Universal graph pre-training has emerged as a key paradigm in graph representation learning, offering a promising way to train encoders to learn transferable representations from unlabeled graphs and to effectively generalize across a wide range of downstream tasks. However, recent explorations in universal graph pre-training primarily focus on homogeneous graphs and it remains unexplored for heterogeneous graphs, which exhibit greater structural and semantic complexity. This heterogeneity makes it highly challenging to train a universal encoder for diverse heterogeneous graphs: (i) the diverse types with dataset-specific semantics hinder the construction of a unified representation space; (ii) the number and semantics of meta-paths vary across datasets, making encoding and aggregation patterns learned from one dataset difficult to apply to others. To address these challenges, we propose a novel Meta-path-aware Universal heterogeneous Graph pre-training (MUG) approach. Specifically, for challenge (i), MUG introduces a input unification module that integrates information from multiple node and relation types within each heterogeneous graph into a unified representation. This representation is then projected into a shared space by a dimension-aware encoder, enabling alignment across graphs with diverse schemas. Furthermore, for challenge (ii), MUG trains a shared encoder to capture consistent structural patterns across diverse meta-path views rather than relying on dataset-specific aggregation strategies, while a global objective encourages discriminability and reduces dataset-specific biases. Extensive experiments demonstrate the effectiveness of MUG on some real datasets.

Recent advances in generic large models, such as GPT and DeepSeek, have motivated the introduction of universality to graph pre-training, aiming to learn rich and generalizable knowledge across diverse domains using graph representations to improve performance in various downstream applications. However, most existing methods face challenges in learning effective knowledge from generic graphs, primarily due to simplistic data alignment and limited training guidance. The issue of simplistic data alignment arises from the use of a straightforward unification for highly diverse graph data, which fails to align semantics and misleads pre-training models. The problem with limited training guidance lies in the arbitrary application of in-domain pre-training paradigms to cross-domain scenarios. While it is effective in enhancing discriminative representation in one data space, it struggles to capture effective knowledge from many graphs. To address these challenges, we propose a novel Latent sEmantic Distribution Alignment (LEDA) model for universal graph pre-training. Specifically, we first introduce a dimension projection unit to adaptively align diverse domain features into a shared semantic space with minimal information loss. Furthermore, we design a variational semantic inference module to obtain the shared latent distribution. The distribution is then adopted to guide the domain projection, aligning it with shared semantics across domains and ensuring cross-domain semantic learning. LEDA exhibits strong performance across a broad range of graphs and downstream tasks. Remarkably, in few-shot cross-domain settings, it significantly outperforms in-domain baselines and advanced universal pre-training models.

Graph Neural Networks (GNNs) have recently achieved significant success in several graph-related tasks. However, traditional GNNs and their variants are constantly limited by the implicit homophily, assuming neighboring nodes belong to the same class. This results in weak performance on heterophilic graphs where most nodes are linked to neighbors of different classes. Despite the numerous attempts to adequately deal with heterophily, most methods still use the uniform propagation aggregation mechanism. In this paper, we argue that identifying neighbors with different class labels and exploiting them individually is crucial for heterophilic GNNs. We then propose a simple and efficient novel co-training approach, EG-GCN, which uses group aggregation to handle homophilic and heterophilic neighbors separately. In EG-GCN, we first use an edge discriminator to classify edges and split the neighborhood of every node into two parts. We then apply group graph convolution to the divided neighborhoods to obtain node representations. During training, we continuously optimize the edge discriminator to improve neighborhood partition and use the node classification results to identify highly confident unlabeled nodes to expand the edge training set. This co-training strategy enables both components to enhance each other mutually. Extensive experiments demonstrate that EG-GCN significantly outperforms the state-of-the-art approaches.

Heterogeneous graph neural network (HGNN) is a popular technique for modeling and analyzing heterogeneous graphs. Most existing HGNN-based approaches are supervised or semi-supervised learning methods requiring graphs to be annotated, which is costly and time-consuming. Self-supervised contrastive learning has been proposed to address the problem of requiring annotated data by mining intrinsic properties in the given data. However, the existing contrastive learning methods are not suitable for heterogeneous graphs because they construct contrastive views only based on data perturbation or pre-defined structural properties (e.g., meta-path) in graph data while ignoring noises in node attributes and graph topologies. We develop a robust heterogeneous graph contrastive learning approach, namely HGCL, which introduces two views on respective guidances of node attributes and graph topologies and integrates and enhances them by a reciprocally contrastive mechanism to better model heterogeneous graphs. In this new approach, we adopt distinct but suitable attribute and topology fusion mechanisms in the two views, which are conducive to mining relevant information in attributes and topologies separately. We further use both attribute similarity and topological correlation to construct high-quality contrastive samples. Extensive experiments on four large real-world heterogeneous graphs demonstrate the superiority and robustness of HGCL over several state-of-the-art methods.

