Exit Time Research Articles

Maximum Likelihood Estimation for an Ornstein–Uhlenbeck Model for Neural Activity

The Ornstein–Uhlenbeck process arises from a leaky stochastic integrate-and-fire model of the membrane potential of a neuron, in which its firing corresponds to the first time the process hits a barrier. We address the problem of estimating the parameters of the underlying process when the available data are the neuron’s successive spikes, or spike train. The first-hitting time density is not tractable, so we use its Laplace transform to determine the identifiable parameters of the model, show that their maximum likelihood estimates are consistent and asymptotically normal, and describe computational methods to obtain the estimates and their standard errors.

Exact solutions of the two-side exit time problems for the Vasicek model

Exit times of diffusion processes play an important role in the application of finance, insurance, biology, engineering, and so on. This article investigates the two-side exit time problems for the Vasicek model. By using Strong Markov property, the Laplace–Stieltjes transform (LST) of some exit times are obtained. And then the results are used to figure out the probability and mathematical expectation of the exit times. Finally, numerical examples are given to illustrate the applications of the LST of some exit times.

A Correlated Binary Model for Ignorable Missing Data: Application to Rheumatoid Arthritis Clinical Data

Incomplete data are common phenomenon in research that adopts the longitudinal design approach. If incomplete observations are present in the longitudinal data structure, ignoring it could lead to bias in statistical inference and interpretation. We adopt the disposition model and extend it to the analysis of longitudinal binary outcomes in the presence of monotone incomplete data. The response variable is modeled using a conditional logistic regression model. The nonresponse mechanism is assumed ignorable and developed as a combination of Markov's transition and logistic regression model. MLE method is used for parameter estimation. Application of our approach to rheumatoid arthritis clinical trials is presented.

Influence of Wearing Ballistic Vests on Physical Performance of Danish Police Officers: A Cross-Over Study.

Purpose: We aimed to investigate the influence of wearing a ballistic vest on physical performance in police officers. Methods: We performed a cross-over study to investigate the influence of wearing a ballistic vest on reaction and response time, lumbar muscle endurance and police vehicle entry and exit times. Reaction and response time was based on a perturbation setup where the officers’ pelvises were fixed and EMG of lumbar and abdominal muscles was recorded. We used a modified Biering–Sørensen test to assess the lumbar muscle endurance and measured duration of entry and exit maneuvers in a variety of standard-issue police cars. Results: There was a significant difference of 24% in the lumbar muscle endurance test (no vest: 151 s vs. vest: 117 s), and the police officers experienced higher physical fatigue after the test when wearing a vest. Furthermore, officers took longer to both enter and exit police cars when wearing a vest (range: 0.24–0.56 s) depending on the model of the vehicle. There were no significant differences in reaction and response times between the test conditions (with/without vest). Discussion and Conclusion: Wearing of a ballistic vest significantly influenced the speed of movement in entry and exit of police cars and lumbar muscle endurance, although it does not seem to affect reaction or response times. The ballistic vest seems to impair performance of tasks that require maximal effort, which calls for better designs of such vests.

Aspirin Resistance as a Result of Impaired Interaction of Platelets and Neutrophils in Patients with Coronary Heart Disease

Aim. To study the relationship between the levels of synthesis of reactive oxygen species (ROS) by platelets and neutrophils in patients with coronary heart disease (CHD) before and after coronary artery bypass grafting (CABG), depending on sensitivity to acetylsalicylic acid (ASA).Material and methods. The study included 95 patients with coronary artery disease who are indicated for CABG surgery. The control group consisted of 30 healthy donors. The antiplatelet therapy was stopped for at least 5 days before CABG. In the postoperative period, from the first day, all patients were received 100 mg of an enteric form of acetylsalicylic acid (ASA). Resistance to ASA was determined at the level of platelet aggregation with arachidonic acid ≥20% by optical agregometry at least at one observation point: before CABG, on 1-3 day and on 8-10 day after surgery. We evaluated the spontaneous and induced lucigenin-dependent chemiluminescence (CL) of platelets (ADP induction) and neutrophils (zymosan induction) by the exit time to maximum intensity (Tmax), maximum intensity (Imax) and area (S) under the CL curve.Results. 70.5% sensitive (sASA) and 29.5% resistant (rASA) to ASA patients were revealed. Prior to CABG, in sASA patients, the Imax of spontaneous and zymosan-induced neutrophil CL and CL platelet activity was increased relative to control values. Tmax of spontaneous platelet CL, Imax and S under the ADP-induced platelet CL curve were lower in sASA patients, if to compare with rASA patients. On the 1st and 8-10th day after CABG in sASA patients, the CL indicators of neutrophil and platelet activity also remained elevated compared to control values. On the 1st day after CABG decreased levels of S under the spontaneous CL curve of neutrophils in rASA patients was established compared with sASA patients, and increased levels of Imax and S under the curve of induced neutrophil CL were detected in comparison with the control range. In rASA patients, the values of Tmax of spontaneous platelet CL decreased in relation to the values detected in the control group and sASA patients. On the 8–10th day after CABG, most indicators of spontaneous and zymosan-induced CL neutrophils in rASA patients were also increased compared to control values. In rASA patients a positive correlation of Imax-induced CL was found (r=0.83) on the 1st day after CABG and negative correlations of Tmax of spontaneous CL (r=- 0.75) and S under the curve induced CL (r=-0.70) on the 8-10th day were detected between platelets and neutrophils.Conclusion. In sASA patients with coronary heart disease before and after CABG, a high level of synthesis of superoxide radical by neutrophils and platelets was detected. The relationship between the levels of the synthesis of superoxide radical by neutrophils and platelets was found only after CABG in rASA patients. Increased synthesis of superoxide radical due to metabolic and regulatory relationships in neutrophils and platelets stimulates pro-inflammatory processes in coronary artery disease and determines the sensitivity of platelets to ASA.

