인지적 노화로 인한 시각적 경로 집성(Visual path integration)에서의 원형 효과(Prototype effect)

최수경 연세대학교 대학원 2019 국내석사

Spatial ability decreases with aging. This causes the elderly to have difficulty in carrying out navigation tasks. Successful navigation can be achieved by multiple error-free stages of cognitive and perceptual processes that handle spatial information. Out of many perceptual processes, the elderly are known to exhibit apparent defects in path integration. Path integration combines multiple sensory information generated by self-generated movements to calculate distance and direction. Among three sensory inputs used for path integration, this study focused on visual path integration (VPI), which is a path integration based on visual sensory information(optical flow). This study compared the directional estimation of VPI between young and old groups. In addition, we intended to identify differences between age groups and clarify systematic bias in older people in estimating the direction of the VPI. In experiment 1, we used a virtual environment to compare the errors seen by young and old groups in estimating the direction of the VPI. In experiment 2, we tried to explain what kind of systematic bias is shown in the direction estimation based on the category adjustment model in the aged group. Participant performed tasks after watching first-person video of a certain angle of rotation within the given environment. In experiment 1, participants performed the task of estimating and answering the angle of rotation(direction) based on the amount of perceived optical flow in experiment videos. In experiment 2, participants performed a detection task to answer with O or X whether the rotation angle(direction) they estimated after viewing the video was equal to or different from the center axis angle(direction) of the spatial category. Results showed that the older group had more errors in estimating rotation angles than the younger group. Both groups showed a higher number of estimated errors as the rotation angle of the video increases (Experiment 1). Interestingly, in certain spatial categories (categories with 45 degrees centered), the older group performed tasks as well as younger group did when the rotation angle of the video was significantly different from the center axis angle of the spatial category, but in the cases the difference between rotation angle of the video and center axis angle was small, they showed less detection task capability than younger group. This study demonstrated older people generally have less capability to identify the directional estimation of VPI than younger people. Furthermore when the rotational motion becomes closer to the center axis of the space category, the older group tends to be biased toward the center axis without distinguishing the difference between the two. 노화(aging)에 따라 인간의 공간 인지 능력은 감퇴한다. 이로 인해 고령자는 목적지를 찾아가는 항행(navigation) 과제를 수행함에 있어서 어려움을 겪는다. 성공적인 항행은 공간 정보를 처리하는 여러 단계의 인지 및 지각 과정을 오류 없이 처리해야만 달성할 수 있다. 그 중 고령자는 자기 움직임(self-motion)에 의해 생성되는 여러 감각 정보를 통합하여 거리(distance)와 방향(direction)을 계산해내는 경로 집성(path- integration) 수행에 있어서 뚜렷한 결함을 보이는 것으로 알려져 있다. 본 연구는 경로 집성에 사용되는 세 가지 감각 정보 중에서 시 감각 정보(광학 흐름)에 기반한 경로 집성을 뜻하는 시각적 경로 집성(visual path integration, VPI)을  중점적으로 살펴보았다. 먼저 젊은 집단과 고령 집단 간 VPI의 방향 추정 수행을 비교하여 노화로 인한 차이를 확인하였다. 또한 연령 집단 간 차이를 확인하는 것에서 더 나아가 VPI의 방향 추정에서 나타나는 고령자의 결함이 어떤 특성을 띠는지 밝히고자 하였다. 이를 위해 실험 1에서는 가상 환경을 사용하여 고령 집단과 젊은 집단이 VPI의 방향추정에서 보이는 오차를 비교하였다. 이어서 실험 2에서는 고령 집단이 방향 추정에서 보이는 오차가 어떠한 체계적인 특성을 보이는지를 범주 조정 모델(category adjustm- ent model)에 기반하여 설명하고자 하였다. 구체적으로 고령 집단과 젊은 집단은 가상 환경 내에서 특정 각도만큼 제자리 회전(angular rotation)하는 1인칭 영상을 시청한 후 방향 추정 과제를 수행했다. 실험 1의 참가자들은 영상에서 지각한 광학 흐름의 양을 토대로 회전 각도(방향)를 추정하여 답변하는 과제를 수행하였고, 실험 2의 참가자들은 본인이 영상을 보고 추정한 회전 각도(방향)가 공간 범주의 중심 축 각도(방향)와 같은지 다른지 여부를 O, X로 답변하는 탐지 과제를 수행하였다. 연구 결과 고령 집단은 젊은 집단에 비해 회전 각도 추정에 있어서 오차가 더 크게 나타났으며, 두 집단 모두 영상의 회전 각도가 증가할수록 방향 추정 오차가 증가하는 특징을 보였다(실험1). 또한, 흥미롭게도 고령 집단은 특정 공간 범주(가 중심 축인 범주)에서 영상의 회전 각도가 공간 범주의 중심 축 각도와 차이가 큰 경우에는 젊은 집단만큼 탐지 과제를 잘 수행한 반면, 차이가 작은 경우에는 젊은 집단보다 탐지 과제 능력이 떨어지는 특징을 보였다(실험2). 이는 고령자가 젊은 사람에 비해 전체적으로 VPI의 방향 추정이 부정확하며, 더 나아가 회전 운동이 공간 범주의 중심 축 각도에 가깝게 발생할수록 둘 간의 차이를 구별하지 못하고 중심 축 방향으로 편향되게 부호화하는 원형 효과의 경향이 있음을 시사한다.

