Exit Time Research Articles

“Right here waiting”? Distribution of intentional metro travel groups amid COVID-19 in Hong Kong

During COVID-19, people needed to travel and meet as a group physically to gain benefits such as overcoming loneliness. Using multiday continuous smartcard data, we can identify intentional travel groups (ITGs) in cities. Using the 2020 smartcard data of the Hong Kong metro system, we first construct a dataset of probable ITG trips (PIGTs) where two riders swiped in and out at the same stations within one minute during weekends—we choose weekends because there are fewer co-presenting metro commuters entering and/or exiting the same station. Assuming that ITGs would have more PIGTs and smaller exit time difference than those co-presenting by coincidence, we then identified ITGs as those with at least four PIGTs in a month. To see whether and how the pandemic impacted ITGs, we geo-visualize the quantity of the identified ITGs by metro station and between metro stations on three different Sundays before and during the pandemic. The results indicate that ITGs’ distribution by metro station and between metro stations changed notably after the outbreak of COVID-19.

Application of the first exit time stochastic model with self-repair mechanism to human mortality rates.

The purpose of this study is to construct a mortality model that reasonably explains survival curves and mortality rates in terms of the decline in biological function, which is the phenomenon of ageing. In this model, an individual organism is regarded as a collection of subsystems, and for each subsystem, the model defines human mortality by introducing positive self-repair mechanisms and stochastically generated negative external shocks. The probability density function of the time of death is derived explicitly, and the model parameters are estimated using life tables from Japan and the UK, which demonstrate the existence of multiple parameter sets that fit well with the observed data.

Antipredator responses of bats during short boreal nights with variable climatic conditions

Abstract The threat of predation can influence the behavior of animals. To minimize the impact of predation, animals rely on antipredatory responses and effectively balance these responses with other activities to maximize survival. Boreal bats are nocturnal animals that must forage within a narrow time frame during short, light summer nights with unpredictable weather. Despite having no specialized predators, boreal bats are still subject to predation. However, whether they express antipredatory responses has not been established. We studied antipredatory responses and responses to climatic conditions in boreal bats in 2 settings: 1) during roost emergence; and 2) during foraging within Tawny Owl territories and at locations with no Tawny Owl sightings. Acoustic data were collected at 23 roosts and 10 foraging grounds. Two controlled predation threats were used—playbacks of Tawny Owl calls and fledgling calls. Fledgling calls were only played during roost emergence. In both experiments, music and no treatment were used as controls. We also incorporated weather variables in the model. According to our results, bats tend to delay their emergence by 16 min when Tawny Owl calls were played outside the roost, but this effect was not noticeable when weather variables were included. There was no difference in exit time when music or fledgling sounds were played. While foraging, bats reduced their activity in Tawny Owl territories when calls of owls or music were played compared to no treatment. These results suggest that bats might display variable antipredatory responses, but weather influences behavior of bats more than predation risk, highlighting the importance of energy-saving strategies at northerly latitudes.

Remaining useful life prediction method for jointless track circuits based on multivariate feature fusion and nonlinear Wiener process

Abstract Predicting the Remaining Useful Life (RUL) of track circuits is essential to ensure the safe and reliable operation of high-speed railways. In response to the challenges faced by current machine-learning-based RUL prediction methods, which struggle to represent the uncertainty in the probability distribution of RUL predictions, this paper suggests a hybrid-driven method for estimating remaining life. Firstly, the track circuit Health Index (HI) is constructed by feature dimensionality reduction and fusion of the original multivariate monitoring data through Kernel Principal Component Analysis (KPCA) and Autoencoder (AE); Secondly, the degraded state of the rail circuit is modelled using a nonlinear Wiener degradation model. Finally, the principle of First Hitting Time (FHT) is used to derive the Probability Density Function (PDF) of the anticipated RUL. The efficacy and superiority of the approach presented in this paper are validated by experimental research on the track circuit monitoring dataset. The method enhances forecast accuracy and reduces prediction uncertainty, offering robust technical support for track circuit maintenance decision-making.

