Space-time Paths Research Articles

Examining Personal Air Pollution Exposure, Intake, and Health Danger Zone Using Time Geography and 3D Geovisualization

Expanding traditional time geography, this study examines personal exposure to air pollution and personal pollutant intake, and defines personal health danger zones by accounting for individual level space-time behavior. A 3D personal air pollution and health risk map is constructed to visualize individual space-time path, personal Air Quality Indexes (AQIs), and personal health danger zones. Personal air pollution exposure level and its variation through space and time is measured by a portable air pollutant sensor coupled with a portable GPS unit. Personal pollutant intake is estimated by accounting for air pollutant concentration in immediate surroundings, individual’s biophysical characteristics, and individual’s space-time activities. Personal air pollution danger zones are defined by comparing personal pollutant intake with air quality standard; these zones are particular space-time-activity segments along an individual’s space-time path. Being able to identify personal air pollution danger zones can help plan for proper actions aiming at controlling health impacts from air pollution. As a case study, this paper reports on an examination and visualization of an individual’s two-day ozone exposure, intake and danger zones in Houston, Texas.

Special relativity at the quantum scale.

It has been suggested that the space-time structure as described by the theory of special relativity is a macroscopic manifestation of a more fundamental quantum structure (pre-geometry). Efforts to quantify this idea have come mainly from the area of abstract quantum logic theory. Here we present a preliminary attempt to develop a quantum formulation of special relativity based on a model that retains some geometric attributes. Our model is Feynman's “checker-board” trajectory for a 1-D relativistic free particle. We use this model to guide us in identifying (1) the quantum version of the postulates of special relativity and (2) the appropriate quantum “coordinates”. This model possesses a useful feature that it admits an interpretation both in terms of paths in space-time and in terms of quantum states. Based on the quantum version of the postulates, we derive a transformation rule for velocity. This rule reduces to the Einstein's velocity-addition formula in the macroscopic limit and reveals an interesting aspect of time. The 3-D case, time-dilation effect, and invariant interval are also discussed in term of this new formulation. This is a preliminary investigation; some results are derived, while others are interesting observations at this point.

Adaptive-Velocity Time-Geographic Density Estimation for Mapping the Potential and Probable Locations of Mobile Objects

Time-geographic density estimation (TGDE) provides a method for generating probability density surfaces for mobile objects. The technique operates by fitting distance-weighted geo-ellipses to each pair of points in a tracking dataset and combining them to create a final density surface. The sizes of the geo-ellipses, and thus the amount of smoothing, are determined by a velocity parameter which specifies how fast the object can travel. In prior formulations of TGDE this maximum-velocity parameter was treated as constant or fixed. This can be problematic if an object displays variable movement patterns, such as alternating between movements and stops. In this research we develop a more robust formulation of time-geographic density estimation, termed adaptive-velocity TGDE, which allows the maximum-velocity parameter to vary for each segment of the space-time path. First, the new mathematical formulation is demonstrated and compared with fixed-TGDE through an application to synthetic pedestrian tracking data. Second, both methods are evaluated in the context of accurately mapping the movement patterns of a homing pigeon tracked by GPS. The results of both applications demonstrate that adaptive-velocity TGDE has the potential to more accurately delineate the trajectories of mobile objects than the fixed-velocity version. Implications of these results in the context of developing a probabilistic time geography for general mobile objects are also discussed.

Spatio-Temporal Analytics for Exploring Human Mobility Patterns and Urban Dynamics in the Mobile Age

In this research, we present a spatio-temporal analytical framework including spatio-temporal visualization (STV), space-time kernel density estimation (STKDE), and spatio-temporal-autocorrelation-analysis (STAA), to explore human mobility patterns and intra-urban communication dynamics. Experiments were conducted using large-scale detailed records of mobile phone calls in a city. The space-time path, time series graphs, vertical Bézier curves, STKDE, STAA, and related techniques in 3D GIS as well as statistical tests have been suggested for different spatio-temporal analysis tasks. We also investigated several statistical measures that extend the classic spatial association indices for spatio-temporal autocorrelation analysis. The spatial order of weighted matrix was found to have more significant effects than the temporal neighbors on influencing the autocorrelation strength of hourly phone calls.