(A) novel approach to transmission loss allocation considering path dependency using path integral in power systems

민경일 Graduate School, Yonsei University 2010 국내박사

This study presents a new algorithm of accurate bus-wise transmission loss allocation based on path-integrals and analyzes various path types to consider path-dependency of transmission loss allocation. With rigorous theoretical analysis, a new path integral method is developed by integrating the partial differential of the system loss along a path reflecting the transaction strategy. This path integral enables us to remarkably enhance the accuracy in loss allocation with full consideration of nonlinearity. The accuracy has been further improved by using the AC power flow. Determining the integral path is discussed to reflect various situations of the power market. Given an integral path, the proposed algorithm provides a unique and accurate solution to the loss allocation. We propose various path types which are modeled to embody path-dependency of practical power systems. The path types are classified into two categories: generation increase pattern and transaction strategy. Generation increase pattern implies the information of buswise generation increase rates and amounts, which makes it possible to consider path-dependency by generator commitment order and base points of generators and loads. The path-dependency of power transaction can be realized by various transaction strategies in both bilateral and pool markets. These path types can be politically utilized to satisfy the stakes among power market participants. An effective method is proposed to reduce the computation time remarkably in the integration of bus-wise differential loss. The proposed algorithm has been tested and the results showed that on-line application is possible to large power systems.

