Is breaking of ensemble equivalence monotone in the number of constraints?

Breaking of ensemble equivalence between the microcanonical ensemble and the canonical ensemble may occur for random graphs whose size tends to infinity, and is signaled by a non-zero specific relative entropy between the two ensembles. In Garlaschelli et al. (2017) and Garlaschelli et al. (0000) it was shown that breaking occurs when the constraint is put on the degree sequence (configuration model). It is not known what is the effect on the relative entropy when the number of constraints is reduced, i.e., when only part of the nodes are constrained in their degree (and the remaining nodes are left unconstrained). Intuitively, the relative entropy is expected to decrease. However, this is not a trivial issue because when constraints are removed both the microcanonical ensemble and the canonical ensemble change. In this paper a formula for the relative entropy valid for generic discrete random structures, recently formulated by Squartini and Garlaschelli, is used to prove that the relative entropy is monotone in the number of constraints when the constraint is on the degrees of the nodes. It is further shown that the expression for the relative entropy corresponds, in the dense regime, to the degrees in the microcanonical ensemble being asymptotically multivariate Dirac and in the canonical ensemble being asymptotically Gaussian.     

Optimal uncertainty size in distributionally robust inverse covariance estimation

In a recent paper, Nguyen et al. (2018) built a distributionally robust estimator for the precision matrix of the Gaussian distribution. The distributional uncertainty size is a key ingredient in the construction of this estimator. We develop a statistical theory which shows how to optimally choose the uncertainty size to minimize the associated Stein loss. Surprisingly, rather than the expected canonical square-root scaling rate, the optimal uncertainty size scales linearly with the sample size.     

基于新巴塞尔协议监管下保险人的均值-方差最优投资-再保险问题

本文研究了均值-方差优化准则下,保险人的最优投资和最优再保险问题.我们用一个复合泊松过程模型来拟合保险人的风险过程,保险人可以投资无风险资产和价格服从跳跃-扩散过程的风险资产.此外保险人还可以购买新的业务(如再保险).本文的限制条件为投资和再保险策略均非负,即不允许卖空风险资产,且再保险的比例系数非负.除此之外,本文还引入了新巴塞尔协议对风险资产进行监管,使用随机二次线性(linear-quadratic,LQ)控制理论推导出最优值和最优策略.对应的哈密顿-雅克比-贝尔曼(Hamilton-Jacobi-Bellman,HJB)方程不再有古典解.在粘性解的框架下,我们给出了新的验证定理,并得到有效策略(最优投资策略和最优再保险策略)的显式解和有效前沿.     

Existence of solutions for integral inclusions of Urysohn type with nonconvex-valued orientor field

In this paper, we prove the existence of solutions for an integral inclusion of Urysohn type with nonconvex orientor field and with delay. We make standard boundedness and continuity assumptions on the data, and we assume that the orientor field is l.s.c. in the state variable. Using a selection theorem of Fryszkowski, we are able to prove the existence of solutions, extending an earlier result of Angell.This research was supported by NSF Grant No. DMS-86-02313.     

Effect of bias in ferroelectric-antiferroelectric relaxation

The ferroelectric-antiferroelectric transition in greyscale generation of antiferroelectric liquid crystal displays (AFLC) is a heterogeneous process. The process has been described as the growth of finger-like domains [1]. We have previously studied the ferroelectric-antiferroelectric phase transition, relaxation that follows the data pulse in surface stabilized asymmetric antiferroelectric liquid crystal displays using biasless video frequency waveforms [2]. This relaxation involves an intensity decay of the light transmitted by a pixel and depends on several parameters such as surface stabilization, rotational viscosity of the AFLC, magnitude of the data pulse, and bias voltage. The usual multiplexed driving of AFLC displays leads to long-term stabilisation of the grey levels induced by the data pulses within the selection time. However, depending on the bias level, alternative greyscale mechanisms may be obtained by allowing the grey levels to decay during the frametime. These greyscales may be advantageous in some instances since they improve the dynamic response of the AFLC device and reduce the reset time of the waveform. In this study we extend the previous work to include the effect of bias. We present the measured data, in terms of growth pattern and speed and present an extension of the previously model on order to explain the results.     

