Fang-Xiang Wu

Recurrent Neural Network for Non-Smooth Convex Optimization Problems With Application to the Identification of Genetic Regulatory Networks

A recurrent neural network is proposed for solving the non-smooth convex optimization problem with the convex inequality and linear equality constraints. Since the objective function and inequality constraints may not be smooth, the Clarkes generalized gradients of the objective function and inequality constraints are employed to describe the dynamics of the proposed neural network. It is proved that the equilibrium point set of the proposed neural network is equivalent to the optimal solution of the original optimization problem by using the Lagrangian saddle-point theorem. Under weak conditions, the proposed neural network is proved to be stable, and the state of the neural network is convergent to one of its equilibrium points. Compared with the existing neural network models for non-smooth optimization problems, the proposed neural network can deal with a larger class of constraints and is not based on the penalty method. Finally, the proposed neural network is used to solve the identification problem of genetic regulatory networks, which can be transformed into a non-smooth convex optimization problem. The simulation results show the satisfactory identification accuracy, which demonstrates the effectiveness and efficiency of the proposed approach.

CytoNCA: a cytoscape plugin for centrality analysis and evaluation of protein interaction networks.

BACKGROUND AND SCOPE Nowadays, centrality analysis has become a principal method for identifying essential proteins in biological networks. Here we present CytoNCA, a Cytoscape plugin integrating calculation, evaluation and visualization analysis for multiple centrality measures. IMPLEMENTATION AND PERFORMANCE (i) CytoNCA supports eight different centrality measures and each can be applied to both weighted and unweighted biological networks. (ii) It allows users to upload biological information of both nodes and edges in the network, to integrate biological data with topological data to detect specific nodes. (iii) CytoNCA offers multiple potent visualization analysis modules, which generate various forms of output such as graph, table, and chart, and analyze associations among all measures. (iv) It can be utilized to quantitatively assess the calculation results, and evaluate the accuracy by statistical measures. (v) Besides current eight centrality measures, the biological characters from other sources could also be analyzed and assessed by CytoNCA. This makes CytoNCA an excellent tool for calculating centrality, evaluating and visualizing biological networks. AVAILABILITY http://apps.cytoscape.org/apps/cytonca.

Modeling gene expression from microarray expression data with state-space equations.

We describe a new method to model gene expression from time-course gene expression data. The modelling is in terms of state-space descriptions of linear systems. A cell can be considered to be a system where the behaviours (responses) of the cell depend completely on the current internal state plus any external inputs. The gene expression levels in the cell provide information about the behaviours of the cell. In previously proposed methods, genes were viewed as internal state variables of a cellular system and their expression levels were the values of the intemal state variables. This viewpoint has suffered from the underestimation of the model parameters. Instead, we view genes as the observation variables, whose expression values depend on the current intemal state variables and any external input. Factor analysis is used to identify the internal state variables, and Bayesian Information Criterion (BIC) is used to determine the number of the internal state variables. By building dynamic equations of the internal state variables and the relationships between the internal state variables and the observation variables (gene expression profiles), we get state-space descriptions of gene expression model. In the present method, model parameters may be unambiguously identified from time-course gene expression data. We apply the method to two time-course gene expression datasets to illustrate it.

Identifying protein complexes and functional modules—from static PPI networks to dynamic PPI networks

Cellular processes are typically carried out by protein complexes and functional modules. Identifying them plays an important role for our attempt to reveal principles of cellular organizations and functions. In this article, we review computational algorithms for identifying protein complexes and/or functional modules from protein-protein interaction (PPI) networks. We first describe issues and pitfalls when interpreting PPI networks. Then based on types of data used and main ideas involved, we briefly describe protein complex and/or functional module identification algorithms in four categories: (i) those based on topological structures of unweighted PPI networks; (ii) those based on characters of weighted PPI networks; (iii) those based on multiple data integrations; and (iv) those based on dynamic PPI networks. The PPI networks are modelled increasingly precise when integrating more types of data, and the study of protein complexes would benefit by shifting from static to dynamic PPI networks.

Detecting protein complexes based on uncertain graph model

Advanced biological technologies are producing large-scale protein-protein interaction (PPI) data at an ever increasing pace, which enable us to identify protein complexes from PPI networks. Pair-wise protein interactions can be modeled as a graph, where vertices represent proteins and edges represent PPIs. However most of current algorithms detect protein complexes based on deterministic graphs, whose edges are either present or absent. Neighboring information is neglected in these methods. Based on the uncertain graph model, we propose the concept of expected density to assess the density degree of a subgraph, the concept of relative degree to describe the relationship between a protein and a subgraph in a PPI network. We develop an algorithm called DCU (detecting complex based on uncertain graph model) to detect complexes from PPI networks. In our method, the expected density combined with the relative degree is used to determine whether a subgraph represents a complex with high cohesion and low coupling. We apply our method and the existing competing algorithms to two yeast PPI networks. Experimental results indicate that our method performs significantly better than the state-of-the-art methods and the proposed model can provide more insights for future study in PPI networks.