오프로드 환경에서의 굴절식 차량 전복 방지를 위한 Model Predictive Path Integral 기반 경로 계획 및 제어 기법 개발

김태완 국민대학교 자동차모빌리티대학원 2024 국내석사

The global construction industry faces the dual challenges of enhancing productivity and ensuring safety, with the automation and unmanned operation of construction equipment emerging as key solutions. However, conventional autonomous driving technologies have shown clear limitations in effectively addressing the complex, variable environments of construction sites and the unique characteristics of construction machinery. To overcome these technical challenges, this study proposes the Model Predictive Path Integral (MPPI) control method. This paper aims to prevent rollover accidents that may occur during off-road driving of articulated construction vehicles by developing an MPPI-based autonomous driving algorithm. The proposed approach overcomes the limitations of traditional path planning methods by precisely reflecting the vehicle’s dynamic characteristics and constraints, with a particular focus on preventing rollovers that can lead to serious accidents on construction sites. To this end, an MPPI framework optimized for articulated vehicles was designed to capture the vehicle’s dynamic behavior and integrate real-time rollover prevention and active obstacle avoidance. To accurately represent the unstructured terrain of construction sites, a grid map containing normal vector information was generated from 3D point cloud data. The RANSAC (Random Sample Consensus) algorithm was employed to robustly estimate normal vectors by minimizing the influence of noise and outliers in the terrain data. RANSAC iteratively samples random subsets to generate models and selects the model supported by the largest number of inliers, making it highly effective for extracting reliable parameters from real-world data prone to measurement errors. Based on the constructed grid map and the vehicle’s current yaw angle, a real-time roll angle estimation algorithm was developed. The MPPI controller probabilistically samples multiple candidate control sequences and predicts future states for each sequence using a nonlinear dynamic model. The optimal control input is then determined by evaluating a cost function that comprehensively considers rollover risk, collision risk, path tracking accuracy, and terrain adaptability. For rollover prevention, the controller calculates dynamic stability indices in real time using the vehicle’s dynamic state and estimated terrain information, integrating these indices as key elements in the MPPI cost function. If the calculated stability index or estimated roll angle exceeds a predefined safety threshold, a large penalty is imposed on the corresponding control sequence, effectively excluding unsafe trajectories through strong constraints. Furthermore, when encountering unexpected obstacles, the MPPI immediately incorporates obstacle information into the cost function, enabling rapid replanning of safe avoidance paths. The performance of the proposed integrated controller in rollover prevention and obstacle avoidance was comprehensively validated in various rough-terrain driving scenarios using Vortex Studio, a simulation environment specialized for construction equipment. The evaluation focused on the appropriateness of path generation, path tracking accuracy, safety during operation, and real-time control feasibility 전 세계 건설 산업의 관심사는 현재 생산성 향상과 안전 확보에 집중되고 있으며, 이에 대한 해결 방안으로 건설기계의 자동화 및 무인화에 많은 투자가 이루어지고 있다. 그러나 기존 자율주행 기술은 비정형적이고 복잡한 오프로드 현장과 건설기계의 특성을 효과적으로 다루는 데 한계가 있다. 본 연구는 이러한 한계를 해결하기 위해 모델 예측 경로 적분 제어(Model Predictive Path Integral, MPPI) 기법을 제안한다. 본 논문은 굴절식 건설기계 차량이 오프로드 주행 시 발생할 수 있는 전복 사고를 방지하며 경로를 계획 및 제어하는, MPPI 기반의 건설기계 자율주행 알고리즘을 개발했다. 이는 차량의 동역학적 특성과 전복 방지를 위한 제약조건을 반영한 경로를 설계함으로써 기존 경로계획 방식의 한계를 극복하였다. 건설 현장의 비정형적인 지형 특성을 정밀하게 반영하고자, 먼저 지형의 3차원 포인트 클라우드 데이터로부터 법선벡터 정보를 포함하는 Grid Map을 생성했다. 이 과정에서 RANSAC(Random Sample Consensus) 알고리즘을 활용하여 지형 데이터에 포함된 노이즈나 이상치(outlier)의 영향을 최소화하고 강인하게 법선벡터를 추정했다. RANSAC은 임의 표본을 반복적으로 추출하여 모델을 생성하고, 가장 많은 데이터 포인트(inlier)로부터 지지받는 모델을 최종적으로 선택함으로써, 측정 오류가 빈번한 실제 환경 데이터로부터 신뢰도 높은 파라미터를 추출하는 데 매우 효과적이다. 이렇게 구축된 Grid Map과 차량의 현재 Yaw Angle를 기반으로 실시간 Roll Angle를 추정하는 알고리즘을 개발했다. MPPI 기법은 다수의 후보 제어 시퀀스를 확률적으로 샘플링하고, 예측 모델을 통해 각 시퀀스에 따른 미래 상태를 예측한다. 이후, 예측된 상태를 바탕으로 전복 위험, 장애물 충돌 여부, 목표 경로 추종 오차, 그리고 지형 정보 등을 종합적으로 평가하는 비용 함수를 통해 최적의 제어 입력을 결정한다. 차량의 동적 상태와 지형 정보를 활용하여 실시간으로 차량의 Roll Angle을 계산하고, 건설기계 차량의 전복 방지를 위하여 거동안정성 지표를 계산하여 이를 MPPI의 비용함수 및 제약 조건의 주요 요소로 통합했다. 이때, 거동안정성 지표는 건설기계와 오프로드 환경의 특성에 적합한 거동안정성 지표인 Zero-Moment Point(ZMP)와 Lateral Load Transfer Ratio estimation(LT Re)을 사용했다. 나아가, 계산된 건설기계의 전복 방지를 위한 거동안정성 지표나 지형기반 Roll Angle이 사전에 정의된 안전 임계치를 초과할 경우, 해당 제어 시퀀스에 매우 큰 비용을 부여하여 사실상 해당 경로가 선택되 지 않도록 하는 제약 조건을 구현했다. 마지막으로, 예측하지 못한 장애물과 조우 시, MPPI가 장애물 정보와 차량의 위치를 통한 충돌 여부를 비용 함수에 반영하여 안전한 회피 경로를 재탐색하는 장애물 회피 알고리즘을 구현했다. 제안된 MPPI기반 자율주행 알고리즘의 전복 방지 및 장애물 회피 성능은 CMLabs사의 건설기계 특화 시뮬레이션 환경인 Vortex Studio를 사용하여 구성된 다양한 시나리오에서 경로 생성의 적절성, 주행 중 전복 방지 능력 및 실시간 제어 연산 가능성을 종합적으로 검증했다.