Contrastive Learning (CL) has emerged as a popular self-supervised representation learning paradigm that has been shown in many applications to perform similarly to traditional supervised learning methods. A key component of CL is mining the latent discriminative relationships between positive and negative samples and using them as self-supervised labels. We argue that this discriminative contrastive task is, in essence, similar to a classification task, and the “either positive or negative” hard label sampling strategies are arbitrary. To solve this problem, we explore ideas from data distillation, which considers probabilistic logit vectors as soft labels to transfer model knowledge. We attempt to abandon the classical hard sampling labels in CL and instead explore self-supervised soft labels. We adopt soft sampling labels that are extracted, without supervision, from the inherent relationships in data pairs to retain more information. We propose a new self-supervised graph learning method, Distill and Contrast (D&C), for learning representations that closely approximate natural data relationships. D&C extracts node similarities from the features and structures to derive soft sampling labels, which also eliminate noise in the data to increase robustness. Extensive experimental results on real-world datasets demonstrate the effectiveness of the proposed method.

Graph Contrastive Learning (GCL) has emerged as a powerful approach for generating graph representations without the need for manual annotation. Most advanced GCL methods fall into three main frameworks: node discrimination, group discrimination, and bootstrapping schemes, all of which achieve comparable performance. However, the underlying mechanisms and factors that contribute to their effectiveness are not yet fully understood. In this paper, we revisit these frameworks and reveal a common mechanism—representation scattering—that significantly enhances their performance. Our discovery highlights an essential feature of GCL and unifies these seemingly disparate methods under the concept of representation scattering. To leverage this insight, we introduce Scattering Graph Representation Learning (SGRL), a novel framework that incorporates a new representation scattering mechanism designed to enhance representation diversity through a center-away strategy. Additionally, consider the interconnected nature of graphs, we develop a topology-based constraint mechanism that integrates graph structural properties with representation scattering to prevent excessive scattering. We extensively evaluate SGRL across various downstream tasks on benchmark datasets, demonstrating its efficacy and superiority over existing GCL methods. Our findings underscore the significance of representation scattering in GCL and provide a structured framework for harnessing this mechanism to advance graph representation learning. The code of SGRL is at https://github.com/hedongxiao-tju/SGRL.

Heterogeneous information networks (HINs) are potent models of complex systems. In practice, many nodes in an HIN have their attributes unspecified, resulting in significant performance degradation for supervised and unsupervised representation learning. We developed an unsupervised heterogeneous graph contrastive learning approach for analyzing HINs with missing attributes (HGCA). HGCA adopts a contrastive learning strategy to unify attribute completion and representation learning in an unsupervised heterogeneous framework. To deal with a large number of missing attributes and the absence of labels in unsupervised scenarios, we proposed an augmented network to capture the semantic relations between nodes and attributes to achieve a fine-grained attribute completion. Extensive experiments on three large real-world HINs demonstrated the superiority of HGCA over several state-of-the-art methods. The results also showed that the complemented attributes by HGCA can improve the performance of existing HIN models.

Graph Contrastive Learning (GCL) has recently enjoyed great success as an efficient self-supervised representation learning approach. However, the existing methods have focused on designing of contrastive modes and used data augmentation with a rigid and inefficient one-to-one sampling strategy. We adopted node neighborhoods to extend positive samplings and made avoided resorting to data augmentation to create different views. We also considered the homophily problem in Graph Neural Networks (GNNs) between the inter-class node pairs. The key novelty of our method hinged upon analyzing this GNNs problem and integrating the GCL sampling strategy with homophily discrimination, where we solved these two significant problems using one approach. We introduced a new parameterized neighbor sampling component to replace the conventional sub-optimal samplings. By keeping and updating the neighbor sets, both the positive sampling of GCL and the message passing of GNNs can be optimized. Moreover, we theoretically proved that the new method provided a lower bound of mutual information for unsupervised semantic learning, and it can also keep the lower bound with downstream tasks. In essence, our method is a new self-supervised approach, which we refer to as group discrimination, and it can make the downstream fine-tuning efficient. Our extensive empirical results demonstrate that the new method can significantly outperform the existing GCL methods because the former can solve the homophily problem in a self-supervised way with the new group discrimination method used.

Community detection, a fundamental task for network analysis, aims to partition a network into multiple sub-structures to help reveal their latent functions. Community detection has been extensively studied in and broadly applied to many real-world network problems. Classical approaches to community detection typically utilize probabilistic graphical models and adopt a variety of prior knowledge to infer community structures. As the problems that network methods try to solve and the network data to be analyzed become increasingly more sophisticated, new approaches have also been proposed and developed, particularly those that utilize deep learning and convert networked data into low dimensional representation. Despite all the recent advancement, there is still a lack of insightful understanding of the theoretical and methodological underpinning of community detection, which will be critically important for future development of the area of network analysis. In this paper, we develop and present a unified architecture of network community-finding methods to characterize the state-of-the-art of the field of community detection. Specifically, we provide a comprehensive review of the existing community detection methods and introduce a new taxonomy that divides the existing methods into two categories, namely probabilistic graphical model and deep learning. We then discuss in detail the main idea behind each method in the two categories. Furthermore, to promote future development of community detection, we release several benchmark datasets from several problem domains and highlight their applications to various network analysis tasks. We conclude with discussions of the challenges of the field and suggestions of possible directions for future research.

