Sequential adaptive variables and subject selection for GEE methods.

Modeling correlated or highly stratified multiple-response data is a common data analysis task in many applications, such as those in large epidemiological studies or multisite cohort studies. The generalized estimating equations method is a popular statistical method used to analyze these kinds of data, because it can manage many types of unmeasured dependence among outcomes. Collecting large amounts of highly stratified or correlated response data is time-consuming; thus, the use of a more aggressive sampling strategy that can accelerate this process-such as the active-learning methods found in the machine-learning literature-will always be beneficial. In this study, we integrate adaptive sampling and variable selection features into a sequential procedure for modeling correlated response data. Besides reporting the statistical properties of the proposed procedure, we also use both synthesized and real data sets to demonstrate the usefulness of our method.

Myocardial infarction evaluation from stopping time decision toward interoperable algorithmic states in reinforcement learning.

BACKGROUND: The Elliot wave principle commonly characterizes the impulsive and corrective wave trends for both financial market trends and electrocardiograms. The impulsive wave trends of electrocardiograms can annotate several wave components of heart-beats including pathological heartbeat waveforms. The stopping time inquires which ordinal element satisfies the assumed mathematical condition within a numerical set. The proposed work constitutes several algorithmic states in reinforcement learning from the stopping time decision, which determines the impulsive wave trends. Each proposed algorithmic state is applicable to any relevant algorithmic state in reinforcement learning with fully numerical explanations. Because commercial electrocardiographs still misinterpret myocardial infarctions from extraordinary electrocardiograms, a novel algorithm needs to be developed to evaluate myocardial infarctions. Moreover, differential diagnosis for right ventricle infarction is required to contraindicate a medication such as nitroglycerin. METHODS: The proposed work implements the stopping time theory to impulsive wave trend distribution. The searching process of the stopping time theory is equivalent to the actions toward algorithmic states in reinforcement learning. The state value from each algorithmic state represents the numerically deterministic annotated results from the impulsive wave trend distribution. The shape of the impulsive waveform is evaluated from the interoperable algorithmic states via least-first-power approximation and approximate entropy. The annotated electrocardiograms from the impulsive wave trend distribution utilize a structure of neural networks to approximate the isoelectric baseline amplitude value of the electrocardiograms, and detect the conditions of myocardial infarction. The annotated results from the impulsive wave trend distribution consist of another reinforcement learning environment for the evaluation of impulsive waveform direction. RESULTS: The accuracy to discern myocardial infarction was found to be 99.2754% for the data from the comma-separated value format files, and 99.3579% for those containing representative beats. The clinical dataset included 276 electrocardiograms from the comma-separated value files and 623 representative beats. CONCLUSIONS: Our study aims to support clinical interpretation on 12-channel electrocardiograms. The proposed work is suitable for a differential diagnosis under infarction in the right ventricle to avoid contraindicated medication during emergency. An impulsive waveform that is affected by myocardial infarction or the electrical direction of electrocardiography is represented as an inverse waveform.

Existence and Uniqueness of the Local Smooth Solution to 3D Stochastic MHD Equations without Diffusion.

In this paper, we consider the existence of local smooth solution to stochastic magneto-hydrodynamic equations without diffusion forced by additive noise in R 3 . We first transform the system into a random system via a simple change of variable and borrow the result obtained for classical magneto-hydrodynamic equations, then we show that this random transformed system is measurable with respect to the stochastic element. Finally we extend the solution to the maximality solution. Due to the coupled construction of this system, we need more elaborate and complicated estimates with respect to stochastic Euler equation.

A Game-Theoretical Winner and Loser Model of Dominance Hierarchy Formation.

Many animals spend large parts of their lives in groups. Within such groups, they need to find efficient ways of dividing available resources between them. This is often achieved by means of a dominance hierarchy, which in its most extreme linear form allocates a strict priority order to the individuals. Once a hierarchy is formed, it is often stable over long periods, but the formation of hierarchies among individuals with little or no knowledge of each other can involve aggressive contests. The outcome of such contests can have significant effects on later contests, with previous winners more likely to win (winner effects) and previous losers more likely to lose (loser effects). This scenario has been modelled by a number of authors, in particular by Dugatkin. In his model, individuals engage in aggressive contests if the assessment of their fighting ability relative to their opponent is above a threshold [Formula: see text]. Here we present a model where each individual can choose its own value [Formula: see text]. This enables us to address questions such as how aggressive should individuals be in order to take up one of the first places in the hierarchy? We find that a unique strategy evolves, as opposed to a mixture of strategies. Thus, in any scenario there exists a unique best level of aggression, and individuals should not switch between strategies. We find that for optimal strategy choice, the hierarchy forms quickly, after which there are no mutually aggressive contests.

A stochastic framework for evaluating CAR T cell therapy efficacy and variability.

Based on a deterministic and stochastic process hybrid model, we use white noises to account for patient variabilities in treatment outcomes, use a hyperparameter to represent patient heterogeneity in a cohort, and construct a stochastic model in terms of Ito stochastic differential equations for testing the efficacy of three different treatment protocols in CAR T cell therapy. The stochastic model has three ergodic invariant measures which correspond to three unstable equilibrium solutions of the deterministic system, while the ergodic invariant measures are attractors under some conditions for tumor growth. As the stable dynamics of the stochastic system reflects long-term outcomes of the therapy, the transient dynamics provide chances of cure in short-term. Two stopping times, the time to cure and time to progress, allow us to conduct numerical simulations with three different protocols of CAR T cell treatment through the transient dynamics of the stochastic model. The probability distributions of the time to cure and time to progress present outcome details of different protocols, which are significant for current clinical study of CAR T cell therapy.