Brownian net with killing

Motivated by its relevance for the study of perturbations of one-dimensional voter models, including stochastic Potts models at low temperature, we consider diffusively rescaled coalescing random walks with branching and killing. Our main result is convergence to a new continuum process, in which the random space–time paths of the Sun–Swart Brownian net are terminated at a Poisson cloud of killing points. We also prove existence of a percolation transition as the killing rate varies. Key issues for convergence are the relations of the discrete model killing points and their intensity measure to the continuum counterparts: these convergence issues make the addition of killing considerably more difficult for the Brownian net than for the Brownian web.

A Coordinated Routing Model with Optimized Velocity for Train Scheduling on a Single-Track Railway Line

Train scheduling aims to seek a set of space-time paths for multiple trains on a railway line such that resources can be utilized efficiently with respect to prespecified criteria. By representing the train trajectory through a time-space path in its space-time network, this paper proposes an integer programming model for train scheduling on a single-track railway line, in which velocity choice is particularly considered to further decrease the expected energy consumption and interactions between different trains, and the link energy consumption is derived by the Davis formula with respect to different train speeds. The proposed model is implemented in the GAMS optimization software to solve an approximate optimal solution. Numerical examples show that the optimal timetable with optimized velocities can further decrease the energy consumption and coupling effects in comparison to the fixed velocity based schedule.

High-Speed Rail Train Timetabling Problem: A Time-Space Network Based Method with an Improved Branch-and-Price Algorithm

A time-space network based optimization method is designed for high-speed rail train timetabling problem to improve the service level of the high-speed rail. The general time-space path cost is presented which considers both the train travel time and the high-speed rail operation requirements: (1) service frequency requirement; (2) stopping plan adjustment; and (3) priority of train types. Train timetabling problem based on time-space path aims to minimize the total general time-space path cost of all trains. An improved branch-and-price algorithm is applied to solve the large scale integer programming problem. When dealing with the algorithm, a rapid branching and node selection for branch-and-price tree and a heuristic train time-space path generation for column generation are adopted to speed up the algorithm computation time. The computational results of a set of experiments on China’s high-speed rail system are presented with the discussions about the model validation, the effectiveness of the general time-space path cost, and the improved branch-and-price algorithm.

Towards exposure-based time-space pedestrian crash analysis in facing the challenges of ageing societies in Asia

The global ageing phenomenon leads to major road safety concerns. This paper represents a pioneer but preliminary attempt to propose an exposure-based time-space approach to examine elderly pedestrians' crashes in a district in Hong Kong. A disaggregate Geographical Information Systems (GIS)-based three-dimensional (3D) time-space framework is used to relate individual travel activities with crash patterns. In an attempt to integrate the activity-based and spatial crash analysis models, this study combines three rich relational databases to better describe elderly pedestrian behavior in a road network. In the model calibration, space-time paths of the elderly were first generated, they were then superimposed on crash data which were snapped to the link-node system in a 3D environment, with the additional dimension of the time to supplement the traditional 2D analysis. Finally, one- and four-hourly snapshots of vehicle-pedestrian crashes involving the elderly within the district are derived to identify possible associations between the space-time slices of crash frequency and crash risk. The results show that the district's center during the afternoon rush hours was the most hazardous for elderly pedestrians.

