Space-time Paths Research Articles

Advancing human mobility modeling: a novel path flow approach to mining traffic congestion dynamics

Mining traffic congestion dynamics presents difficulties in data structure and spatiotemporal analysis. Existing studies mainly provide insights from a supply perspective, with a restricted examination of why congestion occurs and how travel demands affect congestion. This study introduces an innovative framework to mine congestion dynamics from the perspective of human mobility. In human mobility modeling, we refine the conventional origin-destination representation of activity flow by introducing "path flow" (PF) which considers space-time paths and movement patterns. In congestion scenarios, congestion-related path flow (CPF) and congested path sub-flow (CPSF) are extended to track individuals’ congestion exposure and explore the correlations between congestion and human mobility. To finely classify congestion-related travel demands, a Bayesian inference approach, incorporating destination and spatiotemporal heterogeneities, is developed to deduce trip purposes. The experiments conducted in Wuhan demonstrate the availability and importance of PF in spatiotemporal dynamics analysis of human mobility. Interestingly, we find that 1) the job-housing relationship is imbalanced, with massive residents opting for cross-district living and working; 2) individuals tend to visit tertiary hospitals on weekends and secondary medical facilities with less congestion on weekdays. Notably, path flow can promote the fine-grained modeling of human mobility and provide theoretical support for many urban issues.

Theoretical and Experimental Framework for Estimating Cyber Victimization Risk in a Hybrid Physical-Virtual World

This study proposes a framework integrating Routine Activities Theory into a hybrid physical-virtual space. Utilizing a space-time path metaphor, it explores phishing susceptibility in relation to daily activities in the hybrid physical-virtual environments. The mixed-method approach includes surveys and experiments, such as simulated phishing emails, to assess response patterns in both settings and investigate travel behavior’s impact on cyber victimization. This hybrid model seeks to understand how physical and virtual interactions affect cybercrime vulnerability, aiding in developing prevention strategies. Additionally, the research underscores the role of visual analytics in cybersecurity, turning complex data into visual forms for effective threat analysis.

Bootstrapping smooth conformal defects in Chern-Simons-matter theories

The expectation value of a smooth conformal line defect in a CFT is a conformal invariant functional of its path in space-time. For example, in large N holographic theories, these fundamental observables are dual to the open-string partition function in AdS. In this paper, we develop a bootstrap method for studying them and apply it to conformal line defects in Chern-Simons matter theories. In these cases, the line bootstrap is based on three minimal assumptions — conformal invariance of the line defect, large N factorization, and the spectrum of the two lowest-lying operators at the end of the line. On the basis of these assumptions, we solve the one-dimensional CFT on the line and systematically compute the defect expectation value in an expansion around the straight line. We find that the conformal symmetry of a straight defect is insufficient to fix the answer. Instead, imposing the conformal symmetry of the defect along an arbitrary curved line leads to a functional bootstrap constraint. The solution to this constraint is found to be unique.

Door to door space-time path planning of intercity multimodal transport network using improved ripple-spreading algorithm

The main objective of this study is to solve the problem of recommending door-to-door space–time paths in an intercity multimodal transport network. The available modes include railway, metro, bus, rapid-bus, and walking. In terms of mathematical modeling, the reconstructed space–time path planning model considers multiple constraints, such as acyclic constraint, flow balance constraint and transfer constraints, to ensure the viability of the path, which is significantly different from the path in the traditional graph theory and road network. To attain the K shortest paths in two situations, the improved ripple-spreading algorithm (hereafter referred to as IRSA) is introduced, which is inspired by the ripple-spreading phenomenon and can find global optimal paths through only one iteration. A method for reducing the search space is applied to speed up the computing process. We demonstrate the feasibility and effectiveness of the proposed model and algorithm by comparing it with Gurobi Solver and Dijkstra algorithm using a small-scale network. The experiment results are evaluated by solving the door-to-door itinerary problem from Taiyuan to Beijing. Results indicate that the proposed approach can find constrained K shortest paths within an acceptable computing time. A set of experiments are conducted to test the performance of different methods, and results show that the speed-up method provides a significant improvement in problem-solving efficiency, while attempting to guarantee path optimality, which could reduce the CPU time by 51% to 92% for the tested OD pairs.