High-Fidelity Simulations of Flight Dynamics and Trajectory of a Parachute–Payload System Leaving the C-17 Aircraft

This article examines the flight dynamics and trajectory analysis of a parachute–payload system deployed from a C-17 aircraft. The aircraft is modeled with an open cargo door, extended flaps, and four turbo-fan engines operating at an altitude of 2000 feet Above Ground Level (AGL) and an airspeed of 150 knots. The payloads consist of simplified CONEX containers measuring either 192 inches or 240 inches in length, 9 feet in width, and 5.3 feet in height, with their mass and moments of inertia specified. At positive deck angles, gravitational forces cause these payloads to begin a gradual descent from the rear of the aircraft. For aircraft at zero deck angle, a ring-slot parachute with approximately 20% geometric porosity is utilized to extract the payload from the aircraft. This study specifically employs the CREATE-AV Kestrel simulation software to model the chute-payload system. The extraction and suspension lines are represented using Kestrel’s Catenary capability, with the extraction line connected to the floating confluence points of the CONEX container and the chute. The chute and payload will experience coupled motion, allowing for an in-depth analysis of the flight dynamics and trajectory of both elements. The trajectory data obtained will be compared to that of a payload (without chute and cables) exiting the aircraft at positive deck angles. An adaptive mesh refinement technique is applied to accurately capture the engine exhaust flow and the wake generated by the C-17, chute, and payloads. Friction and ejector forces are estimated to align the exit velocity and timing with those recorded during flight testing. The results indicate that the simulation of extracted payloads aligns with expected trends observed in flight tests. Notably, higher deck angles result in longer distances from the ramp, leading to increased exit velocities and reduced payload rotation rates. All payloads exhibit clockwise rotation upon leaving the ramp. The parachute extraction method yields significantly higher exit velocities and shorter exit times, while the payload-chute acceleration correlates with the predicted drag of the chute as demonstrated in prior studies.

Energy optimal path planning for wheeled mobile robots with circular obstacle

AbstractThe energy optimal motion planning algorithm for a differential drive robot with a circular obstacle in the maneuver space is introduced in this article. Rather than the traditional unicycle model, a non‐canonical state space model of the kinematics of a wheeled mobile robot is used to formulate the optimal control problem. The necessary conditions for optimality are formally derived using calculus of variations, resulting in constraints for the costates when the inequality constraint become active, revealing that the controls are required to be continuous. The optimality conditions permit decomposing the motion planning problem in two independent segments: prior to and after activation of the inequality constraints. Analytical expressions for the evolving states and control are found to be a function of Jacobi elliptic functions, permitting reducing the optimal control problem to a root‐finding problem. A comprehensive parametric study is included to demonstrate the impact on the optimal trajectories by varying the radius of the obstacle. The study shows that there are three distinct maneuver strategies with respect to the size of the obstacle. Furthermore, by including entering and exit time as optimization variables, a methodology for generalizing the development to any given motion scenario is developed and numerically illustrated.

Factors affecting the accuracy of prehospital triage application and prehospital scene time in simulated mass casualty incidents

BackgroundThe contemporary management of mass casualty incidents (MCIs) relies on the effective application of predetermined, dedicated response plans based on current best evidence. Currently, there is limited evidence regarding the factors influencing the accuracy of first responders (FRs) in applying the START protocol and the associated prehospital times during the response to MCIs. The objective of this study was to investigate factors affecting FRs’ accuracy in performing prehospital triage in a series of simulated mass casualty exercises. Secondly, we assessed factors affecting triage-to-scene exit time in the same series of exercises.MethodsThis retrospective study focused on simulated casualties in a series of simulated MCIs Full Scale Exercises. START triage was the triage method of choice. For each Full-Scale Exercise (FSEx), collected data included exercise and casualty-related information, simulated casualty vital parameters, simulated casualty anatomic lesions, scenario management times, and responder experience.ResultsAmong the 1090 casualties included in the primary analysis, 912 (83.6%) were correctly triaged, 137 (12.6%) were overtriaged, and 41 (3.7%) were undertriaged. The multinomial regression model indicated that increasing heart rate (RRR = 1.012, p = 0.008), H-AIS (RRR = 1.532, p < 0.001), and thorax AIS (T-AIS) (RRR = 1.344, p = 0.007), and lower ISS (RRR = 0.957, p = 0.042) were independently associated with overtriage. Undertriage was significantly associated with increasing systolic blood pressure (RRR = 1.013, p = 0.005), AVPU class (RRR = 3.104 per class increase), and A-AIS (RRR = 1.290, p = 0.035). The model investigating the factors associated with triage-to-scene departure time showed that the assigned prehospital triage code red (TR = 0.841, p = 0.002), expert providers (TR = 0.909, p = 0.015), and higher peripheral oxygen saturation (TR = 0.998, p < 0.001) were associated with a reduction in triage-to-scene departure time. Conversely, increasing ISS was associated with a longer triage-to-scene departure time (TR = 1.004, 0.017).ConclusionsUnderstanding the predictors influencing triage and scene management decision-making by healthcare professionals responding to a mass casualty may facilitate the development of tailored training pathways regarding mass casualty triage and scene management.

