Exit Time Research Articles

CSR Program Social Return on Investment Analysis Case Study: PT PLN Indonesia Power PLTGU Cilegon OMU

Responsibility and sustainability play a larger role in the activities of global businesses. The practice of Corporate Social Responsibility (CSR) can be used to promote more responsible and sustainable behavior. PT PLN Indonesia Power PLTGU Cilegon OMU is a sub holding of an Indonesian state-owned corporation committed to fostering a responsible and sustainable culture through CSR. The old CSR program in Margasari village, the company’s first ring area, must be replaced because it has come to its exit time. Based on the Social Mapping Document 2022 and interviews, a SWOT analysis is conducted taking into account the current situation of the community. The analysis indicates that a new sewing group named Pujasari could be implemented as the new CSR program in the village of Margasari. Nevertheless, since a CSR program is a social investment, the company must be confident in the program’s future return for the community. This study aims to determine the program’s economic feasibility, Social Return on Investment (SROI) value, variables that may influence SROI achievement, and contribution to the Sustainable Development Goals (SDGs). In calculating SROI, the triple bottom line concept will be used, while the economic feasibility will use capital budgeting method. A sensitivity analysis will be conducted to determine the critical variable for achieving SROI. The study demonstrates that the calculation utilizing the triple bottom line concept (considering economic, social, and environmental benefit) over a 5-year project period yields an NPV of IDR 1,988 mio, an IRR of 109%, with a WACC of 13.349%. The program’s SROI is 20.39, indicating that for every IDR 1 invested by the company in this program, IDR 20.39 in social benefit will be generated. Analysis of sensitivity reveals that WACC, the selling price of rags, working productivity, and price of rag primary materials are, in order, the most sensitive variables affecting the project’s SROI value. In addition, the program demonstrates contribution to SDGs 1, 5, 8, 12, and 13.

Controlling mean exit time of stochastic dynamical systems based on quasipotential and machine learning

The mean exit time escaping basin of attraction in the presence of white noise is of practical importance in various scientific fields. In this work, we propose a strategy to control mean exit time of general stochastic dynamical systems to achieve a desired value based on the quasipotential concept and machine learning. Specifically, we develop a neural network architecture to compute the global quasipotential function. Then we design a systematic iterated numerical algorithm to calculate the controller for a given mean exit time. Moreover, we identify the most probable path between metastable attractors with the help of the effective Hamilton–Jacobi scheme and the trained neural network. Numerical experiments with various dimensions and structures demonstrate that our control strategy is effective and sufficiently accurate.

Escrutinio para el cáncer de colon: ¿cuál fue el impacto en los primeros 2 años de la pandemia de COVID-19? Experiencia en una clínica privada ambulatoria.

COVID-19 pandemic had a negative impact on colorectal cancer (CRC) screening programs. The care strategy was modified throughout the pandemic, this paper evaluates its impact and short-term consequences. A retrospective, descriptive and cross-sectional study was carried out in a private ambulatory endoscopic center, in average risk subjects. The study compared two periods: pre-pandemic and pandemic (subdivided into pre-vaccination and vaccination). During this period, 54.4% of scheduled colonoscopies were due to the screening program. The average age was 60.4 ± 7 years. Women were 52.0%. The overall cancellation rate was 41.1%, higher during pre-vaccination period. There were no differences in the degree of colonic cleansing, colonoscope exit time, and patient satisfaction. The adenoma detection rate (38.4% vs. 42.8% vs. 36.4%; p = 0.8) and the total number of adenomas (p = 0.02) was statistically significant during the pre-vaccination period. The rate of adenoma/patient showed a higher trend during this period (p = 0.06). The number of colorectal cancers was 10, without differences between periods. In conclusion, the impact of the decrease in screening colonoscopy procedures for CRC detection was similar to what was seen worldwide. In this period no increase in cancer cases, although this effect may be observed in the long term.

