A probabilistic dynamic technique for the distributed generation of very large state spaces

Conventional methods for state space exploration are limited to the analysis of small systems because they suffer from excessive memory and computational requirements. We have developed a new dynamic probabilistic state exploration algorithm which addresses this problem for general, structurally unrestricted state spaces.

Our method has a low state omission probability and low memory usage that is independent of the length of the state vector. In addition, the algorithm can be easily parallelised. This combination of probability and parallelism enables us to rapidly explore state spaces that are an order of magnitude larger than those obtainable using conventional exhaustive techniques.

We derive a performance model of this new algorithm in order to quantify its benefits in terms of distributed run-time, speedup and efficiency. We implement our technique on a distributed-memory parallel computer and demonstrate results which compare favourably with the performance model. Finally, we discuss suitable choices for the three hash functions upon which our algorithm is based.     

Wavelet-based feature extraction using probabilistic finite state automata for pattern classification

Real-time data-driven pattern classification requires extraction of relevant features from the observed time series as low-dimensional and yet information-rich representations of the underlying dynamics. These low-dimensional features facilitate in situ decision-making in diverse applications, such as computer vision, structural health monitoring, and robotics. Wavelet transforms of time series have been widely used for feature extraction owing to their time-frequency localization properties. In this regard, this paper presents a symbolic dynamics-based method to model surface images, generated by wavelet coefficients in the scale-shift space. These symbolic dynamics-based models (e.g., probabilistic finite state automata (PFSA)) capture the relevant information, embedded in the sensor data, from the associated Perron-Frobenius operators (i.e., the state-transition probability matrices). The proposed method of pattern classification has been experimentally validated on laboratory apparatuses for two different applications: (i) early detection of evolving damage in polycrystalline alloy structures, and (ii) classification of mobile robots and their motion profiles.     

A data model and algebra for probabilistic complex values

We present a probabilistic data model for complex values. More precisely, we introduce probabilistic complex value relations, which combine the concept of probabilistic relations with the idea of complex values in a uniform framework. We elaborate a model-theoretic definition of probabilistic combination strategies, which has a rigorous foundation on probability theory. We then define an algebra for querying database instances, which comprises the operations of selection, projection, renaming, join, Cartesian product, union, intersection, and difference. We prove that our data model and algebra for probabilistic complex values generalizes the classical relational data model and algebra. Moreover, we show that under certain assumptions, all our algebraic operations are tractable. We finally show that most of the query equivalences of classical relational algebra carry over to our algebra on probabilistic complex value relations. Hence, query optimization techniques for classical relational algebra can easily be applied to optimize queries on probabilistic complex value relations.     

Extending the relational model to deal with probabilistic data

According to the soundness and completeness of information in databases,the expressive form and the semantics of incomplete information are discussed in this paper.On the basis of the discussion,the current studies on incomplete data in relational databases are reviewed.In order to represent stochastic uncertainty in most general sense in the real world,probabilistic data are introduced into relational databases.An extended relational data model is presented to express and manipulate probabilistic data and the operations in relational algebra based on the extended model are defined in this paper.     

随机进程代数新技术综述

本文以PEPA语言为例,对近年来发展起来的随机进程代数的缓解状态空间爆炸问题的新技术做一个综述．     

概率逻辑系统是与集合代数同态的布尔代数

联结词的本质是命题的运算,只有对所有命题都适用的真值函数才能用于定义联结词.概率逻辑中由于命题的内涵相关性,任何[0,1]上的函数都不能完全适用于任意命题的运算,概率逻辑的联结词不能定义成真值函数.各种算子可以作为一种计算方法使用和研究,但不能代表一个逻辑系统研究系统的性质.概率逻辑系统是概率空间的逻辑表示,是与概率空间中的事件域(集合代数)同态的布尔代数.用事件域上的集合函数精确定义各种联结词,与经典二值逻辑相容,与事实相符,能够在经典逻辑框架内实现概率命题演算.     