Graph-Convolution-based methods have been successfully applied to representation learning on homophily graphs where nodes with the same label or similar attributes tend to connect with one another. Due to the homophily assumption of Graph Convolutional Networks (GCNs) that these methods use, they are not suitable for heterophily graphs where nodes with different labels or dissimilar attributes tend to be adjacent. Several methods have attempted to address this heterophily problem, but they do not change the fundamental aggregation mechanism of GCNs because they rely on summation operators to aggregate information from neighboring nodes, which is implicitly subject to the homophily assumption. Here, we introduce a novel aggregation mechanism and develop a RAndom Walk Aggregation-based Graph Neural Network (called RAW-GNN) method. The proposed approach integrates the random walk strategy with graph neural networks. The new method utilizes breadth-first random walk search to capture homophily information and depth-first search to collect heterophily information. It replaces the conventional neighborhoods with path-based neighborhoods and introduces a new path-based aggregator based on Recurrent Neural Networks. These designs make RAW-GNN suitable for both homophily and heterophily graphs. Extensive experimental results showed that the new method achieved state-of-the-art performance on a variety of homophily and heterophily graphs.

Abnormal expressions of long non-coding RNAs (lncRNAs) are associated with various human diseases. Identifying disease-related lncRNAs can help clarify complex disease pathogeneses. The latest methods for lncRNA-disease association prediction rely on diverse data about lncRNAs and diseases. These methods, however, cannot adequately integrate the neighbour topological information of lncRNA and disease nodes. Moreover, more intrinsic features of lncRNA-disease node pairs can be explored to better predict their latent associations. We developed a novel method, named GTAN, to predict the association propensities between lncRNAs and diseases. GTAN integrates various information about lncRNAs and diseases, and exploits neighbour topology and attribute representations of a pair of lncRNA-disease nodes. We adopted in GTAN a graph neural network architecture with three attention mechanisms and multi-layer convolutional neural networks. First, a neighbour-level self-attention mechanism is constructed to learn the importance of each neighbour for an interested lncRNA or disease node. Second, topology-level attention is proposed to enhance contextual dependencies among multiple local topology representations. An attention-enhanced graph neural network framework is then established to learn a topology representation of top-ranked neighbours. GTAN also has attribute-level attention to distinguish various contributions of attributes of the lncRNA-disease pair. Finally, attribute representation is learned by multi-layer CNN to integrate detailed features and representative features of the pair. Extensive experimental results demonstrated that GTAN outperformed state-of-the-art methods. The ablation studies confirmed the important contributions of three attention mechanisms. Case studies on three cancers further showed GTAN's ability in discovering potential lncRNA candidates related to diseases.

Community detection has been extensively studied for various applications. Recent research has started to explore node contents to identify semantically meaningful communities. However, links in real networks typically have semantic descriptions and communities of links can better characterize community behaviors than communities of nodes. The second issue in community finding is that the most existing methods assume network topologies and descriptive contents carry the same or compatible information of node group membership, restricting them to one topic per community, which is generally violated in real networks. The third issue is that the existing methods use top ranked words or phrases to label topics when interpreting communities, which is often inadequate for comprehension. To address these issues altogether, we propose a new Bayesian probabilistic approach for modeling real networks and developing an efficient variational algorithm for model inference. Our new method explores the intrinsic correlation between communities and topics to discover link communities and extract semantically meaningful community summaries at the same time. If desired, it is able to derive more than one topical summary per community to provide rich explanations. We present experimental results to show the effectiveness of our new approach and evaluate the method by a case study.

Community detection, aiming at partitioning a network into multiple substructures, is practically importance. Graph convolutional network (GCN), a new deep-learning technique, has recently been developed for community detection. Markov Random Fields (MRF) has been combined with GCN in the MRFasGCN method to improve accuracy. However, the existing GCN community-finding methods are semi-supervised, even though community finding is essentially an unsupervised learning problem. We developed a new GCN approach for unsupervised community detection under the framework of Autoencoder. We cast MRFasGCN as an encoder and then derived node community membership in the hidden layer of the encoder. We introduced a community-centric dual decoder to reconstruct network structures and node attributes separately in an unsupervised fashion, for faithful community detection in the input space. We designed a scheme of local enhancement to accommodate nodes to have more common neighbors and similar attributes with similar community memberships. Experimental results on real networks showed that our new method outperformed the best existing methods, showing the effectiveness of the novel decoding mechanism for generating links and attributes together over the commonly used methods for reconstructing links alone.