Iteration method for predicting essential proteins based on orthology and protein-protein interaction networks

BackgroundIdentification of essential proteins plays a significant role in understanding minimal requirements for the cellular survival and development. Many computational methods have been proposed for predicting essential proteins by using the topological features of protein-protein interaction (PPI) networks. However, most of these methods ignored intrinsic biological meaning of proteins. Moreover, PPI data contains many false positives and false negatives. To overcome these limitations, recently many research groups have started to focus on identification of essential proteins by integrating PPI networks with other biological information. However, none of their methods has widely been acknowledged.ResultsBy considering the facts that essential proteins are more evolutionarily conserved than nonessential proteins and essential proteins frequently bind each other, we propose an iteration method for predicting essential proteins by integrating the orthology with PPI networks, named by ION. Differently from other methods, ION identifies essential proteins depending on not only the connections between proteins but also their orthologous properties and features of their neighbors. ION is implemented to predict essential proteins in S. cerevisiae. Experimental results show that ION can achieve higher identification accuracy than eight other existing centrality methods in terms of area under the curve (AUC). Moreover, ION identifies a large amount of essential proteins which have been ignored by eight other existing centrality methods because of their low-connectivity. Many proteins ranked in top 100 by ION are both essential and belong to the complexes with certain biological functions. Furthermore, no matter how many reference organisms were selected, ION outperforms all eight other existing centrality methods. While using as many as possible reference organisms can improve the performance of ION. Additionally, ION also shows good prediction performance in E. coli K-12.ConclusionsThe accuracy of predicting essential proteins can be improved by integrating the orthology with PPI networks.

Nonlinear PD control for trajectory tracking with consideration of the design for control methodology

This paper presents a study of examining nonlinear PD (NPD) control of multi-degree-of-freedom parallel manipulator systems for a generic task, i.e., trajectory tracking. The motivation of this study is the well-known observation that NPD control method can offer a means to improve the performance of plant systems. This study is also to examine how the mechanical structure of the manipulator affects dynamic performance. The design of mechanical structure follows the design-for-control (DFC) principle, and in particular it renders to a full force balanced mechanism. Simulation studies confirm that the concurrent consideration of mechanical structure design and NPD control can obtain good trajectory tracking performance for the parallel manipulators.

Dynamic protein interaction network construction and applications.

With more dynamic information available, researchers’ attention has recently shifted from static properties to dynamic properties of protein–protein interaction networks. To compensate the limited ability of technologies of detecting dynamic protein–protein interactions, dynamic protein interaction networks (DPINs) can be constructed by involving proteomic, genomic, and transcriptome analyses. Two groups of DPIN construction methods are classified based on the different focuses on dynamic information extracted from gene expression data. The dynamics of one kind of DPINs is reflected by the changes in protein presence varying with time, while that of the other kind of DPINs is reflected by the differences of coexpression under different conditions. In this review, the applications on DPINs will be discussed, including protein complexes/functional modules and network organization analysis, biomarkers detection in the progression or prognosis of the disease, and network medicine. We also point out the challenges in DPINs construction and future directions in the research of DPINs at the end of this review.

Integrated Design and PD Control of High-Speed Closed-loop Mechanisms

The performance of an electromechanical system not only depends on its controller design, but also on the design of its mechanical structure. In order to achieve the excellent performance of the four-bar-link mechanism byemploying the simple PD control, we redesign the structure of the four-bar-link mechanism by a mass-redistribution scheme to simplify the dynamic model. Theoretically, we analyze the stability of the closed-loop system consisting of the PD controller and several kinds of four-bar-link mechanisms, and discuss the relations between the performance of the PD controller and its gains and the mechanical design. The obtained results show that the performance of the PD controller may be significantly improved by using the methodology of Design For Control (DFC). The effectiveness of the proposed methodology has also been verified by some simulation studies.

Global and Robust Stability Analysis of Genetic Regulatory Networks With Time-Varying Delays and Parameter Uncertainties

The study of stability is essential for designing or controlling genetic regulatory networks. This paper addresses global and robust stability of genetic regulatory networks with time delays and parameter uncertainties. Most existing results on this issue are based on the linear matrix inequalities (LMIs) approach, which results in checking the existence of a feasible solution to high dimensional LMIs. Based on M-matrix theory, we will present several novel global stability conditions for genetic regulatory networks with time-varying and time-invariant delays. All of these stability conditions are given in terms of M-matrices, for which there are many and very easy ways to be verified. Then, we extend these results to genetic regulatory networks with time delays and parameter uncertainties. To illustrate the effectiveness of our theoretical results, several genetic regulatory networks are analyzed. Compared with existing results in the literature, we also show that our results are less conservative than existing ones with these illustrative genetic regulatory networks.The study of stability is essential for designing or controlling genetic regulatory networks. This paper addresses global and robust stability of genetic regulatory networks with time delays and parameter uncertainties. Most existing results on this issue are based on the linear matrix inequalities (LMIs) approach, which results in checking the existence of a feasible solution to high dimensional LMIs. Based on M-matrix theory, we will present several novel global stability conditions for genetic regulatory networks with time-varying and time-invariant delays. All of these stability conditions are given in terms of M-matrices, for which there are many and very easy ways to be verified. Then, we extend these results to genetic regulatory networks with time delays and parameter uncertainties. To illustrate the effectiveness of our theoretical results, several genetic regulatory networks are analyzed. Compared with existing results in the literature, we also show that our results are less conservative than existing ones with these illustrative genetic regulatory networks.