Entropy Maximization and Geometric Programming

This paper surveys the main developments in the area of sensitivity analysis for geometric programming problems, including both the theoretical and computational aspects. It presents results which characterize solution existence, continuity, and differentiability properties for primal and dual geometric programs as well as the optimal value function differentiability properties for primal and dual programs. It also provides an overview of main computational approaches to sensitivity analysis in geometric programming which attempt to estimate new optimal solutions resulting from perturbations in some problem parameters.

The calculation of the composition of a reacting mixture when it reaches equilibrium can be regarded as a dual Geometric Program; there is a related primal Geometric Program with fewer variables than the dual. Both primal and dual formulations were compared using the Generalized Reduced Gradient (GRG) algorithm for systems containing 8, 10 and 24 reacting species. The primal proved to be faster (30%) than the dual, and more robust.A sensitivity analysis method suggested by Rijckaert (1974) was tested and the results were compared with re‐solving the original problem. Sensitivity analysis was faster than re‐optimization (50%) but the accuracy of the results depended strongly on the particular problem.

The entropy model has attached a good deal of attention in transportation analysis, urban and regional planning as well as in other areas. This paper shows the equivalence of entropy maximization models to geometric programs. To provide a better understanding of this entropy based transportation model they are analyzed by geometric programming. Dual mathematical programs and algorithms are also obtained and are supported by an illustrative example. .

Geometric programming is now a well-established branch of optimization theory which has its origin in the analysis of posynomial programs. Geometric programming transforms a mathematical program with nonlinear objective function and nonlinear inequality constraints into a dual problem with nonlinear objective function and linear constraints. Although the dual problem is potentially simpler to solve, there are certain computational difficulties to be overcome. The gradient of the dual objective function is not defined for components whose values are zero. Moreover, certain dual variables may be constrained to be zero (geometric programming degeneracy).To resolve these problems, a means to find a solution in the relative interior of a set of linear equalities and inequalities is developed. It is then applied to the analysis of dual geometric programs.

The theme of this paper is the application of linear analysis to simplify and extend convex analysis. The central problem treated is the standard convex program — minimize a convex function subject to inequality constraints on other convex functions. The present approach uses the support planes of the constraint region to transform the convex program into an equivalent linear program. Then the duality theory of infinite linear programming shows how to construct a new dual program of bilinear type. When this dual program is transformed back into the convex function formulation it concerns the minimax of an unconstrained Lagrange function. This result is somewhat similar to the Kuhn—Tucker theorem. However, no constraint qualifications are needed and yet perfect duality maintains between the primal and dual programs.

Simulation and analysis of red-crowned crane habitat suitability using maximum entropy and information entropy models

Empirical evidence of scaling behaviors in neuronal avalanches suggests that neuronal populations in the brain operate near criticality. Departure from scaling in neuronal avalanches has been used as a measure of distance to criticality and linked to brain disorders. A distinct line of evidence for brain criticality has come from thermodynamic signatures in maximum entropy (ME) models. Both of these approaches have been widely applied to the analysis of neuronal data. However, the relationship between deviations from avalanche criticality and thermodynamics of ME models of neuronal populations remains poorly understood. To address this question, we study spontaneous activity of organotypic rat cortex slice cultures in physiological and drug-induced hypo- or hyper-excitable conditions, which are classified as critical, subcritical and supercritical based on avalanche dynamics. We find that ME models inferred from critical cultures show signatures of criticality in thermodynamic quantities, e.g. specific heat. However, such signatures are also present, and equally strong, in models inferred from supercritical cultures—despite their altered dynamics and poor functional performance. On the contrary, ME models inferred from subcritical cultures do not show thermodynamic hints of criticality. Importantly, we confirm these results using an interpretable neural network model that can be tuned to and away from avalanche criticality. Our findings indicate that maximum entropy models correctly distinguish subcritical from critical/supercritical systems. However, they may not be able to discriminate between avalanche criticality and supercriticality, although they may still capture a number of important features from neuronal data.