An Active Handoff Algorithm based on The Retention Time of Complementary Nodes

Due to the frequent joining and quitting of nodes in P2P network, it often leads to the failure of accessing nodes, and the decrease of system availability. Some of the existing methods are to switch a node’s service to its backup node after it is found to exit, and the backup node will continue to provide services. But the actual results are not ideal. The reason is that the service request of the node is always not responded from the time when the node exits the network to the time when the service switches to the backup node. This paper proposes an active handoff algorithm based on the retention time characteristics of complementary nodes. By predicting the exit time of the node, it finds the node complementary to the node in time as the backup node, and actively switches to the backup node before the node exits the network, so as to realize the service continuity. Experimental results show that the algorithm reduces the access failure and improves the system availability.

Robust scenario-based concept for stochastic energy management of an energy hub contains intelligent parking lot considering convexity principle of CHP nonlinear model with triple operational zones

In this paper, an energy management system is taken into account to control some distributed energy resources spread into an entity. The included facilities are aggregated by an energy hub (EH) and also equipped by some control and communication in a smart environment. Through this system, the stakeholder can prepare energy operational planning in the form of energy markets. In this paper, a novel convexity principle is presented to face the nonlinearity of combined heat and power (CHP) unit model considering triple operational zones. Here, the energy hub acts as a price taker in the energy markets. Here, some stochastic parameters such as day-ahead market price, wind power output, and plug-in hybrid electric vehicles (PHEVs) entry and exit time and their battery characteristics are considered; therefore a robust scenario-based optimization strategy is proposed to deal with them. The robust optimization is employed by upper and lower bounds for market price uncertain parameter by historical behaviors and also is presented through confidence bounds. Also, to deal with the wind power uncertainty, the scenario-based method is performed by scenario generation based on historical wind data. To demonstrate the effectiveness of the proposed strategy, a real case study is investigated and some prominent results are provided. As obtained, the CHP unit can work actively in the winter day so that the 3rd operational zone will be active and also with increasing the percentage of PHEV units to 100 % within the EH in the summer day, the percentage of power sold to the network will be increased to 68.1 % compared with no vehicle situation.

First Exit-Time Analysis for an Approximate Barndorff-Nielsen and Shephard Model with Stationary Self-Decomposable Variance Process

In this paper, an approximate version of the Barndorff-Nielsen and Shephard model, driven by a Brownian motion and a L\'evy subordinator, is formulated. The first-exit time of the log-return process for this model is analyzed. It is shown that with certain probability, the first-exit time process of the log-return is decomposable into the sum of the first exit time of the Brownian motion with drift, and the first exit time of a L\'evy subordinator with drift. Subsequently, the probability density functions of the first exit time of some specific L\'evy subordinators, connected to stationary, self-decomposable variance processes, are studied. Analytical expressions of the probability density function of the first-exit time of three such L\'evy subordinators are obtained in terms of various special functions. The results are implemented to empirical S&P 500 dataset.

Comparison of the Time to Extubation and Length of Stay in the PACU after Sugammadex and Neostigmine Use in Two Types of Surgery: A Monocentric Retrospective Analysis.

