Random Time Research Articles

Abstract GS03-02: Mammographic surveillance in early breast cancer patients aged 50 years or over: results of the Mammo-50 non-inferiority trial of annual versus less frequent mammography

Abstract Introduction: Annual surveillance mammograms for an unspecified period, after treatment for early breast cancer, are widely practised in USA and Europe and represent a significant healthcare cost. Current UK guidelines recommend annual mammograms up to 5 years, then reverts to 3 year screening without specified risk stratification. Further evidence is needed to determine the optimum frequency and duration of mammographic surveillance. Methods: A multi-centre, randomised controlled, phase III trial of annual mammography versus 2-yearly for conservation surgery and 3-yearly mammograms for mastectomy patients up to 9 years. Women were eligible if aged 50 years or over at initial diagnosis of breast cancer (invasive or DCIS), and recurrence free 3 years post curative surgery. Primary outcome was breast cancer specific survival (BCSS). Secondary outcomes include recurrence free interval (RFI) and overall survival (OS). BCSS event was defined as deaths from breast cancer and RFI as any locoregional or distant invasive recurrence or new breast primary. 5000 women were needed to detect a 3% absolute non-inferiority (NI) margin for BCSS with 2.5% one-sided alpha and at least 85% power. Analyses were carried out on intention-to-treat basis. Results: 5235 women were randomised between April 2014 and September 2018. 4347 (83%) women were aged 55-75 years, 4203 (80%) had undergone conservation surgery, 4564 (87%) had invasive disease, 1162 (22%) had node positive disease, 4330 (83%) had ER positive tumours and 3812 (73%) were taking hormone therapy at the time of randomisation. Patient characteristics were balanced across arms. With a median of 5.4 years follow-up (interquartile range 4.6-5.9), 319 women have died; 104 of breast cancer (53 on annual arm; 51 on less frequent arm). BCSS at 5 years was 98.2% (95% CI 97.5-98.6%) on annual arm and 98.3% (95% CI 97.7-98.8%) on less frequent arm. Hazard ratio (HR) was 1.04 (95% CI 0.71 -1.54), demonstrating non-inferiority of less frequent mammograms at the 3% margin (NI p< 0.0001; critical value 2.71) and the 1% margin (NI p=0.02; critical value 1.56). 320 (6%) women had a new invasive breast cancer event (55 loco-regional recurrences, 85 new breast primaries, 139 distant recurrences and 41 with multiple invasive events); 164 on the annual arm compared to 156 on the less frequent arm. Five-year RFI was 94.2% (95% CI 93.2-95.1%) for the annual arm and 94.4% (95% CI 93.4-95.3%) for the less frequent arm; HR= 1.03; (95% CI 0.83-1.28) demonstrating non-inferiority at a 2% margin (NI p=0.006; critical value 1.36). OS at 5 years was 94.9% (95% CI 93.9-95.7%) on the annual arm and 94.3% (95% CI 93.3-95.2%) on the less frequent arm. Hazard ratio (HR) was 1.18 (95% CI 0.94 -1.47), demonstrating non-inferiority of less frequent mammograms at the 3% margin (NI p=0.003; critical value 1.61) and the 2.5% margin (NI p=0.02; critical value 1.51). A total of 14987 mammograms have been performed on the annual arm and 8047 on the less frequent arm. 1967 (75%) of 2618 women on the annual arm complied with their allocated schedule compared to 1775 (68%) of 2617 women on the less frequent arm. COVID-19 pandemic affected compliance; it is estimated that 345 (7%) women missed mammograms during the pandemic. A sensitivity analysis was performed on the 72% of women who fully complied with their scheduled mammograms as per protocol, and again NI was demonstrated for BCSS, RFI and OS. Conclusions: For patients aged 50 or older and 3 years post diagnosis, Mammo-50 demonstrated that less frequent mammograms were no worse than annual mammograms. These results provide evidence for less frequent mammographic surveillance for this patient population. Citation Format: Janet Dunn, Peter Donnelly, Nada Elbeltagi, Andrea Marshall, Alastair Thompson, Riccardo Audisio, Sarah Pinder, David Cameron, Amy Campbell, Sue Hartup, Lesley Turner, Annie Young, Helen Higgins, Eila Watson, Sophie Gasson, Peter Barrett-Lee, Claire Hulme, Bethany Shinkins, Peter Hall, Andy Evans. Mammographic surveillance in early breast cancer patients aged 50 years or over: results of the Mammo-50 non-inferiority trial of annual versus less frequent mammography [abstract]. In: Proceedings of the 2023 San Antonio Breast Cancer Symposium; 2023 Dec 5-9; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2024;84(9 Suppl):Abstract nr GS03-02.