PPoSOM: A new variant of PolSOM by using probabilistic assignment for multidimensional data visualization

A new Self-Organizing Map algorithm, called the probabilistic polar self-organizing map (PPoSOM), is proposed. PPoSOM is a new variant of PolSOM, which is constructed on 2-D polar coordinates. Two variables: radius and angle are used to reflect the data characteristics. PPoSOM, developed to enhance the visualization performance, provides more data characteristics compared with the traditional methods that use Euclidian distance as the only variable. The weight-updating rule of PPoSOM is associated with a cost function. Instead of using the hard assignment, PPoSOM employs the soft assignment that the assignment of data to neuron is based on a probabilistic function. The obtained results are compared with the conventional SOM and ViSOM. The presented results show that the proposed PPoSOM is an effective method for multidimensional data visualization. In addition, the quality measurement of mapping, synthetical cluster density (SCD) is applied and it shows PPoSOM exhibits an improved result compared with PolSOM.     

On control of discrete-time state-dependent jump linear systems with probabilistic constraints: A receding horizon approach

In this article, we consider a receding horizon control of discrete-time state-dependent jump linear systems, a particular kind of stochastic switching systems, subject to possibly unbounded random disturbances and probabilistic state constraints. Due to the nature of the dynamical system and the constraints, we consider a one-step receding horizon. Using inverse cumulative distribution function, we convert the probabilistic state constraints to deterministic constraints, and obtain a tractable deterministic receding horizon control problem. We consider the receding horizon control law to have a linear state-feedback and an admissible offset term. We ensure mean square boundedness of the state variable via solving linear matrix inequalities off-line, and solve the receding horizon control problem on-line with control offset terms. We illustrate the overall approach applied on a macroeconomic system.     

A hybrid data-fusion system using modal data and probabilistic neural network for damage detection

This paper addresses a novel hybrid data-fusion system for damage detection by integrating the data fusion technique, probabilistic neural network (PNN) models and measured modal data. The hybrid system proposed consists of three models, i.e. a feature-level fusion model, a decision-level fusion model and a single PNN classifier model without data fusion. Underlying this system is the idea that we can choose any of these models for damage detection under different circumstances, i.e. the feature-level model is preferable to other models when enormous data are made available through multi-sensors, whereas the confidence level for each of multi-sensors must be determined (as a prerequisite) before the adoption of the decision-level model, and lastly, the single model is applicable only when data collected is somehow limited as in the cases when few sensors have been installed or are known to be functioning properly. The hybrid system is suitable for damage detection and identification of a complex structure, especially when a huge volume of measured data, often with uncertainties, are involved, such as the data available from a large-scale structural health monitoring system. The numerical simulations conducted by applying the proposed system to detect both single- and multi-damage patterns of a 7-storey steel frame show that the hybrid data-fusion system cannot only reliably identify damage with different noise levels, but also have excellent anti-noise capability and robustness.     

A probabilistic relaxation labeling framework for reducing the noise effect in geometric biclustering of gene expression data

Biclustering is an important method in DNA microarray analysis which can be applied when only a subset of genes is co-expressed in a subset of conditions. Unlike standard clustering analyses, biclustering methodology can perform simultaneous classification on two dimensions of genes and conditions in a microarray data matrix. However, the performance of biclustering algorithms is affected by the inherent noise in data, types of biclusters and computational complexity. In this paper, we present a geometric biclustering method based on the Hough transform and the relaxation labeling technique. Unlike many existing biclustering algorithms, we first consider the biclustering patterns through geometric interpretation. Such a perspective makes it possible to unify the formulation of different types of biclusters as hyperplanes in spatial space and facilitates the use of a generic plane finding algorithm for bicluster detection. In our algorithm, the Hough transform is employed for hyperplane detection in sub-spaces to reduce the computational complexity. Then sub-biclusters are combined into larger ones under the probabilistic relaxation labeling framework. Our simulation studies demonstrate the robustness of the algorithm against noise and outliers. In addition, our method is able to extract biologically meaningful biclusters from real microarray gene expression data.     

A probabilistic principal component analysis-based approach in process monitoring and fault diagnosis with application in wastewater treatment plant

Probabilistic principal component analysis (PPCA) based approaches have been widely used in the field of process monitoring. However, the traditional PPCA approach is still limited to linear dimensionality reduction. Although the nonlinear projection model of PPCA can be obtained by Gaussian process mapping, the model still lacks robustness and is susceptible to process noise. Therefore, this paper proposes a new nonlinear process monitoring and fault diagnosis approach based on the Bayesian Gaussian latent variable model (Bay-GPLVM). Bay-GPLVM can obtain the posterior distribution rather than point estimation for latent variables, so the model is more robust. Two monitoring statistics corresponding to latent space and residual space are constructed for PM-FD purpose. Further, the cause of fault is analyzed by calculating the gradient value of the variable at the fault point. Compared with several PPCA-based monitoring approaches in theory and practical application, the Bay-GPLVM-based process monitoring approach can better deal with nonlinear processes and show high efficiency in process monitoring.     