Sugammadex provides a rapid pharmacological reversal of aminosteroid, as well as fewer pulmonary complications, a better physiological recovery, and shorter stays in the postanesthetic recovery unit (PACU). This retrospective analysis of our Centricity anesthesia database in 2017–2019 assessed the efficiency of sugammadex in real-life situations in two groups of surgical cancer patients (breast and abdominal surgery) based on the extubation time, operating room exit time, and length of PACU stay. Overall, 382 anesthesia records (131 breast and 251 abdominal surgeries) were extracted for the pharmacological reversal of neuromuscular blockades by neostigmine or sugammadex. Sugammadex was used for reversal in 91 breast and 204 abdominal surgeries. Sugammadex use did not affect the extubation time, operating room exit time, or length of PACU stay. However, the time to reach a 90% train of four (TOF) recovery was significantly faster in sugammadex patients: 2 min (1.5–8) in breast surgery and 2 min (1.5–7) in abdominal surgery versus 10 (6–20) and 9 min (5–20), respectively, for neostigmine (p < 0.05). Most patients who were reversed with sugammadex (91%) reached a TOF ratio of at least 90%, while 54% of neostigmine patients had a 90% TOF ratio recorded (p < 0.05). Factors other than pharmacological reversal probably influence the extubation time, operating room exit time, or PACU stay; however, sugammadex reliably shortened the time so as to reach a 90% TOF ratio with a better level of reversal.

Deep reinforcement learning with a particle dynamics environment applied to emergency evacuation of a room with obstacles

Efficient emergency evacuation is crucial for survival. A very successful model for simulating emergency evacuation is the social-force model. At the heart of the model is the self-driven force that is applied to an agent and is directed towards the exit. However, it is not clear if the application of this force results in optimal evacuation, especially in complex environments with obstacles. In this paper, we develop a deep reinforcement learning algorithm in association with the social force model to train agents to find the fastest evacuation path. During training, we penalize every step of an agent in the room and give zero reward at the exit. We adopt the Dyna-Q learning approach, which incorporates both the model-free Q-learning algorithm and the model-based reinforcement learning method, to update a deep neural network used to approximate the action value functions. We first show that in the case of a room without obstacles the resulting self-driven force points directly towards the exit as in the social force model. To quantitatively validate our method, we compare the total time elapsed when agents escape a room with one door and without obstacles employing the Dyna-Q model with the result obtained using the social-force model. We find that the median exit time intervals calculated using the two methods are not significantly different. We confirm that the proposed method obtains trajectories that minimize the travel time by comparing our results to results generated by geodesics-based adaptive pedestrian dynamics. Then, we investigate evacuation of a room with one obstacle and one exit. We show that our method produces similar results with the social force model when the obstacle is convex. However, in the case of concave obstacles, which sometimes can act as traps for agents governed purely by the social force model and prohibit complete room evacuation, our approach is clearly advantageous since it derives a policy that results in object avoidance and complete room evacuation without additional assumptions. We also study evacuation of a room with multiple exits. We show that agents are able to evacuate efficiently from the nearest exit through a shared network trained for a single agent. Finally, we test the robustness of the Dyna-Q learning approach in a complex environment with multiple exits and obstacles. Overall, we show that our model, based on the Dyna-Q reinforcement learning approach, can efficiently handle modeling of emergency evacuation in complex environments with multiple room exits and obstacles where it is difficult to obtain an intuitive rule for fast evacuation.

Diffusion transients in convection rolls

Abstract

RELIABILITY INDEX AND OPTION PRICING FORMULAS OF THE FIRST-HITTING TIME MODEL BASED ON THE UNCERTAIN FRACTIONAL-ORDER DIFFERENTIAL EQUATION WITH CAPUTO TYPE

Since the ability to control the investor’s income or loss within a certain range, barrier option has been among the most popular path-dependent options where its payoff depends on whether or not the underlying asset’s price reaches a given “barrier”. First, assuming the underlying asset as an uncertain variable for the case that the Caputo fractional-order derivative is adopted instead of the ordinary derivative, the real financial market is better modeled by the uncertain fractional-order differential equation with Caputo type. Then, a first-hitting time model which can measure the exercise ability is innovatively presented. Second, based on the first-hitting time theorem of the uncertain fractional-order differential equation, the reliability index (including validity and survival index) for the proposed model is obtained, and four types of European barrier option (including up-and-in call, down-and-in put, up-and-out put, and down-and-out call options) pricing formulas are obtained accordingly. Lastly, applying the predictor–corrector method, numerical algorithms are provided for calculating European barrier and the reliability index, numerical experiments and corresponding sensitivity analysis are also illustrated concerning various conditions.

On the asymptotics of the distribution of the exit time beyond a non-increasing boundary for a compound renewal process

On the asymptotics of the distribution of the exit time beyond a non-increasing boundary for a compound renewal process

On the Distribution of the Last Exit Time over a Slowly Growing Linear Boundary for a Gaussian Process

For a class of Gaussian stationary processes, we prove a limit theorem on the convergence of the distributions of the scaled last exit time over a slowly growing linear boundary. The limit is a dou...

