Space-time Paths Research Articles

Energy-Efficient Data Transmission in Mobility-Aware Wireless Networks

Data transmission scheme is an effective mode to improve the energy-efficiency in packet delivery. In this paper, we investigate the energy-efficient data transmission over reliable links and unreliable links in mobility-aware wireless networks. The network topologies in mobility-aware wireless networks are changed from one time slot to another, and they could be described by a sequence of static graphs. We first model these network topologies in a time period as a virtual space-time graph. On the virtual space-time graph, energy-efficient data transmission problems over reliable links and unreliable links are defined. The aim of the two data transmission problems is to find a spatial-temporal path with the minimum energy cost. Next, we propose an Energy-Efficient Data Transmission algorithm over Reliable Links (EEDT-RL) to find the optimal space-time path. Based on EEDT-RL, we also develop a heuristic data transmission protocol over unreliable links (named EEDT-UL), in which the path reliability is taken into consideration. Simulation results show that our proposed algorithms perform well in terms of energy cost and transmission count compared with some existing algorithms.

Estimating Spatiotemporal Contacts Between Individuals in Underground Shopping Streets Based on Multi-Agent Simulation

Coronavirus disease 2019 (COVID-19) has exposed the public safety issues. Obtaining inter-individual contact and transmission in the underground spaces is an important issue for simulating and mitigating the spread of the pandemic. Taking the underground shopping streets as an example, this study aimed to verify commercial facilities’ influence on the spatiotemporal distribution of inter-individual contact in the underground space. Based on actual surveillance data, machine learning techniques are adopted to obtain utilizers’ dynamics in underground pedestrian system and shops. Firstly, an entropy maximization approach is adopted to estimate pedestrians’ origin-destination (OD) information. Commercial utilization behaviors at different shops are modeled based on utilizers’ entering frequency and staying duration, which are obtained by re-identifying individuals’ disappearances and appearances at storefronts. Based on observed results, a simulation method is proposed to estimate utilizers’ spatiotemporal contact by recreating their space-time paths in the underground system. Inter-individual contact events and exposure duration are obtained in view of their space-time vectors in passages and shops. A social contact network is established to describe the contact relations between all individuals in the whole system. The exposure duration and weighted clustering coefficients were defined as indicators to measure the contact degree of individual and the social contact network. The simulation results show that the individual and contact graph indicators are similar across time, while the spatial distribution of inter-individual contact within shops and passages are time-varying. Through simulation experiments, the study verified the effects of self-protection and commercial type adjustment measures.

Capacity-Oriented Train Scheduling of High-Speed Railway Considering the Operation and Maintenance of Rolling Stock

The capacity of some busy rail lines is increasingly tight and passenger demand far exceeds the railway capacity. To schedule as many trains as possible in order to satisfy more transportation demands, we studied the capacity-oriented train scheduling problem. While most approaches focus only on increasing the capacity of the rail line, this research considers both the time-space distribution of transportation demands and the operation and maintenance of rolling stock. To solve this problem, we first constructed a time-space network to describe the time-space path of rolling stock. We then proposed an integer planning model with rolling stock maintenance and the OD service frequency constraints to maximize the number of running arcs in rail sections. After decomposing this model by introducing some Lagrangian multipliers to relax its hard constraints, we proposed a Lagrangian relaxation-based decomposition algorithm, including two path search sub-algorithms for rolling stock to optimize both the relaxed and the feasible solutions. Finally, we conducted a computation study on a practical double-track high-speed railway line to test the performance of this algorithm. It reports that the train timetables and the operation of rolling stock are well managed.

Isolated Objects and Their Evolution: A Derivation of the Propagator\u2019s Path Integral for Spinless Elementary Particles

We formalize the notion of isolated objects (units), and we build a consistent theory to describe their evolution and interaction. We further introduce a notion of indistinguishability of distinct spacetime paths of a unit, for which the evolution of the state variables of the unit is the same, and a generalization of the equivalence principle based on indistinguishability. Under a time reversal condition on the whole set of indistinguishable paths of a unit, we show that the quantization of motion of spinless elementary particles in a general potential field can be derived in this framework, in the limiting case of weak fields and low velocities. Extrapolating this approach to include weak relativistic effects, we explore possible experimental consequences. We conclude by suggesting a primitive ontology for the theory of isolated objects.