Partial order reduction for state/event LTL with application to component-interaction automata

Software systems assembled from a large number of autonomous components become an interesting target for formal verification due to the issue of correct interplay in component interaction. State/event LTL (Chaki et al. (2004, 2005) [1] and [2]) incorporates both states and events to express important properties of component-based software systems.The main contribution of this paper is a partial order reduction technique for verification of state/event LTL properties. The core of the partial order reduction is a novel notion of stuttering equivalence which we call state/event stuttering equivalence. The positive attribute of the equivalence is that it can be resolved with existing methods for partial order reduction. State/event LTL properties are, in general, not preserved under state/event stuttering equivalence. To this end we define a new logic, called weak state/event LTL, which is invariant under the new equivalence.To bring some evidence of the method’s efficiency, we present some of the results obtained by employing the partial order reduction technique within our tool for verification of component-based systems modelled using the formalism of component-interaction automata (Brim et al. (2005) [3]).     

A derivative-free affine scaling trust region methods based on probabilistic models with new nonmonotone line search technique for linear inequality constrained minimization without strict complementarity

ABSTRACT

In this paper, a derivative-free trust region methods based on probabilistic models with new nonmonotone line search technique is considered for nonlinear programming with linear inequality constraints. The proposed algorithm is designed to build probabilistic polynomial interpolation models for the objective function. We build the affine scaling trust region methods which use probabilistic or random models within a classical trust region framework. The new backtracking linear search technique guarantee the descent of the objective function, and new iterative points are in the feasible region. In order to overcome the strict complementarity hypothesis, under some reasonable conditions which are weaker than strong second order sufficient condition, we give the new and more simple identification function to structure the affine matrix. The global and local fast convergence of the algorithm are shown and the results of numerical experiments are reported to show the effectiveness of the proposed algorithm.     

A method for adaptive estimation of ARMA processes

When the noise process in adaptive identification of linear stochastic systems is correlated, and can be represented by a moving average model, extended least squares algorithms are commonly used, and converge under a strictly positive real (SPR) condition on the noise model. In this paper, we present an adaptive algorithm for the estimation of autoregressive moving average (ARMA) processes, and show that it is convergent without any SPR condition, and has a convergence rate of O({loglog t)/t}^1/2).     

A symbolic manipulator for automated verification of reactive systems with heterogeneous data types

In this paper, we present the design and implementation of the Composite Symbolic Library, a symbolic manipulator for model checking systems with heterogeneous data types. Our tool provides a common interface for different symbolic representations, such as BDDs, for representing Boolean logic formulas and polyhedral representations for linear arithmetic formulas. Based on this common interface, these data structures are combined using a disjunctive composite representation. We propose several heuristics for efficient manipulation of this composite representation and present experimental results that demonstrate their performance. We used an object-oriented design to implement the Composite Symbolic Library. We imported the CUDD library (a BDD library) and the Omega Library (a linear arithmetic constraint manipulator that uses polyhedral representations) to our tool by writing wrappers around them which conform to our symbolic representation interface. Our tool supports polymorphic verification procedures which dynamically select symbolic representations based on the input specification. Our symbolic representation library can be used as an interface between different symbolic libraries, model checkers, and specification languages. We expect our tool to be useful in integrating different tools and techniques for symbolic model checking, and in comparing their performance.     

Parameter uncertainty and temporal dynamics of sensitivity for hydrologic models: A hybrid sequential data assimilation and probabilistic collocation method

