BACKGROUND: Gene regulatory networks (GRNs) can be inferred from both gene expression data and genetic perturbations. Under different conditions, the gene data of the same gene set may be different from each other, which results in different GRNs. Detecting structural difference between GRNs under different conditions is of great significance for understanding gene functions and biological mechanisms. RESULTS: In this paper, we propose a Bayesian Fused algorithm to jointly infer differential structures of GRNs under two different conditions. The algorithm is developed for GRNs modeled with structural equation models (SEMs), which makes it possible to incorporate genetic perturbations into models to improve the inference accuracy, so we name it BFDSEM. Different from the naive approaches that separately infer pair-wise GRNs and identify the difference from the inferred GRNs, we first re-parameterize the two SEMs to form an integrated model that takes full advantage of the two groups of gene data, and then solve the re-parameterized model by developing a novel Bayesian fused prior following the criterion that separate GRNs and differential GRN are both sparse. CONCLUSIONS: Computer simulations are run on synthetic data to compare BFDSEM to two state-of-the-art joint inference algorithms: FSSEM and ReDNet. The results demonstrate that the performance of BFDSEM is comparable to FSSEM, and is generally better than ReDNet. The BFDSEM algorithm is also applied to a real data set of lung cancer and adjacent normal tissues, the yielded normal GRN and differential GRN are consistent with the reported results in previous literatures. An open-source program implementing BFDSEM is freely available in Additional file 1.

We identify two families of canonical representations called ROBDD[/\i^]_C and ROBDD[/\T^,i]_T by augmenting ROBDD with two types of conjunctive decompositions. These representations cover the three existing languages ROBDD, ROBDD with as many implied literals as possible (ROBDD-L_&infin), and AND/OR BDD. We introduce a new time efficiency criterion called rapidity which reflects the idea that exponential operations may be preferable if the language can be exponentially more succinct. Then we demonstrate that the expressivity, succinctness and operation rapidity do not decrease from ROBDD[/\T^,i]_T to ROBDD[/\i^]_C, and then to ROBDD[/\i+1^]_C. We also demonstrate that ROBDD[/\i^]_C (i > 1) and ROBDD[/\T^,i]_T are not less tractable than ROBDD-L_&infin and ROBDD, respectively. Finally, we develop a compiler for ROBDD[/\&infin^]_C which significantly advances the compiling efficiency of canonical representations.

We identify two families of canonical knowledge compilation languages. Both families augment ROBDD with conjunctive decomposition bounded by an integer i ranging from 0 to ∞. In the former, the decomposition is finest and the decision respects a chain C of variables, while both the decomposition and decision of the latter respect a tree T of variables. In particular, these two families cover the three existing languages ROBDD, ROBDD with as many implied literals as possible, and AND/OR BDD. We demonstrate that each language in the first family is complete, while each one in the second family is incomplete with expressivity that does not decrease with incremental i. We also demonstrate that the succinctness does not decrease from the i-th language in the second family to the i-th language in the first family, and then to the (i+1)-th language in the first family. For the operating efficiency, on the one hand, we show that the two families of languages support a rich class of tractable logical operations, and particularly the tractability of each language in the second family is not less than that of ROBDD; and on the other hand, we introduce a new time efficiency criterion called rapidity which reflects the idea that exponential operations may be preferable if the language can be exponentially more succinct, and we demonstrate that the rapidity of each operation does not decrease from the i-th language in the second family to the i-th language in the first family, and then to the (i+1)-th language in the first family. Furthermore, we develop a compiler for the last language in the first family (i = ∞). Empirical results show that the compiler significantly advances the compiling efficiency of canonical representations. In fact, its compiling efficiency is comparable with that of the state-of-the-art compilers of non-canonical representations. We also provide a compiler for the i-th language in the first family by translating the last language in the first family into the i-th language (i < ∞). Empirical results show that we can sometimes use the i-th language instead of the last language without any obvious loss of space efficiency.

Discovery of communities in networks is a fundamental data analysis problem. Most of the existing approaches have focused on discovering communities of nodes, while recent studies have shown great advantages and utilities of the knowledge of communities of links. Stochastic models provides a promising class of techniques for the identification of modular structures, but most stochastic models mainly focus on the detection of node communities rather than link communities. We propose a stochastic model, which not only describes the structure of link communities, but also considers the heterogeneous distribution of community sizes, a property which is often ignored by other models. We then learn the model parameters using a method of maximum likelihood based on an expectation-maximization algorithm. To deal with large complex real networks, we extend the method by a strategy of iterative bipartition. The extended method is not only efficient, but is also able to determine the number of communities for a given network. We test our approach on both synthetic benchmarks and real-world networks including an application to a large biological network, and also compare it with two existing methods. The results demonstrate the superior performance of our approach over the competing methods for detecting link communities.

The real-world continuous double auction (CDA) market is a dynamic environment. However, most of the existing agent bidding strategies are simply designed for static markets. A new detecting method for bidding strategy is necessary for more practical

Complex network theory provides a means for modeling and analyzing complex systems that consist of multiple and interdependent components. Among the studies on complex networks, structural analysis is of fundamental importance as it presents a natural route to understanding the dynamics, as well as to synthesizing or optimizing the functions, of networks. A wide spectrum of structural patterns of networks has been reported in the past decade, such as communities, multipartites, bipartite, hubs, authorities, outliers, and bow ties, among others. In this paper, we are interested in tackling the challenging task of characterizing and extracting multiplex patterns (multiple patterns as mentioned previously coexisting in the same networks in a complicated manner), which so far has not been explicitly and adequately addressed in the literature. Our work shows that such multiplex patterns can be well characterized as well as effectively extracted by means of a granular stochastic blockmodel, together with a set of related algorithms proposed here based on some machine learning and statistical inference ideas. These models and algorithms enable us to further explore complex networks from a novel perspective.

