Packing of Unequal Spheres and Automated Radiosurgical Treatment Planning

We study an optimization problem of packing unequal spheres into a three-dimensional (3D) bounded region in connection with radiosurgical treatment planning. Given an input (R, V, S, L), where R is a 3D bounded region, V a positive integer, S a multiset of spheres, and L a location constraint on spheres, we want to find a packing of R using the minimum number of spheres in S such that the covered volume is at least V; the location constraint L is satisfied; and the number of points on the boundary of R that are touched by spheres is maximized. Such a packing arrangement corresponds to an optimal radiosurgical treatment planning. Finding an optimal solution to the problem, however, is computationally intractable. In particular, we show that this optimization problem and several related problems are NP-hard. Hence, some form of approximations is needed. One approach is to consider a simplified problem under the assumption that spheres of arbitrary (integral) diameters are available with unlimited supply, and there are no location constraints. This approach has met with certain success in medical applications using a dynamic programming algorithm (Bourland and Wu, 1996; Wu, 1996). We propose in this paper an improvement to the algorithm that can greatly reduce its computation cost.     

Behavior in Multi‐Unit Demand Auctions: Experiments with Uniform Price and Dynamic Vickrey Auctions

We experimentally investigate the sensitivity of bidders demanding multiple units of a homogeneous commodity to the demand reduction incentives inherent in uniform price auctions. There is substantial demand reduction in both sealed bid and ascending price clock auctions with feedback regarding rivals' drop‐out prices. Although both auctions have the same normal form representation, bidding is much closer to equilibrium in the ascending price auctions. We explore the behavioral process underlying these differences along with dynamic Vickrey auctions designed to eliminate the inefficiencies resulting from demand reduction in the uniform price auctions.     

ECX碳排放期货与欧美股市联动性研究——基于DCC-MVGARCH模型的实证分析

碳排放交易是人类利用市场力量解决全球气候变暖问题的尝试,分析碳期货市场与资本市场的动态相关性,有利碳排放交易策略的制定。本文利用DCC-MVGARCH模型,分析主要股票市场与EU ETS碳排放期货价格的联动关系。实证结果表明,主要的股票市场对EU ETS期货价格具有直接或间接的联动关系,且是单方面的引导关系,印证了股市反映实体经济,实体经济的波动影响碳排放期货市场的需求这样一个动态联动性。     

Is There a Curse of Dimensionality for Contraction Fixed Points in the Worst Case?

This paper analyzes the complexity of the contraction fixed point problem: compute an ε‐approximation to the fixed point V*Γ(V*) of a contraction mapping Γ that maps a Banach space B_d of continuous functions of d variables into itself. We focus on quasi linear contractions where Γ is a nonlinear functional of a finite number of conditional expectation operators. This class includes contractive Fredholm integral equations that arise in asset pricing applications and the contractive Bellman equation from dynamic programming. In the absence of further restrictions on the domain of Γ, the quasi linear fixed point problem is subject to the curse of dimensionality, i.e., in the worst case the minimal number of function evaluations and arithmetic operations required to compute an ε‐approximation to a fixed point V*∈B_d increases exponentially in d. We show that the curse of dimensionality disappears if the domain of Γ has additional special structure. We identify a particular type of special structure for which the problem is strongly tractable even in the worst case, i.e., the number of function evaluations and arithmetic operations needed to compute an ε‐approximation of V* is bounded by Cε^−p where C and p are constants independent of d. We present examples of economic problems that have this type of special structure including a class of rational expectations asset pricing problems for which the optimal exponent p1 is nearly achieved.     

跨域环境治理的组合式协同机制与运作逻辑——长三角生态绿色一体化示范区的个案研究

在迈向中国式现代化的伟大征程中,环境治理现代化是中国式现代化的治理回应与检证载体。以“环境治理现代化”表征的这种中国式现代化是对现代性本身的再现代化,需要重新去认识和把握跨域环境治理模式的“现代”属性。从环境污染正在经历的由局部向广域转变的解域化过程来看,跨区域环境协同治理是多辖区间联结与互动的动态演化过程。既有研究已从多层面和多维度视域构建了跨域环境协同治理的理论框架,对于回答协同的应然状态以及如何锻造良好的协同秩序进行了叙事性再现和动态关联考察,但就协同进程中动力机制对协同结果的塑造作用探讨不乏“意犹未尽”之处。基于长三角一体化示范区环境协同治理,构建“理念-制度-实践”理论图式,并从触发机制、驱动机制和行动机制3个维度探索了开启跨域生态合作动力来源的机制之钥。研究发现,长三角一体化示范区在环境治理中的协同模式是典型的组合式协同,存在以系统协同牵引绿色协同的发展倾向,更具有不变体制变机制的内在属性,此种模式是长三角一体化示范区在激励约束与功能分割双重作用下的理性择定。“组合式协同”在应对长三角一体化示范区跨界环境污染问题上能够获得有效的合法性与合宪性回馈,并因其秉持共生、共进以及共...     