Constraints propagation and backtracking are two basic techniques for solving constraint satisfaction problems (CSPs). During the search for a solution, the variable and value pairs that do not belong to any solution can be discarded by constraint propagation to ensure generalized arc consistency so as to avoid the fruitless search. However, constraint propagation is frequently invoked often with little effect on many CSPs. Much effort has been devoted to predicting when to invoke constraint propagation for solving a CSP; however, no effective approach has been developed for the alldifferent constraint. Here we present a novel theorem for identifying the edges in a value graph of alldifferent constraint whose removal can significantly reduce useless constraint propagation. We prove that if an alternating cycle exists for a prospectively removable edge that represents a variable-value assignment, the edge (and the assignment) can be discarded without constraint propagation. Based on this theorem, we developed a novel optimizing technique for early detection of useless constraint propagation which can be incorporated in any existing algorithm for alldifferent constraint. Our implementation of the new method achieved speedup by a factor of 1-5 over the state-of-art approaches on 93 benchmark problem instances in 8 domains. Furthermore, the new algorithm is scalable well and runs increasingly faster than the existing methods on larger problems.

Identification of disease-associated microRNAs (disease miRNAs) is an essential step towards discovering causal miRNAs and understanding disease pathogenesis. Two sources of information can be exploited for predicting disease miRNAs: one includes the connections between miRNAs, between diseases, and between miRNAs and diseases, and the other has the attributes of miRNA nodes. The former contains information of miRNA similarities, disease similarities, and miRNA-disease associations. The latter includes the information of the families and clusters that miRNAs belong to. Similar diseases are usually associated with miRNAs that have similar functions and common attributes. However, most of the existing methods for disease miRNA prediction focus only on the connections of miRNAs and diseases. It remains challenging to adequately integrate the connections and miRNA node attributes to identify more reliable candidate disease miRNAs. We propose a non-negative matrix factorization based method, FamCluRank, for predicting disease miRNAs in heterogeneous networks with node attributes. One of the novelties of FamCluRank is to fully utilize these two oversighted characteristics of miRNAs and focuses particularly on a deep integration of miRNA families and cluster attributes. In particular, the integration was achieved by three different means. We first constructed a miRNA-disease heterogeneous network with node attributes where the miRNA nodes have their family and cluster attributes. Second, miRNAs sharing more common families and clusters are more likely to be associated with the diseases that are also related to these families and clusters. On the basis of the biological premise, we constructed a novel prediction model of FamCluRank to deeply integrate the family and cluster attributes of miRNAs. Third, two similar diseases tend to be associated with more common miRNA families and clusters, and vice versa. Hence, FamCluRank's prediction model is constructed by concerning not only the possible associations between miRNAs and diseases but also the possible disease-family and disease-cluster associations. Comparison with the state-of-the-art methods showed FamCluRank's superior performance not only on the well-characterized diseases but also on the new ones. Case studies on colorectal neoplasms, pancreatic neoplasms, lung neoplasms, and 32 new diseases demonstrated its ability for discovering potential disease miRNAs. FamCluRank is a potent prioritization tool for screening the reliable candidates for subsequent studies concerning their involvement in the pathogenesis of diseases. The web service of FamCluRank, the candidate disease miRNAs for 329 diseases, and the dataset used to develop FamCluRank are available at http://www.famclurank.top.

Overlapping community detection has triggered recent research in network analysis. One of the promising techniques for finding overlapping communities is the popular stochastic models, which, unfortunately, have some common drawbacks. They do not support an important observation that highly connected nodes are more likely to reside in the overlapping regions of communities in the network. These methods are in essence not truly unsupervised, since they require a threshold on probabilistic memberships to derive overlapping structures and need the number of communities to be specified a priori . We develop a new method to address these issues for overlapping community detection. We first present a stochastic model to accommodate the relative importance and the expected degree of every node in each community. We then infer every overlapping community by ranking the nodes according to their importance. Second, we determine the number of communities under the Bayesian framework. We evaluate our method and compare it with five state-of-the-art methods. The results demonstrate the superior performance of our method. We also apply this new method to two applications, showing its superb performance on practical problems.

Community detection is a fundamental problem in network science with various applications. The problem has attracted much attention and many approaches have been proposed. Among the existing approaches are the latest methods based on Graph Convolutional Networks (GCN) and on statistical modeling of Markov Random Fields (MRF). Here, we propose to integrate the techniques of GCN and MRF to solve the problem of semi-supervised community detection in attributed networks with semantic information. Our new method takes advantage of salient features of GNN and MRF and exploits both network topology and node semantic information in a complete end-to-end deep network architecture. Our extensive experiments demonstrate the superior performance of the new method over state-of-the-art methods and its scalability on several large benchmark problems.

