Space-time Diagrams Research Articles

Data Infrastructure for Connected Vehicle Applications

Ann Arbor Connected Vehicle Test Environment (AACVTE) is the world’s largest operational, real-world deployment of connected vehicles (CVs) and connected infrastructure, with over 2,500 vehicles and 74 infrastructure sites, including intersections, midblocks, and highway ramps. The AACVTE generates a massive amount of data on a scale not seen in the traditional transportation systems, which provides a unique opportunity for developing a wide range of connected vehicle (CV) applications. This paper introduces a data infrastructure that processes the CV data and provides interfaces to support real-time or near real-time CV applications. There are three major components of the data infrastructure: data receiving, data pre-processing, and visualization including the performance measurements generation. The data processing algorithms include signal phasing and timing (SPaT) data compression, lane phase mapping identification, trajectory data map matching, and global positioning system (GPS) coordinates conversion. Simple performance measures are derived from the processed data, including the time–space diagram, vehicle delay, and observed queue length. Finally, a web-based interface is designed to visualize the data. A list of potential CV applications including traffic state estimation, traffic control, and safety, which can be built on this connected data infrastructure is discussed.

Development and application effects of visualization materials based on space-time diagram for special relativity

Development and application effects of visualization materials based on space-time diagram for special relativity

Defect-mediated turbulence in bubbly Taylor-Couette flow

We investigate experimentally the defect-mediated turbulence (DMT) which is induced by bubbles injection in a Taylor-Couette flow when the inner cylinder is rotating while the outer cylinder is fixed. Bubbles of 1.2 mm in diameter are injected at the bottom of a Taylor-Couette device of radii ratio equal to 0.91. The tangential Reynolds number range is [2 200, 19 300] and the air injection rate varies up to 800 ml/min. For these conditions of the experiments, bubbles are trapped in the gap by the Taylor vortices and arranged as patterns (toroidal, wavy toroidal, spirals, and wavy spirals). Visualizations of the bubble patterns were carried out. When decreasing the Reynolds number or increasing the air injection rate, spiral and toroidal patterns can coexist in a composite flow. Defects occur in the bubble’s patterns (merging or splitting of the Taylor vortex pairs). By analyzing the space-time diagram of bubbles patterns and their complex demodulation, we highlight different regimes and transitions in the DMT of the bubbly Taylor-Couette flow. The control parameter of the transitions is the air volumetric fraction, which evolves as the ratio between the axial injection Reynolds number and the tangential Reynolds number. By increasing the air volumetric fraction, the defects in the DMT flows are classified as three flow regimes: (i) structured composite flow where the defects are periodic in space and time, (ii) intermittency defects chaos where the defects zones alternate randomly with the patterns in time and space, and (iii) developed defects chaos with a large defects density. The statistical properties of these three regimes of the DMT are analyzed in the framework of the complex Ginzburg-Landau equation.

Visualizing Distributed System Executions

Distributed systems pose unique challenges for software developers. Understanding the system’s communication topology and reasoning about concurrent activities of system hosts can be difficult. The standard approach, analyzing system logs, can be a tedious and complex process that involves reconstructing a system log from multiple hosts’ logs, reconciling timestamps among hosts with non-synchronized clocks, and understanding what took place during the execution encoded by the log. This article presents a novel approach for tackling three tasks frequently performed during analysis of distributed system executions: (1) understanding the relative ordering of events, (2) searching for specific patterns of interaction between hosts, and (3) identifying structural similarities and differences between pairs of executions. Our approach consists of XVector , which instruments distributed systems to capture partial ordering information that encodes the happens-before relation between events, and ShiViz , which processes the resulting logs and presents distributed system executions as interactive time-space diagrams. Two user studies with a total of 109 students and a case study with 2 developers showed that our method was effective, helping participants answer statistically significantly more system-comprehension questions correctly, with a very large effect size.

