Stochastic Maximum Principle for Optimal Advertising Models with Delay and Non-Convex Control Spaces

In this paper we study optimal advertising problems that model the introduction of a new product into the market in the presence of carryover effects of the advertisement and with memory effects in the level of goodwill. In particular, we let the dynamics of the product goodwill to depend on the past, and also on past advertising efforts. We treat the problem by means of the stochastic Pontryagin maximum principle, that here is considered for a class of problems where in the state equation either the state or the control depend on the past. Moreover the control acts on the martingale term and the space of controls U can be chosen to be non-convex but now the space of controls U can be chosen to be non-convex. The maximum principle is thus formulated using a first-order adjoint Backward Stochastic Differential Equations (BSDEs), which can be explicitly computed due to the specific characteristics of the model, and a second-order adjoint relation.

Effective approach for conformal subarray design based on maximum entropy of planar mappings

In this paper,an effective algorithm for optimizing the subarray of conformal arrays is proposed.The method first divides theconformal array into several first-level subarrays.It uses the X algorithm to solve the feasible solution of first-level subarray tiling and employs the particle swarm algorithm to optimize the conformal array subarray tiling scheme with the maximum entropy of the planar mapping as the fitness function.Subsequently,convex optimization is applied to optimize the subarray amplitude phase.Data results verify that the method can effectively find the optimal conformal array tiling scheme.

Predicting Potential Distribution of Tibetan Spruce (Picea smithiana) in Qomolangma (Mount Everest) National Nature Preserve Using Maximum Entropy Niche-based Model

Tibetan spruce (Picea smithiana) is an endemic species of the Himalayas,and it distributes only in a re-stricted area with very low number.To address the lack of detailed distributional information,we used maximum en-tropy (Maxent) niche-based model to predict the species' potential distribution from limited occurrence-only records.The location data of P.smithiana,relative bioclimatic variables,vegetation data,digital elevation model (DEM),and the derived data were analyzed in Maxent.The receiver operating characteristic (ROC) curve was applied to assess the prediction accuracy.The Maxent jackknife test was performed to quantify the training gains from data layers and the response of P.smithiana distribution to four typical environmental variables was analyzed.Results show that the model performs well at the regional scale.There is a potential for continued expansion of P.smithiana population numbers and distribution in China.P.smithiana potentially distributes in the lower reaches of Gyirong Zangbo and Poiqu rivers in Gyirong and Nyalam counties in Qomolangma (Mount Everest) National Nature Preserve (QNNP),China.The species prefers warm temperate climate in mountain area and mainly distributes in needle-leaved evergreen closed to open forest and mixed forest along the river valley at relatively low altitudes of about 2000-3000 m.Model simulations suggest that distribution patterns of rare species with few species numbers can be well predicted by Max-ent.

The Application of a Grey Markov Model to Forecasting Annual Maximum Water Levels at Hydrological Stations

Compared with traditional real-time forecasting,this paper proposes a Grey Markov Model(GMM) to forecast the maximum water levels at hydrological stations in the estuary area.The GMM combines the Grey System and Markov theory into a higher precision model.The GMM takes advantage of the Grey System to predict the trend values and uses the Markov theory to forecast fluctuation values,and thus gives forecast results involving two aspects of information.The procedure for forecasting annul maximum water levels with the GMM contains five main steps:1) establish the GM(1,1) model based on the data series;2) estimate the trend values;3) establish a Markov Model based on relative error series;4) modify the relative errors caused in step 2,and then obtain the relative errors of the second order estimation;5) compare the results with measured data and estimate the accuracy.The historical water level records(from 1960 to 1992) at Yuqiao Hydrological Station in the estuary area of the Haihe River near Tianjin,China are utilized to calibrate and verify the proposed model according to the above steps.Every 25 years' data are regarded as a hydro-sequence.Eight groups of simulated results show reasonable agreement between the predicted values and the measured data.The GMM is also applied to the 10 other hydrological stations in the same estuary.The forecast results for all of the hydrological stations are good or acceptable.The feasibility and effectiveness of this new forecasting model have been proved in this paper.

AXIAL HEAT CONDUCTION MODEL TO PREDICT MAXIMUM HEAT REMOVE OF MINIATURE HEAT PIPE BASED ON GREY MODEL THEORY

Computer chip is always accompanied by the increase of heat dissipation and miniaturization. The miniature heat pipes are widely used in notebook computer to resolve the heat dissipation problems. Maximum heat removed model of miniature heat pipes building by grey model is presented. In order to know the foundation for modeling, the smooth grade of error examination is inquired and the accuracy of grey relational grade is verified. The model can be used to select a suitable heat pipes to solve electric heat problems in the future. Final results show that the grey model only needs four experiment data and its error value is less than 10%, further, it is better than computational fluid dynamics （CFD） model.