Network embedding (NE) maps a network into a low-dimensional space while preserving intrinsic features of the network. Variational Auto-Encoder (VAE) has been actively studied for NE. These VAE-based methods typically utilize both network topologies and node semantics and treat these two types of data in the same way. However, the information of network topology and information of node semantics are orthogonal and are often from different sources; the former quantifies coupling relationships among nodes, whereas the latter represents node specific properties. Ignoring this difference affects NE. To address this issue, we develop a network-specific VAE for NE, named as NetVAE. In the encoding phase of our new approach, compression of network structures and compression of node attributes share the same encoder in order to perform co-training to achieve transfer learning and information integration. In the decoding phase, a dual decoder is introduced to reconstruct network topologies and node attributes separately. Specifically, as a part of the dual decoder, we develop a novel method based on a Gaussian mixture model and the block model to reconstruct network structures. Extensive experiments on large real-world networks demonstrate a superior performance of the new approach over the state-of-the-art methods.

Markov Random Field (MRF) is a powerful framework for developing probabilistic models of complex problems. MRF models possess rich structures to represent properties and constraints of a problem. It has been successful on many application problems, particularly those of computer vision and image processing, where data are structured, e.g., pixels are organized on grids. The problem of identifying communities in networks, which is essential for network analysis, is in principle analogous to finding objects in images. It is surprising that MRF has not yet been explored for network community detection. It is challenging to apply MRF to network analysis problems where data are organized on graphs with irregular structures. Here we present a network-specific MRF approach to community detection. The new method effectively encodes the structural properties of an irregular network in an energy function (the core of an MRF model) so that the minimization of the function gives rise to the best community structures. We analyzed the new MRF-based method on several synthetic benchmarks and real-world networks, showing its superior performance over the state-of-the-art methods for community identification.

Community detection has been extensively studied for various applications, focusing primarily on network topologies. Recent research has started to explore node contents to identify semantically meaningful communities and interpret their structures using selected words. However, links in real networks typically have semantic descriptions, e.g., comments and emails in social media, supporting the notion of communities of links. Indeed, communities of links can better describe multiple roles that nodes may play and provide a richer characterization of community behaviors than communities of nodes. The second issue in community finding is that most existing methods assume network topologies and descriptive contents to be consistent and to carry the compatible information of node group membership, which is generally violated in real networks. These methods are also restricted to interpret one community with one topic. The third problem is that the existing methods have used top ranked words or phrases to label topics when interpreting communities. However, it is often difficult to comprehend the derived topics using words or phrases, which may be irrelevant. To address these issues altogether, we propose a new unified probabilistic model that can be learned by a dual nested expectation-maximization algorithm. Our new method explores the intrinsic correlation between communities and topics to discover link communities robustly and extract adequate community summaries in sentences instead of words for topic labeling at the same time. It is able to derive more than one topical summary per community to provide rich explanations. We present experimental results to show the effectiveness of our new approach, and evaluate the quality of the results by a case study.

Network embedding is to learn a low-dimensional representation for a network in order to capture intrinsic features of the network. It has been applied to many applications, e.g., network community detection and user recommendation. One of the recent research topics for network embedding has been focusing on exploitation of diverse information, including network topology and semantic information on nodes of networks. However, such diverse information has not been fully utilized nor adequately integrated in the existing methods, so that the resulting network embedding is far from satisfactory. In this paper, we develop a weight-free multi-component network embedding approach by network reconstruction via a deep Autoencoder. Three key components make our new approach effective, i.e., a uniformed graph representation of network topology and semantic information, enhancement to the graph representation using local network structure (i.e., pairwise relationship on nodes) by sampling with latent space regularization, and integration of the diverse information in graph forms in a deep Autoencoder. Extensive experimental results on seven real-world networks demonstrate a superior performance of our method over nine state-of-the-art methods for embedding.

The alldifferent constraint is an essential ingredient of most Constraints Satisfaction Problems (CSPs). It has been known that the generalized arc consistency (GAC) of alldifferent constraints can be reduced to the maximum matching problem in a value graph. The redundant edges, which do not appear in any maximum matching of the value graph, can and should be removed from the graph. The existing methods attempt to identify these redundant edges by computing the strongly connected components after finding a maximum matching for the graph. Here, we present a novel theorem for identification of the redundant edges. We show that some of the redundant edges can be immediately detected after finding a maximum matching. Based on this theoretical result, we present an efficient algorithm for processing alldifferent constraints. Experimental results on real problems show that our new algorithm significantly outperforms the-state-of-art approaches.