基于RS和SVM的动态供应链成员选择算法

良好的成员选择方法是动态供应链平稳运行的重要基础,针对动态供应链成员选择时面临决策属性多且可供决策分析数据样本少的难题,提出了基于粗糙集和支持向量机的动态供应链成员选择算法,核心是应用粗糙集进行属性约简,然后结合支持向量机进行链上成员分类.方法在保证不会降低分类性能的前提下,达到降低数据维数和分类过程中复杂度的目的.     

西范坪矿区土壤铜元素的高光谱响应与反演模型研究

为解决传统的土壤地球化学测量方法成本高、效率低等问题,研究了利用可见-近红外光谱技术检测土壤重金属含量的简易方法。研究对西范坪矿区土壤反射光谱进行微分、连续统去除等六种变换,利用逐步回归法和皮尔逊相关系数选出对土壤铜含量敏感的特征波段,组成综合特征变量集,再应用不同的特征变量选取方法和参数建立估算模型并检验。结果表明：不同的光谱变换方法对土壤铜含量信息提取能力不同,每种光谱变换都对应特定的敏感波谱区间;基于综合光谱变换信息建立的土壤铜含量反演模型精度优于基于单种光谱变换信息建立的模型;利用综合光谱变换信息建立土壤铜含量反演模型,后向剔除法优于前向引入法和逐步回归法,当Removal取0.20时得到最优回归模型,其模型决定系数R2和预测模型决定系数R2_pre分别达到了0.851和0.830,建模均方根误差RMSEC和预测均方根误差RMSEP分别为0.349和0.468 mg·kg-1,能较好地检测土壤铜含量,同时为其他土壤重金属元素的光谱检测提供了思路。     

Searching for a near neighbor particle in DSMC cells using pseudo-subcells

LeBeau et al. (2003) [4] introduced the ‘virtual-subcell’ (VSC) method of finding a collision partner for a given DSMC particle in a cell; all potential collision partners in the cell are examined to find the nearest neighbor, which becomes the collision partner. Here I propose a modification of the VSC method, the ‘pseudo-subcell’ (PSC) method, whereby the search for a collision partner stops whenever a ‘near-enough’ particle is found, i.e. whenever another particle is found within the ‘pseudo-subcell’ of radius δ centered on the first particle. The radius of the pseudo-subcell is given by δ = Fd_n, where d_n is the expected distance to the nearest neighbor and F is a constant which can be adjusted to give a desired trade-off between CPU time and accuracy as measured by a small mean collision separation (MCS). For 3D orthogonal cells, of various aspect ratios, d_n/L ≈ 0.746/N^0.383 where N is the number of particles in the cell and L is the cube root of the cell volume. There is a good chance that a particle will be found in the pseudo-subcell and there is a good chance that such a particle is in fact the nearest neighbor. If no particle is found within the pseudo-subcell the closest particle becomes the collision partner.     

On the Relationship Between Markov chain Monte Carlo Methods for Model Uncertainty

This article considers Markov chain computational methods for incorporating uncertainty about the dimension of a parameter when performing inference within a Bayesian setting. A general class of methods is proposed for performing such computations, based upon a product space representation of the problem which is similar to that of Carlin and Chib. It is shown that all of the existing algorithms for incorporation of model uncertainty into Markov chain Monte Carlo (MCMC) can be derived as special cases of this general class of methods. In particular, we show that the popular reversible jump method is obtained when a special form of Metropolis–Hastings (M–H) algorithm is applied to the product space. Furthermore, the Gibbs sampling method and the variable selection method are shown to derive straightforwardly from the general framework. We believe that these new relationships between methods, which were until now seen as diverse procedures, are an important aid to the understanding of MCMC model selection procedures and may assist in the future development of improved procedures. Our discussion also sheds some light upon the important issues of “pseudo-prior” selection in the case of the Carlin and Chib sampler and choice of proposal distribution in the case of reversible jump. Finally, we propose efficient reversible jump proposal schemes that take advantage of any analytic structure that may be present in the model. These proposal schemes are compared with a standard reversible jump scheme for the problem of model order uncertainty in autoregressive time series, demonstrating the improvements which can be achieved through careful choice of proposals.