagnant daily ridership of 0.25–0.28 million passengers in the last half decade. The composite index map serves as a planning tool for optimizing the utilization of available resources and guiding future policy implementations.

Machine Learning for public transportation demand prediction: A Systematic Literature Review

Within the Intelligent Public Transportation Systems (IPTS) field, the prediction of public transportation demand is a key point for enhancing the quality of the services. These predictions can be exploited by transit operators, for service planning and management, as well as by passengers, for planning their trips. Hence, the public transportation demand prediction problem is being more and more investigated by the scientific community, with several different proposals in terms of Machine Learning (ML) techniques, employed sensors, considered external features, and so on. However, there is a lack of comprehensive reviews that summarize and organize the available proposals on this topic. Hence, researchers intending to propose novel ML solutions, and practitioners willing to implement such solutions, may be overwhelmed by the plethora and heterogeneity of scientific work.To support these kinds of profiles, in this paper, we provide a Systematic Literature Review on ML techniques for predicting public transportation demand. This review highlights a growing interest by the scientific community on this topic, but also the lack of open datasets (useful for benchmarking), and in general of reproducible studies. Moreover, while deep learning techniques are frequently favored for their potential in terms of accuracy, associated costs, interpretability, and energy consumption are often overlooked.

A Comprehensive Research Agenda for Integrating Ecological Principles into the Transportation Sector

The paper examines the integration of novel Transportation Ecology principles into transit operations, aiming to address the environmental impacts associated with surface services in urban areas and with the purpose of creating a comprehensive agenda for integrating ecological principles into transit planning and management. The research problem is to quantify the tangible benefits for transit operators, particularly in the context of mitigating wildlife-vehicle collisions and improving overall operational efficiency as a motivator for transit managers to adopt Transportation Ecology principles. The study design, after analyzing the regulatory requirements, implements scenario-based methodology, utilizing data from an average Italian bus fleet to estimate potential monetary savings and benefits. Key parameters, such as maintenance costs, insurance premiums, and collision-related expenses, are analyzed to provide a realistic assessment of the economic advantages of implementing Transportation Ecology measures. The findings reveal that significant cost reductions can be achieved by minimizing accidents involving wildlife, alongside other operational improvements. The scenario demonstrates that even a small fleet, when adopting these principles, can yield substantial financial benefits, thereby making a compelling case for broader implementation. The paper concludes that while the qualitative nature of the analysis necessitates conservative estimates, the results underscore the value of incorporating ecological considerations into transit planning and management. These insights are vital for transit operators and policymakers seeking to balance environmental sustainability with operational profitability and protect urban ecosystems. This also implies the need for a more holistic and interdisciplinary approach to transportation planning and management.