A unified subdivision approach for multi-dimensional non-manifold modeling

This paper presents a new unified subdivision scheme that is defined over a k-simplicial complex in n-D space with k≤3. We first present a series of definitions to facilitate topological inquiries during the subdivision process. The scheme is derived from the double (k+1)-directional box splines over k-simplicial domains. Thus, it guarantees a certain level of smoothness in the limit on a regular mesh. The subdivision rules are modified by spatial averaging to guarantee C¹ smoothness near extraordinary cases. Within a single framework, we combine the subdivision rules that can produce 1-, 2-, and 3-manifolds in arbitrary n-D space. Possible solutions for non-manifold regions between the manifolds with different dimensions are suggested as a form of selective subdivision rules according to user preference. We briefly describe the subdivision matrix analysis to ensure a reasonable smoothness across extraordinary topologies, and empirical results support our assumption. In addition, through modifications, we show that the scheme can easily represent objects with singularities, such as cusps, creases, or corners. We further develop local adaptive refinement rules that can achieve level-of-detail control for hierarchical modeling. Our implementation is based on the topological properties of a simplicial domain. Therefore, it is flexible and extendable. We also develop a solid modeling system founded on our subdivision schemes to show potential benefits of our work in industrial design, geometric processing, and other applications.     

智能电网监控运行大数据分析系统统一建模方法研究

随着电网监控运行一体化运行趋势愈发明显,大数据技术应用的不断成熟、普及,为具有多源、高维、异构等特征的电网监控大数据的分析与应用提供了解决方案。本文提出了面向智能电网监控运行大数据分析系统的统一建模方法,分析了监控大数据的数据源、数据范围及现状与存在问题,指出了数据建模所需解决的问题与思路,采用元数据思想构建了公共模型,基于业务需要构建了应用模型,对于数据接入与存储管理方面,定义了元数据模型,其目的是在接入、汇总监控业务相关数据源的基础上,构建以设备为中心的监控数据关联模型,实现数据对象统一建模,为实现多源数据高效、规范接入提供了模型支撑,同时定义了符合该建模思路的元模型,元模型约束了建模行为,保证建立的模型遵行领域约束,为上层智能监控大数据分析应用奠定了基础。     

Goodness-of-fit tests for modeling longitudinal ordinal data

Longitudinal studies involving categorical responses are extensively applied in many fields of research and are often fitted by the generalized estimating equations (GEE) approach and generalized linear mixed models (GLMMs). The assessment of model fit is an important issue for model inference. The purpose of this article is to extend Pan’s (2002a) goodness-of-fit tests for GEE models with longitudinal binary data to the tests for logistic proportional odds models with longitudinal ordinal data. Two proposed methods based on Pearson chi-squared test and unweighted sum of residual squares are developed, and the approximate expectations and variances of the test statistics are easily computed. Four major variants of working correlation structures, independent, AR(1), exchangeable and unspecified, are considered to estimate the variances of the proposed test statistics. Simulation studies in terms of type I error rate and the power performance of the proposed tests are presented for various sample sizes. Furthermore, the approaches are demonstrated by two real data sets.     

A unified data model for representing multimedia, timeline, andsimulation data

This paper describes a unified data model that represents multimedia, timeline, and simulation data utilizing a single set of related data modeling constructs. A uniform model for multimedia types structures image, sound, video, and long text data in a consistent way, giving multimedia schemas and queries a degree of data independence even for these complex data types. Information that possesses an intrinsic temporal element can all be represented using a construct called a stream. Streams can be aggregated into parallel multistreams, thus providing a structure for viewing multiple sets of time-based information. The unified stream construct permits real-time measurements, numerical simulation data, and visualizations of that data to be aggregated and manipulated using the same set of operators. Prototypes based on the model have been implemented for two medical application domains: thoracic oncology and thermal ablation therapy of brain tumors. Sample schemas, queries, and screenshots from these domains are provided. Finally, a set of examples is included for an accompanying visual query language discussed in detail in another document     