Mode conversion behavior of guided wave in glass fiber reinforced polymer with fatigue damage accumulation

This paper presents a study on the mode conversion effect of guided wave in glass fiber reinforced polymer (GFRP) with fatigue damage accumulation. By using a laser ultrasonic system, a series of time-space diagrams of guided wave has been obtained, which shows the failure process of the specimen under tension-tension fatigue loading. An interesting phenomenon that the mode conversion effect becomes increasing more pronounced with the micro-damage accumulation can be observed in the experiment and further quantitatively evaluated by defining an index MMR (Mode-to-Mode Ratio). An investigation of the relationship between mode conversion effect and matrix crack density is then carried out by means of the finite element method. Influences of various factors such as the density and the randomness of the simulative matrix crack distribution are discussed. Results show that the matrix crack density makes a major contribution to the mode conversion effect in despite of the limited influence caused by the random distributions of the matrix cracks, which offers great potential for composite fatigue evaluation by using the mode conversion effect.

Traffic Data Imputation Using Deep Convolutional Neural Networks

We propose a statistical learning-based traffic speed estimation method that uses sparse vehicle trajectory information. Using a convolutional encoder-decoder based architecture, we show that a well trained neural network can learn spatio-temporal traffic speed dynamics from time-space diagrams. We demonstrate this for a homogeneous road section using simulated vehicle trajectories and then validate it using real-world data from NGSIM. Our results show that with probe vehicle penetration levels as low as 5\%, the proposed estimation method can provide a sound reconstruction of macroscopic traffic speeds and reproduce realistic shockwave patterns, implying applicability in a variety of traffic conditions. We further discuss the model's reconstruction mechanisms and confirm its ability to differentiate various traffic behaviors such as congested and free-flow traffic states, transition dynamics, and shockwave propagation.

Lorentzian-geometry-based analysis of airplane boarding policies highlights "slow passengers first" as better.

We study airplane boarding in the limit of a large number of passengers using geometric optics in a Lorentzian metric. The airplane boarding problem is naturally embedded in a (1+1)-dimensional space-time with a flat Lorentzian metric. The duration of the boarding process can be calculated based on a representation of the one-dimensional queue of passengers attempting to reach their seats in a two-dimensional space-time diagram. The ability of a passenger to delay other passengers depends on their queue positions and row designations. This is equivalent to the causal relationship between two events in space-time, whereas two passengers are timelike separated if one is blocking the other and spacelike if both can be seated simultaneously. Geodesics in this geometry can be utilized to compute the asymptotic boarding time, since space-time geometry is the many-particle (passengers) limit of airplane boarding. Our approach naturally leads to the introduction of an effective refractive index that enables an analytical calculation of the average boarding time for groups of passengers with different aisle-clearing time distribution. In the past, airline companies attempted to shorten the boarding times by trying boarding policies that allow either slow or fast passengers to board first. Our analytical calculations, backed by discrete-event simulations, support the counterintuitive result that the total boarding time is shorter with the slow passengers boarding before the fast passengers. This is a universal result, valid for any combination of the parameters that characterize the problem: the percentage of slow passengers, the ratio between aisle-clearing times of the fast and the slow group, and the density of passengers along the aisle. We find an improvement of up to 28% compared with the fast-first boarding policy. Our approach opens up the possibility to unify numerous simulation-based case studies under one framework.

Electric charge in hyperbolic motion: the special conformal transformation solution

As a simple application of special conformal transformations, we derive the electromagnetic field produced by an electric charge in hyperbolic motion. Unlike other purely algebraic derivations, here we develop a more intuitive geometrical description, based on Minkowski diagrams.

Spacetime Metamaterials—Part I: General Concepts

This article deals with the general concepts underpinning spacetime metamaterials and related systems. It first introduces spacetime metamaterials as a generalization of (bianisotropic) metamaterials, presented in the holistic perspective of direct and inverse spacetime scattering, where spacetime variance and dispersion offer unprecedented medium diversity despite some limitations related to the uncertainty principle. Then, it describes the fundamental physical phenomena occurring in spacetime systems, such as frequency transitions, nonreciprocity, Fizeau dragging, bianisotropy transformation, and superluminality, allowed when the medium moves perpendicularly to the direction of the wave. Next, it extends some principles and tools of relativity physics, particularly a medium-extended version of the spacetime (or Minkowski) diagrams, elaborates a general strategy to compute the fields scattered by spacetime media, and presents a gallery of possible spacetime media, including the spacetime step discontinuity, which constitutes the building brick of any spacetime metamaterial. Finally, the conclusion section provides a list of 16 items that concisely summarizes the key results and teachings of the overall document. The second part establishes the theory and overviews some current and potential applications of spacetime metamaterials.