Unraveling Quantum Gravity Through the Gravitational Path Integral: Geometries, Entropies, and Algebras

Wang, Zhencheng University of California, Santa Barbara ProQuest D 2023 해외박사(DDOD)

The gravitational path integral has long served as a crucial tool in deciphering mysteries within quantum gravity. In recent years, studies of the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence have offered many valuable insights into comprehending those mysteries, and many fruitful results have been yielded from utilizing the gravitational path integral within the framework of AdS/CFT.This dissertation is devoted to studying certain aspects of the gravitational path integral, discussing its relation with gravitational entropies, spacetime geometries, and its algebraic aspects. We explore contexts from Euclidean to Lorentz signature, from holographic theories to general theories, with a goal of understanding quantum gravity in the real world.In Part I, we discuss the fixed-(HRT)-area states in the gravitational path integral. The fixed-area states are holographic states where the area of the Hubeny-Rangamani-Takayanagi (HRT) surface, the holographic dual of entanglement entropy for a region in the boundary CFT, is constrained to a small window when prepared by the gravitational path integral. The study of those fixed-area states helps understand quantum gravity beyond the leading semiclassical order. We first show that by decomposing a general holographic state into fixed-area states, an important subleading correction appears to the entanglement entropy near phase transitions. Then we explore the intrinsic spacetime geometries of fixed-area states under Lorentz-signature time evolution.In Part II, we study saddle-point geometries of the real-time gravitational path integral, in the context of computing holographic R´enyi entropies. Unlike their Euclidean counterparts, these real-time saddles necessarily have complex metrics, giving an example where the saddle point is off the original contour of integration. We first present the formalism of this setup, illustrating the relevant variational problem, and features of the complex saddles. Then we demonstrate explicitly the structure of those saddles by showing examples in low dimensions by direct calculation. We also find that it is possible to deform the original integration contour to pass through saddles of this kind constructed in two-dimensional Jackiw-Teitelboim gravity. Finally, we show that the existence of these saddles results in a consequence which is necessary for unitarity to hold in quantum gravity.In Part III, we take a step towards explaining the origin of gravitational entropies, by utilizing the mathematical tool of von Neumann algebras. In particular, we give an explanation of the HRT formula purely from the bulk perspective, without making any reference to holography. This is done by constructing Hilbert spaces and von Neumann algebras from boundary conditions of the gravitational path integral with several natural axioms. The von Neumann algebras we find from this construction allows us to define a notion of entropy, which matches the HRT formula in the semiclassical limit. One of the axioms we assume which is crucial for the construction of von Neumann algebras - the trace inequality, is proven in the semiclassical limit, and it leads to novel positivity conjectures for the gravitational action. .

On Contours and Boundary Conditions for the Gravitational Path Integral

Liu, Xiaoyi University of California, Santa Barbara ProQuest D 2025 해외박사(DDOD)