Optimizing energy consumption in smart buildings: A model for efficient energy management and renewable integration

In the current landscape of sustainable energy, integrating photovoltaic (PV) generation and electric vehicles (EVs) into household energy management systems (EMSs) has become a pivotal strategy to enhance grid sustainability in residential areas and provide economic benefits to homeowners. This article introduces an innovative approach to an energy administration framework designed for intelligent households, to seamlessly integrate EVs, both with and without PV generation. The proposed plan meticulously optimizes residential electricity expenses. It standardizes the load gradient using Time-of-Use (TOU) cost, residential electricity use fluctuations, PV generation patterns, and specific variables of EVs, including entry and exit times and charging statuses. The management method is divided into two distinct phases based on charging constraints and initial charge status. Stage A comprises three operational states contingent upon the availability of PV generation, while Stage B involves five operational states predicted based on anticipated PV generation. Through this research, the advanced control strategy facilitates precise adjustment of energy absorption by EVs from the grid and/or PV generation, along with injected energy derived from EVs to the grid. It ensures minimal residential electricity expenses and synchronizes the electrical load profiles. The findings indicate a significant reduction in residential electricity expenses and a substantial normalization of power load characteristics. Furthermore, simulation results emphasize the superior performance of the proposed plan for intelligent households fitted with both EVs and PV generation, compared to households with EVs alone, in terms of lowering expenses and normalizing load scenarios.

Exit Time and Principal Eigenvalue of Non-reversible Elliptic Diffusions

Exit Time and Principal Eigenvalue of Non-reversible Elliptic Diffusions

Growth, poverty trap and escape

The well-known Solow growth model is the workhorse model of the theory of economic growth, which studies capital accumulation in a model economy as a function of time with capital stock, labour and technology-based production as the basic ingredients. The capital is assumed to be in the form of manufacturing equipment and materials. Two important parameters of the model are: the saving fraction s of the output of a production function and the technology efficiency parameter A , appearing in the production function. The saved fraction of the output is fully invested in the generation of new capital and the rest is consumed. The capital stock also depreciates as a function of time due to the wearing out of old capital and the increase in the size of the labour population. We propose a stochastic Solow growth model assuming the saving fraction to be a sigmoidal function of the per capita capital kp . We derive analytically the steady state probability distribution P(kp) and demonstrate the existence of a poverty trap, of central concern in development economics. In a parameter regime, P(kp) is bimodal with the twin peaks corresponding to states of poverty and well-being, respectively. The associated potential landscape has two valleys with fluctuation-driven transitions between them. The mean exit times from the valleys are computed and one finds that the escape from a poverty trap is more favourable at higher values of A. We identify a critical value of Ac below (above) which the state of poverty (well-being) dominates and propose two early signatures of the regime shift occurring at Ac . The economic model, with conceptual foundations in nonlinear dynamics and statistical mechanics, shares universal features with dynamical models from diverse disciplines like ecology and cell biology.

Design and implementation of a mechatronic system for monitoring worker exposure in cold storage facilities

In response to the increasing need for enhanced occupational safety in cold storage facilities, this study presents the design and validation of a mechatronic time control device specifically developed for monitoring the exposure times of warehouse operators in a multinational company. Over the past two decades, Ecuador has significantly increased regulations to safeguard worker health and safety. In compliance with these regulations, this research addresses the challenges operators face when exposed to sub-zero temperatures during their work shifts. The proposed system integrates mechanical, electronic, and control components to systematically track and manage operators' time within cold rooms, ensuring compliance with predefined safety thresholds. A NodeMCU microcontroller, digital temperature sensors, and a robust communication interface form the device's core. This device records entry and exit times, monitors ambient conditions, and triggers alerts when exposure limits are approached. Extensive validation was conducted using a 3D-printed resin prototype, demonstrating the device's capability to function effectively in harsh environments. The system's efficacy was evaluated through real-world testing, where operators used the prototype during their shifts. Data collected confirmed the device's reliability in tracking exposure times and enhancing worker safety.

