分泌性癌是一种罕见低度恶性肿瘤, 发生于眼睑者极为罕见。本文回顾性分析1例眼睑分泌性癌患者的临床病理资料。探讨其临床病理学、免疫组织化学及分子遗传学特征和鉴别诊断要点, 并复习相关文献, 以期提高临床病理医师对原发眼睑分泌性癌的认识。

Alkaline metal oxides have received significant attention recently due to their abundance, inherent conductivity, optical absorption, and thermal stability. Here, a straightforward co-precipitation method was employed to obtain both undoped BaO and Mo-doped BaO nanoparticles. Various techniques were used to characterize the synthesized nanoparticles’ structural, Raman spectral, optical, thermal, and electrical properties. X-ray diffraction (XRD) results revealed that Mo was successfully doped into tetragonal nanocrystalline BaO. The W-H plot showed that as Mo doping increases from 2 % to 6 %, the crystallite size grows while the lattice structure remains well-ordered with even strain distribution. Scanning electron microscopy (SEM) was used to examine its surface features. The purity and crystalline character of the samples were further confirmed via Raman spectroscopy, which shows that the peak intensity of the spectra increases with the increase of particle size owing to the rise in the force constant. UV spectroscopy was used to observe the energy band gap, which is found to decrease from 4.2 eV to 3.8 eV, and then it drops to 3.4 eV as the Mo content increases. This is reasonable because of the size-dependent attraction between metallic ions and conduction electrons. PL spectra concluded that Mo doping leads to the enhancement of the optical characteristics of BaO. Adding Mo to BaO also modifies the material’s thermal properties, potentially affecting its suitability for applications that require thermal durability. This finding exhibits that even slight doping of Mo4+ into BaO can significantly impact their structural, thermal, optical, and electrical characteristics. It enriches the existing body of knowledge of BaO nanoparticles and lays the foundation for its future research

For a Markov decision process with countably infinite states, the optimal value may not be achievable in the set of stationary policies. In this paper, we study the existence conditions of an optimal stationary policy in a countable-state Markov decision process under the long-run average criterion. With a properly defined metric on the policy space of ergodic MDPs, the existence of an optimal stationary policy can be guaranteed by the compactness of the space and the continuity of the long-run average cost with respect to the metric. We further extend this condition by some assumptions which can be easily verified in control problems of specific systems, such as queueing systems. Our results make a complementary contribution to the literature in the sense that our method is capable to handle the cost function unbounded from both below and above, only at the condition of continuity and ergodicity. Several examples are provided to illustrate the application of our main results.

In this chapter, we focus on relative optimization of the long-run average of time-nonhomogeneous continuous-time and continuous-state stochastic processes, with a general Markov model. The under-selectivity issue (meaning that the long-run average does not depend on the actions taken in any finite period) is solved and necessary and sufficient optimality conditions are derived; bias optimization is addressed. State classification is implemented with the notion of state comparability and weak ergodicity: all the states can be classified into weakly ergodic states and branching states, which is slightly different from the ergodic and transient states in time-homogeneous systems; and we show that the former is more natural for optimization. Optimality conditions for multi-class stochastic processes are derived with relative optimization. Optimality conditions for discounted performance are also derived.

Relative optimization is based on a direct comparison of the performance measures of any two policies. When the two policies under comparison is infinitesimally close, the performance-difference formula becomes the performance-derivative formula. The performance-derivative-based approach is more suitable for non-linear or non-additive performance measure. In this chapter, we derive the first-order optimality conditions (or the differential version of HJB equation). As an example, we study the optimization of a distorted utility measured with distorted probability. We prove that by changing a probability measure the sample derivative is an unbiased estimate of the derivative of the distorted utility. The optimality condition can be derived. This analysis can be applied to study the non-linear behaviour in finance.

In this chapter, we first discuss the stochastic calculus of multi-dimensional diffusion processes with semi-smooth functions, and we derive the Tanaka formula for multi-dimensional semi-smooth functions with the local time on the semi-smooth curve along its gradient direction. With this formula, we extend the relative optimization approach to stochastic control to multi-dimensional systems. Optimality conditions are derived for systems with semi-smooth value functions and no viscosity solution is involved. This approach provides new insights and motivates the research on stochastic control and stochastic calculus of multi-dimensional systems, in particular, for problems with non-smooth features and degenerate points. The analysis is intuitive and results are preliminary, and hopefully they would motivate new research topics.