Abstract PO2-12-06: Comparative Study on Bone Mineral Density in Premenopausal Patients with Estrogen Receptor-Positive Breast cancer in ASTRRA study: a 5-year follow-up study

Abstract Background With the positive outcomes associated with Ovarian Function Suppression (OFS) treatment as reported in the ASTRRA study, which compare two therapeutic strategies, tamoxifen alone and ovarian function suppression (OFS) in premenopausal patients after chemotherapy, the role of OFS has getting important. However, considering the increased risk of bone density reduction associated with postmenopause in women, the understanding these effects is crucial in devising strategies that not only effectively combat the cancer but also concurrently safeguard the patients’ bone health. This study aimed to compare the impacts of two therapeutic strategies, tamoxifen alone and OFS on bone mineral density (BMD) in premenopausal patients after chemotherapy. Methods Of the 1483 premenopausal enrolled in ASTRRA study, we focused on a subset of 522 patients who had undergone BMD examinations at diagnosis, 3 years and 5 years after diagnosis. Patients were stratified into three categories: normal, osteopenia, osteoporosis, and we examined the changes in their classifications over the 3-year and 5-year periods from baseline to identify any deterioration in bone density. Also, Patients were examined ovarian function every 6 months for 2 years and have different randomization times. Further categorization was carried out according to the time of randomization, which means starting time of OFS after recovery of ovary function. Lastly, we conducted a subset analysis using data from the Asan Medical Center (AMC), specially focused on the absolute value of one density measured in g/cm3. Results The median age of 522 patients was 41.1 and at baseline, a higher incidence of osteopenia was observed in the OFS addition group (p=0.028). Both analysis of change in BMD categories of from baseline to 3-year and baseline to 5-year period showed no significant differences between TAM only and TAM+OFS group (3-year: p=0.567, 5-year: p=0.600). However, there was a significant increased risk of bone density deterioration in the OFS addition group, when randomization occurred at the first visit (HR= 2.970, p=0.008). Within the AMC subset, statistically significant decrease in BMD were observed in the OFS addition group at the spine (p=0.023) and femur (p=0.040) over a baseline to 3-year period. Although a decrease in BMD was also observed over a baseline to 5-year period at both the spine and femur, this change was not statistically significant. Conclusion This study revealed a deleterious impact on bone density associated with the addition of OFS, compared to tamoxifen-only treatment. Remarkably, our findings also indicated that early suppression of ovarian function exerts even more detrimental influence on bone health in premenopausal, estrogen receptor-positive breast cancer patients, who have recovered ovarian function. Change between baseline to 5 years according to randomization time interval The table shows the risk associated with bone health deterioration according to the duration of randomization, thus specifying the time interval between the recovery and suppression of ovarian function. Citation Format: Eunju Shin, Seung Il Kim, Min-ho Park, Hyun-Ah Kim, Yongsik Jung, Jai Min Ryu, Eun Hwa Park, Sung Yong Kim, Eun-Gyeong Lee, Min Hyuk Lee, Jung Ho Park, Seock-Ah Im, Soong June Bae, Su Hwan Kang, Woosung Lim, Hyun Jo Youn, Heung Kyu Park, Kyong Hwa Park, Tae-Hyun Kim, Shin-Young Park, Cheol wan Lim, Geum-Hee Kwak, Chanheun Park, Hyuk-Jae Shin, Young Bum Yoo, Sun Hee Kang, Bong Kyun Kim, Hee Jeong Kim. Comparative Study on Bone Mineral Density in Premenopausal Patients with Estrogen Receptor-Positive Breast cancer in ASTRRA study: a 5-year follow-up study [abstract]. In: Proceedings of the 2023 San Antonio Breast Cancer Symposium; 2023 Dec 5-9; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2024;84(9 Suppl):Abstract nr PO2-12-06.