Mean Exit Times from Submanifolds with Bounded Mean Curvature

Mean Exit Times from Submanifolds with Bounded Mean Curvature

A novel equipment remaining useful life prediction approach considering dynamic maintenance threshold

AbstractIn conventional remaining useful life (RUL) prediction approaches grounded on maintenance, the maintenance threshold is typically established as a stationary value. However, the actual maintenance threshold may exceed its preset value due to the uncertainty of degradation and other factors. Therefore, it is necessary to consider the dynamic maintenance threshold to improve the precision of remaining useful life prediction. By considering the Wiener process, the maintenance threshold error is introduced to reflect the dynamic nature of the maintenance threshold. The influence of maintenance on degradation amount, degradation rate, and degradation path are comprehensively considered to establish a multi‐stage maintenance‐affected degradation process model. The RUL formula of the equipment is derived using the first hitting time (FHT). The maximum likelihood estimation (MLE) approach and Bayesian theory are employed to estimate the model's parameters. The proposed approach is validated using simulation data and gyroscope degradation data. The outcomes reveal that the proposed approach can significantly enhance the precision of life prediction for the equipment.

Efficiency of Foot and Ankle Surgeries Completed on the Preoperative Stretcher vs Operating Room Table: A Randomized Controlled Trial.

Extremity surgeons frequently operate on the preoperative stretcher rather than the operating room (OR) table. This study sought to identify differences between stretcher-based (SB) and OR table-based (TB) procedures with regard to time efficiency and OR team member preferences. We conducted a prospective randomized controlled trial comparing the efficiency of SB vs OR TB foot and ankle procedures. Fifty-two patients undergoing a hardware removal, isolated gastrocnemius recession, soft tissue procedure, or foreign body removal at our day surgery unit were included. Start time and exit time were recorded. "Start time" was the number of minutes between the patient entering the OR and first incision. "Exit time" was the number of minutes between the procedure ending and the patient exiting the OR. Surveys were disseminated to OR staff who participated in the included cases. The total measured time in the OR was an average 6 minutes shorter in the Stretcher group compared to the OR Table group (10 minutes vs 16 minutes, P < .001). SB procedures were associated with a significantly shorter start time (median difference = 4 minutes, P = .001), but not exit time (median difference = 1 minute, P = .058). No difference was found in actual surgical time. Thirty (96.8%) OR team members perceived SB procedures as enhancing OR efficiency, and 30 (96.8%) respondents considered SB procedures to be equal or superior to OR TB procedures in terms of patient safety. All would recommend or strongly recommend SB procedures. We found SB foot and ankle procedures to require less room time than OR TB procedures. Particularly for high-volume specialties, an average 6 minutes saved per case may meaningfully improve overall OR efficiency. Most OR team members believed that SB surgery improves OR efficiency and is the safer option for OR team members. Level II, randomized controlled trial, survey.

Instability in the quantum restart problem.

Repeatedly monitored quantum walks with a rate 1/τ yield discrete-time trajectories which are inherently random. With these paths the first-hitting time with sharp restart is studied. We find an instability in the optimal mean hitting time, which is not found in the corresponding classical random-walk process. This instability implies that a small change in parameters can lead to a rather large change of the optimal restart time. We show that the optimal restart time versus τ, as a control parameter, exhibits sets of staircases and plunges. The plunges, are due to the mentioned instability, which in turn is related to the quantum oscillations of the first-hitting time probability, in the absence of restarts. Furthermore, we prove that there are only two patterns of staircase structures, dependent on the parity of the distance between the target and the source in units of lattice constant. The global minimum of the hitting time is controlled not only by the restart time, as in classical problems, but also by the sampling time τ. We provide numerical evidence that this global minimum occurs for the τ minimizing the mean hitting time, given restarts taking place after each measurement. Last, we numerically show that the instability found in this work is relatively robust against stochastic perturbations in the sampling time τ.

Kinetic Network in Milestoning: Clustering, Reduction, and Transition Path Analysis.

We present a reduction of the Milestoning (ReM) algorithm to analyze the high-dimensional Milestoning kinetic network. The algorithm reduces the Milestoning network to low dimensions but preserves essential kinetic information, such as local residence time, exit time, and mean first passage time between any two states. This is achieved in three steps. First, nodes (milestones) in the high-dimensional Milestoning network are grouped into clusters based on the metastability identified by an auxiliary continuous-time Markov chain. Our clustering method is applicable not only to time-reversible networks but also to nonreversible networks generated from practical simulations with statistical fluctuations. Second, a reduced network is established via network transformation, containing only the core sets of clusters as nodes. Finally, transition pathways are analyzed in the reduced network based on the transition path theory. The algorithm is illustrated using a toy model and a solvated alanine dipeptide in two and four dihedral angles.