In a Markov chain, an $$( N+1)$$ th bias is the bias of an Nth bias, $$N=1,2,\ldots $$ . with 1st bias being the standard bias. The Nth biases measure the transient performance of the Markov chain at different levels. In this chapter, we study the optimization problems of the Nth biases for time-nonhomogeneous Markov chains (TNHMCs). We derive the optimality conditions for all the Nth biases, $$N =1,2,\cdots $$ . We show that the discounted performance can be expressed as a Laurent series in all the Nth biases, and the Blackwell optimal policy is a policy that is optimal for all the Nth biases, $$N =0,1,\cdots $$ . The results show that the Nth-bias optimality and the Blackwell optimality overcome the under-selectivity issue associated with the long-run average performance. The theory in this chapter corresponds to the sensitive discount optimality in the literature, but there are two distinctions: the Nth-bias optimality approach does not require discounting, and the results presented in this chapter are for TNHMCs. Again, the problem is solved by the relative optimization approach. The theory has wide applications because many engineering, economic, physical, and social systems experience a transient period before reaching the steady state.

In this chapter, we study the optimization of the long-run average and bias of single class (or uni-chain) time-nonhomogeneous Markov chains. With confluencity, we define the most central notion in performance optimization, the performance potentials, and discuss its properties. With the performance potentials, we derive the difference formula for the average rewards of any two policies; and based on which we obtain the necessary and sufficient optimality conditions for average rewards. In addition, we study the bias optimality, which optimizes transient performance in the initial period. Bias potentials are defined, and bias optimality conditions are derived. The approach is called relative optimization since it is based on the performance difference formula that gives the difference of the performance measures of any two policies on the entire infinite horizon. The under-selectivity is reflected in the optimality conditions because from the difference formula, it is clear that the optimality conditions do not need to hold in any finite period, or in any “non-frequently” visited sequence of time instants.

We derive the Tanaka formula for multidimensional semismooth functions with the local time on the semismooth curve along the gradient direction. With this formula, we extend the relative optimization based approach to stochastic control to multidimensional systems. Optimality conditions are derived for systems with semismooth value functions, and no viscosity solution is involved. This approach provides new insights and motivates the research on stochastic control and stochastic calculus, in particular, for problems with nonsmooth features and degenerate points.

In this chapter, we show that the degenerate points may separate the state space into different regions for multiple classes, and we discuss the optimization of multi-class degenerate diffusion processes. We also show that under some conditions, the performance function of finite-horizon optimization problems, or the potential function of the long-run average optimization problems, is semi-smooth at degenerate points and smooth at non-degenerate points. Thus, degenerate points coincide with semi-smooth points. Furthermore, there are some special features at the degenerate points: the local time at these points are zero, and the process can only move toward one direction. Therefore, the effect of semi-smoothness of a function can be ignored at these degenerate points in the Ito-Tanaka formula. With these special features in consideration, various optimization problems such as long-run average, finite-horizon, optimal stopping, and singular control, become simpler.

In this chapter, we study optimization problems with diffusion processes for long-run average, finite-horizon, optimal stopping, and singular control. The value function for finite-horizon problems, or the potential function for long-run average, can be smooth or semi-smooth (both one-sided first-order derivatives exist, but not equal). Explicit optimality conditions are derived at both smooth and semi-smooth points. This extends the famous Hamilton-Jacobi-Bellman (HJB) equations from smooth value functions to semi-smooth value functions, which cover the degenerate diffusion processes. Viscosity solution is not used. The performance-difference formula is based on the Ito-Tanaka formula for semi-smooth functions, which involves local time in \([t, t+ dt]\) with a mean of the order of \(\sqrt{dt}\). We also show that under some conditions, the semi-smoothness of the value (or potential) functions can simply be ignored.

We address the long-standing problem of state classification and multiclass optimization of the time-nonhomogeneous continuous-time and continuous-state Markov processes (CTCSMPs). The fundamental property required for state classification is weak ergodicity, with which the state space can be grouped into multiple classes of weak ergodic and branching states. The fundamental property for performance optimization is the state comparability. Optimality conditions are derived for long-run average problems for multiclass CTCSMPs; they take the same form as those for discrete-state Markov processes. It is shown that a stochastic diffusion process is separated by degenerate points into multiple classes. The results also cover the underselectivity issue for long-run average and optimization with nonsmooth value functions. The problem is solved by the relative optimization approach that has been successfully applied to many optimization problems that are not very amenable to dynamic programming.

