From Boolean to probabilistic Boolean networks as models of genetic regulatory networks

Mathematical and computational modeling of genetic regulatory networks promises to uncover the fundamental principles governing biological systems in an integrative and holistic manner. It also paves the way toward the development of systematic approaches for effective therapeutic intervention in disease. The central theme in this paper is the Boolean formalism as a building block for modeling complex, large-scale, and dynamical networks of genetic interactions. We discuss the goals of modeling genetic networks as well as the data requirements. The Boolean formalism is justified from several points of view. We then introduce Boolean networks and discuss their relationships to nonlinear digital filters. The role of Boolean networks in understanding cell differentiation and cellular functional states is discussed. The inference of Boolean networks from real gene expression data is considered from the viewpoints of computational learning theory and nonlinear signal processing, touching on computational complexity of learning and robustness. Then, a discussion of the need to handle uncertainty in a probabilistic framework is presented, leading to an introduction of probabilistic Boolean networks and their relationships to Markov chains. Methods for quantifying the influence of genes on other genes are presented. The general question of the potential effect of individual genes on the global dynamical network behavior is considered using stochastic perturbation analysis. This discussion then leads into the problem of target identification for therapeutic intervention via the development of several computational tools based on first-passage times in Markov chains. Examples from biology are presented throughout the paper.     

基于概率布尔网络的基因调控网络研究及应用

几乎所有的生命活动都受基因调控网络的影响,对基因调控网络的研究可以让人们从基因层面认识人类的生命活动。癌症在我国的发病率和死亡率日益上升,严重威胁了人类健康。文章在基因调控网络的基础上,以癌症的研究为例,在原有的布尔网络的基础上,通过引入更适合生物体内复杂环境的概率布尔网络,对癌症网络进行分析和预测,减少由于布尔网络的确定性产生的错误规则。     

Comparative study between traditional and modified probabilistic neural networks

Probabilistic neural network (PNN) is a kind of supervised neural network, proposed by Specht as an alternative to back-propagation neural network. The key advantages of PNN are that, training requires only a single pass, and decision surfaces are guaranteed to approach the Bayes-optimal decision boundaries, as the number of training samples grows. Furthermore, shape of the decision surface can be made as complex as necessary, or as simple as desired, by choosing an appropriate value of the smoothing parameter; erroneous samples can be tolerated, and sparse samples are adequate for network performance. This paper reviews the PNN, modified PNN, various learning approaches employed to train the PNN and some comparisons of various types of PNN. Experimental results have been carried out to verify the ability of modified PNN in achieving good classification rate over traditional PNN, BPNN and KNN.     

Vehicle detection in aerial surveillance using dynamic Bayesian networks

We present an automatic vehicle detection system for aerial surveillance in this paper. In this system, we escape from the stereotype and existing frameworks of vehicle detection in aerial surveillance, which are either region based or sliding window based. We design a pixelwise classification method for vehicle detection. The novelty lies in the fact that, in spite of performing pixelwise classification, relations among neighboring pixels in a region are preserved in the feature extraction process. We consider features including vehicle colors and local features. For vehicle color extraction, we utilize a color transform to separate vehicle colors and nonvehicle colors effectively. For edge detection, we apply moment preserving to adjust the thresholds of the Canny edge detector automatically, which increases the adaptability and the accuracy for detection in various aerial images. Afterward, a dynamic Bayesian network (DBN) is constructed for the classification purpose. We convert regional local features into quantitative observations that can be referenced when applying pixelwise classification via DBN. Experiments were conducted on a wide variety of aerial videos. The results demonstrate flexibility and good generalization abilities of the proposed method on a challenging data set with aerial surveillance images taken at different heights and under different camera angles.     

ArgMax and ArgMin: transitional probabilistic models in cognitive radio mesh networks

The erratic nature of spectrum availability and diversity imposes the use of a probabilistic framework for channel selection in cognitive radio networks protocol design. In this work, two probability distributions called ArgMax and ArgMin are proposed, which have broad applications in channel selection mechanisms, routing, and media access control protocols. The ArgMax probability distribution locates the maximum random variable among a set of random variables, while the ArgMin locates the minimum random variable. We show that the ArgMax probability distribution is a better candidate than the frequently used odds‐on‐mean probability distribution through theoretical analysis and simulation. The ArgMin probability distribution has a variety of applications and is shown to be useful in achieving a lower bound on the network's minimum spectral capacity. In simulation, we develop a probabilistic selection routing procedure (PSRP) that adopts the ArgMax probability distribution to guide packets throughout the network. The stochastic framework of probabilistic selection routing procedure is also an appropriate skeleton for building stochastic‐based routing protocols for dynamic networks such as cognitive radio networks. The simulation results suggest that ArgMax enables the routing scheme to adapt to the network dynamic more quickly and to more accurately locate the best candidate to route to than the odds‐on‐mean probability distribution. The ArgMax enhances the network throughput and end‐to‐end delay by over 30% when network load increases. Copyright © 2013 John Wiley & Sons, Ltd.     