The Lagrangian structure, the Euler equation, and second Newton’s law of ultrafast nonlinear optics

With a notable exception of space–time variable swap, pulse evolution equations of ultrafast optics are mathematically similar to the equations of quantum mechanics and beam dynamics. The Lagrangian structure of these equations is, however, much less intuitive. Here, we show that such a structure can be identified via a path-integral analysis of the pulse evolution equation, offering useful insights into the Lagrangian underpinning of ultrafast nonlinear optics. The Euler–Lagrange equation applied to the optical analog of the Lagrange function leads to a second-order differential equation that parallels in its structure second Newton’s law. Stationary-phase space–time paths found by solving such an equation reveal the hidden inner workings behind a vast class of field-waveform transformations in ultrafast optics, including the buildup of nonlinear phase, modulation instabilities, and soliton breather dynamics.

Construction and Analysis of Space–Time Paths for Moving Polygon Objects Based on Time Geography: A Case Study of Crime Events in the City of London

Time geography considers that the motion of moving objects can be expressed using space–time paths. The existing time geography methods construct space-time paths using discrete trajectory points of a moving point object to characterize its motion patterns. However, these methods are not suitable for moving polygon objects distributed by point sets. In this study, we took a type of crime event as the moving object and extracted its representative point at each moment, using the median center to downscale the polygon objects distributed by the point sets into point objects with timestamps. On this basis, space–time paths were generated by connecting the representative points at adjacent moments to extend the application scope of space–time paths, representing the motion feature from point objects to polygon objects. For the case of the City of London, we constructed a space–time path containing 13 nodes for each crime type (n = 14). Then, each edge of the space–time paths was considered as a monthly vector, which was analyzed statistically from two dimensions of direction and norm, respectively. The results showed that crime events mainly shifted to the east and west, and crime displacement was the greatest in April. Therefore, space–time paths as proposed in this study can characterize spatiotemporal trends of polygon objects (e.g., crime events) distributed by point sets, and police can achieve improved success by implementing targeted crime prevention measures according to the spatiotemporal characteristics of different crime types.

GIS‐enabled historiography to determine travel routes during the Western Han period via agent‐based models and least‐cost path analysis

AbstractGIS‐enabled historiography allows us to shed light on missing or poorly understood aspects of historical events. Here, we use agent‐based models (ABMs), least cost path analysis (LCPA), and space–time paths to recreate and evaluate possible modes and routes of travel undertaken by Shi Rao, a Western Han official. A diary was found in Shi Rao's tomb that includes information about his travels over 1 year (11 BCE), including start and end times of his journeys. But it leaves out details regarding modes of transport or exact routes. Using Tan Qixiang's historical atlas, we digitized river networks and utilized modern topographic data to digitally recreate the landscape as it was during Shi Rao's travels. This was then used to evaluate possible journeys via rivers (using ABMs) and roads (using LCPA), and compared to historical speed of boats, carts and horses, with findings indicating that horseback may have been the viable option.

High-speed railway-based fast logistics service network design problem

Different from the conventional logistics service network design problem, we design a fast logistics service network based on high-speed railway. An integrative optimization model which is applicable for solving practical problems is established. This paper simultaneously considers three subproblems: Train timetabling, freight flow assignment and electrical multiple units (EMU) routing plan, in which the objectives are simultaneous to minimize the total train travel time, the operation cost and transportation cost of freight transport, the number of freight EMU and the number of maintenance tasks. The constraints imposed in the model include space-time path resource assignment restriction, node operation capability, train safety interval time, train connection time restriction, freight service time window, train loading capacity restriction and EMU routing restriction. Based on the thoughts of divide and conquer, the original problem is decomposed by using the decomposition mechanism of the Lagrange relaxation algorithm to solve the integrated optimization model. To verify the feasibility and effectiveness of the model and algorithm proposed in this paper, a case study is conducted based on Harbin Dalian high-speed railway.