Likelihood approach for count data in longitudinal experiments

In many cancer studies and clinical research, repeated observations of response variables are taken over time on each individual in one or more treatment groups. In such cases the repeated observations of each vector response are likely to be correlated and the autocorrelation structure for the repeated data plays a significant role in the estimation of regression parameters. A random intercept model for count data is developed using exact maximum-likelihood estimation via numerical integration. A simulation study is performed to compare the proposed methodology with the traditional generalized linear mixed model (GLMM) approach and with the GLMM when penalized quasi-likelihood method is used to perform maximum-likelihood estimation. The methodology is illustrated by analyzing data sets containing longitudinal measures of number of tumors in an experiment of carcinogenesis to study the influence of lipids in the development of cancer.     

Likelihood approach for count data in longitudinal experiments

In many cancer studies and clinical research, repeated observations of response variables are taken over time on each individual in one or more treatment groups. In such cases the repeated observations of each vector response are likely to be correlated and the autocorrelation structure for the repeated data plays a significant role in the estimation of regression parameters. A random intercept model for count data is developed using exact maximum-likelihood estimation via numerical integration. A simulation study is performed to compare the proposed methodology with the traditional generalized linear mixed model (GLMM) approach and with the GLMM when penalized quasi-likelihood method is used to perform maximum-likelihood estimation. The methodology is illustrated by analyzing data sets containing longitudinal measures of number of tumors in an experiment of carcinogenesis to study the influence of lipids in the development of cancer.     

A unified framework for modeling, simulating and explaining engineering systems

We present a unified framework which suffices to represent and manipulate physical objects and their relevant relations interactively in the context of modeling, simulating and explaining engineering systems, and which is demonstrated by an example of modeling river networks--environmental engineering systems[9].     

A unified approach of energy and data cooperation in energy harvesting WSNs

Energy harvesting (EH) provisioned wireless sensor nodes are key enablers to increase network life time in modern wireless sensor networks (WSNs). However, the intermittent nature of the EH process necessitates management of nodes’ limited data and energy buffer capacity. In this paper, a unified mathematical model for a cooperative EHWSN with an opportunistic relay is presented. The energy and data causality constraints are expressed in terms of throughput, available energy, delay and transmission time. Considering finite energy buffers, data buffers and discrete transmission rates (as defined in the standard IEEE 802.15.4) at the nodes, different intuitive online power allocation policies at the relay are studied. The results show that a policy achieving high throughput is less fair and vice versa. Therefore, a joint rate and power allocation policy (JRPAP) is proposed in this study which provides a better trade off between fairness, throughput and energy over intuitive policies. Based on the JRPAP results, we propose to use data aggregation (DA) to achieve throughput gain at lower buffer sizes. In addition, the notion of energy aggregation (EA) is introduced to achieve throughput gain at higher buffer sizes. Combining both EA and DA further improves the overall throughput at all buffer sizes.     

A robust unified approach to analyzing methylation and gene expression data

Microarray technology has made it possible to investigate expression levels, and more recently methylation signatures, of thousands of genes simultaneously, in a biological sample. Since more and more data from different biological systems or technological platforms are being generated at an incredible rate, there is an increasing need to develop statistical methods that are applicable to multiple data types and platforms. Motivated by such a need, a flexible finite mixture model that is applicable to methylation, gene expression, and potentially data from other biological systems, is proposed. Two major thrusts of this approach are to allow for a variable number of components in the mixture to capture non-biological variation and small biases, and to use a robust procedure for parameter estimation and probe classification. The method was applied to the analysis of methylation signatures of three breast cancer cell lines. It was also tested on three sets of expression microarray data to study its power and type I error rates. Comparison with a number of existing methods in the literature yielded very encouraging results; lower type I error rates and comparable/better power were achieved based on the limited study. Furthermore, the method also leads to more biologically interpretable results for the three breast cancer cell lines.     