We propose a novel joint pricing and lot sizing model to enable manufacturers plan production and pricing. These types of models have proven to be very popular and are collectively known as the Joint Pricing and Lot sizing Models. We include a discount factor in our model to increase profit for the manufacturer. Our proposed model relies on the fact that demand influences production cost indirectly, while it is dependent on price and the discount offered. By considering the form of demand and production cost, it is apparent that the presented model is a Signomial Geometric Programming problem. We obtain optimal solutions for price, lot size and discount factor by applying the modified transformation method of geometric programming. Numerical examples, which include sensitivity analysis of the objective function and parameters, illustrate our model. References C. J. Corbett and X. de Groote. A supplier's optimal quantity discount policy under asymmetric information. Management Science, 46(3):444--450, 2000. R. J Duffin, E. L Peterson, and C. Zener. Geometric programming, Theory and Application. John Wiely and Sons, 1967. J. R. Freeland. Coordination strategies for production and marketing in a functionally decentralized firm. AIIE Transactions, 12:126--132, 1982. Woon J.Lee, Daesoo Kim, and A. Cabot. Optimal demand rate, lot sizing, and process reliability improvement decisions. IIE Transactions, 28:941--952, 1996. http://cat.inist.fr/?aModele=afficheN&cpsidt=2490704. Daesoo Kim and Woon J. Lee. Optimal joint pricing and lot sizing with fixed and variable capacity. European Journal of Operational Research, 109(1):212--227, 1998. http://www.sciencedirect.com/science/article/B6VCT-3TMR6M6-H/2/2d166a9b5fc0a9a27e923c495f256663. Woon J. Lee. Determining order quantity and selling price by geometric programming. Decision Sciences, 24:76--87, 1993. doi:10.1111/j.1540-5915.1993.tb00463.x. Woon J. Lee and Daesoo Kim. Optimal and heuristic decision strategies for integrated product and marketing planning. Decision Sciences, 24(6):1203--1213, 1993, doi:10.1111/j.1540-5915.1993.tb00511.x. Seyed J. Sajadi, Maryam Orouge, and M. B. Aryanezhad. Optimal production and marketing planning. Computational Optimization and Applications, 30(2):195--203, 2005. http://portal.acm.org/citation.cfm?id=1062644.1062668. Richard J. Tersine. Principles of Inventory And Materials Management. PTR Prentice Hall, Englewood Cliffs, New Jersey 07632, 1994. S. Viswanathan and Q.Wang. Discount pricing decisions in distribution channels with price sensitive demand. European Journal of Operational Research, 149(3):571--587, 2003. http://ideas.repec.org/a/eee/ejores/v149y2003i3p571-587.html. Prakash L. Abad. Determining optimal selling price and the lot size when the supplier offers all-unit quantity discounts. Decision Sciences, 3(19):622--634, 1988. Z. Kevin Weng. Channel coordination and quantity discounts. Management Sciences, 41(9):1509--1522, 1995. http://www.jstor.org/view/00251909/di012962/01p03025/0. Prakash L. Abad. Supplier pricing and lot sizing when demand is price sensitive. European Journal of Operational Research, (78):334--354, 1994. http://cat.inist.fr/?aModele=afficheN&cpsidt=3309143. Charles S. Beightler. Applied Geometric Programming. John Wiely and Sons, 1976. C. W. Chiang, J. Fitzsimmons, Z. Huang, and S. Li. A game theoretic approach to quantity discount problem. Decision Sciences, 25(1):153--168, 1994. doi:10.1111/j.1540-5915.1994.tb00521.x.

In a channel distribution system, the function of an intermediate firm is to purchase products and to sell those purchased products to the public or to other firms. In this paper, for the intermediate firms, an inventory model under return-on-inventory-investment maximization is proposed to determine optimally the quality level, the selling quantity and the purchasing price of a product. The selling price and the supply rate of the product as well as the fixed selling cost are assumed to be power functions of one or more of the decision variables. Under this assumption, the global optimal closed-form solution is derived for the inventory model by utilizing geometric programming techniques. In addition, sensitivity analyses on primal and dual geometric programming problems for the inventory model are presented.

We propose a probabilistic model for estimating word confidence by fusing predictor features. Starting from the maximum entropy (ME) method, we first prove that ME model is equivalent to the best model with certain form to the minimum expected cross entropy (MECE) criterion. Under the MECE criterion, We extend the form of ME model by introducing a hidden state. We call the new model hidden-state maximum entropy (HSME) model. In a keyword-spotting task, we combine predictor features from both phonetic and word-level systems. Compared to lattice posterior alone, recall at 80% precision is improved from 38.1% to 49.5% on voicemail and from 37.1% to 51.9% on Switchboard. Compared with other fusion methods, HSME consistently outperforms decision tree, and most cases SVM.