In this study, a hybrid sequential data assimilation and probabilistic collocation (HSDAPC) approach is proposed for analyzing uncertainty propagation and parameter sensitivity of hydrologic models. In HSDAPC, the posterior probability distributions of model parameters are first estimated through a particle filter method based on streamflow discharge data. A probabilistic collocation method (PCM) is further employed to show uncertainty propagation from model parameters to model outputs. The temporal dynamics of parameter sensitivities are then generated based on the polynomial chaos expansion (PCE) generated by PCM, which can reveal the dominant model components for different catchment conditions. The maximal information coefficient (MIC) is finally employed to characterize the correlation/association between model parameter sensitivity and catchment precipitation, potential evapotranspiration and observed discharge. The proposed method is applied to the Xiangxi River located in the Three Gorges Reservoir area. The results show that: (i) the proposed HSDAPC approach can generate effective 2nd and 3rd PCE models which provide accuracy predictions; (ii) 2^nd-order PCE, which can run nearly ten time faster than the hydrologic model, can capably represent the original hydrological model to show the uncertainty propagation in a hydrologic simulation; (iii) the slow (R_s) and quick flows (R_q) in Hymod show significant sensitivities during the simulation periods but the distribution factor (α) shows a least sensitivity to model performance; (iv) the model parameter sensitivities show significant correlation with the catchment hydro-meteorological conditions, especially during the rainy period with MIC values larger than 0.5. Overall, the results in this paper indicate that uncertainty propagation and temporal sensitivities of parameters can be effectively characterized through the proposed HSDAPC approach.     

A sparse probabilistic approach with chaotic artificial bee colony optimization for sea clutter soft computing

A novel soft computing method of sea clutter based on sparse probabilistic learning frameworks with an optimizing approach is proposed, where a probabilistic dynamic computing method of electromagnetic signals by relevance vector machine (RVM) is developed with sensor parameters optimization using a novel chaotic artificial bee colony (CABC) algorithm. LS-SVM, WLS-SVM and ABC-RVM soft computing models of sea clutter are also developed as the comparative basis. The experimental results show that new optimizing method outperforms the basic ABC both in convergence speed and calculation precision, and then an efficient CABC-RVM approach for computing sea clutter is presented and confirmed through real sea clutter data. Furthermore, the performance of CABC-RVM is analyzed and compared to above sea clutter sensors and literature reported sea clutter sensors in detail. The research results show effectiveness of the proposed approach.     

A combined molecular docking-based and pharmacophore-based target prediction strategy with a probabilistic fusion method for target ranking

Herein, a combined molecular docking-based and pharmacophore-based target prediction strategy is presented, in which a probabilistic fusion method is suggested for target ranking. Establishment and validation of the combined strategy are described. A target database, termed TargetDB, was firstly constructed, which contains 1105 drug targets. Based on TargetDB, the molecular docking-based target prediction and pharmacophore-based target prediction protocols were established. A probabilistic fusion method was then developed by constructing probability assignment curves (PACs) against a set of selected targets. Finally the workflow for the combined molecular docking-based and pharmacophore-based target prediction strategy was established. Evaluations of the performance of the combined strategy were carried out against a set of structurally different single-target compounds and a well-known multi-target drug, 4H-tamoxifen, which results showed that the combined strategy consistently outperformed the sole use of docking-based and pharmacophore-based methods. Overall, this investigation provides a possible way for improving the accuracy of in silico target prediction and a method for target ranking.     

Consensus reaching process for fuzzy behavioral TOPSIS method with probabilistic linguistic q-rung orthopair fuzzy set based on correlation measure

The paper proposes a consensus reaching process for fuzzy behavioral TOPSIS method with probabilistic linguistic q-rung orthopair fuzzy sets (PLq-ROFSs) based on correlation measure. First, the operational laws of adjusted PLq-ROFSs based on linguistic scale function (LSF) for semantics of linguistic terms are introduced, where the PLq-ROFSs have same probability space. In addition, we define the score function and accuracy function of PLq-ROFS based on the proposed operational laws to compare the PLq-ROFSs. Furthermore, we propose the probabilistic linguistic q-rung orthopair fuzzy weighted averaging (PLq-ROFWA) operator and the probabilistic linguistic q-rung orthopair fuzzy order weighted averaging (PLq-ROFOWA) operator to aggregate the linguistic decision information. Considering the inconsistency between the individual information and aggregated information in decision-making process and the demiddle of given linguistic sets tocision makers' behavioral factors, we define a new correlation measure based on LSF to develop a consensus reaching process for fuzzy behavioral TOPSIS method with PLq-ROFSs. Finally, a numerical example concerning the selection of optimal green enterprise is given to illustrate the feasibility of the proposed method and some comparative analyses with the existing methods are given to show its effectiveness. The sensitivity analysis and stability analysis of the proposed method on the ranking results are also discussed.