Using Recurrent Neural Networks for the Performance Analysis and Optimization of Stochastic Milkrun-Supplied Flow Lines

Long-term throughput, as a key performance indicator of a stochastic flow line, is affected by numerous parameters describing the features of the flow line, such as processing time and buffer size. Fast and accurate evaluation methods for a given set of values for those parameters are a prerequisite to systematically optimize such a flow line. In this paper, we consider the case of a flow line with random processing times, limited buffer capacities and so-called milkruns that supply the machines with material parts that are required to perform, e.g., assembly operations on workpieces. In such a system, shortages in the supply of material parts can limit the performance of the flow line. Up to now, there are no accurate analytical approaches to quantify the complex interactions in such milkrun-supplied flow lines for realistic problem sizes. We propose to use recurrent neural networks to determine the long-term throughput of such flow lines enabling us to evaluate production systems of flexible size. Our results show that the throughput can be determined accurately and quickly via recurrent neural networks. Furthermore, we use this new evaluation procedure as a building block to optimize this type of flow line using gradient and local search techniques.

Shortage Policies for a Jump Process with Positive and Negative Batch Arrivals in a Random Environment

We study a continuous-review stock management of a retailer for a single item in a limited storage (buffer) in a random environment. The stock level fluctuates according to two independent compound Poisson processes with discrete amounts of items (batches) that enter and leave the storage facility. The storage facility is controlled by a three-parameter base-stock replenishment policy. All items exceeding the storage capacity are transferred to an unlimited foreign facility. In addition, a restricted backlogging possibility is permitted; additional demands for items are lost sales. We further assume a random shelf life, the possibility of total inventory collapse, and a random lead time. Applying Markov theory, we derive the optimal control parameters minimizing the long-run expected total cost. A sensitivity analysis is conducted focusing on the comparison between the pure lost-sales policy and a partial backordering policy. Accordingly, we identify cases where one policy is cost effective compared to the other, particularly with respect to the batch patterns (sign, rate, average, and variability), and the associated costs.

A stochastic and time-delay evolutionary game of food safety regulation under central government punishment mechanism

Food safety is a pressing issue affecting public health, and strengthening food safety regulation has become a widespread consensus. This study addresses the three-party game involving food production enterprises, third-party testing agencies, and government regulatory authorities. Considering the influence of random disturbances and time delays on the strategy-choosing and behavioral evolution of game players, a three-party stochastic evolutionary game model for food safety regulation with time delays is established. The stability of the model is analyzed by using Lyapunov's method, and the strategy evolution of the game players is investigated while combining numerical simulations. The study shows that the net benefit of the players' expected strategies is key in determining whether the overall game system can reach the optimal equilibrium. The level of penalties imposed by the central government on local government regulators is key to food safety. The main factors influencing the strategy-choosing of game players are the level of penalties imposed by the local government regulators on third-party testing agencies, together with the supervision costs of the local government regulators. Random disturbances have a certain impact on strategy-choosing of the game players, with a greater impact on testing agencies, followed by food production enterprises, and a weaker impact on government regulatory authorities. The time delay factors exhibit a certain delay effect on the evolutionary path of strategy-choosing among the game players, which aligns with the actual situation. The findings of the study have implications for food safety regulation.

Stochastic Compartment Model with Mortality and Its Application to Epidemic Spreading in Complex Networks.