Residents’ activity-travel behavior variation by communities in Beijing, China

China’s transition from a planned economy to a market economy has resulted in many changes in its urban structure and society and provided an opportunity for a quasi-longitudinal case study on the relationship between the built environment and activity-travel behavior. This paper draws upon data from an activity diary survey conducted in Beijing in 2007. The survey sample comprised 652 residents living in Danwei (work unit), commodity housing, and affordable housing neighborhoods. On the basis of the three-dimensional geo-visualization analysis of the space-time path and statistical multivariate regression models of daily travel and leisure time, it was found that both residential spatial factors and socio-demographics influence residents’ daily behaviors. The findings show that Danwei residents have less daily travel time than those who live in commodity housing, but people living in affordable housing endure the longest travel time. Daily leisure time is associated more with individual attributes. We argue that although China’s transition is currently gradual, the Danwei system may continue to play significant roles in daily life, and it might provide a valuable model for neighborhood spatial planning.

Bundled camera paths for video stabilization

We present a novel video stabilization method which models camera motion with a bundle of (multiple) camera paths. The proposed model is based on a mesh-based, spatially-variant motion representation and an adaptive, space-time path optimization. Our motion representation allows us to fundamentally handle parallax and rolling shutter effects while it does not require long feature trajectories or sparse 3D reconstruction. We introduce the 'as-similar-as-possible' idea to make motion estimation more robust. Our space-time path smoothing adaptively adjusts smoothness strength by considering discontinuities, cropping size and geometrical distortion in a unified optimization framework. The evaluation on a large variety of consumer videos demonstrates the merits of our method.

A High Performance Scalable Data Collection System for Moving Objects

help Locations Based Services systems to meet market demands, a performance and scalable collection framework was provided to gather different kinds of geographical data (from GPS devices, RFID, Data base transactions, etc.) based on the unified moving object trajectories' Meta-model. Basically, the collection framework offers components to collect spatio-temporal data from GPS enabling devices using .Net sockets, and benefits from executing all code in .NET Common Language Runtime to increase the system performance compared to unmanaged codes that decrease performance because of additional requirement security checks. In order to test the scalability of the proposed collection system, a vehicle tracking simulator was developed to generate and simulate tremendous spatio-temporal data of different moving objects. The main goal of this manuscript is to illustrate the importance of the collection framework and analyze the worst-case testing. Following this strategy, monitoring how scalable the proposed data collection framework is possible when dealing with very large and simultaneous moving objects trajectories datasets in real time. Keywordsdata modeling, Trajectory data collection framework, moving object database, space time path, spatial data engineering, trajectory meta-model.

An Approach to Representing Movement Data

A moving object is an object of which position changes continuously in space. The movement of an object is represented by the change of its position through space and the change of its attributes over time or location. In temporal geography, the model of space-time cube (STC) represents movements as polylines time-ordered connecting spatio-temporal positions of moving objects. The space-time cubes do not represent attributes of moving objects, which change over time or along trajectories. Several authors used two cubes to represent a moving object, one for spatio-temporal positions and another for attributes changing over location. This article proposes an approach to representing multivariate data of moving objects in a Cartesian coordinate system. The main idea of this article is to join the coordinate system representing location data with the coordinate system representing attributes by sharing the time axis. In this case, attributes that are recorded by the location-based method are inferred visually through the space-time path of the movement. This approach can apply for two cases, given route and ungiven route. For movements of ungiven route, the visualization system combines a 3-dimension system representing locations with a 2-dimension system representing attributes. For movements of given route, the visualization system is a 3-dimension Cartesian coordinate system, where the trajectory is extended as an axis representing the distance from departure place to current place, two other axes indicate time and attributes. In both modes, colors are employed as dimensions to show various attributes. The two modes can be switched reciprocally in a system tracking moving objects on ground.