Joint occupation times in an infinite interval for spectrally negative Lévy processes on the last exit time

Joint occupation times in an infinite interval for spectrally negative Lévy processes on the last exit time

Optimal integration of CCHP with electric Vehicle parking lots in energy hub

Nowadays, due to environmental problems and the lack of fossil fuels, the use of Electric Vehicles (EVs) is extended. These systems need optimal planning and management, like all energy tools. With another look at electrical generation systems, the combined energy production units have also increased dramatically, with only one kind of fuel, it is possible to produce any kind of energy such as electrical, thermal, and cooling energies at the same time. This production type is called the energy hub. The main goal of creating an energy hub is to meet several types of demand at the same time and to increase the flexibility of the system. The Combined Cooling, Heat, and Power (CCHP) unit, which has a higher efficiency ratio to traditional systems, could be referred to as the main component of the energy hub. To reduce the losses of these systems, their planning could be implemented in coordination with the EV parking lot. The energy hub system could provide the mentioned conditions in the presence of renewable energy sources and energy storage units in a coordinated and optimal way. In this paper, the presence of an EV parking lot in an energy hub is investigated that includes a CCHP, a photovoltaic unit in the presence of demand response programs, and its effects on optimizing power consumption to reduce cost. The demand response programs are used to reduce the operating costs of the energy hub. Moreover, the uncertainties of EV consist of entry and exit times and charge level, solar irradiation, and loads value are applied in the model. Finally, the cost of risk by the conditional value–at–risk method is investigated. The simulations are done by determining 3 various case studies for better investigation of the proposed model. The results show that the proposed solution method of the demand response program could decrease the total cost of the energy hub by about 1.90 % in both summer and winter, under risk-averse conditions.

Climate change for global warming 1.5∘C under the influence of multiplicative Gaussian noise

We propose a stochastic energy balance differential equation with multiplicative Gaussian noise, which better captures the influence of the atmosphere as external noise on climate change. Meanwhile, we apply the Milstein method with stronger convergence to approximate the stochastic climate change trajectory. Further, the numerical approach can efficiently calculate two exit concepts: the mean first exit time and the first escape probability. These two quantities are used to examine the transition of the climate from one state to another. For global warming of [Formula: see text]C and [Formula: see text]C, we find that the enhanced noise intensity is more likely to induce a shorter mean first exit time or a higher first escape probability. These results provide important insights into the underlying mechanisms of climate change for global warming.

Homogenization of non-symmetric jump processes

AbstractWe study homogenization for a class of non-symmetric pure jump Feller processes. The jump intensity involves periodic and aperiodic constituents, as well as oscillating and non-oscillating constituents. This means that the noise can come both from the underlying periodic medium and from external environments, and is allowed to have different scales. It turns out that the Feller process converges in distribution, as the scaling parameter goes to zero, to a Lévy process. As special cases of our result, some homogenization problems studied in previous works can be recovered. We also generalize the approach to the homogenization of symmetric stable-like processes with variable order. Moreover, we present some numerical experiments to demonstrate the usage of our homogenization results in the numerical approximation of first exit times.

Physical mechanisms of exit dynamics in microchannels of nonequilibrium transport systems

In the field of molecular nonequilibrium transports, physical mechanisms of multiple reaction dynamics of these systems are the core of deep understanding complex reactions and transport mechanisms. In order to explore related mechanisms, establishing multiple systems coupled with tremendous exit dynamics and studying their exit dynamics properties are quite vital. Beyond previous researches, new stochastic transport processes are emphasized here. Multiple new exit dynamic systems are established, which are motivated by the multiplicity of paths and products of real biochemical processes in organisms. In order to ensure research universality, core system modeling factors are fully considered. Countable parallel orbits, uniform connection with external sources, countable parallel orbits as subsystems in middle lattices and influences of all lattices on transport trajectories on dynamic properties are analyzed. Dynamic properties of different particles located in orbits are explored by deeply studying average exit time and time scale. Quantitative spatiotemporal impacts are extensively studied. The rationality of average exit time as a time scale in the universal exit dynamic system is proved. Main findings and fruitful results can not only serve as theoretical bases for broadening reaction path modeling, but also be helpful to support understanding nonequilibrium transport mechanisms, especially stochastic biochemical processes.