Climate change impacts on tropical forests and tree species have been documented as changes in distribution, growing period, phenology, habitat, productivity, species composition, and migration. This study attempts to assess the current and future habitat suitability distribution of two dominant species of Central India, teak (Tectona grandis Linn. f.) and sal (Shorea robusta Gaertn. f.) using a maximum entropy (MaxEnt) model to predict species occurrences by finding the distribution that has the most spread. The future suitable habitat ranges of the species were modeled for two time periods (2050 and 2070) and two representative concentration pathways (RCP 2.6 and 8.5). Representative concentration pathways are scenarios that describe alternative trajectories for carbon dioxide emissions and the resulting atmospheric concentration from 2000 to 2100. We collected and modeled the spatially well-dispersed species occurrence points of teak and sal. The results suggested an increase in suitable habitat range for teak and a decrease for sal for both time periods and RCPs. Furthermore, the jackknife analysis identified temperature and precipitation seasonality as the major variables that influence the distribution of teak. In the case of sal, minimum temperature makes the maximum contribution to distribution changes. The suitable silvicultural strategies for forest management are proposed based on the future distribution of species in relation to the climate variables responsible for the change in their distribution range. These findings and strategies will help forest departments build future management plans for teak and sal forest with a focus on minimizing the impact of climate change. Study Implications: Our study used maximum entropy (MaxEnt) modeling to understand the impact of changing climate on the distribution of teak and sal forests of central India and to propose future silvicultural strategies. The study used MaxEnt model for two time periods and two climate change scenarios at highest resolution. An increase in future suitable habitat for teak and a decrease for sal is predicted by the model. Temperature for teak and precipitation for sal were identified as the major influencing climatic variables. We recommend forest and other related government departments to commission focused research to understand the changing patterns of species with climate change and design appropriate silviculture strategies for effective management.

Intrusion detection is a critical component of secure information systems. Current intrusion detection systems (IDS) especially NIDS (Network Intrusion Detection System) examine all data features to detect intrusions. However, some of the features may be redundant or contribute little to the detection process and therefore they have great impact on the system performance. This paper proposes a lightweight intrusion detection model that is computationally efficient and effective based on feature selection and Maximum Entropy (ME) model. Firstly, the issue of identifying important input features is addressed. Since elimination of the insignificant and/or useless inputs leads to a simplification of the problem, therefore results to faster and more accurate detection. Secondly, classic ME model is used to learn and detect intrusions using the selected important features. Experimental results on the well-known KDD 1999 dataset show the proposed model is effective and can be applied to real-time intrusion detection environments.