Long-Horizon Multi-Robot Rearrangement Planning for Construction Assembly

Robotic assembly planning enables architects to explicitly account for the assembly process during the design phase, and enables efficient building methods that profit from the robots' different capabilities. Previous work has addressed planning of robot assembly sequences and identifying the feasibility of architectural designs. This paper extends previous work by enabling planning with large, heterogeneous teams of robots. We present a planning system which enables parallelization of complex task and motion planning problems by iteratively solving smaller subproblems. Combining optimization methods to solve for manipulation constraints with a sampling-based bi-directional space-time path planner enables us to plan cooperative multi-robot manipulation with unknown arrival-times. Thus, our solver allows for completing subproblems and tasks with differing timescales and synchronizes them effectively. We demonstrate the approach on multiple case-studies to show the robustness over long planning horizons and scalability to many objects and agents of our algorithm. Finally, we also demonstrate the execution of the computed plans on two robot arms to showcase the feasibility in the real world.

Assessing the cognition of movement trajectory visualizations: interpreting speed and direction

ABSTRACT This paper evaluates cognitively plausible geovisualization techniques for mapping movement data. With the widespread increase in the availability and quality of space-time data capturing movement trajectories of individuals, meaningful representations are needed to properly visualize and communicate trajectory data and complex movement patterns using geographic displays. Many visualization and visual analytics approaches have been proposed to map movement trajectories (e.g. space-time paths, animations, trajectory lines, etc.). However, little is known about how effective these complex visualizations are in capturing important aspects of movement data. Given the complexity of movement data which involves space, time, and context dimensions, it is essential to evaluate the communicative efficiency and efficacy of various visualization forms in helping people understand movement data. This study assesses the effectiveness of static and dynamic movement displays as well as visual variables in communicating movement parameters along trajectories, such as speed and direction. To do so, a web-based survey is conducted to evaluate the understanding of movement visualizations by a nonspecialist audience. This and future studies contribute fundamental insights into the cognition of movement visualizations and inspire new methods for the empirical evaluation of geovisualizations.

Analyzing national parks visitor activities using geotagged social media photos

Visitor activities within national parks are important information for park management. Currently, national parks and nature-based recreation area worldwide have no systematic visitor activity data collection schemes. Traditional visitor movement or activity data collection methods used in tourism studies are often costly in money and time and difficult to implement. This paper presents a framework and formal procedure that uses geotagged photos crowdsourced from social media platforms to uncover visitor activities within national parks. First, the daily individual space-time paths are constructed from the photo geotags and timestamps for all visitors. Then the following information is derived from the space-time paths: 1) four activity types including stationary, walking, vehicle riding, and flying; 2) the total time of various visitor activities in a park; 3) visitor flow directions aggregated to a grid; 4) a graph constructed from space-time paths and the directed and undirected connections (flows) between POIs; and 5) the centrality of POIs derived from the graph. A case study of four highly visited U.S. national park units from 2008 to 2021 demonstrates the process and capabilities of the method. It also reveals a trend of increased walking time and decreased stationary time in the case study parks over the years. Although this study is only based on Flickr photos, the method can be implemented with data derived from any social media platforms as long as geotags and timestamps are available. The method may be used to monitor visitor activities and movements within national parks and other outdoor recreation areas, especially remote and unmonitored locations.

Exact instantons via worldline deformations

The imaginary part of the one loop effective action in external backgrounds can be efficiently computed using worldline instantons which are closed periodic paths in spacetime. Exact solutions for nonstatic backgrounds are only known in certain cases. In this paper, we propose a novel technique allowing the construction of further exactly solvable models. In order to do so, we introduce a deformation function which maps the worldline instantons for a given model to the closed periodic stationary paths of a new model. Executing this procedure iteratively results in a chain of infinitely many solvable models. Similar ideas were applied to topological and nontopological defects in quantum field theory. We explicitly discuss the tunneling exponential in the Schwinger pair creation rate and illustrate the validity of the proposed technique for well-known cases.