We study epidemic spreading in complex networks by a multiple random walker approach. Each walker performs an independent simple Markovian random walk on a complex undirected (ergodic) random graph where we focus on the Barabási-Albert (BA), Erdös-Rényi (ER), and Watts-Strogatz (WS) types. Both walkers and nodes can be either susceptible (S) or infected and infectious (I), representing their state of health. Susceptible nodes may be infected by visits of infected walkers, and susceptible walkers may be infected by visiting infected nodes. No direct transmission of the disease among walkers (or among nodes) is possible. This model mimics a large class of diseases such as Dengue and Malaria with the transmission of the disease via vectors (mosquitoes). Infected walkers may die during the time span of their infection, introducing an additional compartment D of dead walkers. Contrary to the walkers, there is no mortality of infected nodes. Infected nodes always recover from their infection after a random finite time span. This assumption is based on the observation that infectious vectors (mosquitoes) are not ill and do not die from the infection. The infectious time spans of nodes and walkers, and the survival times of infected walkers, are represented by independent random variables. We derive stochastic evolution equations for the mean-field compartmental populations with the mortality of walkers and delayed transitions among the compartments. From linear stability analysis, we derive the basic reproduction numbers RM,R0 with and without mortality, respectively, and prove that RM<R0. For RM,R0>1, the healthy state is unstable, whereas for zero mortality, a stable endemic equilibrium exists (independent of the initial conditions), which we obtained explicitly. We observed that the solutions of the random walk simulations in the considered networks agree well with the mean-field solutions for strongly connected graph topologies, whereas less well for weakly connected structures and for diseases with high mortality. Our model has applications beyond epidemic dynamics, for instance in the kinetics of chemical reactions, the propagation of contaminants, wood fires, and others.

Intuitionistic fuzzy time series forecasting method based on dendrite neuron model and exponential smoothing

Methods based on artificial neural networks for intuitionistic fuzzy time series forecasting can produce successful forecasting results. In the literature, exponential smoothing methods are hybridised with artificial neural networks due to their simple and efficient structures to improve the forecasting performance. The contribution of this paper is to propose a new forecasting approach combining exponential smoothing methods and intuitionistic fuzzy time series. In this study, a forecasting algorithm based on the dendrite neuron model and simple exponential smoothing methods is proposed for modelling intuitionistic fuzzy time series. In the fuzzification stage of the proposed method, the intuitionistic fuzzy c-means method is used. The proposed method is a modular method using two separate dendrite neuron model neural networks and the grey wolf optimisation algorithm is used to estimate all parameters of the method. The performance of the proposed method is applied on four different random time series obtained for Index of Coin Market Cap and the performance of the method is compared with some other fuzzy forecasting methods. As a result of the analyses, it is concluded that the proposed modular method has better forecasting results than other methods.

On Non-Occurrence of the Inspection Paradox

The well-known inspection paradox or waiting time paradox states that, in a renewal process, the inspection interval is stochastically larger than a common interarrival time having a distribution function F, where the inspection interval is given by the particular interarrival time containing the specified time point of process inspection. The inspection paradox may also be expressed in terms of expectations, where the order is strict, in general. A renewal process can be utilized to describe the arrivals of vehicles, customers, or claims, for example. As the inspection time may also be considered a random variable T with a left-continuous distribution function G independent of the renewal process, the question arises as to whether the inspection paradox inevitably occurs in this general situation, apart from in some marginal cases with respect to F and G. For a random inspection time T, it is seen that non-trivial choices lead to non-occurrence of the paradox. In this paper, a complete characterization of the non-occurrence of the inspection paradox is given with respect to G. Several examples and related assertions are shown, including the deterministic time situation.

The Optimal Stopping Problem under a Random Horizon

This paper considers a pair (F,τ), where F is a filtration representing the “public” flow of information that is available to all agents over time, and τ is a random time that might not be an F-stopping time. This setting covers the case of a credit risk framework, where τ models the default time of a firm or client, and the setting of life insurance, where τ is the death time of an agent. It is clear that random times cannot be observed before their occurrence. Thus, the larger filtration, G, which incorporates F and makes τ observable, results from the progressive enlargement of F with τ. For this informational setting, governed by G, we analyze the optimal stopping problem in three main directions. The first direction consists of characterizing the existence of the solution to this problem in terms of F-observable processes. The second direction lies in deriving the mathematical structures of the value process of this control problem, while the third direction singles out the associated optimal stopping problem under F. These three aspects allow us to deeply quantify how τ impacts the optimal stopping problem and are also vital for studying reflected backward stochastic differential equations that arise naturally from pricing and hedging of vulnerable claims.

Effects of Tetrahydrolipstatin on Glioblastoma in Mice: MRI-Based Morphologic and Texture Analysis Correlated with Histopathology and Immunochemistry Findings-A Pilot Study.