Dimensional Dependence of Binding Kinetics.

In the context of protein-protein binding, the dissociation constant is used to describe the affinity between two proteins. For protein-protein interactions, most experimentally-measured dissociation constants are measured in solution and reported in units of volume concentration. However, many protein interactions take place on membranes. These interactions have dissociation constants with units of areal concentration, rather than volume concentration. Here, we present a novel, stochastic approach to understanding the dimensional dependence of binding kinetics. Using stochastic exit time calculations, in discrete and continuous space, we derive general reaction rates for protein-protein binding in one, two, and three dimensions and demonstrate that dimensionality greatly affects binding kinetics. Further, we present a formula to transform three-dimensional experimentally-measured dissociation constants to two-dimensional dissociation constants. This conversion can be used to mathematically model binding events that occur on membranes.

A remaining useful life prediction framework with adaptive dynamic feedback

Remaining useful life (RUL) prediction of components is a crucial aspect of mechanical systems prognostic and health management. However, during the online RUL prediction of components, the existing method cannot use the prediction results for feedback and optimize the prediction model. To address this issue, this paper proposes a framework for RUL prediction with adaptive dynamic feedback. First, a feedback multi-feature fusion (FMFF) method is designed. It introduces a series of non-exceeding threshold positive constants, that is fraction thresholds (FT), to perform division of the degradation state dimension. Besides, the first hitting time (FHT) from the current moment to FT is the fraction remaining useful life (FRUL). It is used to construct and update the fusion factors. Then, the feedback multi-model selection (FMMS) method is proposed for adaptive feedback and to select the degradation model based on the FRUL prediction results in different stages. The probability density function of RUL based on the FHT is calculated based on the FMMS method to realize the RUL prediction of the component. Finally, the effectiveness and superiority of the proposed framework are validated based on XJTU-SY dataset and run-to-failure test.

Loop corrections in the separate universe picture

In inflationary models that produce a spike of power on short scales, back-reaction of small-scale substructure onto large-scale modes is enhanced. Loop corrections that quantify this back-reaction have been evaluated by a number of authors. We argue that the separate universe framework provides a highly convenient tool for such computations. Each loop of interest is characterized by large hierarchies in wavenumber and horizon exit time. The separate universe framework highlights important factorizations involving these hierarchies. We interpret each loop correction in terms of a simple, classical, back-reaction model, and clarify the meaning of the different volume scalings that have been reported in the literature. We argue that significant back-reaction requires both short-scale nonlinearities and long-short couplings that modulate the short-scale power spectrum. In the absence of long-short couplings, only incoherent “shot noise”-like effects are present, which are volume-suppressed. Dropping the shot noise, back-reaction from a particular scale is controlled by a product of f NL-like parameters: an equilateral configuration measuring the nonlinearity of the short-scale modes, and a squeezed configuration measuring the long-short coupling. These may carry important scale dependence controlling the behaviour of the loop in the decoupling limit where the hierarchy of scales becomes large. In single-field models the long-short coupling may be controlled by this hierarchy, in which case the net back-reaction would be safely suppressed. We illustrate our framework using explicit computations in a 3-phase ultra-slow-roll scenario. Our analysis differs from earlier treatments of this model, which did not consistently include the effect of small-scale modes. Finally, we discuss different choices for the smoothing scale used in the separate universe framework and argue the effect can be absorbed into a renormalization of local operators. This complicates interpretation of the loop, because the analytic part of each loop integral is degenerate with unknown, ultraviolet-sensitive contributions.

Uncovering the multifractality of Lagrangian pair dispersion in shock-dominated turbulence

Lagrangian pair dispersion provides insights into mixing in turbulent flows. By direct numerical simulations (DNSs) we show that the statistics of pair dispersion in the randomly forced two-dimensional Burgers equation, which is a typical model of shock-dominated turbulence, is very different from its incompressible counterpart because Lagrangian particles get trapped in shocks. We develop a heuristic theoretical framework that accounts for this—a generalization of the multifractal model—whose prediction of the scaling of Lagrangian exit times agrees well with our DNS. Published by the American Physical Society 2024