The gravitational path integral has been a useful tool in studying quantum gravity. This thesis is devoted to studying certain aspects of the gravitational path integral, discussing the choices of contours of integration and boundary conditions for the gravitational path integral, in both Euclidean and Lorentzian signatures.In Part I, we discuss the choice of contours of integration for the gravitational path integral. The Euclidean gravitational action is unbounded from below, which means we cannot take the contour of the Euclidean path integral to all real Euclidean geometries. We propose a Wick-rotation contour prescription for the Euclidean gravitational path integral, and test this prescription by computing the stability of black hole saddles and comparing it with standard thermodynamic stability. We also study contours for Lorentzian gravitational path integral, where the original contour of integration is taken to be over all real Lorentzian geometries. We use Jackiw-Teitelboim (JT) gravity as an example, and explicitly demonstrate that it is possible to deform the original contour to pass through complex saddles that reproduce the correct Renyi entropy of JT gravity. In addition, we consider more complicated wormhole geometries in Euclidean anti-de Sitter spacetimes, which resemble the wormholes that are important in ensuring the black hole Hilbert space dimension is finite. We discuss their genericity with large Euclidean sources at the conformal infinity and compute the stability of these Euclidean wormholes.In Part II, we discuss the choice of boundary conditions for the gravitational path integral. We propose a one-parameter family of boundary conditions for Euclidean gravity that yields a well-posed elliptic system, and study Euclidean stability of various saddles with such boundary conditions. These boundary conditions can be used to define a generalized thermal canonical ensemble. They are then applied in Lorentzian signature to study real-time evolution in a spherical cavity. By analyzing the quasi-normal modes of empty flat space, we demonstrate that the same boundary conditions fail to define a well-posed initial-boundary value problem in Lorentzian signature.

Quantum-Classical and Semiclassical Path Integral Methods for Condensed Phase Dynamics

Wang, Fei ProQuest Dissertations & Theses University of Illi 2018 해외박사(DDOD)

Chemical dynamics are essentially quantum mechanical processes. A great variety of chemical processes such as electron transfer and energy relaxation occur in condensed phase, reactants and products embedding in a non-reactive solution/environment. Therefore, quantum dynamics in condensed phase is the study of the behavior of the quantum system coupled to an interacting bath. The development of robust methodologies and efficient computational tools for condensed phase dynamics remains central to theoretical chemistry. Since the full quantum treatment only limits to a system with a few degrees of freedom, the partition of the entire system into a subsystem for which quantum mechanical description is necessary and the bath which can be modeled by the less expensive classical dynamics, is a common strategy. Due to the decoherence nature of the bath on the system, the quantum dynamics of the system is often described by the density matrix. Path integral formulation of the density matrix provides a versatile tool for studying quantum dynamics in condensed phase. Unlike the Schro ̈dinger equation in which the wavefunction is central, Feynman’s path integral formulation is trajectory based, and therefore offers a natural connection between quantum mechanics and classical mechanics. This work will investigate path integral formulation in treating a quantum system coupled to anharmonic environment and the semiclassical formulation of path integral. A big achievement in using Feynman’s path integral to study condensed phase dynamics is the development of quantum-classical path integral (QCPI) methodology. Taking advantage that the non-reactive environment can be modeled accurately by classical mechanics, a great reduction of computational cost is achieved. Previous studies have been largely focusing on a quantum system interacting with harmonic environment, mainly because the analytical expressions of harmonic oscillator can be obtained. In this work, we extend the QCPI method to anharmonic environment by making numerically accurate approximations. Semiclassical approach reduces all the possible quantum paths into one or several classical trajectories, therefore automatically eliminates the exponential growth of paths with time evolution. The distinct forward and backward trajectories in the density matrix allows quantum interference. This work explores the semiclassical-system classical-bath formulation of path integral. The stationary phase condition makes the phase smooth and makes Monte Carlo sampling very efficient with respect to the bath initial phase space distribution. The continuous coordinate formulation offers a potential utility of the method to treating multi-level systems.

강건한 험지 자율주행: 경로 계획 알고리즘의 벤치마크와 Hybrid A*-guided Model Predictive Path Integral의 개발