The impact of gasoline price changes on traffic safety: a time geography explanation

The impact of gasoline price changes on traffic safety has received increasing attention in empirical studies. In this study, we use time geography to provide a theoretical framework for examining the effects of time-varying fluctuations in gasoline prices and their relationship to traffic safety in a case study of Mississippi from April 2004 to December 2010. Application of time geography theory suggests that gasoline prices act as one type of capability constraint of the space–time path. As gasoline prices increase (that is, as the capability constraint becomes stronger), we hypothesize traffic crash rates decrease, and they decrease more for groups for whom the constraint is stronger. The results corroborate the hypotheses and suggest that gasoline prices have stronger effects on reducing less severe crashes and negligible effects on reducing fatal crashes. Gasoline price effects on reducing crashes start at a 9-month lag, peak at a 12-month lag, and diminish after an 18-month lag.

Young people and the hidden meanings of the everyday: time-space path as a methodological opportunity

The article explores the ways in which young people use their everyday environments and how they give meanings to their surroundings. It concentrates on the potential of the re-interpretations of 1970s time-geography by applying the method of time-space paths to educational contexts in both universities and schools. The point of view is methodological. The piloting phase took place during a number of courses on environmental education of the university level and, based on the experience gained, the method was re-developed for secondary school levels. The data were gathered from eight schools in Finland as part of the ‘Liikkeelle!’ (‘On the move!’) project, funded by the Finnish National Board of Education, where the main aim was to take students’ own neighbourhoods into account in teaching. The students were asked to make observations of their environment over a one-day period and to take photographs, which could all be used later as material for the construction of their unique time-space paths. The main contents of the paths have been analysed in the article, but more emphasis have been placed on an evaluation of the exercise in order to offer ideas for further development of these methods.

Spatiotemporal analysis of critical transportation links based on time geographic concepts: a case study of critical bridges in Wuhan, China

Critical transportation infrastructure has been studied extensively in recent years. This paper presents a spatiotemporal analysis of critical transportation links based on time geographic concepts. With widespread adoption of information and communication technologies (ICT) and location-aware mobile devices, large tracking datasets have become readily available. This study uses a tracking dataset of approximately 12,000 taxis in Wuhan, China over 1week to analyze spatiotemporal origin–destination (O–D) patterns of trips that use three critical bridges connecting the three districts of Wuchang, Hankou, and Hanyang separated by the Yangtze River and the Han River. We use the space–time prism concept to identify alternative space–time paths passing through different bridges that observe the spatial and temporal constraints between each O–D pair derived from the taxi trajectory data. This case study illustrates the feasibility and benefits of using the proposed time geographic approach to analyze spatiotemporal patterns of travel demands on the critical links and their alternative paths in a transportation system.

Moving Object Trajectories Meta-Model and Spatio-Temporal Queries

In this paper, a general moving object trajectories framework is put forward to allow independent applications processing trajectories data benefit from a high level of interoperability, information sharing as well as an efficient answer for a wide range of complex trajectory queries. Our proposed meta-model is based on ontology and event approach, incorporates existing presentations of trajectory and integrates new patterns like space-time path to describe activities in geographical space-time. We introduce recursive Region of Interest concepts and deal mobile objects trajectories with diverse spatio-temporal sampling protocols and different sensors available that traditional data model alone are incapable for this purpose.

Bringing emotions to time geography: the case of mobilities of poverty

Although there is ample evidence that the way we feel and anticipate feeling in certain situations or places can assert great influence on our behavior, this emotional component of the space–time path has for the most part remained external to time geographical analyses. Working from within a time geographical framework, this paper shows that spatio-temporal and emotional boundaries are both relevant and interacting while persons travel their paths through time and space. To that purpose we suggest a reinterpretation of authority constraints and to take into account the biological and cultural expressions of individuals. The rather static conceptualizations of the poverty–context relationship in poverty studies could benefit from an emotionally sensitive time geography. We draw from a small case study of low-income single mothers in San Francisco, California.