Generalized Path Planning for UTM Systems With a Space-Time Graph

Motivated by the increased use of UAS in commercial applications, in this paper we tackle the problem of path planning when requests are submitted by UAS managed by different operators. We propose the new problem of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">generalized path planning</i> for UAS Traffic Management, where the UAS path is described by operators with a sequence of waypoint groups and a solution trajectory must pass through a waypoint in each group. This problem is typical for applications where multiple charging stations and pickup/drop-off locations are distributed in a flight area. Our solution builds upon prior work on discretized space-time graph path planning and proposes a novel multi-source/multi-destination graph search algorithm that generates collision-free trajectories for pre-flight CDR. Our efficient algorithm has runtime proportional to the number of groups and avoids combinatorial explosion. We apply our mechanism to the energy-constrained UAS package delivery problem with multiple warehouses and battery charging stations. Simulation results show that our algorithm is efficient and scalable with the number of requests and graph size. The addition of charging stations and the option for multiple warehouses increases the request admission ratio and reduces the overall trajectory duration, effectively improving both the planner’s quality of service and the efficiency of airspace usage.

Theory of spacetime impetus

This article introduces the theory of spacetime impetus (SI). The theory unites Newtonian theory (NT) and the theory of general relativity (GR). To develop SI, we reformulated NT in spacetime and replaced the particle primitive in NT with the fragment of energy primitive in field theory. SI replaces Newton’s second law F = ma governing the motion of particles, where F, m, and a are, respectively, interaction force, mass, and acceleration, with the change equation P = k governing the motion of fragments of energy, where P and k are, respectively, action force and the curvature of a path in spacetime. To verify SI, we conducted three tests: Test 1 predicted the precession angles of Mercury and Jupiter, test 2 predicted the bending angle of light as it grazes the surface of the sun, and test 3 predicted the radius of the photon sphere. All three tests were in agreement with GR, the third corresponding to strong Riemannian curvature in GR. The equations of motion in SI are in terms of Cartesian coordinates and time and are relatively simple to solve. Undergraduate students in science and engineering and others with similar mathematical skills can validate the results for themselves.

The Visualization Representation of Space-Time-Path in The Space-Time-Cube

Map is a traditional visualization tool to represent distribution and interaction of spatial objects or spatial phenomenon. However, with the continuous development of acquisition and processing technologies for spatio-temporal data, traditional map can hardly meet the visualization requirement for this type of data. In other words, the dynamic information about spatial object or phenomenon cannot be expressed fully by traditional map. The Space-Time-Cube (STC), as a three-dimensional visualization environment, whose base represents the two-dimensional geographical space and whose height represents the temporal dimension, can simultaneously represent the spatial distribution as well as the temporal changes of spatio-temporal data. For some spatial object or phenomenon, its moving trajectory can be visualized in STC as a Space-Time-Path (STP), by which the speed and state of motion can be clearly reflected. Noticeably, the problem of visual clutter about STP is inevitably due to the complexity of three-dimensional visualization. In order to reduce the impact of visual clutter, this paper discusses different aspects about visualization representation of STP in the STC. The multiple scales representation and the multiple views display can promote interactive experience of users, and the application of different visual variables can help to represent different kinds of attribute information of STP. With the visualization of STP, spatio-temporal changes and attributive characters of spatial object or phenomenon can be represented and analysed.

Time–space paths and the experiences of vulnerable young people in alternative educational settings

ABSTRACT We use the concept of time–space paths (Gordon, Holland and Lahelma 2000) to explore how young people negotiate manageable educational pathways and experience educational engagement in alternative educational settings. For many young people in alternative settings, tight time–space paths (e.g. attending school on time) led to their disengagement from mainstream school settings, as mainstream schools did not accommodate the lives and needs of these young people. We draw on interviews with young people in alternative educational settings in Finland and Australia. We extend the discussion to two alternative time–space paths to explore how young people in alternative educational settings, while expressing a like and need for looser time–space paths to accommodate their difficult life circumstances, still need aspects of tight time–space paths to engage with education. We discuss strategies used in the alternative educational settings that enable the young people to develop a rhythm within their own time–space paths and a sense of agency and control in their learning environment. These strategies enabled communication and the development of positive relationships with teachers that led to a sense of belonging and their engagement with education.