양준열 경희대학교 대학원 2025 국내석사

Autonomous navigation in rough terrains is challenging because physical properties of the terrain, such as slope and surface roughness, have a direct impact on driving stability, making it difficult to ensure reliable traversal using path planning based solely on obstacle avoidance. This study compares the performance of representative local path planning algorithms, including Dynamic Window Approach(DWA), Timed Elastic Band(TEB), Regulated Pure Pursuit(RPP), and Model Predictive Path Integral(MPPI), based on 2.5D costmap that incorporates traversability information, and experimentally demonstrates that existing algorithms suffer from instability, inefficient paths, and collisions in unstructured terrains. To overcome these limitations, this paper proposes an integrated planning framework called Hybrid A*-guided MPPI. In the proposed method, Hybrid A* generates a reference path that prioritizes regions with low slope and roughness based on traversability evaluation, and MPPI optimizes local control inputs along this path. This structure enables global path strategy and local control optimization to be organically combined within a single framework, maintaining consistency and stability of the overall navigation path while adapting to real-time environmental changes. Experimental results conducted in various rough terrain scenarios show that the proposed method consistently improves key performance indicators, including reduced roll and pitch oscillations, enhanced path smoothness, and increased navigation success rate compared to existing approaches.

(An) Algorithm for Searching Optimum Path using Car-hailing as Transit Feeder

이하식 서울대학교 대학원 2019 국내석사

Promoting the use of transit helps alleviate many problems caused by excessive use of private autos, such as traffic congestion, parking problems and air pollution. In Seoul, the modal split of transit has declined in the past five years and that of private autos has increased. This means that transit is less competitive than private autos, and in order to enhance transit competitiveness, it should first evaluate its competitiveness. Most of the studies evaluating transit focused on the accessibility of transit, which can be measured using factors such as travel time, distance and fare. This study compares the two modes by using five-weekday smart card data in Seoul to obtain the passengers of transit, and by acquiring the travel time of auto and transit through application programming (API) services. Not only travel time is compared, but the number of transit passengers is considered to define transit vulnerable ODs (Origin and Destination) in Seoul. The travel occurred during the morning peak hours where traffic is concentrated is analyzed, and the OD is selected as the transit vulnerable OD when the difference in travel time between transit and auto is more than 5 minutes and the number of passengers of transit is more than 500 in 5 days. By using four multimodal integrated route generating algorithms of each vulnerable OD, combined paths between transit and car-hailing service were generated and compared with existing unimodal paths to identify how the transit competitiveness has improved. Among the multimodal paths generated by the algorithm, the optimum path is selected by calculating the generalized cost, and the optimum paths selected by each algorithm are compared. As a result, the second algorithm, which replaces the bus with the car-hailing service and selects the transfer points before and after the transfer stations of transit path as the origin and the destination of the car-hailing service, is found to find multimodal paths most efficiently. Although the multimodal paths have the shortest travel time at a specific OD in a certain time period, at the majority of the ODs, the multimodal paths have about 30% of the travel time between the car-hailing only and the transit paths. Also, the competitiveness of multimodal path was low for ODs with short travel distance, and the competitiveness of multimodal paths was high at ODs with long travel distance. It is most effective to use the car-hailing service as transit feeder where the access time is long. 대중교통의 이용을 활성화하는 것은 교통혼잡, 주차문제, 대기오염 등 과도한 승용차의 이용으로 인해 발생하는 여러 문제들을 완화하는데 도움을 준다. 서울의 경우 최근 5년동안 대중교통의 수단분담률이 감소하고 승용차의 수단분담률이 증가하고 있다. 이는 승용차 대비 대중교통의 경쟁력이 낮다는 것을 의미하고, 경쟁력을 제고하기 위해서는 먼저 대중교통의 경쟁력을 평가해야 한다. 대중교통을 평가한 대다수의 논문들은 대중교통의 접근성에 초점을 두었고, 대중교통 접근성은 통행시간, 거리, 요금 등의 요소들을 이용하여 측정할 수 있다. 본 연구는 서울시 평일 5일치 교통카드 데이터를 이용하여 대중교통의 탑승객 수를 구하고, API 서비스를 이용하여, 승용차와 대중교통의 통행시간을 구득하여, 대중교통과 승용차의 통행시간을 비교하고자 한다. 단순히 통행시간만을 비교한 것이 아니라, 해당하는 출발지와 도착지를 통행했던 대중교통 탑승객 수도 같이 고려하여 서울시의 대중교통 취약 OD를 선정한다. 통행이 집중되는 오전 첨두시에 발생한 통행을 분석하고, 대중교통과 승용차의 통행시간 차이가 5분 이상 나고, 대중교통 탑승객 수가 5일동안 500명 이상인 OD를 취약 OD로 선정한다. 선정된 취약 OD에 대하여 총 네가지의 통합 수단 경로 생성 알고리즘을 이용해 car-hailing 서비스와 대중교통이 결합된 경로를 생성하여, 기존의 단일 수단 경로와 비교하고, 대중교통 경쟁력이 얼마나 개선되는지 파악한다. 알고리즘을 이용해 생성된 통합 수단 경로들 중에서 최적 경로는 일반화 비용을 계산하여 선정하고, 알고리즘 별로 선정된 최적 경로를 비교한다. 그 결과 버스를 Car-hailing 서비스로 대체하고, 환승지점 앞, 뒤 정류장들을 Car-hailing의 출발지와 도착지로 선정하는 두번째 알고리즘이 가장 효율적으로 최적의 수단 통합 경로를 찾는 것으로 나타난다. 통합 수단 경로는 특정 시간대에 특정 OD에서는 가장 짧은 통행시간을 갖기도 하지만, 대다수의 OD에서 수단이 통합된 경로는 car-hailing만 이용한 통행과 대중교통만 이용하는 통행사이의 30% 정도 수준의 통행 시간을 갖는 것으로 나타난다. 또한 통행거리가 짧은 OD에 대해서는 통합수단의 경쟁력이 낮았고, 통행거리가 긴 OD에서 통합수단의 경쟁력이 높았다. 이를 통해 통행거리가 긴 OD 중 접근 시간이 긴 곳에 Car-hailing 서비스를 대중교통 연계수단으로 도입하는 것이 가장 효과적이라 할 수 있다.