Improving the Feasibility of Moment-Based Safety Analysis for Stochastic Dynamics

Given a dynamical system modelled via stochastic differential equations (SDEs), we evaluate the safety of the system through its exit time moments. Using appropriate semidefinite positive matrix constraints, an SDP moment-based approach can be used to compute moments of the exit time. However, the approach is impeded when analyzing higher dimensional physical systems as the dynamics are limited to polynomials. Computational scalability is also poor as the dimensionality of the state grows, largely due to the combinatorial growth of the optimization program. We propose methods to make feasible the safety analysis of higher dimensional physical systems. The restriction to polynomial dynamics is lifted by using state augmentation which allows one to generate the optimization for a broader class of nonlinear stochastic systems. We then reformulate the constraints to mitigate the computational limitations associated with an increase in state dimensionality. We employ our methods on two example processes to characterize their safety via exit times and show the ability to handle multi-dimensional systems that were previously unsupported by the existing SDP method of moments.

Raspberry Pi-based wireless automatic assistance control system used by health center staff

The ongoing COVID-19 pandemic has severely strained healthcare systems worldwide, necessitating the implementation of various biosecurity measures by governments to mitigate further virus transmission. Consequently, researchers have increasingly focused on developing automation technologies to minimize direct human contact. However, within healthcare centers, some work assistance processes still rely on inefficient methods wherein each worker fills out an assistance form in the presence of a supervisor. This outdated approach not only leads to time wastage but also introduces errors in the records. To address this issue, we propose the development of a wireless automatic attendance control system utilizing a Raspberry Pi device. This system will be implemented for the staff of healthcare centers, enabling them to record their entry and exit times using either a mobile device or a fingerprint reader. The recorded data will be accessible through a user interface and securely stored in the cloud. By adopting this system, it will be possible to monitor and enforce labor discipline among workers automatically. Through the implementation of the attendance control system, we have observed its optimal functionality, achieving an efficiency rate of 97.16% in registering and storing the entry and exit times of all workers in the database. This level of efficiency is deemed acceptable, given the swift and secure nature of the process.

Can one hear the shape of a target zone?

We develop an exchange rate target zone model with finite exit time and non-Gaussian tails. We show how the tails are a consequence of time-varying investor risk aversion, which generates mean-preserving spreads in the fundamental distribution. We solve explicitly for stationary and non-stationary exchange rate paths, and show how both depend continuously on the distance to the exit time and the target zone bands. This enables us to show how central bank intervention is endogenous to both the distance of the fundamental to the band and the underlying risk. We discuss how the feasibility of the target zone is shaped by the set horizon and the degree of underlying risk, and we determine a minimum time at which the required parity can be reached. We prove that increases in risk beyond a certain threshold can yield endogenous regime shifts where the “honeymoon effects” vanish and the target zone cannot be feasibly maintained. None of these results can be obtained by means of the standard Gaussian or affine models. Numerical simulations allow us to recover all the exchange rate densities established in the target zone literature. The generality of our framework has important policy implications for modern target zone arrangements.

Mean first exit times of Ornstein–Uhlenbeck processes in high-dimensional spaces

The d-dimensional Ornstein–Uhlenbeck process (OUP) describes the trajectory of a particle in a d-dimensional, spherically symmetric, quadratic potential. The OUP is composed of a drift term weighted by a constant and a diffusion coefficient weighted by σ > 0. In the absence of drift (i.e. θ = 0), the OUP simply becomes a standard Brownian motion (BM). This paper is concerned with estimating the mean first-exit time (MFET) of the OUP from a ball of finite radius L for large . We prove that, asymptotically for , the OUP takes (on average) no longer to exit than BM. In other words, the mean-reverting drift of the OUP (scaled by ) has asymptotically no effect on its MFET. This finding might be surprising because, for small , the OUP exit time is significantly larger than BM by a margin that depends on θ. As it allows for the drift to be ignored, it might simplify the analysis of high-dimensional exit-time problems in numerous areas.Finally, our short proof for the non-asymptotic MFET of OUP, using the Andronov–Vitt–Pontryagin formula, might be of independent interest.