This study aimed to investigate the effects of tetrahydrolipstatin (orlistat) on heterotopic glioblastoma in mice by applying MRI and correlating the results with histopathology and immunochemistry. Human glioblastoma cells were injected subcutaneously into the groins of immunodeficient mice. After tumor growth of >150 mm3, the animals were assigned into a treatment group (n = 6), which received daily intraperitoneal injections of orlistat, and a control group (n = 7). MRI was performed at the time of randomization and before euthanizing the animals. Tumor volumes were calculated, and signal intensities were analyzed. The internal tumor structure was evaluated visually and with texture analysis. Western blotting and protein expression analysis were performed. At histology, all tumors showed high mitotic and proliferative activity (Ki67 ≥ 10%). Reduced fatty acid synthetase expression was measured in the orlistat group (p < 0.05). Based on the results of morphologic MRI-based analysis, tumor growth remained concentric in the control group and changed to eccentric in the treatment group (p < 0.05). The largest area under the receiver operating curve of the predictors derived from the texture analysis of T2w images was for wavelet transform parameters WavEnHL_s3 and WavEnLH_s4 at 0.96 and 1.00, respectively. Orlistat showed effects on heterotopically implanted glioblastoma multiforme in MRI studies of mice based on morphologic and texture analysis.

Optimal investment and reinsurance to reach a bequest goal with random time solvency regulation

ABSTRACT This paper studies optimal investment and proportional reinsurance policies for an insurer with Markov regime-switching model and random time solvency regulation. The goal of the insurer is to maximise the probability that its wealth exceeds a predetermined level l before the regulatory time arrives. By constructing an auxiliary control problem without regime switching, together with the classical results on Hamilton-Jacobi-Bellman (HJB) equation and fixed-point method, we prove the regularity of the value function. When the current state of the Markov chain is given, we found that the optimal policies for an insurer in a multiple-regime market is the same as those in a single-regime market. Explicit optimal policies can be derived when the premium is calculated by the expectation principle. For more general cases, numerical schemes for value functions and feedback optimal policies are given by the Markov chain approximating method.

Distinction of Chaos from Randomness Is Not Possible from the Degree Distribution of the Visibility and Phase Space Reconstruction Graphs.

We investigate whether it is possible to distinguish chaotic time series from random time series using network theory. In this perspective, we selected four methods to generate graphs from time series: the natural, the horizontal, the limited penetrable horizontal visibility graph, and the phase space reconstruction method. These methods claim that the distinction of chaos from randomness is possible by studying the degree distribution of the generated graphs. We evaluated these methods by computing the results for chaotic time series from the 2D Torus Automorphisms, the chaotic Lorenz system, and a random sequence derived from the normal distribution. Although the results confirm previous studies, we found that the distinction of chaos from randomness is not generally possible in the context of the above methodologies.

Optimal resilience-based restoration of a system subject to recurrent dependent hazards

Many engineered systems are faced with multiple natural and manmade hazards during operation. Since such hazards may cause system disruptions (e.g., catastrophic failure and performance deterioration), timely and effective restoration needs to be conducted to minimize the negative impacts of the hazards. In practice, these hazards are recurrent and often interact dynamically with each other. This causes a major challenge in assessing the performance of the systems and determining the optimal restoration policy from a holistic perspective. In this paper, we model the availability and resilience of a system subject to recurrent and dependent hazards and develop the optimal restoration policies for decision makers with different risk preferences. Particularly, we first model the random occurrence times and severities of a set of hazards whose occurrence frequencies and severities are dynamically dependent. Next, we derive the analytical expressions for the system's availability metrics. Third, we investigate the optimal restoration policies for both risk-neutral (RN) and risk-averse (RA) decision makers by solving two related optimization problems. A case study on the pipelines in the Mid-Atlantic area of the U.S. is provided to illustrate the practical values of the proposed availability assessment and resilience optimization methods.