Control approaches for probabilistic gene regulatory networks - What approaches have been developed for addreassinig the issue of intervention?

This article presents a tutorial survey of some of the recent results on intervention in the context of probabilistic gene regulatory networks, which, owing to their original binary formulation and their usual application using binary and ternary gene-expression quantization, are generically called probabilistic Boolean networks (PBNs). These are essentially probabilistic generalizations of the standard Boolean networks introduced by Kauffman that allow the incorporation of uncertainty into the intergene relationships. Given a PBN, the transition from one state to the next takes place in accordance with certain transition probabilities and their dynamics, and hence intervention can be studied in the context of homogeneous Markov chains with finite state spaces     

Boosted learning in dynamic Bayesian networks for multimodal speaker detection

Bayesian network models provide an attractive framework for multimodal sensor fusion. They combine an intuitive graphical representation with efficient algorithms for inference and learning. However, the unsupervised nature of standard parameter learning algorithms for Bayesian networks can lead to poor performance in classification tasks. We have developed a supervised learning framework for Bayesian networks, which is based on the Adaboost algorithm of Schapire and Freund. Our framework covers static and dynamic Bayesian networks with both discrete and continuous states. We have tested our framework in the context of a novel multimodal HCI application: a speech-based command and control interface for a Smart Kiosk. We provide experimental evidence for the utility of our boosted learning approach.     

一种构建基因调控网络的混合算法

基因调控网络的重构是系统生物学一个热门研究领域,其中条件互信息是一种很实用的方法。文中提出一种基于条件互信息和爬山搜索策略相结合的混合算法,并应用于大量的基因表达数据,结果证明能提高基因调控网络构建的精确度。条件互信息可以确定变量之间的条件独立性,既可以识别变量间线性关系,也可以识别变量间的非线性关系。这种方法使用打分搜索策略来确定变量X或者Y的邻接点。在有n个变量和n个样本的DREAM数据集以及包含9个变量和9个样本的大肠杆菌数据集中,应用文中方法进行仿真测试,结果显示文中方法能提高基因调控网络的构建精度。     

Recognition of dynamic video contents with global probabilistic models of visual motion.

The exploitation of video data requires methods able to extract high-level information from the images. Video summarization, video retrieval, or video surveillance are examples of applications. In this paper, we tackle the challenging problem of recognizing dynamic video contents from low-level motion features. We adopt a statistical approach involving modeling, (supervised) learning, and classification issues. Because of the diversity of video content (even for a given class of events), we have to design appropriate models of visual motion and learn them from videos. We have defined original parsimonious global probabilistic motion models, both for the dominant image motion (assumed to be due to the camera motion) and the residual image motion (related to scene motion). Motion measurements include affine motion models to capture the camera motion and low-level local motion features to account for scene motion. Motion learning and recognition are solved using maximum likelihood criteria. To validate the interest of the proposed motion modeling and recognition framework, we report dynamic content recognition results on sports videos.     

Relationships between antennas as scatterers and as radiators

The field scattered by an antenna contains a component that is the short circuit scattered field normalized by the short circuit current and a second component that is the radiation field normalized by the transmitting current and multiplied by a factor (1-Γ). The RCS is the magnitude squared of the difference between two terms, one being the square root of a complex `structural' cross section, and the other (1-Γ) times the square root of a complex `antenna' cross section. These relationships, and the role of the load impedance are clarified. The connection between antenna directivity and load effective receiving area is also derived     

Functionality of multilayer Boolean neural networks

The authors present a method for calculating the functionality of a multilayer neural network (MLN) using logical nodes. The method is demonstrated with reference to six network topologies, and a cost/functionality ratio is proposed as an assessment metric for MLNs.<>     

Bayesian methods for pharmacokinetic models in dynamic contrast-enhanced magnetic resonance imaging

This paper proposes a new method for estimating kinetic parameters of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) based on adaptive Gaussian Markov random fields. Kinetic parameter estimates using neighboring voxels reduce the observed variability in local tumor regions while preserving sharp transitions between heterogeneous tissue boundaries. Asymptotic results for standard errors from likelihood-based nonlinear regression are compared with those derived from the posterior distribution using Bayesian estimation with and without neighborhood information. Application of the method to the analysis of breast tumors based on kinetic parameters has shown that the use of Bayesian analysis combined with adaptive Gaussian Markov random fields provides improved convergence behavior and more consistent morphological and functional statistics.     