Pricing of the Bus-Truck Co-Delivery Mode of Last Mile Delivery Considering Social Welfare Maximization

In order to solve the problems of low delivery efficiency and high cost at the end of express delivery, and the impact of express trucks on urban road traffic, the co-delivery mode of trucks and buses is proposed. In this mode, without affecting the normal operation of the bus, it uses the idle resources of the bus to cooperate with the trucks to complete the delivery. The express company pays the bus delivery service fee to the bus operator, so as to improve the revenue of the bus operator. At the same time, the delivery efficiency can be improved, the express delivery cost can be reduced, and the impact of express trucks on urban traffic can be lower. A two-layer optimization model is constructed to solve the bus delivery service pricing and express space-time path selection scheme under the co-delivery mode. An example analysis is carried out through the actual bus routes and express delivery demand in Dalian. The results show that the co-delivery mode can provide consumers with more efficient services, reduce costs for express companies, provide additional revenue for bus operators, and improve social welfare. Unless the timeliness of delivery is extremely considered, the measure of using the co-delivery mode is better than the measure of relaxing restrictions on express delivery vehicles.

Personalizing the dichotomy of fixed and flexible activities in everyday life: deriving prism anchors from GPS-enabled survey data.

Space-time prism is a fundamental concept in time geography that can model an individual's accessibility to resources under space-time constraints. A prism anchor is often defined by work, school, or home activity with a fixed location and schedule. Trips and other activities are relatively flexible and scheduled between prism anchors. This fixity-flexibility dichotomy may not capture the increasing complexity of human mobility behaviors or variations among individuals. Recent developments in location-aware technologies allow us to collect person-level mobility data with detailed space-time paths and contextual information. This article develops methods to extract prism anchors from these GPS-based survey data and examines whether home, work, and school activities can always be used to define prism anchors for everyone. To illustrate our methods, we use data collected in Minnesota and Beijing as two study cases. Results in both study cases suggest that not everyone has home, work, or school anchors, and people with the same socio-demographic background tend to have similar anchor types. By deriving home, work, and school anchors, we can better understand how a person's everyday schedules are governed by home, work, and school and refine person-based accessibility measures.

Minimizing Coordination in Multi-Agent Path Finding with Dynamic Execution

Multi-agent Path Finding (MAPF) is an important problem in large games with many dynamic agents that need to follow space-time trajectories without inter-agent collisions. Modern MAPF solvers plan assuming that agents directly follow the space-time trajectories at known constant speeds without delays or speedups, resulting in rigid plans which need to be replanned if there are changes during execution. Instead we would like agents to be able to follow their computed paths with dynamic velocities while requiring minimal coordination with others to prevent collisions and deadlocks. One way to address this problem is to first produce collision free space-time paths and then compute a coordination controller that prevents collisions and deadlock during dynamic execution. This two step process prevents fully minimizing coordination as the initially planned space-time paths do not reason about coordination and can be arbitrarily bad. We introduce a novel paradigm and show how planning in space-coordination level, rather than space-time, allows us to simultaneously plan paths and a coordination controller. Our method, Space-Level Conflict-Based Search (SL-CBS), builds on the Conflict-Based Search framework and allows us to reason explicitly about coordination, producing paths as well as a coordination controller with bounded suboptimal minimal coordination. We show experimentally that this results in a 20-50% reduction in coordination compared to the closest state of the art solver.

Identifying Tourist Spatial and Temporal Patterns Using GPS and Sequence Alignment Method

This study identified the spatial and temporal patterns of national park visitors by combining global positioning system (GPS) technologies and surveys using the sequence alignment method (SAM) based on the concept of space–time path of time geography. Data were collected from a sample of 344 GPS tracks and questionnaires obtained from Gyeryongsan National Park in South Korea. A complex random stratified sampling method was employed to represent a national sample based on mobile positioning data. The result of the SAM analysis revealed that the derived visitor typologies constituted three groups from 83 unique paths extracted from 341 sequences. Significant intergroup differences were found for the paths based on average travel distance, average visit duration, and average travel speed. The main theoretical contribution of this study is in expanding the application of the theory by providing methodological improvements using SAM and GPS analysis of the theoretical basis of time geography.