On the space-time statistics of motion pictures.

It is well known that natural images possess statistical regularities that can be captured by bandpass decomposition and divisive normalization processes that approximate early neural processing in the human visual system. We expand on these studies and present new findings on the properties of space-time natural statistics that are inherent in motion pictures. Our model relies on the concept of temporal bandpass (e.g., lag) filtering in lateral geniculate nucleus (LGN) and area V1, which is similar to smoothed frame differencing of video frames. Specifically, we model the statistics of the differences between adjacent or neighboring video frames that have been slightly spatially displaced relative to one another. We find that when these space-time differences are further subjected to locally pooled divisive normalization, statistical regularities (or lack thereof) arise that depend on the local motion trajectory. We find that bandpass and divisively normalized frame differences that are displaced along the motion direction exhibit stronger statistical regularities than for other displacements. Conversely, the direction-dependent regularities of displaced frame differences can be used to estimate the image motion (optical flow) by finding the space-time displacement paths that best preserve statistical regularity.

A Space-Time Analysis of Rural Older People's Outdoor Mobility and Its Impact on Self-Rated Health: Evidence from a Taiwanese Rural Village.

With the aggravation of rural aging, the well-being and self-rated health level of older people in rural communities are significantly lower than those in urban communities. Past studies hold that mobility is essential to the quality of life of the elderly, and well-being depends on their own adaptation strategies in the built environment. Therefore, this study combines three key factors related to active aging: environment, health and mobility, and assumes that the elderly with good health status will have environmental proactivity and a wider range of daily mobility in a poor rural built environment. This study attempts to track daily mobility by using a space–time path method in time geography and then to explore the relationship between outdoor mobility and older people’s self-rated health. A 1-week mobility path survey for 20 senior citizens of Xishi Village, a typical rural village in Taiwan, was conducted by wearing a GPS sports watch. A questionnaire survey and in-depth interviews were done to provide more information about the seniors’ personal backgrounds and lifestyles. The results show that when the built environment is unfit to the needs of daily activities, half of the participants can make adjustment strategies to go beyond the neighborhoods defined by administrative units. Correlation analysis demonstrated that mental health is associated with daily moving time and distance. In addition, men have higher self-rated health scores than women, and there are significant statistical differences between married and widowed seniors in daily outing time and distance. This exploratory study suggests that in future research on rural health and active aging in rural areas, understanding the daily outdoor mobility of the elderly can help to assess their health status and living demands and quickly find out whether there is a lack of rural living services or environmental planning.

Geodesic Incompleteness and Partially Covariant Gravity

We study the issue of length renormalization in the context of fully covariant gravity theories as well as non-relativistic ones such as Hořava–Lifshitz gravity. The difference in their symmetry groups implies a relation among the lengths of paths in spacetime in the two types of theory. Provided that certain asymptotic conditions hold, this relation allows us to transfer analytic criteria for the standard spacetime length to be finite and the Perelman length to be likewise finite, and therefore formulate conditions for geodesic incompleteness in partially covariant theories. We also discuss implications of this result for the issue of singularities in the context of such theories.

Comparing Commercial Vehicle Fuel Consumption Models using Real-World Data under Calibration Constraints

Assessing commercial road vehicle fuel use at a high spatiotemporal resolution helps in understanding underlying usage patterns and informs future interventions toward fuel-efficient freight planning and operations. With the use of global navigation satellite systems in fleet tracking and advancements in driver activity surveys, instantaneous fuel consumption models can calculate fuel use in high resolution using inputs like speed and acceleration derived from GPS data. Given that several models exist, there is a need to compare fuel use estimates from different models, especially under the constraint of limited data for calibration. This study evaluates the accuracy of fuel use estimates from three fuel consumption models (COPERT 4, SIDRA TRIP, and MOVES) applied to 10 diesel commercial road vehicles in Singapore over a standardized drive cycle (NEDC) and real-world activity data derived from GPS traces using the method of space-time path segments and road grade obtained from a digital elevation model. Changes in model performance are examined when supplementary on-board diagnostics (OBD) data and payload information are used. The models gave varying fuel use estimates over the NEDC, especially for heavier vehicles in the sample. When applied to real-world data, SIDRA TRIP was found to be the most accurate for the context studied. SIDRA TRIP’s performance improved consistently when supplemented with OBD and payload information. This comparison approach allows analysts to select the most suitable model for a given context, and take steps toward more sustainable freight transportation.