PDF HTML阅读 XML下载 导出引用 引用提醒 气候变化情景下基于最大熵模型的青海云杉潜在分布格局模拟 DOI: 10.5846/stxb201809151999 作者: 作者单位: 甘肃农业大学林学院,兰州大学生命科学学院,甘肃农业大学林学院,甘肃农业大学林学院 作者简介: 通讯作者: 中图分类号: 基金项目: 甘肃农业大学科技创新基金-公招博士科研启动基金项目（GSAU-RCZX01707）；学科建设专项基金项目（GAU-XKJS-2018-099）；国家自然基金项目（31860197） Simulation of the potential distribution patterns of Picea crassifolia in climate change scenarios based on the maximum entropy (Maxent) model Author: Affiliation: Gansu Agricultural University, Lanzhou 730070 Fund Project: 摘要 | 图/表 | 访问统计 | 参考文献 | 相似文献 | 引证文献 | 资源附件 | 文章评论 摘要:青海云杉（Picea crassifolia）是我国青藏高原东北缘特有树种，在维系我国西北地区生态平衡、水土保持、水源涵养和生物多样性等方面发挥着重要作用。基于其分布范围内的69个地理分布样点，利用最大熵（Maxent）模型对现实气候条件下青海云杉的潜在分布及其分布的主导气候因子进行分析，同时结合3种大气环流模型模拟青海云杉在3种气候变化情景（温室气候排放量不同）下未来2050s和2080s潜在分布区的变化。结果表明：Maxent模型对青海云杉潜在分布区的预测具有极高的准确度，所有模型的平均受试者工作特征曲线下面积（AUC测试值）均高于0.99；Jackknife检验和气候因子响应曲线表明年最低降雨量是限制青海云杉分布的主导因子；当前青海云杉的潜在分布区主要集中于青海东部、甘肃东南部、宁夏大部分地区、西藏东部、四川西部山区以及陕西、新疆和内蒙古部分地区。在未来3种增温情景下，青海云杉在2050s和2080s的潜在分布总面积与当前相比变化不明显，但不同适生等级的潜在分布面积变化较大，其中，中度适生区和低度适生区受气候增温影响显著，中度增温下这些区域在2080s的面积明显增大，而高度适生区（核心分布）则在所有增温情景下均呈缩小趋势。同时，在未来3种增温情景下，青海云杉在2050s和2080s的潜在分布区有向北移动趋势，但其心分布区域（高度适生区）仍然以青海东部、甘肃北部为主，无明显变迁趋势。从气候因素角度考虑，本研究表明未来气候变化情景下，青海云杉依然在西部高山地区，特别是作为我国重要生态屏障的祁连山、贺兰山等山区具有重要的经济价值并将持续其生态服务功能。 Abstract:Qinghai spruce (Picea crassifolia) is the endemic tree species in the northeastern margin of the Qinghai-Tibet Plateau (QTP) in China. It plays an important role in maintaining ecological balance, biodiversity, and soil and water conservation in northwestern China. In this study, the current potential distribution of Qinghai spruce and its dominant climatic factors were analyzed firstly based on 69 distributional records via the maximum entropy model (Maxent). Then the distribution patterns of Qinghai spruce under three climate change scenarios (i.e., the lowest, a moderate, and the highest greenhouse gas emission scenarios; RCP2.6, RCP4.5 and RCP8.5) with three general atmospheric circulation models were predicted by Maxent for two future decades:the 2050s and 2080s. The results showed that the accuracy of the Maxent model was pretty high for modeling potential distribution regions of Qinghai spruce, and the average values of the area under the receiver operator characteristic curve (AUC) were higher than 0.99. The results from the Jackknife test and climate factor response curves revealed that the annual lowest precipitation is the key factor that limited the distribution of Qinghai spruce; the current potential distribution regions of Qinghai spruce are mainly concentrated in eastern Qinghai, southeastern Gansu, most of Ningxia, eastern Tibet, mountainous areas of western Sichuan, and parts of Shaanxi, Xinjiang, and Inner Mongolia. The total potential distribution area of Qinghai spruce in the 2050s and 2080s was changed little compared to the current distribution in all three scenarios, but its potential distribution area at different levels of fitness was changed a lot. Among them, the regions with fitness of less than 0.1 and in the range of 0.1-0.3 were significantly affected by the climate changes, and their area was largely increased in the medium emission scenario. In contrast, the regions with fitness in the range of 0.5-0.8 were shrunk in all scenarios. At the same time, the distribution patterns of Qinghai spruce in the 2050s and 2080s had a tendency to move northward in all scenarios, whereas its central distributional regions (more suitable regions) were still kept in eastern Qinghai and northern Gansu, with no obvious trend to change. From the perspective of climatic factors, this study showed that Qinghai spruce would continue to have important economic values and ecological service functions in the western mountains, especially in the Qilian Mountains and Helan Mountains, which are the important ecological barriers in China. 参考文献 相似文献 引证文献

While radiologists regularly issue follow-up recommendations, our preliminary research has shown that anywhere from 35 to 50% of patients who receive follow-up recommendations for findings of possible cancer on abdominopelvic imaging do not return for follow-up. As such, they remain at risk for adverse outcomes related to missed or delayed cancer diagnosis. In this study, we develop an algorithm to automatically detect free text radiology reports that have a follow-up recommendation using natural language processing (NLP) techniques and machine learning models. The data set used in this study consists of 6000 free text reports from the author's institution. NLP techniques are used to engineer 1500 features, which include the most informative unigrams, bigrams, and trigrams in the training corpus after performing tokenization and Porter stemming. On this data set, we train naive Bayes, decision tree, and maximum entropy models. The decision tree model, with an F1 score of 0.458 and accuracy of 0.862, outperforms both the naive Bayes (F1 score of 0.381) and maximum entropy (F1 score of 0.387) models. The models were analyzed to determine predictive features, with term frequency of n-grams such as "renal neoplasm" and "evalu with enhanc" being most predictive of a follow-up recommendation. Key to maximizing performance was feature engineering that extracts predictive information and appropriate selection of machine learning algorithms based on the feature set.

The convergence rates of generalized iterative scaling (GIS) and improved iterative scaling (IIS) algorithms for fitting maximum entropy (ME) models are investigated and also a particular linear dynamic system monitoring with partial active measurements is studied. An information-theoretic based measurement scheme is derived to select informative hidden states, which is validated on a problem of origin-destination matrix estimation for Internet traffic.