Storage capacity of multilayer Boolean neural networks

A method for determining the statistical storage capacity of a multilayer Boolean neural network is presented. Theoretical values are compared with those obtained by computer simulation of a number of small networks.<>     

Weak state versus strong state: an analysis of a probabilistic state mechanism for dynamic networks

Network protocols coordinate their decision making using information about entities in remote locations. Such information is provided by state entries. To remain valid, the state information needs to be refreshed via control messages. When it refers to a dynamic entity, the state has to be refreshed at a high rate to prevent it from becoming stale. In capacity constrained networks, this may deteriorate the overall performance of the network. The concept of weak state has been proposed as a remedy to this problem in the context of routing in mobile ad-hoc networks. Weak state is characterized by probabilistic semantics and local refreshes as opposed to strong state that is interpreted as absolute truth. A measure of the probability that the state remains valid, i.e. confidence, accompanies the state. The confidence is decayed in time to adapt to dynamism and to capture the uncertainty in the state information. This way, weak state remains valid without explicit state refresh messages. We evaluate the consistency of weak state and strong state using two notions of distortion. Pure distortion measures the average difference between the actual value of the entity and the value that is provided by the remote state. Informed distortion captures both this difference and the effect of confidence value on state consistency. Using a mathematical analysis and simulations, we show that weak state reduces the distortion values when it provides information about highly dynamic entities and/or it is utilized for protocols that is required to incur a low amount of overhead.     

Intervention in gene regulatory networks via a stationary mean-first-passage-time control policy

A prime objective of modeling genetic regulatory networks is the identification of potential targets for therapeutic intervention. To date, optimal stochastic intervention has been studied in the context of probabilistic Boolean networks, with the control policy based on the transition probability matrix of the associated Markov chain and dynamic programming used to find optimal control policies. Dynamical programming algorithms are problematic owing to their high computational complexity. Two additional computationally burdensome issues that arise are the potential for controlling the network and identifying the best gene for intervention. This paper proposes an algorithm based on mean first-passage time that assigns a stationary control policy for each gene candidate. It serves as an approximation to an optimal control policy and, owing to its reduced computational complexity, can be used to predict the best control gene. Once the best control gene is identified, one can derive an optimal policy or simply utilize the approximate policy for this gene when the network size precludes a direct application of dynamic programming algorithms. A salient point is that the proposed algorithm can be model-free. It can be directly designed from time-course data without having to infer the transition probability matrix of the network.      

用多时延信息论构建基因调控网络

最近涌现出大量基因调控网络重构的模型和方法,但是都没有涉及到基因数据尺寸大小对算法精度的影响问题。文中研究了基因数据尺寸大小对信息论方法构建基因调控网络精度的影响,实验表明基因调控网络构建的精度会在一定数据尺寸规模下达到一个稳态。为了克服互信息的一些缺点,引入文中多时延互信息值来计算两个基因之间的调控关系,所构建的基因调控网络取得了很好的查全率和查准率。并应用它对两个真实的生物分子网络进行重构,结果表明基于多时延的策略下,所构建的基因调控网络取得了很高的特异度和精确度。     

Nonstationary probabilistic target and clutter scattering models

A probabilistic model for nonstationary and/or nonhomogeneous clutter and target scattering is proposed and developed. The first-order probability density of the scattered power is treated as the expected value of a conditional density that is a function of random parameters. The family of gamma densities is a general solution for the density function of the intensity reflected by objects comprised of several scatterers and is selected as the conditional density. In the general case, the gamma density is a function of two parameters: the mean and the inverse of the normalized variance. Assuming various distributions for a random mean, expressions for the first-order density of the scattered power are derived and used to explain previous experimental and theoretical results. An example of detection performance for nonstationary target fluctuation based on the developed model is also presented.     

Theory of wire addition and removal in combinational Boolean networks

Let w_t be a wire in a combinational Boolean network. There may exist a wire w_a such that when w_a is added and w_t is removed, the overall circuit functionality is unchanged. Redundancy-addition-and-removal (RAR) is an efficient technique to find such a w_a. The idea is to add a redundant alternative wire w_a to make the target wire w_t redundant. However, as long as the addition of w_a together with the removal of w_t does not change the overall functionality of the circuit, wires that are added and removed do not necessarily need to be redundant. This raises a question about the existence of alternative wires. Why can one wire replace another wire in a combinational Boolean network? In this paper, we analyze theoretically the existence of alternative wires and model it as an error-cancellation problem. The two existing rewiring techniques, the redundancy-addition-and-removal and the global flow optimization, are unified under the proposed generalized model.