A MAXIMUM ENTROPY CHUNKING MODEL WITH N-FOLD TEMPLATE CORRECTION

This letter presents a new chunking method based on Maximum Entropy (ME) model with N-fold template correction model.First two types of machine learning models are described.Based on the analysis of the two models,then the chunking model which combines the profits of conditional probability model and rule based model is proposed.The selection of features and rule templates in the chunking model is discussed.Experimental results for the CoNLL-2000 corpus show that this approach achieves impressive accuracy in terms of the F-score:92.93%.Compared with the ME model and ME Markov model,the new chunking model achieves better performance.

Spatial-temporal Evolution and Determinants of the Belt and Road Initiative: A Maximum Entropy Gravity Model Approach

The spatial interaction model is an effective way to explore the geographical disparities inherent in the Belt and Road Initiative(BRI) by simulating spatial flows. The traditional gravity model implies the hypothesis of equilibrium points without any reference to when or how to achieve it. In this paper, a dynamic gravity model was established based on the Maximum Entropy(MaxEnt) theory to estimate and monitor the interconnection intensity and dynamic characters of bilateral relations. In order to detect the determinants of interconnection intensity, a Geodetector method was applied to identify and evaluate the determinants of spatial networks in five dimensions. The empirical study clearly demonstrates a heterogeneous and non-circular spatial structure. The main driving forces of spatial-temporal evolution are foreign direct investment, tourism and railway infrastructure construction, while determinants in different sub-regions show obvious spatial differentiation. Southeast Asian countries are typically multi-island area where aviation infrastructure plays a more important role. North and Central Asian countries regard oil as a pillar industry where power and port facilities have a greater impact on the interconnection. While Western Asian countries are mostly influenced by the railway infrastructure, Eastern European countries already have relatively robust infrastructure where tariff policies provide a greater impetus.

A New Detection Approach Based on the Maximum Entropy Model

The maximum entropy model was introduced and a new intrusion detection approach based on the maximum entropy model was proposed. The vector space model was adopted for data presentation. The minimal entropy partitioning method was utilized for attribute diseretization. Experiments on the KDD CUP 1999 standard data set were designed and the experimental results were shown. The receiver operating eharaeteristie（ROC） curve analysis approach was utilized to analyze the experimental results. The analysis results show that the proposed approach is comparable to those based on support vector maehine（SVM） and outperforms those based on C4.5 and Naive Bayes classifiers. According to the overall evaluation result, the proposed approach is a little better than those based on SVM.

Video segmentation using Maximum Entropy Model

Detecting objects of interest from a video sequence is a fundamental and critical task in automated visual surveillance. Most current approaches only focus on discriminating moving objects by background subtraction whether or not the objects of interest can be moving or stationary. In this paper, we propose layers segmentation to detect both moving and stationary target objects from surveillance video. We extend the Maximum Entropy (ME) statistical model to segment layers with features, which are collected by constructing a codebook with a set of codewords for each pixel. We also indicate how the training models are used for the discrimination of target objects in surveillance video. Our experimental results are presented in terms of the success rate and the segmenting precision.

Prediction of the global potential geographical distribution of Hylurgus ligniperda using a maximum entropy model

Background: Hylurgus ligniperda(Fabricius) is native to Europe but has established populations in many countries and regions. H. ligniperda mainly infests Pinus species, and can cause severe weakness and even death of the host through its boring activity;it can also be a vector of various pathogenic fungi. This study was conducted to investigate the environmental variables limiting the distribution of H. ligniperda and the change trend of its suitable areas under climate change.Results: We used a maximum entropy model to predict the potential geographical distribution of H. ligniperda on a global scale under near current and future climatic scenarios using its occurrence data and environmental variables. The result shows that the areas surrounding the Mediterranean region, the eastern coastal areas of Asia, and the southeastern part of Oceania are highly suitable for H. ligniperda. The environmental variables with the greatest effect on the distribution of H. ligniperda were determined using the jackknife method and Pearson’s correlation analysis and included the monthly average maximum temperature in April, precipitation of driest quarter, the monthly average minimum temperature in December, precipitation of coldest quarter, mean temperature of driest quarter and mean diurnal range.Conclusions: Excessive precipitation in winter and low temperatures in spring had a great effect on the distribution of H. ligniperda. The potential geographical distribution of H. ligniperda was predicted to change under future climatic conditions compared with near current climate conditions. Highly suitable areas, moderately suitable areas and low suitable areas were predicted to increase by 59.99%, 44.43% and 22.92%, respectively, under the2081–2100 ssp245 scenario.