A spatiotemporal data model and an index structure for computational time geography

The availability of Spatiotemporal Big Data has provided a golden opportunity for time geographical studies that have long been constrained by the lack of individual-level data. However, how to store, manage, and query a huge number of time geographic entities effectively and efficiently with complex spatiotemporal characteristics and relationships poses a significant challenge to contemporary GIS platforms. In this article, a hierarchical compressed linear reference (CLR) model is proposed to transform network-constrained time geographic entities from three-dimensional (3D) (x, y, t) space into two-dimensional (2D) space. Accordingly, time geographic entities can be represented as 2D spatial entities and stored in a classical spatial database. The proposed CLR model supports a hierarchical linear reference system (LRS) including not only underlying a link-based LRS but also multiple higher-level route-based LRSs. In addition, an LRS-based spatiotemporal index structure is developed to index both time geographic entities and the corresponding hierarchical network. The results of computational experiments on large datasets of space–time paths and prisms show that the proposed hierarchical CLR model is effective at storing and managing time geographic entities in road networks. The developed index structure achieves satisfactory query performance in milliseconds on large datasets of time geographic entities.

Simulating inter-individual contact in the inter-station passenger transfer system connecting multiple metro stations based on space–time path data

Determining passengers’ inter-individual contact in the metro station area (MSA) is an important issue to simulate and mitigate the spread of the Coronavirus disease 2019 (COVID-19) pandemic. Taking the inter-station passenger transfer system (IPTS) as an example, this study aimed to verify the passenger flows’ influence on the inter-individual contact around the MSA. Based on actual observed data, the passengers’ space–time paths (STP) in the network were obtained through an agent-based simulation. In this study, the direct contact model and the mediate contact model were used to describe the inter-individual contact in view of the passengers’ STP. The contact count and the exposure duration were defined as indicators to measure the contact degree of individual and the system. The results show that the time-varying trip distribution of the metro passengers significantly affected the inter-individual contact degree and the spatial distribution of contact risk region in the MSA. The intersection of passenger flow in different directions and the concentrated movement of passenger flow in the same direction increased the inter-individual contact and prolonged exposure in the morning. Through simulation experiments, the study verified the effects of controlling the flow direction and equalizing passenger flow generation measures aiming to reduce inter-individual contact and cumulative exposure duration.

Time Domain Optimize in an Urban Rail Transit Line Based on Passenger Flow Spatial and Temporal Distribution

Focusing on the time domain optimization problem of an urban rail transit line, this paper constructs a passenger travel network with OD passenger flow data as input, by using a multi-path search algorithm based on dynamic cost to deduce the passenger space-time path. The passenger travel path is restored and the spatial and temporal distribution of passenger flow is calculated. Based on this, considering the influence of passenger flow spatial and temporal distribution on the time domain division, the orderly clustering method is used to optimize the time domain. Factoring in the influence of line capacity constraint, train running sequentially on time domain division and bidirectional time domain, a time domain optimization framework for an urban rail line is proposed in this study to integrate the time domain optimization results and improve the adaptability of optimization method. A practical line is taken as an example to verify the effectiveness of the proposed framework. Compared with the traditional time domain division method, the time domain division result accuracy is significantly improved and lays a foundation for the formulation of train service scheme which accurately matches transport capacity to demand.

A Generalized Model of Activity Space

This article introduces the concept of a generalized activity space to bridge area-based and activity-based representations of geographic context. We argue that microscale space–time paths fail to account for contextual determinants of behavior, because they emphasize “contacts” over “contexts,” a problem that could be solved, in part, by using a broader “generalized” representation of geographic context. This article develops the idea of a generalized activity space and empirically tests the viability of the concept. Support for the viability of the idea is identified through analysis of 34,500 trips by 7,550 individuals in Atlanta. We find that demographic characteristics and residential location jointly shape a person’s geographic context. Through a series of hypothesis tests, we find evidence that these location–demographic groupings are generalizable; that is, people with similar socioeconomic backgrounds and residential locations exhibit similar generalized activity spaces. Residential location, by itself, however, is not an effective descriptor of the configuration of a person’s context. We argue that generalized activity spaces have potential to inform study of how the environment influences behavior by allowing a more robust consideration of interplay between socioeconomic characteristics and the use of space.