MOTIVATION: Identification of disease-associated miRNAs (disease miRNAs) is critical for understanding disease etiology and pathogenesis. Since miRNAs exert their functions by regulating the expression of their target mRNAs, several methods based on the target genes were proposed to predict disease miRNA candidates. They achieved only limited success as they all suffered from the high false-positive rate of target prediction results. Alternatively, other prediction methods were based on the observation that miRNAs with similar functions tend to be associated with similar diseases and vice versa. The methods exploited the information about miRNAs and diseases, including the functional similarities between miRNAs, the similarities between diseases, and the associations between miRNAs and diseases. However, how to integrate the multiple kinds of information completely and consider the biological characteristic of disease miRNAs is a challenging problem. RESULTS: We constructed a bilayer network to represent the complex relationships among miRNAs, among diseases and between miRNAs and diseases. We proposed a non-negative matrix factorization based method to rank, so as to predict, the disease miRNA candidates. The method integrated the miRNA functional similarity, the disease similarity and the miRNA-disease associations seamlessly, which exploited the complex relationships within the bilayer network and the consensus relationship between multiple kinds of information. Considering the correlation between the candidates related to various diseases, it predicted their respective candidates for all the diseases simultaneously. In addition, the sparseness characteristic of disease miRNAs was introduced to generate more reliable prediction model that excludes those noisy candidates. The results on 15 common diseases showed a superior performance of the new method for not only well-characterized diseases but also new ones. A detailed case study on breast neoplasms, colorectal neoplasms, lung neoplasms and 32 other diseases demonstrated the ability of the method for discovering potential disease miRNAs. AVAILABILITY AND IMPLEMENTATION: The web service for the new method and the list of predicted candidates for all the diseases are available at http://www.bioinfolab.top. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

The objective of discovering network communities, an essential step in complex systems analysis, is two-fold: identification of functional modules and their semantics at the same time. However, most existing community-finding methods have focused on finding communities using network topologies, and the problem of extracting module semantics has not been well studied and node contents, which often contain semantic information of nodes and networks, have not been fully utilized. We considered the problem of identifying network communities and module semantics at the same time. We introduced a novel generative model with two closely correlated parts, one for communities and the other for semantics. We developed a co-learning strategy to jointly train the two parts of the model by combining a nested EM algorithm and belief propagation. By extracting the latent correlation between the two parts, our new method is not only robust for finding communities and semantics, but also able to provide more than one semantic explanation to a community. We evaluated the new method on artificial benchmarks and analyzed the semantic interpretability by a case study. We compared the new method with eight state-of-the-art methods on ten real-world networks, showing its superior performance over the existing methods.

Detection of overlapping communities has drawn much attention lately as they are essential properties of real complex networks. Despite its influence and popularity, the well studied and widely adopted stochastic model has not been made effective for finding overlapping communities. Here we extend the stochastic model method to detection of overlapping communities with the virtue of autonomous determination of the number of communities. Our approach hinges upon the idea of ranking node popularities within communities and using a Bayesian method to shrink communities to optimize an objective function based on the stochastic generative model. We evaluated the novel approach, showing its superior performance over five state-of-the-art methods, on large real networks and synthetic networks with ground-truths of overlapping communities.

Identification of modular or community structures of a network is a key to understanding the semantics and functions of the network. While many network community detection methods have been developed, which primarily explore network topologies, they provide little semantic information of the communities discovered. Although structures and semantics are closely related, little effort has been made to discover and analyze these two essential network properties together. By integrating network topology and semantic information on nodes, e.g., node attributes, we study the problems of detection of communities and inference of their semantics simultaneously. We propose a novel nonnegative matrix factorization (NMF) model with two sets of parameters, the community membership matrix and community attribute matrix, and present efficient updating rules to evaluate the parameters with a convergence guarantee. The use of node attributes improves upon community detection and provides a semantic interpretation to the resultant network communities. Extensive experimental results on synthetic and real-world networks not only show the superior performance of the new method over the state-of-the-art approaches, but also demonstrate its ability to semantically annotate the communities.

Link prediction and multi-label learning on graphs are two important but challenging machine learning problems that have broad applications in diverse fields. Not only are the two problems inherently correlated and often appear concurrently, they are also exacerbated by incomplete data. We develop a novel algorithm to solve these two problems jointly under a unified framework, which helps reduce the impact of graph noise and benefits both tasks individually. We reduce multi-label learning problem into an additional link prediction task and solve both problems with marginalized denoising, which we co-regularize with Laplacian smoothing. This approach combines both learning tasks into a single convex objective function, which we optimize efficiently with iterative closed-form updates. The resulting approach performs significantly better than prior work on several important real-world applications with great consistency.

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.

An important problem in analyzing complex networks is discovery of modular or community structures embedded in the networks. Although being promising for identifying network communities, the popular stochastic models often do not preserve node degrees, thus reducing their representation power and applicability to real-world networks. Here we address this critical problem. Instead of using a blockmodel, we adopted a random-graph null model to faithfully capture community structures by preserving in the model the expected node degrees. The new model, learned using nonnegative matrix factorization, is more accurate and robust in representing community structures than the existing methods. Our results from extensive experiments on synthetic benchmarks and real-world networks show the superior performance of the new method over the existing methods in detecting both disjoint and overlapping communities.