Spacetime Paths as a Whole

The mathematical similarities between non-relativistic wavefunction propagation in quantum mechanics and image propagation in scalar diffraction theory are used to develop a novel understanding of time and paths through spacetime as a whole. It is well known that Feynman’s original derivation of the path integral formulation of non-relativistic quantum mechanics uses time-slicing to calculate amplitudes as sums over all possible paths through space, but along a definite curve through time. Here, a 3+1D spacetime wave distribution and its 4-momentum dual are formally developed which have no external time parameter and therefore cannot change or evolve in the usual sense. Time is thus seen “from the outside”. A given 3+1D momentum representation of a system encodes complete dynamical information, describing the system’s spacetime behavior as a whole. A comparison is made to the mathematics of holograms, and properties of motion for simple systems are derived.

Directional-Layered Space-Time Densities: A New Spatiotemporal Trajectory Aggregation and Geographic Visualization Approach

One approach used in GIScience to investigate movement data is adopting time-geography theory and its important principles/methods: space-time paths and space-time cube. Thus, the movement of a moving object can be represented as a 3D polyline in a space-time cube. However, with the advent of larger movement datasets, this type of display can easily become cluttered and incomprehensible. In this article, we propose a new space-time aggregation algorithm, i.e., directional-layered space-time densities (DLSTDs), to solve the problem of trajectory clutter in a space-time cube. The approach is an extension of the pixel (2D raster cell) density around a point in two-dimensional space to the voxel density around a trajectory line segment in three-dimensional space-time $(x-y+t)$ . In the algorithm, the horizontal or vertical voxel layers are first calculated around the trajectory based on the direction of each trajectory line segment. Subsequently, the voxel density is calculated by substituting the distance of the voxel from the trajectory segment into a Gaussian-based attenuation function. Finally, the resulting layered densities are presented using volume rendering techniques. We demonstrate the DLSTDs on 30-day movement data of transport trucks in a mine in China and compare the algorithm with two other algorithms. At the end of the article, we summarize the research and consider further developments of the proposed approach.

The Girl on the Bus: Familiar Faces in Daily Travel and Their Implications for Crime Protection

Hägerstrand proposed that individuals’ daily mobility is constrained to a particular time–space path by capability, coupling, and authority requirements. This tethering of routine activities to particular places at scheduled times facilitates repetitive bundling of individuals at certain nodes. Associations emerging from repeated, cursory encounters between individuals have been coined familiar strangers. “Familiar strangers” is a unique social phenomenon that emerges where individuals experience repeated visual encounters but never verbally interact. Scholarship suggests that increased familiarity among individuals might incur social benefits at places by reducing individual anonymity and enhancing the moral obligation to obey behavioral norms, which in turn could have a crime protection effect. In this study we spatially and temporally integrate a large smart card data set with a database of crime incidents along with census information to examine the relationship between bus stops with varying concentrations of familiar strangers and the occurrence of three crime types (theft, drug, and nuisance offenses). The findings demonstrate the potential for familiar strangers to provide crime guardianship at bus stops and also highlight the influence of surrounding land use and neighborhood sociodemographic environment on crime risk.

4D street view: a video-based visualization method.

We propose a new visualization method for massive supercomputer simulations. The key idea is to scatter multiple omnidirectional cameras to record the simulation via in situ visualization. After the simulations are complete, researchers can interactively explore the data collection of the recorded videos by navigating along a path in four-dimensional spacetime. We demonstrate the feasibility of this method by applying it to three different fluid and magnetohydrodynamics simulations using up to 1,000 omnidirectional cameras.