Automaticity and Invariant Measures of Linear Cellular Automata

AbstractWe show that spacetime diagrams of linear cellular automata $\unicode[STIX]{x1D6F7}:\,\mathbb{F}_{p}^{\mathbb{Z}}\rightarrow \mathbb{F}_{p}^{\mathbb{Z}}$ with $(-p)$-automatic initial conditions are automatic. This extends existing results on initial conditions that are eventually constant. Each automatic spacetime diagram defines a $(\unicode[STIX]{x1D70E},\unicode[STIX]{x1D6F7})$-invariant subset of $\mathbb{F}_{p}^{\mathbb{Z}}$, where $\unicode[STIX]{x1D70E}$ is the left shift map, and if the initial condition is not eventually periodic, then this invariant set is nontrivial. For the Ledrappier cellular automaton we construct a family of nontrivial $(\unicode[STIX]{x1D70E},\unicode[STIX]{x1D6F7})$-invariant measures on $\mathbb{F}_{3}^{\mathbb{Z}}$. Finally, given a linear cellular automaton $\unicode[STIX]{x1D6F7}$, we construct a nontrivial $(\unicode[STIX]{x1D70E},\unicode[STIX]{x1D6F7})$-invariant measure on $\mathbb{F}_{p}^{\mathbb{Z}}$ for all but finitely many $p$.

Influence of coarse toll on the dynamic properties of traffic flow in a single-entry traffic corridor

In this paper, we investigate the effects of coarse toll on the user equilibrium (UE) state in a single-entry traffic corridor with early and late arrivals from analytical and numerical perspective. Unlike previous studies on traffic tolls, the flow congestion model is used to take into account the dynamic propagation of traffic flow. The LWR (Lighthill–Whitham–Richards) model and the Greenshields’ velocity–density function are used to describe the dynamic properties of traffic flow. The quasi-analytic solutions of the three possible cases in UE due to different charges are derived. Both analytical and numerical results indicate that rarefaction waves and shock waves appear in the corridor under the coarse toll. The three-dimensional evolution diagrams of traffic flow and space–time diagrams illustrate that the introduction of course toll lets flow patterns more complicated. This extends the knowledge given by the classical bottleneck model.

Memory, attention and prediction: a deep learning architecture for car-following

Car-following (CF) models are an appealing research area because they fundamentally describe the longitudinal interactions of vehicles and contribute substantially to an understanding of traffic flow. In this study, by combining numerous deep neural network structures to mimic the memory, attention and prediction (MAP) mechanisms of real drivers, a deep learning-based car following model named MAP is built. The proposed MAP learned CF behaviour from real-world datasets. Experiments on predicting future driving behaviour show that the MAP model with memory, attention and prediction mechanisms outperforms models without those mechanisms. Several analysis are conducted to understand the MAP model, and quantitatively provides some explanations of how MAP achieves the CF behaviour. A simulation is also presented and explicitly analysed. The results show that the proposed approach can produce space-time diagrams similar to real traffic. The analysis also shows that the supervised learning models generate the most likely, rather than the best, CF behaviour.