Adaptive promising zone design for cancer immunotherapy with heterogeneous delayed treatment effect

ABSTRACT Indirect mechanisms of cancer immunotherapies result in delayed treatment effects that vary among patients. Consequently, the use of the log-rank test in trial design and analysis can lead to significant power loss and pose additional challenges for interim decisions in adaptive designs. In this paper, we describe patients’ survival using a piecewise proportional hazard model with random lag time and propose an adaptive promising zone design for cancer immunotherapy with heterogeneous delayed effects. We provide solutions for calculating conditional power and adjusting the critical value for the log-rank test with interim data. We divide the sample space into three zones – unfavourable, promising, and favourable –based on re-estimations of the survival parameters, the log-rank test statistic at the interim analysis, and the initial and maximum sample sizes. If the interim results fall into the promising zone, the sample size is increased; otherwise, it remains unchanged. We show through simulations that our proposed approach has greater overall power than the fixed sample design and similar power to the matched group sequential trial. Furthermore, we confirm that critical value adjustment effectively controls the type I error rate inflation. Finally, we provide recommendations on the implementation of our proposed method in cancer immunotherapy trials.

Understanding and Quantifying Network Robustness to Stochastic Inputs.

A variety of biomedical systems are modeled by networks of deterministic differential equations with stochastic inputs. In some cases, the network output is remarkably constant despite a randomly fluctuating input. In the context of biochemistry and cell biology, chemical reaction networks and multistage processes with this property are called robust. Similarly, the notion of a forgiving drug in pharmacology is a medication that maintains therapeutic effect despite lapses in patient adherence to the prescribed regimen. What makes a network robust to stochastic noise? This question is challenging due to the many network parameters (size, topology, rate constants) and many types of noisy inputs. In this paper, we propose a summary statistic to describe the robustness of a network of linear differential equations (i.e. a first-order mass-action system). This statistic is the variance of a certain random walk passage time on the network. This statistic can be quickly computed on a modern computer, even for complex networks with thousands of nodes. Furthermore, we use this statistic to prove theorems about how certain network motifs increase robustness. Importantly, our analysis provides intuition for why a network is or is not robust to noise. We illustrate our results on thousands of randomly generated networks with a variety of stochastic inputs.

Charge fluctuations on the dust grains in the presence of energetic electrons

Abstract Dust charging is an arbitrary process occurring at random times which results in fluctuations of dust charge around its equilibrium value. To have a better insight into the mechanism of charge fluctuations, a numerical simulation of the statistical nature of the dust charging process is investigated. Here, a multicomponent non-Maxwellian hydrogen plasma comprising two electron groups, positive ions, and dust grains is modelled. An increase in the overall negative dust charge number is reported in the presence of non-Maxwellian electrons. Additionally, the study emphasizes the role of electron distribution and hot electron temperature and density on the charge fluctuations of the dust grains.

Universal Glycosyltransferase Continuous Assay for Uniform Kinetics and Inhibition Database Development and Mechanistic Studies Illustrated on ST3GAL1, C1GALT1, and FUT1.

Chemical systems glycobiology requires experimental and computational tools to make possible big data analytics benefiting genomics and proteomics. The impediment to tool development is that the nature of glycan construction and mutation is not template driven but rests on cooperative glycosyltransferase (GT) catalytic synthesis. What is needed is the collation of kinetics and inhibition data in a standardized form to make possible analytics of glycan and glycoconjugate synthesis, mechanism extraction, and pattern recognition. Currently, kinetics assays in use for GTs are not universal in processing nucleoside phosphate UDP, GDP, and CMP donor-based glycosylation reactions due to limitations in accuracy and large substrate volume requirements. Here we present a universal glycosyltransferase continuous (UGC) assay able to measure the declining concentration of the NADH reporter molecule through fluorescence spectrophotometry and, therefore, determine reaction rate parameters. The development and parametrization of the assay is based on coupling the nucleotide released from GT reactions with pyruvate kinase, via nucleoside diphosphate kinase (NDK) in the case of NDP-based donor reactions. In the case of CMP-based reactions, the coupling is carried out via another kinase, cytidylate kinase in combination with NDK, which phosphorylates CMP to CDP, then CDP to CTP. Following this, we conduct kinetics and inhibition assay studies on the UDP, GDP, and CMP-based glycosylation reactions, specifically C1GAlT1, FUT1, and ST3GAL1, to represent each class of donor, respectively. The accuracy of calculating initial rates using the continuous assay compared to end point (noncontinuous) assays is demonstrated for the three classes of GTs. The previously identified natural product soyasaponin1 inhibitor was used as a model to demonstrate the application of the UGC assay as a standardized inhibition assay for GTs. We show that the dose response of ST3GAL1 to a serial dilution of Soyasaponin1 has time-dependent inhibition. This brings into question previous inhibition findings, arrived at using an end point assay, that have selected a seemingly random time point to measure inhibition. Consequently, using standardized Km values taken from the UGC assay study, ST3GAL1 was shown to be the most responsive enzyme to soyasaponin1 inhibition, followed by FUT1, then C1GALT1 with IC50 values of 37, 52, and 886 μM respectively.