An Age-Dependent Prognostic Model for Nonlinear Degrading Devices Based on Diffusion Process

Degradation modeling based remaining useful life (RUL) predicting has become a significant basis of prognotics and system health management (PHM), and has drawn much favor of both scholars and engineers in the field of reliability. Based on a purely time-dependent diffusion process, this paper presents a nonlinear degradation model with special focus on the proportional relationship between the age-dependent expectation and variance of the degradation processes of the concerned devices. Exact probability density function (PDF) and cumulative distribution function (CDF) of life time and RUL in explicit forms are derived under the concept of first hitting time (FHT), incorporating the item-to-item variability. An framework of maximizing the likelihood function has been proposed to estimate the unknown parameters utilizing condition monitoring data of the devices. Case studies of fatigue crack length data of alloy and capacity data of electrolytic capacitors have been presented to illustrate the proposed prognostics model. The results show that the proposed degradation model can be well fitted to the nonlinear degradation data and provide an accurate prediction of RUL, and thus demonstrate the effectiveness of the proposed model.

Dynamic Programming Principle for Classical and Singular Stochastic Control with Discretionary Stopping

We prove the dynamic programming principle (DPP) in a class of problems where an agent controls a d-dimensional diffusive dynamics via both classical and singular controls and, moreover, is able to terminate the optimisation at a time of her choosing, prior to a given maturity. The time-horizon of the problem is random and it is the smallest between a fixed terminal time and the first exit time of the state dynamics from a Borel set. We consider both the cases in which the total available fuel for the singular control is either bounded or unbounded. We build upon existing proofs of DPP and extend results available in the traditional literature on singular control (Haussmann and Suo in SIAM J Control Optim 33(3):916–936, 1995; SIAM J Control Optim 33(3):937–959, 1995) by relaxing some key assumptions and including the discretionary stopping feature. We also connect with more general versions of the DPP (e.g., Bouchard and Touzi in SIAM J Control Optim 49(3):948–962, 2011) by showing in detail how our class of problems meets the abstract requirements therein.

Bounds for exit times of Brownian motion and the first Dirichlet eigenvalue for the Laplacian

For domains in R d \mathbb {R}^d , d ≥ 2 d\geq 2 , we prove universal upper and lower bounds on the product of the bottom of the spectrum for the Laplacian to the power p > 0 p>0 and the supremum over all starting points of the p p -moments of the exit time of Brownian motion. It is shown that the lower bound is sharp for integer values of p p and that for p ≥ 1 p \geq 1 , the upper bound is asymptotically sharp as d → ∞ d\to \infty . For all p > 0 p>0 , we prove the existence of an extremal domain among the class of domains that are convex and symmetric with respect to all coordinate axes. For this class of domains we conjecture that the cube is extremal.

Lévy noise influences basin stability in a delayed vegetation-water dynamical system.

The stochastic stability for the irregular attraction basin in a time-delayed vegetation-water ecosystem disturbed by Lévy noise is explored. We first discuss that average delay time does not change the attractors of the deterministic model but affects the corresponding attraction basins, and we present the generation of Lévy noise. Then, we investigate the influence of stochastic parameters and delay time on the ecosystem by two statistical indicators, the first escape probability (FEP) and the mean first exit time (MFET). The numerical algorithm for calculating the FEP and the MFET in the irregular attraction basin is implemented, which is effectively verified by Monte Carlo simulations. Furthermore, the metastable basin is defined by the FEP and the MFET and confirms the consistency of the two indicators reflecting results. The result shows that the stochastic stability parameter, especially the noise intensity, decreases the basin stability of the vegetation biomass. In this environment, the time delay effect can validly alleviate its instability.

Boundary Conditions for Linear Exit Time Gradient Trajectories Around Saddle Points: Analysis and Algorithm