Asymptotic Comparison of Method of Moments Estimators and Maximum Likelihood Estimators of Parameters in Zero-Inflated Poisson Model

This paper discusses the estimation of parameters in the zero-inflated Poisson (ZIP) model by the method of moments. The method of moments estimators (MMEs) are analytically compared with the maximum likelihood estimators (MLEs). The results of a modest simulation study are presented.

RESEARCH OF PINYIN-TO-CHARACTER CONVERSION BASED ON MAXIMUM ENTROPY MODEL

This paper applied Maximum Entropy (ME) model to Pinyin-To-Character (PTC) conversion in-stead of Hidden Markov Model (HMM) that could not include complicated and long-distance lexical informa-tion. Two ME models were built based on simple and complex templates respectively, and the complex one gave better conversion result. Furthermore, conversion trigger pair of y A → y B cBwas proposed to extract the long-distance constrain feature from the corpus; and then Average Mutual Information (AMI) was used to se-lect conversion trigger pair features which were added to the ME model. The experiment shows that conver-sion error of the ME with conversion trigger pairs is reduced by 4% on a small training corpus, comparing with HMM smoothed by absolute smoothing.

Constructing Confidence Regions for Autoregressive-Model Parameters

We discuss formulas and techniques for finding maximum-likelihood estimators of parameters of autoregressive (with particular emphasis on Markov and Yule) models, computing their asymptotic variance-covariance matrix and displaying the resulting confidence regions;Monte Carlo simulation is then used to establish the accuracy of the corresponding level of confidence. The results indicate that a direct application of the Central Limit Theorem yields errors too large to be acceptable;instead, we recommend using a technique based directly on the natural logarithm of the likelihood function, verifying its substantially higher accuracy. Our study is then extended to the case of estimating only a subset of a model’s parameters, when the remaining ones (called nuisance) are of no interest to us.

Rate of strong consistency of the maximum quasi-likelihood estimator in quasi-likelihood nonlinear models

Quasi-likelihood nonlinear models （QLNM） include generalized linear models as a special case. Under some regularity conditions, the rate of the strong consistency of the maximum quasi-likelihood estimation （MQLE） is obtained in QLNM. In an important case, this rate is O（n-^1/2（loglogn）^1/2）, which is just the rate of LIL of partial sums for i.i.d variables, and thus cannot be improved anymore.

基于CAN和REST物联网技术的智能矿山安全检测系统研发

针对矿井安全生产检测数据传输效率低下和共享性差的特点,综合考虑开发成本与工作环境要求,基于CAN(Controller Area Network)和REST(Representational State Transfer)物联网技术提出了智能矿山安全检测方法,设计了矿山安全检测判别程序,采用最大熵模型算法开发了数据信息预警程序。结合CAN总线技术,将多传感器信息进行有机融合并进行安全数据检测,将井下传感器设备相关信息经过判断分析后传输至总机。将所提安全检测方法进行了系统开发,并在淮北某矿进行了应用。结果表明:基于CAN和REST物联网技术的安全检测方法能够实现多点测量,并可随机增减检测设备,可实现数据实时传输和共享,有助于实现矿山安全实时检测。

Weighted Maximum Likelihood Technique for Logistic Regression

In this paper, a weighted maximum likelihood technique (WMLT) for the logistic regression model is presented. This method depended on a weight function that is continuously adaptable using Mahalanobis distances for predictor variables. Under the model, the asymptotic consistency of the suggested estimator is demonstrated and properties of finite-sample are also investigated via simulation. In simulation studies and real data sets, it is observed that the newly proposed technique demonstrated the greatest performance among all estimators compared.

高可靠舰船装备软件可靠性的两阶段验证方案

针对高可靠舰船装备软件可靠性验证存在的测试周期长、测试剖面难以准确反映真实使用环境等问题,提出了一种两阶段可靠性验证方案。首先,在研发阶段对软件提出可靠性要求,并基于该阶段产生的可靠性增长测试信息,利用软件可靠性增长模型评估软件可靠性水平,验证其是否达到规定的可靠性要求;然后,基于最大后验风险制定贝叶斯验证方案,并在软件试用阶段利用用户现场使用信息验证软件可靠性。实例分析结果表明:所提的两阶段验证方案能缩短软件可靠性验证时长、方便工程实施;利用用户现场使用信息给出验证结论,使结论具备较高的可信性。