Backward stochastic differential equations with non-Markovian singular terminal conditions for general driver and filtration

We consider a class of Backward Stochastic Differential Equations with superlinear driver process f adapted to a filtration supporting at least a d dimensional Brownian motion and a Poisson random measure on Rm∖{0}. We consider the following class of terminal conditions: ξ1=∞⋅1{τ1≤T} where τ1 is any stopping time with a bounded density in a neighborhood of T and ξ2=∞⋅1AT where At, t∈[0,T] is a decreasing sequence of events adapted to the filtration Ft that is continuous in probability at T (equivalently, AT={τ2>T} where τ2 is any stopping time such that P(τ2=T)=0). In this setting we prove that the minimal supersolutions of the BSDE are in fact solutions, i.e., they attain almost surely their terminal values. We note that the first exit time from a time varying domain of a d-dimensional diffusion process driven by the Brownian motion with strongly elliptic covariance matrix does have a continuous density. Therefore such exit times can be used as τ1 and τ2 to define the terminal conditions ξ1 and ξ2. The proof of existence of the density is based on the classical Green’s functions for the associated PDE.

Semi-parametric survival analysis via Dirichlet process mixtures of the First Hitting Time model.

Time-to-event data often violate the proportional hazards assumption inherent in the popular Cox regression model. Such violations are especially common in the sphere of biological and medical data where latent heterogeneity due to unmeasured covariates or time varying effects are common. A variety of parametric survival models have been proposed in the literature which make more appropriate assumptions on the hazard function, at least for certain applications. One such model is derived from the First Hitting Time (FHT) paradigm which assumes that a subject's event time is determined by a latent stochastic process reaching a threshold value. Several random effects specifications of the FHT model have also been proposed which allow for better modeling of data with unmeasured covariates. While often appropriate, these methods often display limited flexibility due to their inability to model a wide range of heterogeneities. To address this issue, we propose a Bayesian model which loosens assumptions on the mixing distribution inherent in the random effects FHT models currently in use. We demonstrate via simulation study that the proposed model greatly improves both survival and parameter estimation in the presence of latent heterogeneity. We also apply the proposed methodology to data from a toxicology/carcinogenicity study which exhibits nonproportional hazards and contrast the results with both the Cox model and two popular FHT models.

Regularity and Stability of Feedback Relaxed Controls

This paper proposes a relaxed control regularization with general exploration rewards to design robust feedback controls for multidimensional continuous-time stochastic exit time problems. We estab...

Bounds on set exit times of affine systems, using Linear Matrix Inequalities

Abstract Efficient computation of trajectories of switched affine systems becomes possible, if for any such hybrid system, we can manage to efficiently compute the sequence of switching times. Once the switching times have been computed, we can easily compute the trajectories between two successive switches as the solution of an affine ODE. Each switching time can be seen as a positive real root of an analytic function, thereby allowing for efficient computation by using root finding algorithms. These algorithms require a finite interval, within which to search for the switching time. In this paper, we study the problem of computing upper bounds on such switching times, and we restrict our attention to stable time-invariant affine systems. We provide semi-definite programming models to compute upper bounds on the time taken by the trajectories of an affine ODE to exit a set described as the intersection of a few generalized ellipsoids. Through numerical experiments, we show that the resulting bounds are tighter than bounds reported before, while requiring only a modest increase in computation time.

Inequalities for the average exit time of a random walk from an interval

Получены двусторонние неравенства для среднего времени выхода из интервала для случайного блуждания с нулевым и отрицательным сносом. Библиография: 13 наименований.

Multiple Relay Nodes Selection Scheme using Exit Time Variation for Efficient Data Dissemination in VANET

Efficient Data dissemination in VANET is still the challenge because of variable speed of vehicles, road conditions, frequent fragmentation etc. In this article a selective forwarding data dissemination scheme using exit time differences in vehicles for highway lanes scenario is proposed that focuses on the solution of broadcast storm, less coverage, transmission delay and reliable data delivery. Our approach is selecting multiple forwarding nodes to increase coverage in less delay. In this article road lanes concept is used to identify the moving node direction. Redundant regions and zones technique in proposed approach is reducing the processing of parameters at significant extents. Simulation of proposed approach is done using NS2 and SUMO. Output of implementation is compared with unidirectional flooding, KB_Selective, and LT_Selective techniques. Result analysis shown that the proposed technique is much efficient and it increases the rate of coverage up to 23%. Also it reduces the delay up to 18% in data delivery ratio. This methodology also improves the performance of system by increasing the throughput and reducing the collision rate in comparison with other methods.