Gradient-related first-order methods have become the workhorse of large-scale numerical optimization problems. Many of these problems involve nonconvex objective functions with multiple saddle points, which necessitates an understanding of the behavior of discrete trajectories of first-order methods within the geometrical landscape of these functions. This paper concerns convergence of first-order discrete methods to a local minimum of nonconvex optimization problems that comprise strict-saddle points within the geometrical landscape. To this end, it focuses on analysis of discrete gradient trajectories around saddle neighborhoods, derives sufficient conditions under which these trajectories can escape strict-saddle neighborhoods in linear time, explores the contractive and expansive dynamics of these trajectories in neighborhoods of strict-saddle points that are characterized by gradients of moderate magnitude, characterizes the non-curving nature of these trajectories, and highlights the inability of these trajectories to re-enter the neighborhoods around strict-saddle points after exiting them. Based on these insights and analyses, the paper then proposes a simple variant of the vanilla gradient descent algorithm, termed Curvature Conditioned Regularized Gradient Descent (CCRGD) algorithm, which utilizes a check for an initial boundary condition to ensure its trajectories can escape strict-saddle neighborhoods in linear time. Convergence analysis of the CCRGD algorithm, which includes its rate of convergence to a local minimum, is also presented in the paper. Numerical experiments are then provided on a test function as well as a low-rank matrix factorization problem to evaluate the efficacy of the proposed algorithm.

Integrating machine layout, transporter allocation and worker assignment into job-shop scheduling solved by an improved non-dominated sorting genetic algorithm

To meet the everchanging production demand and close to the actual scheduling environment, a multi-objective job-shop scheduling problem (MOJSP) with multiple resource constraints is investigated. Specifically, an integrated mathematical model is constructed based on a job-shop scheduling problem (JSP) considering machine layout rearrangement, transporter allocation with capacity limitation, and worker assignment with skill variance to simultaneously minimize the exit time, labor cost, worker workload difference, and transportation time. To tackle the concerned problem, an improved non-dominated sorting genetic algorithm with a hybrid local search (INSGA-HLS) is designed. In the numerical simulation, a test dataset is first constructed according to the literature. Second, an orthogonal experiment is utilized to find the best combination of key parameters for INSGA-HLS. Third, the exploitation competence of the proposed hybrid local search (HLS) is verified. Then, the superiority of the designed INSGA-HLS algorithm is demonstrated by comparing it with the other intelligent algorithms. Thereafter, the influence of three considered factors on the integrated scheduling problem is illustrated: (1) flexible machine layout rearrangement may reduce the handling time, and improve production efficiency to some extent; (2) transporter capacity limitation can prolong the transport time, which extends the exit time; and (3) worker assignment with skill variance can not only improve productivity and reduce the labor cost, but also narrow the workload difference to improve employee satisfaction. Finally, an actual production line application further verifies the practicability and benefit of the model, and the managerial significance is analyzed.

Optimal reinsurance and investment with a common shock and a random exit time

Under the mean-variance framework, we study the continuous-time optimal reinsurance and investment problem with a common shock and a random exit time. To describe the influence of the common shock, we propose a new interdependence mechanism between the insurance market and the financial market. It can reflect both the impact of the occurrence of a common shock and its influence degree on the two markets. Both the termination times of reinsurance and investment are random, and the random exit time is affected simultaneously by exogenous and endogenous random events. The insurer’s objective is to minimize the variance of her terminal wealth under a given level of expected terminal wealth. We derive the explicit optimal reinsurance-investment strategy by employing stochastic optimal control and Lagrange duality techniques. The influences of the market interdependence and the random exit time on the optimal strategy are demonstrated through numerical experiments. The results reveal some meaningful phenomena and provide insightful guidance for reinsurance and investment practice in reality.

Logarithmic heat kernel estimates without curvature restrictions

The main results of the article are short time estimates and asymptotic estimates for the first two order derivatives of the logarithmic heat kernel of a complete Riemannian manifold. We remove all curvature restrictions and also develop several techniques. A basic tool developed here is intrinsic stochastic variations with prescribed second order covariant differentials, allowing to obtain a path integration representation for the second order derivatives of the heat semigroup $P_t$ on a complete Riemannian manifold, again without any assumptions on the curvature. The novelty is the introduction of an $\epsilon^2$ term in the variation allowing greater control. We also construct a family of cut-off stochastic processes adapted to an exhaustion by compact subsets with smooth boundaries, each process is constructed path by path and differentiable in time, furthermore the differentials have locally uniformly bounded moments with respect to the Brownian motion measures, allowing to by-pass the lack of continuity of the exit time of the Brownian motions on its initial position.