Neither past nor present : Authenticity and late twentieth-century architectural heritage

It was the present moment. No one need wonder that Orlando started, pressed her hand to her heart, and turned pale. For what more terrifying revelation can there be than that it is the present moment? That we survive the shock at all is only possible because the past shelters us on one side and the future on another. But we have no time now for reflections.(Virginia Woolf, Orlando)How long does the present moment last? Where and when does the past begin and how does the present end? In physics – or more precisely in the special theory of relativity – the present can be defined as the coordinate origin in a spacetime diagram – an unextended point that separates an observer’s past and future light cones. From that point of view, the present has no duration at all; the past instantly assimilates the future without any hesitation in between. However, time perception tells us that we actually experience a ‘here and now’. Psychologists believe that the time range we perceive as the present, the socalled specious present, lasts about three seconds – the interval duration after which the brain may be said to reset its attention. This is already infinitely more than no duration at all but this recognition is still not enough to explain concepts like the present time or ‘today’ as an indicator of the contemporary. In the domain of history, the present seems to be a much more complex construction. When we speak of phenomena as contemporary, we place them in an extended present. We concede that the present encompasses the recent past and the near future – a temporal range that provides a stage for the actions and reactions that shape our world.

Walking behavior of pedestrian social groups on stairs: A field study

There is growing consensus that most pedestrians in a crowd walk in groups, and these groups have an influence on crowd dynamics whenever under natural or emergency situations. Despite this fact, however, empirical data on group walking behavior on stairs are limited. This paper aims to explore how group members interact with each other and how groups organize on stairs. In order to achieve these, a field study was conducted on stairs in a campus of a university. A total of 105 pedestrian groups descending the stairs were selected as observation subjects. After obtaining their trajectories by the optimal flow algorithm, interpersonal distances and angles between group members, average speed, space-time diagrams offset angles and walking dissimilarity on stairs were calculated and analyzed. Results demonstrate that average distances for groups of different sizes are relatively stable. Groups with different sizes on stairs can form different walking patterns. Members belonging to the same group always seek to move at similar speed and offset angles, and can adjust their motion during the descending process, in order to ensure comfortable group walking and coherence. It is discovered that group size has a significant negative effect on average group speed. Gender and social relationships have little influence on group walking speed and dissimilarity values, except in dyads. These findings have implications for group walking modelling and safe pedestrian facility design.

Capacity approximations for near- and far-side bus stops in dedicated bus lanes

We develop analytical approximations for the bus-carrying capacities at near- and far-side stops with one or multiple curbside berths where buses operate in a dedicated bus lane. The approximations are derived using time-space diagrams of bus trajectories and probabilistic methods. They correctly account for the effects of key operating factors that were ignored or incorrectly addressed by previous methods. These factors include the signal timing and the distance between stop and signal. Comparison against computer simulation shows that our models furnish much more accurate estimates for near- and far-side stop capacities than previous methods in the literature. Numerical case studies are performed to examine how the stop capacity is affected by various operating factors. New findings and their practical implications are discussed.

Oritatami: A Computational Model for Molecular Co-Transcriptional Folding.

We introduce and study the computational power of Oritatami, a theoretical model that explores greedy molecular folding, whereby a molecular strand begins to fold before its production is complete. This model is inspired by our recent experimental work demonstrating the construction of shapes at the nanoscale from RNA, where strands of RNA fold into programmable shapes during their transcription from an engineered sequence of synthetic DNA. In the model of Oritatami, we explore the process of folding a single-strand bit by bit in such a way that the final fold emerges as a space-time diagram of computation. One major requirement in order to compute within this model is the ability to program a single sequence to fold into different shapes dependent on the state of the surrounding inputs. Another challenge is to embed all of the computing components within a contiguous strand, and in such a way that different fold patterns of the same strand perform different functions of computation. Here, we introduce general design techniques to solve these challenges in the Oritatami model. Our main result in this direction is the demonstration of a periodic Oritatami system that folds upon itself algorithmically into a prescribed set of shapes, depending on its current local environment, and whose final folding displays the sequence of binary integers from 0 to with a seed of size . We prove that designing Oritatami is NP-hard in the number of possible local environments for the folding. Nevertheless, we provide an efficient algorithm, linear in the length of the sequence, that solves the Oritatami design problem when the number of local environments is a small fixed constant. This shows that this problem is in fact fixed parameter tractable (FPT) and can thus be solved in practice efficiently. We hope that the numerous structural strategies employed in Oritatami enabling computation will inspire new architectures for computing in RNA that take advantage of the rapid kinetic-folding of RNA.