Missing information is ubiquitous in relational datasets. Imputation of missing relations, a.k.a. link prediction, has become an increasingly crucial problem in relational data analysis as a huge amount of data has been accumulated in various fields. Recent advances in the latent variable models have greatly improved the state-of-the-art in the link prediction accuracy, however it comes at the price of increasing complexity. In this paper, we propose a novel link prediction algorithm, marginalized denoising model (MDM), where the problem of predicting unobserved or missing links in a given relational matrix is cast as a problem of matrix denoising. The method learns a mapping function that models the embedded topological structures of the relational network by capturing the so-called indirect affinities among entities. We train the mapping function by recovering the originally observed matrix from a conceptually “infinite” number of corrupted matrices where some links are randomly masked from the observed matrix. By re-applying the learned function to the observed relational matrix, we aim to “denoise” the observed matrix and thus to recover the unobserved links. Experimental results on several benchmarks demonstrate the superior performance of the new method over several state-of-the-art link prediction methods.

Hundreds of genetic markers have shown associations with various complex diseases, yet the "missing heritability" remains alarmingly elusive. Combinatorial interactions may account for a substantial portion of this missing heritability, but their discoveries have been impeded by computational complexity and genetic heterogeneity. We present BlocBuster, a novel systems-level approach that efficiently constructs genome-wide, allele-specific networks that accurately segregate homogenous combinations of genetic factors, tests the associations of these combinations with the given phenotype, and rigorously validates the results using a series of unbiased validation methods. BlocBuster employs a correlation measure that is customized for single nucleotide polymorphisms and returns a multi-faceted collection of values that captures genetic heterogeneity. We applied BlocBuster to analyze psoriasis, discovering a combinatorial pattern with an odds ratio of 3.64 and Bonferroni-corrected p-value of 5.01×10(-16). This pattern was replicated in independent data, reflecting robustness of the method. In addition to improving prediction of disease susceptibility and broadening our understanding of the pathogenesis underlying psoriasis, these results demonstrate BlocBuster's potential for discovering combinatorial genetic associations within heterogeneous genome-wide data, thereby transcending the limiting "small effects" produced by individual markers examined in isolation.

The importance of writing well can never be overstated for a successful professional career, and the ability to write solid papers is an essential trait of a productive researcher. Writing and publishing a paper has its own life cycle; properly following a course of action and avoiding missteps can be vital to the overall success not only of a paper but of the underlying research as well. Here, we offer ten simple rules for writing and publishing research papers. As a caveat, this essay is not about the mechanics of composing a paper, much of which has been covered elsewhere, e.g., [1], [2]. Rather, it is about the principles and attitude that can help guide the process of writing in particular and research in general. In this regard, some of the discussion will complement, extend, and refine some advice given in early articles of this Ten Simple Rules series of PLOS Computational Biology [3]–[8].

Accurate identification of cis-regulatory elements and their correlated modules is essential for analysis of transcriptional regulation, which is a challenging problem in computational biology. Unsupervised learning has the advantage of compensating for missing annotated data, and is thus promising to be effective to identify cis-regulatory elements and modules. We introduced a Conditional Random Fields model, referred to as CRFEM, to integrate sequence features and long-range dependency of genomic sequences such as epigenetic features to identify cis-regulatory elements and modules at the same time. The proposed method is able to automatically learn model parameters with no labeled data and explicitly optimize the predictive probability of cis-regulatory elements and modules. In comparison with existing methods, our method is more accurate and can be used for genome-wide studies of gene regulation.

Complex traits such as obesity are manifestations of intricate interactions of multiple genetic factors. However, such relationships are difficult to identify. Thanks to the recent advance in high-throughput technology, a large amount of data has been collected for various complex traits, including obesity. These data often measure different biological aspects of the traits of interest, including genotypic variations at the DNA level and gene expression alterations at the RNA level. Integration of such heterogeneous data provides promising opportunities to understand the genetic components and possibly genetic architecture of complex traits. In this paper, we propose a machine learning based method, module-guided Random Forests (mgRF), to integrate genotypic and gene expression data to investigate genetic factors and molecular mechanism underlying complex traits. mgRF is an augmented Random Forests method enhanced by a network analysis for identifying multiple correlated variables of different types. We applied mgRF to genetic markers and gene expression data from a cohort of F2 female mouse intercross. mgRF outperformed several existing methods in our extensive comparison. Our new approach has an improved performance when combining both genotypic and gene expression data compared to using either one of the two types of data alone. The resulting predictive variables identified by mgRF provide information of perturbed pathways that are related to body weight. More importantly, the results uncovered intricate interactions among genetic markers and genes that have been overlooked if only one type of data was examined. Our results shed light on genetic mechanisms of obesity and our approach provides a promising complementary framework to the "genetics of gene expression" analysis for integrating genotypic and gene expression information for analyzing complex traits.