Information-statistical approach for temporal-spatial data with application

A treatment for temporal-spatial data such as atmospheric temperature using an information-statistical approach is proposed. Conditioning on specific spatial nature of the data, the temporal aspect of the data is first modeled parametrically as Gaussian, and Schwarz information criterion is then applied to detect multiple mean change points—thus the Gaussian statistical models—to account for changes of the population mean over time. To examine the spatial characteristics of the data, successive mean change points are qualified by finite categorical values. The distribution of the finite categorical values is then used to estimate a non-parametric probability model through a non-linear SVD-based optimization approach; where the optimization criterion is Shannon expected entropy. This optimal probability model accounts for the spatial characteristics of the data and is then used to derive spatial association patterns subject to chi-square statistic hypothesis test. The proposed approach is applied to examine the weather data set obtained from NOAA. Selected temperature data are studied. These data cover different geographical localities in the United States, with some spanning over 200 years. Preliminary results are reported.     

A unified reanalysis approach for structural analysis,design, and optimization

This study presents a unified reanalysis approach for structural analysis, design, and optimization that is based on the Combined Approximations (CA) method. The method is suitable for various analysis models (linear, nonlinear, elastic, plastic, static, dynamic), different types of structures (trusses, frames, grillages, continuum structures), and all types of design variables (cross-sectional, material, geometrical, topological). The calculations are based on results of a single exact analysis. The computational effort is usually much smaller than that needed to carry out a complete analysis of modified designs. Accurate results are achieved by low-order approximations for significant changes in the design. It is possible to improve the accuracy by considering higher-order terms, and exact solutions can be achieved in certain cases. The solution steps are straightforward, and the computational procedures presented can readily be used with general finite element systems. Typical results are demonstrated by numerical examples.     

A multiple imputation approach to the analysis of interval-censored failure time data with the additive hazards model

This paper discusses regression analysis of interval-censored failure time data, which occur in many fields including demographical, epidemiological, financial, medical, and sociological studies. For the problem, we focus on the situation where the survival time of interest can be described by the additive hazards model and a multiple imputation approach is presented for inference. A major advantage of the approach is its simplicity and it can be easily implemented by using the existing software packages for right-censored failure time data. Extensive simulation studies are conducted which indicate that the approach performs well for practical situations and is comparable to the existing methods. The methodology is applied to a set of interval-censored failure time data arising from an AIDS clinical trial.     

A k-anonymity privacy-preserving approach in wireless medical monitoring environments

With the proliferation of wireless sensor networks and mobile technologies in general, it is possible to provide improved medical services and also to reduce costs as well as to manage the shortage of specialized personnel. Monitoring a person’s health condition using sensors provides a lot of benefits but also exposes personal sensitive information to a number of privacy threats. By recording user-related data, it is often feasible for a malicious or negligent data provider to expose these data to an unauthorized user. One solution is to protect the patient’s privacy by making difficult a linkage between specific measurements with a patient’s identity. In this paper we present a privacy-preserving architecture which builds upon the concept of k-anonymity; we present a clustering-based anonymity scheme for effective network management and data aggregation, which also protects user’s privacy by making an entity indistinguishable from other k similar entities. The presented algorithm is resource aware, as it minimizes energy consumption with respect to other more costly, cryptography-based approaches. The system is evaluated from an energy-consuming and network performance perspective, under different simulation scenarios.     

A Shortest-route approach for optimum aggregation of data with an application to income data

This paper addresses the problem of grouping a large volume of discrete data into a given number of groups. The algorithm is based on the well-known shortest path algorithm. It handles different criteria for minimizing the loss of information which might result during the process of grouping. The given problem is transformed into a directed graph and it then looks for a shortest path with a given number of edges. The algorithm is illustrated through an example of five data items. It has also been coded in Pascal and some test results are presented.     

A framework for an integrated unified modeling language

The unified modeling language (UML) is one of the most commonly used modeling languages in the software industry. It simplifies the complex process of design by providing a set of graphical notations, which helps express the objectoriented analysis and design of software projects. Although UML is applicable to different types of systems, domains, methods, and processes, it cannot express certain problem domain needs. Therefore, many extensions to UML have been proposed. In this paper, we propose a framework for integrating the UML extensions and then use the framework to propose an integrated unified modeling language-graphical (iUML-g) form. iUML-g integrates the existing UML extensions into one integrated form. This includes an integrated diagram for UML class, sequence, and use case diagrams. The proposed approach is evaluated using a case study. The proposed iUML-g is capable of modeling systems that use different domains.     