We prove that for a number of optimal control problems, including finite horizon, long-run average, and optimal stopping, with one-dimensional degenerate diffusion processes, the potential function (solution to Poisson equation) and, hence, the value function (solution to HJB equation) are semismooth at the degenerate points (i.e., the left-and right-hand side derivatives exist but may not be equal). This allows applying the Ito-Tanaka formula in the direct-comparison-based optimization approach, and previous results on semismooth value functions depend heavily on this property. This result will facilitate further research in stochastic optimal control.

The stochastic calculus of non-smooth functions indicates that for a continuous semi-martingale X(t), the changes of a function h[ X(t)] at its semi-smooth point (both right-and left-hand side derivatives exist) X(t) = x in [t, t + dt] is at the scale of the local time of X(t), with a mean of the order root dt in the case of Ito processes. We introduce the relative time which evolves at the scale of local time when the semi-martingale is at a semi-smooth point of h(x). The change of h[X(t)] in [t, t + dt] can be precisely measured in the scale of relative time, while this change is wrongly ignored with regular time scale dt. The optimal control problem is well defined with the regular time replaced by the relative time; however, dynamic programming does not seem work well for this problem. We apply the direct-comparison-based optimization approach to the control problem formulated in relative time and derive the generalized Hamilton-Jacobi-Bellman (HJB) equations, which consist of two parts, the classical HJB equation for smooth points, and some additional relations for semi-smooth points. Under some bounded conditions, the optimal value function is the (classical) solution to the generalized HJB equations, and viscosity solution is not needed. In addition, we show that the singular control problem can be formulated and solved in the same framework with the relative time.

The history of Perturbation Analysis (PA) is intimately related to that of Discrete Event Dynamic Systems (DEDS), starting with a solution of a long-standing problem in the late 1970s and continuing today with the control and optimization of Hybrid Systems and the emergence of event-driven control methods. We review the origins of the PA theory and how it became part of a broader framework for modelling, control and optimization of DEDS. We then discuss the theoretical underpinnings of Infinitesimal Perturbation Analysis (IPA) as a data-driven stochastic gradient estimation method and how it has been applied over the past few decades. We explain how IPA offers a basis for general-purpose stochastic optimization of Markovian systems through the notion of the performance potential and how it has evolved beyond DEDS and now provides a framework for control and optimization of Hybrid Systems and, more generally, event-driven methodologies.

Dear editor:I wish to echo the recent‘modest proposal’by Prof.Yu-Chi Ho on‘a Hippocratic Oath’for academicians of Chinese Academies of Sciences and of Engineering（Natl Sci Rev,2015,2:387）,and to provide additional comments and observations.First,I wish to emphasize that the academic community always has a fair consensus on a researcher’s achievement and

The area of discrete event systems (DES) was established in early 1980s; after more than three decades, it has developed into a mature area.This is evidenced by the healthy number of submissions and citations to our Journal.In the past few years, the number of yearly submissions has averaged about 65 and the number of yearly citations has been in the range of 260-292.Because of its special features, the DES area, as well as this Journal, is facing a number of challenges and opportunities.First, the area of DES deals with theories and applications of systems that are emerging in the new era of information technology; therefore, there is always a need to expand our arena and to accommodate newly emerging subjects.Second, as the founding Editor-in-Chief Yu-Chi (Larry) Ho put it in the inaugural editorial, the key to the answer to the question "Is the baby (journal) …going to be stunted in its development?"is: "Not if we maintain a problem-driven approach."The developments in the past 24 years provide the best answer to this question.However, the challenge is always there.The area of DES, or that of control and optimization in general, is facing the challenge that it does not "own" a problem domain; problem domains such as manufacturing, communication, networks, logistics, sensor networks, management, discrete event simulation, etc., have their own communities.In the past decade, we have maintained a close relationship with a number of major conferences in the DES or related areas, including WODES (International Workshop on Discrete Event Systems), ADHS (Analysis and Design of Hybrid Systems), MSR (Modeling of Reactive Systems), and other related conferences in computer science and operations research.This has allowed us to identify newly emerging topics at the frontier of DESrelated research and publish several special issues on topics such as hybrid systems, eventbased control and optimization, performance evaluation methodologies and tools, optimization of DES, and so forth.We also have created the new category of "short papers" for rapid publication of novel but perhaps not fully developed ideas.We are happy to see that many