Nonlinear Stochastic Dynamics of Structural Systems: A General and Computationally Efficient Wiener Path Integral Formalism

Mavromatis, Ilias G Columbia University ProQuest Dissertations & These 2024 해외박사(DDOD)

This dissertation introduces advances in the Wiener path integral (WPI) technique for determining efficiently and accurately the stochastic response of diverse nonlinear dynamical systems.First, a novel, general, formalism of the WPI technique is developed to account, in a direct manner, also for systems with non-Markovian response processes. Specifically, the probability of a path and the associated transition probability density function (PDF) corresponding to the Wiener excitation process are considered. Next, a functional change of variables is employed, in conjunction with the governing stochastic differential equation, for deriving the system response joint transition PDF as a functional integral over the space of possible paths connecting the initial and final states of the response vector. In comparison to alternative derivations in the literature, the herein-developed formalism does not require the Markovian assumption for the system response process. Overall, the veracity and mathematical legitimacy of the WPI technique to treat also non-Markovian system response processes are demonstrated. In this regard, nonlinear systems with a history-dependent state, such as hysteretic structures or oscillators endowed with fractional derivative elements, can be accounted for in a direct manner-that is, without resorting to any ad hoc modifications of the WPI technique pertaining, typically, to employing additional auxiliary filter equations and state variables.Next, a reduced-order WPI formulation is introduced for efficiently determining the stochastic response of diverse nonlinear systems with fractional derivative elements. This formulation can be also construed as a dimension reduction approach that renders the associated computational cost independent of the total number of stochastic dimensions of the problem. In fact, the proposed technique can determine, directly, any lower-dimensional joint response PDF corresponding to a subset only of the response vector components. This is accomplished by utilizing an appropriate combination of fixed and free boundary conditions in the related variational, functional minimization, problem. Notably, the reduced-order WPI formulation is particularly advantageous for problems where the interest lies in, few only, specific degrees-of-freedom whose stochastic response is critical for the design and optimization of the overall system. Further, an extrapolation approach within the WPI technique is developed that significantly enhances the computational efficiency of the technique without, practically, affecting the associated degree of accuracy. Overall, the WPI technique treats the system response joint transition PDF as a functional integral over the space of all possible paths connecting the initial and the final states of the response vector. Next, the functional integral is evaluated, ordinarily, by considering the contribution only of the most probable path. This corresponds to an extremum of the functional integrand, and is determined by solving a functional minimization problem that takes the form of a deterministic boundary value problem (BVP). This BVP corresponds to a specific grid point of the response PDF domain. Remarkably, the BVPs corresponding to two neighboring grid points not only share the same equations, but also the boundary conditions differ only slightly. This unique aspect of the technique is exploited, and it is shown that solution of a BVP and determination of the response PDF value at a specific grid point can be used for extrapolating and estimating efficiently and accurately the PDF values at neighboring points without the need for considering additional BVPs.Last, a joint time-space extrapolation approach within WPI technique is developed for determining, efficiently and accurately, the non-stationary stochastic response of diverse nonlinear dynamical systems. The approach can be construed as an extension of the above space-domain extrapolation scheme to account also for the temporal dimension. Specifically, it is shown that in-formation inherent in the time-history of an already determined most probable path can be used for evaluating points of the response PDF corresponding to arbitrary time instants, without the need for solving additional BVPs. In a nutshell, relying on the aforementioned unique and advantageous features of the WPI-based BVP, the complete non-stationary response joint PDF is determined, first, by calculating numerically a relatively small number of PDF points, and second, by extrapolating in the joint time-space domain at practically zero additional computational cost. Compared to an alternative brute-force implementation of the WPI technique, and to a standard Monte Carlo simulation (MCS) solution treatment, the developed extrapolation approach reduces the associated computational cost by several orders of magnitude.Several representative numerical examples are considered to demonstrate the reliability of the developed techniques. Juxtapositions with pertinent MCS data are included as well.