Random-time component reallocation and system replacement policy with minimal repair

The maintenance policies based on random working time guarantee the continuity of system functionality. This paper studies a random-time component reallocation and system replacement (RCS) policy, in which the random-time system replacement is to replace the system at the planned preventive time or the random working time, whichever comes first, the random-time component reallocation is to balance the degradation of components by reallocating components at random working time before system replacement, and minimal repair is implemented for failed components. To improve the efficiency and flexibility of RCS policy, we first establish an optimization model to minimize the expected system maintenance cost per unit time based on a given interval for random-time component reallocation, and analytical results are derived by comparing the proposed policy with the preventive component reallocation and random-time system replacement policy, and the simple random-time system replacement policy. Next, we construct another optimization model to maximize the interval length for the random-time component reallocation constrained by the threshold of the efficiency level of RCS policy. Numerical experiments demonstrate the performance of the RCS policy and provide guidance for the interval for the random-time component reallocation.

Target-oriented robust satisficing models for the single machine scheduling problems with release time

In this paper, we investigate single machine scheduling problems with release times and random processing times, where the release times can be either deterministic or random. The objective is to determine a scheduling sequence that exhibits strong out-of-sample performance. To achieve this, we employ target-oriented robust satisficing models to obtain the scheduling sequence. For the scheduling problem with deterministic release times, we derive an equivalent mixed-integer linear program and an approximate reformulation to address cases involving a large number of jobs. For the scheduling problem with random release times, we first demonstrate the challenges associated with providing an equivalent reformulation. To overcome this intractability, we propose an approximate reformulation based on the linear decision rule. Numerical experiments are conducted to demonstrate the superiority of our solutions through comparisons with several benchmarks. Furthermore, the numerical results demonstrate that a relatively higher target should be chosen if the worst-case performance is valued, otherwise, the decision-maker should set a relatively lower target to obtain better average performance.

Local resetting in non-conserving zero-range processes with extensive rates

A non-conserving zero-range process with extensive creation, annihilation and hopping rates is subjected to local resetting. The model is formulated on a large, fully-connected network of states. The states are equipped with a (bounded) fitness level: particles are added to each state at a rate proportional to the fitness level of the state. Moreover, particles are annihilated at a constant rate, and hop at a fixed rate to a uniformly-drawn state in the network. This model has been interpreted in terms of population dynamics: the fitness is the reproductive fitness in a haploid population, and the hopping process models mutation. It has also been interpreted as a model of network growth with a fixed set of nodes (in which particles occupying a state are interpreted as links pointing to this state). In the absence of resetting, the model is known to reach a steady state, which in a certain limit may exhibit a condensate at maximum fitness. If the model is subjected to global resetting by annihilating all particles at Poisson-distributed times, there is no condensation in the steady state. If the system is subjected to local resetting, the occupation numbers of each state are reset to zero at independent random times. These times are distributed according to a Poisson process whose rate (the resetting rate) depends on the fitness. We derive the evolution equation satisfied by the probability law of the occupation numbers. We calculate the average occupation numbers in the steady state. The existence of a condensate is found to depend on the local behavior of the resetting rate at maximum fitness: if the resetting rate vanishes at least linearly at high fitness, a condensate appears at maximum fitness in the limit where the sum of the annihilation and hopping rates is equal to the maximum fitness.