Moving vehicle detection, tracking and traffic parameter estimation from a satellite video: a perspective on a smarter city

ABSTRACTSatellite remote sensing is undergoing a revolution in terms of sensors and temporal coverage. The possibility of acquiring earth’s surface video from space provides an opportunity to investigate broader applications of remote sensing. High-resolution spaceborne videos can become a vital factor in earth observation. Temporally continuous tracking of moving objects, i.e. vehicles, vessels, or even military equipment on Earth’s surface demands high spatial resolution satellite videos. Detecting moving vehicles in the urban areas from space video can lead governments to a new era of traffic monitoring. Satellite videos will find many applications in the field of traffic monitoring. In this article, first, moving vehicles are detected using background subtraction with 94.7% accuracy. Afterwards, vehicles’ trajectories, average velocities, dynamic velocities, and space-time diagram are estimated and trajectories are classified based on velocities. Finally, the total frame traffic density is computed.

Traffic Prediction using Time-Space Diagram: A Convolutional Neural Network Approach

Traffic prediction is a major component of any traffic management system. With the increase in data sources and advancement in connectivity, data analysis and machine learning approaches for traffic prediction have gained a lot of attention. Most of the existing data analysis approaches in traffic prediction rely on aggregated inputs such as flow and density, with limited studies using the individual vehicle-level data. The time-space diagram of the vehicles can be constructed from the connected vehicles’ data. This plot is comprehensive and contains all the information about traffic flow dynamics at both microscopic and macroscopic levels. Accordingly, this study introduces a deep learning-based methodology to directly predict the traffic state based on the time-space diagram with the use of convolutional neural networks (CNN). The time-space diagram is directly used as the input to the traffic prediction model using a CNN. The prediction capability of the proposed model is compared with multilayer perceptron, support vector regression, and autoregressive integrated moving average, and the results indicate a superior capability of CNN in predicting flow and density across all possible values of these parameters.

Adaptive Rolling Smoothing With Heterogeneous Data for Traffic State Estimation and Prediction

Spatial–temporal traffic state estimation and the prediction of urban expressways is a vital component of traffic management and information systems. The adaptive smoothing method is one of the most frequently used approaches to estimate traffic states. However, the fixed filter parameters used in existing approaches sometimes fail to characterize traffic dynamics well. To better capture generation, propagation, and mitigation dynamics of traffic congestion, we propose an adaptive rolling smoothing (ARS) approach by dynamically tuning the filter parameters in a rolling horizon scheme for online applications. The fusion of heterogeneous traffic data combines aggregate traffic measurements (e.g., traffic flow rate, time occupancy, and speed collected by remote microwave sensors) and disaggregate information (e.g., timestamps of individual vehicles detected by license plate recognition cameras). A nonlinear traffic flow filter based on the virtual trajectory algorithm is established to reconstruct the spatial–temporal traffic state and estimate experienced travel times of individual vehicles. The results demonstrate the capability and effectiveness of the proposed ARS approach in the historical traffic state estimation and short-term traffic flow prediction. Complicated traffic states of weaving, merging, and diverging segments can be well distinguished by reconstructing time-space speed diagrams. The proposed approach can be extended to develop efficient missing data imputation algorithms and hierarchical control strategies for heterogeneously congested urban expressways.

Perturbation threshold and hysteresis associated with the transition to turbulence in sudden expansion pipe flow

The complex flow resulting from the laminar-turbulent transition in a sudden expansion pipe flow, with expansion ratio of 1:2, subjected to an inlet parabolic velocity profile and a vortex perturbation, is investigated by means of direct numerical simulations. It is shown that the threshold amplitude for disordered motion is described by a power law scaling, with -3 exponent, as a function of the subcritical Reynolds number. The instability originates from a region of intense shear rate, which results on the flow symmetry breakdown. Above the threshold, several unsteady states are identified using space-time diagrams of the centreline axial velocity fluctuation and their energy. In addition, the simulations show a small hysteresis transition mode due to the reestablishment of the recirculation region in the subcritical range of Reynolds numbers, which depends on: (i) The initial and final quasi-steady states, (ii) the observation time and (iii) the number of intermediate steps taken when increasing and decreasing the Reynolds number.