A unified approach to analyzing models of cellular communication networks with data call buffering

A unified approach to the analysis of models of cellular communication networks with queues of data calls was developed. Consideration was given to the models with two types of strategies for admission to the cell channels and the buffer. In one strategy, admission to the voice call channels is based on reservation of channels for handover of calls of the given type, and in the other strategy, on the scheme of truncating the calls of the given type. In both models, the strategy of buffer admission by the data calls relies on the scheme of place reservation for handover of the calls of the given type. The models with finite and infinite data call queues were studied. For different admission strategies, algorithms to calculate the servicing performance indices were given, and the results of their comparative analysis were presented.     

RE-EM trees: a data mining approach for longitudinal and clustered data

Longitudinal data refer to the situation where repeated observations are available for each sampled object. Clustered data, where observations are nested in a hierarchical structure within objects (without time necessarily being involved) represent a similar type of situation. Methodologies that take this structure into account allow for the possibilities of systematic differences between objects that are not related to attributes and autocorrelation within objects across time periods. A standard methodology in the statistics literature for this type of data is the mixed effects model, where these differences between objects are represented by so-called “random effects” that are estimated from the data (population-level relationships are termed “fixed effects,” together resulting in a mixed effects model). This paper presents a methodology that combines the structure of mixed effects models for longitudinal and clustered data with the flexibility of tree-based estimation methods. We apply the resulting estimation method, called the RE-EM tree, to pricing in online transactions, showing that the RE-EM tree is less sensitive to parametric assumptions and provides improved predictive power compared to linear models with random effects and regression trees without random effects. We also apply it to a smaller data set examining accident fatalities, and show that the RE-EM tree strongly outperforms a tree without random effects while performing comparably to a linear model with random effects. We also perform extensive simulation experiments to show that the estimator improves predictive performance relative to regression trees without random effects and is comparable or superior to using linear models with random effects in more general situations.     

A unified framework for input-to-state stability in systems with two time scales

This paper develops a unified framework for studying robustness of the input-to-state stability (ISS) property and presents new results on robustness of ISS to slowly varying parameters, to rapidly varying signals, and to generalized singular perturbations. The common feature in these problems is a time-scale separation between slow and fast variables which permits the definition of a boundary layer system like in classical singular perturbation theory. To address various robustness problems simultaneously, the asymptotic behavior of the boundary layer is allowed to be complex and it generates an average for the derivative of the slow state variables. The main results establish that if the boundary layer and averaged systems are ISS then the ISS bounds also hold for the actual system with an offset that converges to zero with the parameter that characterizes the separation of time-scales. The generality of the framework is illustrated by making connection to various classical two time-scale problems and suggesting extensions.     

A multi-fidelity surrogate modeling approach for incorporating multiple non-hierarchical low-fidelity data

Multi-fidelity (MF) surrogate models have been widely used in simulation-based design problems to reduce the computational cost by integrating the data with different fidelity levels. Most of the existing MF modeling methods are only applicable to the problems with hierarchical low-fidelity (LF) models, namely the fidelity levels of multiple LF models can be identified. However, the fidelity levels of the LF models that are obtained from different simplification methods often vary over the design space. To address this challenge, a non-hierarchical Co-Kriging modeling (NHLF-Co-Kriging) method that can flexibly handle multiple non-hierarchical LF models is developed in this work. In the proposed method, multiple LF models are scaled by different scale factors, and a discrepancy model is utilized to depict the differences between the HF model and the ensembled LF models. To make the discrepancy Gaussian process (GP) model easy to be fitted, an optimization problem whose objective is to minimize the second derivative of the prediction values of the discrepancy GP model is defined to obtain optimal scale factors of the LF models. The performance of the NHLF-Co-Kriging method is compared with the extended Co-Kriging model and linear regression MF surrogate model through several analytical examples and an engineering case. Results show that the proposed method selects more reasonable scale factors for the multiple LF models and provides more accurate MF surrogate models under a limited computational budget.