Intra-attraction Tourist Spatial-Temporal Behaviour Patterns

This paper focuses on tourist spatial-temporal behaviour patterns and develops a combination approach to clarify such behaviour patterns quantitatively and qualitatively using the concept of the space–time path of time geography. A case study of the Summer Palace verifies that this approach is feasible. Tourist spatial-temporal behaviour can be described and determined by temporal behaviour factors, spatial behaviour factors, activity choice factors and path characteristics factors. The research results of the Summer Palace case study revealed seven clusters of spatial-temporal behaviour patterns. Temporal behaviour factors made the largest contribution to the clustering analysis, and the phenomenon of space–time tension was clearly present in tourists’ behaviour in the Summer Palace. Tourists’ stay time displayed a clear decreasing trend, with an increase in the constraint of exit time. Describing and portraying tourist spatial-temporal behaviour patterns results in a better understanding of tourist activities. A better understanding of tourist behaviour patterns may, in turn, provide a scientific basis for industry practices, such as attraction management, product renewal and attraction marketing. This study has practical significance for the upgrading of attraction facilities and the ultimate improvement of the quality of tourist experiences.

Analysing infrequently sampled animal tracking data by incorporating generalized movement trajectories with kernel density estimation

When analysing the movements of an animal, a common task is to generate a continuous probability density surface that characterises the spatial distribution of its locations, termed a home range. Traditional kernel density estimation (KDE), the Brownian Bridges kernel method, and time-geographic density estimation are all commonly used for this purpose, although their applicability in some practical situations is limited. Other studies have argued that KDE is inappropriate analysing moving objects, while the latter two methods are only suitable for tracking data collected at frequent enough intervals such that an object’s movement pattern can be adequately represented using a space–time path created by connecting consecutive points. This research formulates and evaluates KDE using generalised movement trajectories approximated by Delaunay triangulation (KDE-DT) as a method for analysing infrequently sampled animal tracking data. In this approach, a DT is constructed from a point pattern of tracking data in order to approximate the network of movement trajectories for an animal. This network represents the generalised movement patterns of an animal rather than its specific, individual trajectories between locations. Then, kernel density estimates are calculated with distances measured using that network. First, this paper describes the method and then applies it to generate a probability density surface for a Florida panther from radio-tracking data collected three times per week. Second, the performance of the technique is evaluated in the context of delineating wildlife home ranges and core areas from simulated animal locational data. The results of the simulations suggest that KDE-DT produces more accurate home range estimates than traditional KDE, which was evaluated with the same data in a previous study. In addition to animal home range analysis, the technique may be useful for characterising a variety of spatial point patterns generated by objects that move through continuous space, such as pedestrians or ships.

Localized qubits in curved spacetimes

We provide a systematic and self-contained exposition of the subject of localized qubits in curved spacetimes. This research was motivated by a simple experimental question: if we move a spatially localized qubit, initially in a state |ψ1〉, along some spacetime path Γ from a spacetime point x1 to another point x2, what will the final quantum state |ψ2〉 be at point x2? This paper addresses this question for two physical realizations of the qubit: spin of a massive fermion and polarization of a photon. Our starting point is the Dirac and Maxwell equations that describe respectively the one-particle states of localized massive fermions and photons. In the WKB limit we show how one can isolate a two-dimensional quantum state which evolves unitarily along Γ. The quantum states for these two realizations are represented by a left-handed 2-spinor in the case of massive fermions and a four-component complex polarization vector in the case of photons. In addition we show how to obtain from this WKB approach a fully general relativistic description of gravitationally induced phases. We use this formalism to describe the gravitational shift in the Colella–Overhauser–Werner 1975 experiment. In the non-relativistic weak field limit our result reduces to the standard formula in the original paper. We provide a concrete physical model for a Stern–Gerlach measurement of spin and obtain a unique spin operator which can be determined given the orientation and velocity of the Stern–Gerlach device and velocity of the massive fermion. Finally, we consider multipartite states and generalize the formalism to incorporate basic elements from quantum information theory such as quantum entanglement, quantum teleportation, and identical particles. The resulting formalism provides a basis for exploring precision quantum measurements of the gravitational field using techniques from quantum information theory.