Webs of Care: Qualitative GIS Research on Aging, Mobility, and Care Relations in Singapore

The connections between time and space have been studied considerably in quantitative and qualitative research on the geographies of care; however, researchers tend to prioritize one approach over the other. Our article integrates analyses of activity spaces and space–time paths with conceptualizations of care developed in qualitative studies to deepen understanding of the spatiotemporal care routines of older adults in Singapore. Using qualitative geographic information systems (QualiGIS), we develop a comparative frame to understand the differential sociopolitical logics that shape the care routines of older adults who are Singapore citizens and nonmigrants vis-à-vis temporary migrants from the People’s Republic of China. Building on recent writing about care assemblages, we conceptualize webs of care as the interlinked chains, in and through which individuals—in this case, older adults—exercise agency to give and receive care in the context of political, institutional, and social structures. Our article shows how the relational thinking of assemblage theory can inform geographic information systems analyses of activity space and space–time paths. We advance research on care assemblages by identifying in actual time–space how various resources within care assemblages (or the lack of) can diminish or enhance the capacity and resilience of older adults to give and receive care.

A spatial data model for urban spatial-temporal accessibility analysis.

Time geography represents the uncertainty of the space–time position of moving objects through two basic structures, the space–time path and space–time prism, which are subject to the speed allowed in the travel environment. Thus, any attempt at a quantitative time-geographic analysis must consider the actual velocity with respect to space. In a trip, individuals tend to pass through structurally varying spaces, such as linear traffic networks and planar walking surfaces, which are not suitable for use in a single GIS spatial data model (i.e., network, raster) that is only applicable to a single spatial structure (i.e., point, line, polygon). In this study, a velocity model is developed for a traffic network and walking surface-constrained travel environment through the divide-and-conquer principle. The construction of this model can be divided into three basic steps: the spatial layering of the dual-constrained travel environment; independent modelling of each layer using different spatial data models; and generation of layer-based time-geographic framework by merging models of each layer. We demonstrate the usefulness of the model for studying the space–time accessibility of a moving object over a study area with varying spatial structures. Finally, an example is given to analyse the effectiveness of the proposed model.

How Neighborhood Effect Averaging Might Affect Assessment of Individual Exposures to Air Pollution: A Study of Ozone Exposures in Los Angeles

The neighborhood effect averaging problem (NEAP) can be a serious methodological problem that leads to erroneous assessments when studying mobility-dependent exposures (e.g., air or noise pollution) because people’s daily mobility could amplify or attenuate the exposures they experienced in their residential neighborhoods. Specifically, the NEAP suggests that individuals’ mobility-based exposures tend toward the mean level of the participants or population of a study area when compared to their residence-based exposures. This research provides an in-depth examination of the NEAP and how the NEAP is associated with people’s daily mobility through an assessment of individual exposures to ground-level ozone using the activity-travel diary data of 2,737 individuals collected in the Los Angeles metropolitan statistical area. The results obtained with exploratory analysis (e.g., a scatterplot and histograms) and spatial regression models indicate that the NEAP exists when assessing individual exposures to ozone in the study area. Further, high-income, employed, younger, and male participants (when compared to low-income, nonworking, older, and female participants) are associated with higher levels of neighborhood effect averaging because of their higher levels of daily mobility. Finally, three-dimensional interactive geovisualizations of the space-time paths and hourly ozone exposures of seventy-one selected participants who live in the same neighborhood corroborate the findings obtained from the spatial regression analysis.

A Cost and Passenger Responsible Optimization Method for the Operation Plan of Additional High-Speed Trains in a Peak Period

In the peak period of a railway system, operators typically add additional trains to provide increased capacity to satisfy the increasing passenger demand. The paper proposes a new optimization framework for designing the operation plan, which includes the number of additional trains, train type, stop plan, and timetable, for additional trains in a peak period. A space-time network representation is used to obtain a feasible primary operation plan by finding a set of feasible space-time paths in the space-time network. Considering simultaneously the passenger demand and the trains’ total travel times, we formulate a biobjective integer programming model for generating a cost and passenger responsible primary operation plan. A set of loading capacity constraints are formulated in the model to guarantee a suitable loading capacity for each station’s passenger demand and better service for passengers. The CPLEX solver is used to solve the proposed model and to generate the optimal operation plan. Two sets of numerical experiments are conducted on a small-scale rail corridor and on the Wuhan-Guangzhou rail corridor to evaluate the performance of the proposed method. The results of the experiments show that the primary operation plan can be obtained within an acceptable computation time.