Nonparametric Shiryaev-Roberts change-point detection procedures based on modified empirical likelihood.

Sequential change-point analysis, which identifies a change of probability distribution in an infinite sequence of random observations, has important applications in many fields. A good method should detect a change point as soon as possible, and keep a low amount of false alarms. As one of the most popular methods, Shiryaev-Roberts (SR) procedure holds many optimalities. However, its implementation requires the pre-change and post-change distributions to be known, which is not achievable in practice. In this paper, we construct a nonparametric version of the SR procedure by embedding different versions of empirical likelihood, assuming two training samples, before and after change, are available for parameter estimations. Simulations are conducted to compare the performance of the proposed method with existing methods. The results show that when the underlying distribution is unknown, and training sample sizes are small, the proposed modified procedure shows advantage by giving a smaller delay of detection.

Effect of labour income on the optimal bankruptcy problem.

In this paper we deal with the optimal bankruptcy problem for agents who can optimally allocate their consumption rate, the amount of capital invested in the risky asset, as well as their leisure time. In our framework, the agents are endowed by an initial debt, and they are required to repay their debt continuously. Declaring bankruptcy, the debt repayment is exempted at the cost of a wealth shrinkage. We implement the duality method to solve the problem analytically and conduct a sensitivity analysis to the bankruptcy cost and benefit parameters. Introducing the flexible leisure/working rate, and therefore the labour income, into the bankruptcy model, we investigate its effect on the optimal strategies. Supplementary Information: The online version contains supplementary material available at 10.1007/s10479-023-05166-z.

Study of Carbon Reduction and Marketing Decisions with the Envisioning of a Favorable Event under Cap-and-Trade Regulation.

To achieve SDGs (sustainable development goals) and carbon neutrality goals, the Chinese government have been adopting the cap-and-trade regulation to curb carbon emissions. With this background, members in the supply chain should properly arrange their carbon reduction and marketing decisions to acquire optimal profits, especially when the favorable event may happen, which tends to elevate goodwill and the market demand. However, the event may not be of their benefit when the cap-and-trade regulation is conducted, since the increase in market demand is always associated with an increase in carbon emissions. Hence, questions arise about how the members adjust their carbon reduction and marketing decisions while envisioning the favorable event under the cap-and-trade regulation. Given the fact that the event occurs randomly during the planning period, we use the Markov random process to depict the event and use differential game methodology to dynamically study this issue. After solving and analyzing the model, we acquire the following conclusions: (1) the occurrence of the favorable event splits the whole planning period into two regimes and the supply chain members should make optimal decisions in each regime to maximize the overall profits. (2) The potential favorable event will elevate the marketing and carbon reduction efforts, as well as the goodwill level before the event. (3) If the unit emissions value is relatively low, the favorable event will help to decrease the emissions quantity. However, if the unit emissions value is relatively large, then the favorable event will help to increase the emissions quantity.

Firm Exit during the COVID-19 Pandemic: Evidence from Japan.

Firms have exited the market since the start of the COVID-19 pandemic. To evaluate the number of firms exiting the market and their exit rate, we construct a simple model, in which firms optimally choose stopping time for their exit. We estimate the model using firm-level data on firm exits before the pandemic. Subsequently, using recent survey data on firm sales growth, we simulate potential firm exits during the pandemic under the condition that the institutional background, represented by activities such as bankruptcy procedures and government rescue plans, did not change the exit option value. Our main findings are as follows. First, we find sizable heterogeneity with respect to the number and rate of firm exits across industries and regions. Second, in aggregate, the pandemic potentially increased firm exits by around 20 % compared to the previous year under the assumption that the recent reduction in firm sales is temporary and, thus, partially incorporated into firms' expectations for future trend sales growth. In two extreme cases in which the recent sales reduction has a full or no impact on firms' expectations for future sales, firm exits increased by 110 % and 10 % , respectively. Third, these increases are mainly due to the decrease in the expected sales growth rate, rather than the increase in uncertainty. Finally, we quantify the hypothetical amount of government subsidies needed to prevent excess increases in potential firm exits, which is around 10 - 3 of Japan's GDP.

Consumption-portfolio choice with subsistence consumption and risk aversion change at retirement.

This paper considers subsistence consumption of an economic agent both before and after retirement in analyzing the optimal consumption, portfolio, and retirement problem. We allow the relative risk aversion of the economic agent to make a one-off jump at retirement. With a Cobb-Douglas utility function, we obtain explicit expressions for the optimal policies. Numerical results show that, whereas post-retirement subsistence consumption tends to delay retirement, pre-retirement subsistence consumption and the magnitude of jump in relative risk aversion may stimulate early retirement. Also, the consumption drop at retirement deepens as post-retirement subsistence consumption increases, but it weakens as pre-retirement subsistence consumption increases.

Precise large deviations of aggregate claims in a size-dependent renewal risk model with stopping time claim-number process.

In this paper, we consider a size-dependent renewal risk model with stopping time claim-number process. In this model, we do not make any assumption on the dependence structure of claim sizes and inter-arrival times. We study large deviations of the aggregate amount of claims. For the subexponential heavy-tailed case, we obtain a precise large-deviation formula; our method substantially relies on a martingale for the structure of our models.