Quantum Gravity as a Holographic Theory: Lessons from the Gravitational Path Integral

Hernandez-Cuenca, Sergio University of California, Santa Barbara ProQuest D 2022 해외박사(DDOD)

Holographic dualities like AdS/CFT provide a non-perturbative definition of a bulk theory of quantum gravity in terms of a lower-dimensional boundary quantum field theory. Elucidating quantum gravity thus becomes the challenge of deciphering the dictionary between bulk and boundary physics, and using it to translate basic properties of the latter into lessons about the former. A crucial intermediary between these two realms is the gravitational path integral, which defines the bulk theory in terms of an integral over spacetimes subject to conditions from the boundary theory. Though shallowly understood and rather formal, this piece of technology has thus far been able to provide deep insights into quantum gravity. This thesis is organized in three parts, each focusing on a different basic property in quantum theory and its consequences for quantum gravity through the gravitational path integral: entanglement, causality, and factorization. Part I addresses the emergence of spacetime from entanglement, with a focus on understanding constraints on the entanglement structure of quantum states to posses classical geometries as holographic bulk duals. These constraints can be expressed as linear inequalities and used to define the holographic entropy cone (HEC). A systematic study of the HEC is accomplished by reformulating the holographic computation of von Neumann entropies as a graph-theoretic one, thereby recasting a complicated problem in differential geometry as a purely combinatorial one. This allows to prove important properties of the HEC, devise proof methods and algorithms for constructing it, derive precise relations to other polytope structures, and ultimately pursue a top-down understanding of the HEC from the universal quantum inequality of subadditivity. This part concludes with an exploration of how the machinery involved in the study of the HEC may also be generalized to settings where the von Neumann entropy receives contributions from bulk quantum fields, a regime where the graph-theoretic apparatus has to be upgraded.Part II presents an alternative perspective on spacetime emergence, both in classical and quantum regimes, based on causality. Starting at a classical level, we explain how the conformal bulk geometry can be reconstructed by encoding its causal structure in data accessible from the boundary field theory. Through the use of field theory correlators, we propose a method for obtaining the full-dimensional bulk geometry up to a conformal factor. This generalizes the approach to bulk metric reconstruction based on light-cone cuts to a prescription which allows for recovering even those dimensions which become compact asymptotically. Moving away from the classical limit, we then resolve a known puzzle that arises from a tension between the bulk and boundary causal structures when the bulk theory is understood as a genuine gravitational path integral over spacetimes.Finally, part III delves into the consequences of the lack of factorization that occurs in holography when wormholes are included in the gravitational path integral. In particular, we study generating functionals in quantum gravity and propose a recipe for their computation which accounts for the contribution of such connected topologies. This allows to differentiate between quenched and annealed quantities in quantum gravity, a distinction which may be used as a consistency test-ground for foundational aspects of the gravitational path integral regarding summing over topologies.