广义 $d$-$\rho$-$(\eta,\theta)$-type I 一致凸非可微多目标规划

In this puper, on the basis of notions of d-p-（η, θ）-invex function, type I function and univex function, we present new classes of generalized d-p-（η, θ）-type I univex functions. By using these new concepts, we obtain several sufficient optimality conditions for a feasible solution to be an efficient solution, and derive some Mond-Weir type duality results.     

Empirical Bayes Test for the Parameter of Rayleigh Distribution with Error of Measurement

For the data with error of measurement in historical samples, the empirical Bayes test rule for the parameter of Rayleigh distribution is constructed, and the asymptotically optimal property is obtained. It is shown that the convergence rate of the proposed EB test rule can be arbitrarily close to O（n-1/2） under suitable conditions.     

On sufficiency and duality for a class of interval-valued programming problems

In this paper, we are concerned with an interval-valued programming problem. Sufficient optimality conditions are established under generalized convex functions for a feasible solution to be an efficient solution. Appropriate duality theorems for Mond-Weir and Wolfe type duals are discussed in order to relate the efficient solutions of primal and dual programs.     

Average sample-path optimality for continuous-time Markov decision processes in Polish spaces

In this paper we study the average sample-path cost(ASPC) problem for continuous-time Markov decision processes in Polish spaces.To the best of our knowledge,this paper is a first attempt to study the ASPC criterion on continuous-time MDPs with Polish state and action spaces.The corresponding transition rates are allowed to be unbounded,and the cost rates may have neither upper nor lower bounds.Under some mild hypotheses,we prove the existence of ε(ε≥ 0)-ASPC optimal stationary policies based on two differe...     

Infinite horizon asymptotic average optimality for large-scale parallel server networks

We study infinite-horizon asymptotic average optimality for parallel server networks with multiple classes of jobs and multiple server pools in the Halfin–Whitt regime. Three control formulations are considered: (1) minimizing the queueing and idleness cost, (2) minimizing the queueing cost under constraints on idleness at each server pool, and (3) fairly allocating the idle servers among different server pools. For the third problem, we consider a class of bounded-queue, bounded-state (BQBS) stable networks, in which any moment of the state is bounded by that of the queue only (for both the limiting diffusion and diffusion-scaled state processes). We show that the optimal values for the diffusion-scaled state processes converge to the corresponding values of the ergodic control problems for the limiting diffusion. We present a family of state-dependent Markov balanced saturation policies (BSPs) that stabilize the controlled diffusion-scaled state processes. It is shown that under these policies, the diffusion-scaled state process is exponentially ergodic, provided that at least one class of jobs has a positive abandonment rate. We also establish useful moment bounds, and study the ergodic properties of the diffusion-scaled state processes, which play a crucial role in proving the asymptotic optimality.     

Model-adaptive optimal discretization of stochastic integrals*

We study the optimal discretization error of stochastic integrals driven by a multidimensional continuous Brownian semimartingale. In the previous works a pathwise lower bound for the renormalized quadratic variation of the error was provided together with an asymptotically optimal discretization strategy, i.e. for which the lower bound is attained. However the construction of the optimal strategy involved the knowledge about the diffusion coefficient of the semimartingaleunder study. In this work we provide a model-adaptive asymptotically optimal discretization strategy that does not require any prior knowledge about the model. We prove the optimality for quite general class of discretization strategies based on kernel techniques for adaptive estimation and previously obtained optimal strategies that use random ellipsoid hitting times.     

OPTIMAL CONTROL PROBLEM OF PARABOLIC DIFFERENTIAL EQUATION WITH TWO POINT BOUNDARY CONDITION

This paper deals with optimal control problem of parabolic differential equation with two point boundary conditions (in the time variable). The results here extend those in [3] on optimal control of the heat equations. Moreover, the technique used in this paper is based on some smooth approximations of “tangent cones” in the sense of Clarke and some maximal monotone operators.     

时变种群扩散系统最优生育率控制的非线性问题

本文讨论了一类时变种群扩散系统最优生育率控制的非线性问题，证明了最优生育率控制的存在性，给出了控制为最优的必要条件及其最优性组，本结果可为种群扩散系统最优控制问题的实际研究提供物理理论基础。     

Asymptotical optimality in cluster analysis

The problem of optimality and performance evaluation for cluster analysis procedures is investigated. For the situations where the classes are described by known or unknown prior probabilities and regular probability density functions with unknown parameters the asymptotic expansions of classification error probability are constructed. The results are illustrated for the case of well‐known Fisher classification model. Copyright © 1999 John Wiley & Sons, Ltd.     

The Eco-Evo Mandala: Simplifying Bacterioplankton Complexity into Ecohealth Signatures

The microbiome emits informative signals of biological organization and environmental pressure that aid ecosystem monitoring and prediction. Are the many signals reducible to a habitat-specific portfolio that characterizes ecosystem health? Does an optimally structured microbiome imply a resilient microbiome? To answer these questions, we applied our novel Eco-Evo Mandala to bacterioplankton data from four habitats within the Great Barrier Reef, to explore how patterns in community structure, function and genetics signal habitat-specific organization and departures from theoretical optimality. The Mandala revealed communities departing from optimality in habitat-specific ways, mostly along structural and functional traits related to bacterioplankton abundance and interaction distributions (reflected by ϵ and λ as power law and exponential distribution parameters), which are not linearly associated with each other. River and reef communities were similar in their relatively low abundance and interaction disorganization (low ϵ and λ) due to their protective structured habitats. On the contrary, lagoon and estuarine inshore reefs appeared the most disorganized due to the ocean temperature and biogeochemical stress. Phylogenetic distances (D) were minimally informative in characterizing bacterioplankton organization. However, dominant populations, such as Proteobacteria, Bacteroidetes, and Cyanobacteria, were largely responsible for community patterns, being generalists with a large functional gene repertoire (high D) that increases resilience. The relative balance of these populations was found to be habitat-specific and likely related to systemic environmental stress. The position on the Mandala along the three fundamental traits, as well as fluctuations in this ecological state, conveys information about the microbiome’s health (and likely ecosystem health considering bacteria-based multitrophic dependencies) as divergence from the expected relative optimality. The Eco-Evo Mandala emphasizes how habitat and the microbiome’s interaction network topology are first- and second-order factors for ecosystem health evaluation over taxonomic species richness. Unhealthy microbiome communities and unbalanced microbes are identified not by macroecological indicators but by mapping their impact on the collective proportion and distribution of interactions, which regulates the microbiome’s ecosystem function.