The ability to discover community structures from explorative networks is useful for many applications. Most of the existing methods with regard to community mining are specifically designed for assortative networks, and some of them could be applied to address disassortative networks by means of intentionally modifying the objectives to be optimized. However, the types of the explorative networks are unknown beforehand. Consequently, it is difficult to determine what specific algorithms should be used to mine appropriate structures from exploratory networks. To address this issue, a novel concept, generalized community structure, has been proposed with the attempt to unify the two distinct counterparts in both types of networks. Furthermore, based on the proposed random network ensemble model, a generalized community mining algorithm, so called G-NCMA, has been proposed, which is promisingly suitable for both types of networks. Its performance has been rigorously tested, validated and compared with other related algorithms against real-world networks as well as synthetic networks. Experimental results show the G-NCMA algorithm is able to detect communities, without any prior, from explorative networks with a good accuracy.

Detecting communities from complex networks has triggered considerable attention in several application domains. Targeting this problem, a local search based genetic algorithm (GALS) which employs a graph-based representation (LAR) has been proposed in this work. The core of the GALS is a local search based mutation technique. Aiming to overcome the drawbacks of the existing mutation methods, a concept called marginal gene has been proposed, and then an effective and efficient mutation method, combined with a local search strategy which is based on the concept of marginal gene, has also been proposed by analyzing the modularity function. Moreover, in this paper the percolation theory on ER random graphs is employed to further clarify the effectiveness of LAR presentation; A Markov random walk based method is adopted to produce an accurate and diverse initial population; the solution space of GALS will be significantly reduced by using a graph based mechanism. The proposed GALS has been tested on both computer-generated and real-world networks, and compared with some competitive community mining algorithms. Experimental result has shown that GALS is highly effective and efficient for discovering community structure.

Research has shown that many social networks come into being hierarchically based on some basic building blocks called communities, within which the social interactions are very intensive, but between which they are very weak. Network community mining algorithms aim at efficiently and effectively discovering all such communities from a given network. Many related methods have been proposed and applied to different areas including social network analysis, gene network analysis and web clustering engine. Most of the existing methods for mining communities are centralized. In this paper, we present a multi-agent based decentralized algorithm, in which a group of autonomous agents work together to mine a network through a proposed self-aggregation and self-organization mechanism. Thanks to its decentralized feature, our method is potentially suitable for dealing with distributed networks, whose global structures are hard to obtain due to their geographical distributions, decentralized controls or huge sizes. The effectiveness of our method has been tested against different benchmark networks.

Recently, the sizes of networks are always very huge, and they take on distributed nature. Aiming at this kind of network clustering problem, in the sight of local view, this paper proposes a fast network clustering algorithm in which each node is regarded as an agent, and each agent tries to maximize its local function in order to optimize network modularity defined by function Q, rather than optimize function Q from the global view as traditional methods. Both the efficiency and effectiveness of this algorithm are tested against computer-generated and real-world networks. Experimental result shows that this algorithm not only has the ability of clustering large-scale networks, but also can attain very good clustering quality compared with the existing algorithms. Furthermore, the parameters of this algorithm are analyzed.

The term of social network communities refers to groups of individuals within which social interactions are intense and between which they are weak. A social network community mining problem (SNCMP) can be stated as the problem of finding all such communities from a given social network. A wide variety of applications can be formulated into SNCMPs, ranging from Web intelligence to social intelligence. So far, many algorithms addressing the SNCMP have been developed; most of them are either optimization or heuristic based methods. Different from all existing work, this paper explores the notion of a social network community and its intrinsic properties, drawing on the dynamics of a stochastic model naturally introduced. In particular, it uncovers an interesting connection between the hierarchical community structure of a network and the metastability of a Markov process constructed upon it. A lot of critical topological information regarding to communities hidden in networks can be inferred from the derived spectral signatures of such networks, without actually clustering them with any particular algorithms. Based upon the above connection, we can obtain a frameworkfor characterizing and analyzing social network communities.

For the NURBS curve that hold the arbitrary degrees and generally structured knots, under the assumption of unchanging the knot vector and the degree of NURBS curve, we present the constraint conditions for elevating the parametric continuity order of NURBS curve at the interior knots by modifying their control points and weights. Meanwhile, we obtain the freedom degree of the control points and the weights when the parametric continuity order of NURBS curve elevates by one. Furthermore, we obtain the conditions for elevating the parametric continuity order of NURBS surface along its isoparametric line by modifying their control points and weights. Meanwhile, the freedom degree of the control points and the weights when the parametric continuity order of NURBS surface elevates by one is presented at the end.

In transaction processing, an association is said to exist between two sets of items when a transaction containing one set is likely to also contain the other. In information retrieval, an association between two sets of keywords occurs when they cooccur in a document. Similarly, in data mining, an association occurs when one attribute set occurs together with another. As the number of such associations may be large, maximal association rules are sought, e.g., Feldman et al. (1997, 1998). Rough set theory is a successful tool for data mining. By using this theory, rules similar to maximal associations can be found. However, we show that the rough set approach to discovering knowledge is much simpler than the maximal association method.

This paper presents a novel method for classification, which makes use of models built by the lattice machine (LM). The LM approximates data resulting in, as a model of data, a set of hyper tuples that are equilabelled, supported and maximal. The method presented uses the LM model of data to classify new data with a view to maximising the density of the model. Experiments show that this method, when used with the LM, outperforms the C2 algorithm and is comparable to the C5.0 classification algorithm.