动态经济系统分析的经济计量模型与方法

综述可有效阐明动态经济系统长期关系和因果关系的因果测度理论. 首先简要介绍多变 量时间序列的协整过程及与此相关的若干概念,并总结了在经济计量学领域评价较高的多变 量自回归模型的统计识别方法. 基于多变量时间序列协整过程的向量自回归模型,较详细讨论 了多变量时间序列间各种因果测度的定义及其沃尔德检验. 所述单方向因果测度及其统计检 验理论作为C1W. J . Granger 非因果性理论的扩张,不仅可以检验两组时间序列间的因果影响 存在与否,还可以定量描述影响的程度. 单方向因果测度理论为分析复杂经济系统提     

两阶段价格和需求变动产品的供应链协调

通过建立两阶段动态模型研究了价格和需求变动产品的供应链协调问题。首先建立了集中协调、分散无协调和分散收入共享协调三种模式下供应链的动态规划模型;证明价格和需求变动时供应链在不同模式下存在最优解,应用改进的收入共享契约可以协调供应链系统并取得集中协调供应链系统的绩效,并可实现供应链利润的任意分配;给出了协调契约参数的确定方法;讨论了价格、市场需求风险变化对供应链协调绩效及最优契约参数的影响;通过数值实验分析证明了改进的收入共享契约可以使系统各方共同承担风险及分享利润,使各方绩效达到Pareto最优。     

新能源汽车补贴政策与保有量影响研究:单位补贴、销售奖励与产品差异化

以提升新能源汽车市场保有量和整体质量的补贴政策为背景,建立包括政府、制造商、零售商和消费者在内的动态博弈模型,将产业数量目标、高质量发展目标及补贴预算约束等政策特征纳入模型,对单位补贴、销售奖励以及差异化单位补贴政策的影响进行理论研究发现：在确保政府补贴绩效为正的条件下,政府对制造商和消费者的单位补贴可增加新能源汽车的 市场需求量,并提高制造商和零售商的利润水平;叠加的销售奖励不仅可改善单位补贴的市场结果,还可提高政府补贴绩效.考虑汽车质量的差异化单位补贴在不降低市场需求总量的同时,可减少低质量车的需求量并增加高质量车的需求量.单位补贴的最优值主要由政府设定的数量目标和制造商单位成本决定,数量目标和单位成本越高,则单位补贴越高,但政府补贴绩效越低.     

Covariate handling approaches in combination with dynamic borrowing for hybrid control studies

Borrowing data from external control has been an appealing strategy for evidence synthesis when conducting randomized controlled trials (RCTs). Often named hybrid control trials, they leverage existing control data from clinical trials or potentially real-world data (RWD), enable trial designs to allocate more patients to the novel intervention arm, and improve the efficiency or lower the cost of the primary RCT. Several methods have been established and developed to borrow external control data, among which the propensity score methods and Bayesian dynamic borrowing framework play essential roles. Noticing the unique strengths of propensity score methods and Bayesian hierarchical models, we utilize both methods in a complementary manner to analyze hybrid control studies. In this article, we review methods including covariate adjustments, propensity score matching and weighting in combination with dynamic borrowing and compare the performance of these methods through comprehensive simulations. Different degrees of covariate imbalance and confounding are examined. Our findings suggested that the conventional covariate adjustment in combination with the Bayesian commensurate prior model provides the highest power with good type I error control under the investigated settings. It has desired performance especially under scenarios of different degrees of confounding. To estimate efficacy signals in the exploratory setting, the covariate adjustment method in combination with the Bayesian commensurate prior is recommended.     

基于多阶段随机规划模型的国债动态积极投资策略

本文提出国债组合投资的多阶段随机规划模型,导出基于未来利率市场不确定信息的具备动态调整特点的国债组合主动投资策略。该模型采用基于利率水平、斜率和曲率"三位一体"的离散情景树刻画未来利率期限结构动态演化过程,其中特别考虑了广义货币供给变动的影响;通过最小化国债组合收益的条件风险价值,对国债组合进行主动动态调整;同时兼顾国债投资安全性、流动性和收益性等要求,实现了国债组合投资管理中利率风险规避和收益能力的有效匹配。实证研究表明,与传统久期配比免疫模型相比,该模型确定的最优策略不仅能够为国债组合提供更强的抵御利率风险能力,而且能够稳步提升其收益空间,为金融机构实现国债投资的主动管理提供决策支持。