基于混合建模的新型微槽刀具外冷通道结构优化设计

这里提出了一种有限元法(FEM)和计算流体力学(CFD)的混合建模方法。通过单因素试验生成响应曲面,分析了喷嘴的直径、角度、压力对刀具最高温度的单因素和交互影响规律。采用正交试验设计方法,以刀具最高温度为评价指标,以微流道的截面形状、宽度,深度和微流道分布的角度为影响因素,通过仿真分析,研究以上四个因素对刀具降温的影响。研究表明,截面宽度较大的矩形微流道对刀具降温效果较好,微流道的角度、深度影响次之,微流道的形状影响最小。通过对模型的验证,证明了模型的有效性。

三种PTFs方法获取的侵蚀黑土水分特征曲线的比较

采用3种土壤转换方程(PTFs)获取不同侵蚀程度黑土的土壤水分特征曲线(SWCC),并与实测数据进行了比较,以选择适合黑土SWCC间接获取的PTFs方法。以4种不同侵蚀程度的黑土为供试土壤,采用常用的PTFs计算机模型:Rosetta3、CalcPTF和以最大吸湿量为残余含水量(θ_(r))发展的PTFs方法(编号:PTFs3),进行了SWCC的van Genuchten (VG)模型参数的预报。Rosetta3模型的输入参数包括土壤机械组成、土壤密度、33 kPa压力下的土壤含水率(θ_(33 kPa))和1 500 kPa压力下土壤含水量(θ_(1 500 kPa));CalcPTF模型的输入参数包括土壤机械组成、土壤密度和有机碳含量;PTFs3的输入参数包括饱和含水量(θ_(0))、最大吸湿量(θ_(97%RH))、θ_(33 kPa)和θ_(1 500 kPa)。将上述3种方法获取的参数带入VG模型,得出供试土壤在不同水吸力下的土壤含水量,并与实测结果进行对比。结果显示,使用3种PTFs模型输出参数的VG模型预报值与实测值都有极显著的相关性,总体计算结果与实测结果也比较接近。PTFs3预报值与实测值的差值在±0.05 cm^(3)/cm^(3)内;CalcPTF-Var模型差值在-0.08~0.05 cm^(3)/cm^(3)之间;而Rosetta3模型的差值在-0.10~0.06 cm^(3)/cm^(3)之间。在土壤含水率压力小于33 kPa情况下时,SWCC差值相对较大。Rosetta3和PTFs3因为有θ_(33 kPa)和θ_(1 500 kPa)两点的水分进行校正,精确性比较可控,效果优于CalcPTF-Var。预报值与实测值差异的百分比也说明了这一点。具体到每个供试土壤样本,3种PTFs对剧烈侵蚀的黑土预报偏差百分比都较大,但PTFs3表现较优于其他两种模型。CalcPTF-Var在微度侵蚀样本S1的模拟上也出现了相对较大的偏差。综上,PTFs3模型是一种比较适合预报黑土SWCC的VG模型参数的PTFs方法。Rosetta3模型误差主要来源于较严重的低估了≤1 kPa SWCC的土壤含水量,而高估了6~33 kPa的土壤含水量。仅输入土壤理化性质的CalcPTF-Var模型需注意在部分黑土样本上的较大偏差。

考虑微裂纹力学行为的岩石单轴压缩损伤模型

针对目前岩石压缩损伤模型未能很好地同时考虑微裂纹滑移与扩展对岩石总变形的贡献、微裂纹复合扩展准则及岩石损伤程度对被激活裂纹数量影响等不足,基于细观力学对微裂纹在单轴压缩荷载下的滑移及扩展机理展开研究。首先根据微裂纹滑移模型及能量平衡原理,建立了岩石单轴压缩应力应变关系,并认为微裂纹服从Weibull分布模型;进而以应变能密度准则作为微裂隙扩展判据,采用迭代法求解复合型断裂的翼裂纹扩展长度,并获得用翼裂纹扩展长度表示的岩石损伤变量演化方程,由此提出了一个新的岩石单轴压缩损伤模型,并验证了其合理性;最后,采用参数敏感性分析研究了微裂纹长度及摩擦系数和岩石断裂韧度对岩石力学特性的影响。结果表明:由本模型预测得到的岩石单轴压缩峰值强度与试验结果吻合较好,说明了其合理性。同时发现随着微裂纹长度增加及其摩擦系数减小、岩石断裂韧度增加,岩石单轴抗压峰值强度及峰值应变均随之减小。当微裂纹长度由60μm增加到120μm时,岩石单轴抗压峰值强度近似线性降低;而当微裂纹摩擦系数由0.5增加到0.8及岩石断裂韧度由0.3 MPa·m^(1/2)增加到0.6 MPa·m1/2时,岩石单轴抗压峰值强度均是先缓慢增加,而后迅速增加。本研究为岩石压缩损伤本构模型的建立提供了一条新的思路,具有重要的理论意义。