Complex features, such as temporal dependencies and numerical cost constraints, are hallmarks of real-world planning problems. In this article, we consider the challenging problem of cost-sensitive temporally expressive (CSTE) planning, which requires concurrency of durative actions and optimization of action costs. We first propose a scheme to translate a CSTE planning problem to a minimum cost (MinCost) satisfiability (SAT) problem and to integrate with a relaxed parallel planning semantics for handling true temporal expressiveness. Our scheme finds solution plans that optimize temporal makespan, and also minimize total action costs at the optimal makespan. We propose two approaches for solving MinCost SAT. The first is based on a transformation of a MinCost SAT problem to a weighted partial Max-SAT (WPMax-SAT), and the second, called BB-CDCL, is an integration of the branch-and-bound technique and the conflict driven clause learning (CDCL) method. We also develop a CSTE customized variable branching scheme for BB-CDCL which can significantly improve the search efficiency. Our experiments on the existing CSTE benchmark domains show that our planner compares favorably to the state-of-the-art temporally expressive planners in both efficiency and quality.

BACKGROUND: Nucleosome distribution along chromatin dictates genomic DNA accessibility and thus profoundly influences gene expression. However, the underlying mechanism of nucleosome formation remains elusive. Here, taking a structural perspective, we systematically explored nucleosome formation potential of genomic sequences and the effect on chromatin organization and gene expression in S. cerevisiae. RESULTS: We analyzed twelve structural features related to flexibility, curvature and energy of DNA sequences. The results showed that some structural features such as DNA denaturation, DNA-bending stiffness, Stacking energy, Z-DNA, Propeller twist and free energy, were highly correlated with in vitro and in vivo nucleosome occupancy. Specifically, they can be classified into two classes, one positively and the other negatively correlated with nucleosome occupancy. These two kinds of structural features facilitated nucleosome binding in centromere regions and repressed nucleosome formation in the promoter regions of protein-coding genes to mediate transcriptional regulation. Based on these analyses, we integrated all twelve structural features in a model to predict more accurately nucleosome occupancy in vivo than the existing methods that mainly depend on sequence compositional features. Furthermore, we developed a novel approach, named DLaNe, that located nucleosomes by detecting peaks of structural profiles, and built a meta predictor to integrate information from different structural features. As a comparison, we also constructed a hidden Markov model (HMM) to locate nucleosomes based on the profiles of these structural features. The result showed that the meta DLaNe and HMM-based method performed better than the existing methods, demonstrating the power of these structural features in predicting nucleosome positions. CONCLUSIONS: Our analysis revealed that DNA structures significantly contribute to nucleosome organization and influence chromatin structure and gene expression regulation. The results indicated that our proposed methods are effective in predicting nucleosome occupancy and positions and that these structural features are highly predictive of nucleosome organization.The implementation of our DLaNe method based on structural features is available online.

Planning as satisfiability is a principal approach to planning with many eminent advantages. The existing planning as satisfiability techniques usually use encodings compiled from STRIPS. We introduce a novel SAT encoding scheme (SASE) based on the SAS+ formalism. The new scheme exploits the structural information in SAS+, resulting in an encoding that is both more compact and efficient for planning. We prove the correctness of the new encoding by establishing an isomorphism between the solution plans of SASE and that of STRIPS based encodings. We further analyze the transition variables newly introduced in SASE to explain why it accommodates modern SAT solving algorithms and improves performance. We give empirical statistical results to support our analysis. We also develop a number of techniques to further reduce the encoding size of SASE, and conduct experimental studies to show the strength of each individual technique. Finally, we report extensive experimental results to demonstrate significant improvements of SASE over the state-of-the-art STRIPS based encoding schemes in terms of both time and memory efficiency.

Planning as satisfiability is a principal approach to planning with many eminent advantages. The existing planning as satisfiability techniques usually use encodings compiled from the STRIPS formalism. We introduce a novel SAT encoding scheme based on the SAS+ formalism. It exploits the structural information in the SAS+ formalism, resulting in more compact SAT instances and reducing the number of clauses by up to 50 fold. Our results show that this encoding scheme improves upon the STRIPS-based encoding, in terms of both time and memory efficiency.

The Hamiltonian cycle problem (HCP) is an important combinatorial problem with applications in many areas. It is among the first problems used for studying intrinsic properties, including phase transitions, of combinatorial problems. While thorough theoretical and experimental analyses have been made on the HCP in undirected graphs, a limited amount of work has been done for the HCP in directed graphs (DHCP). The main contribution of this work is an effective algorithm for the DHCP. Our algorithm explores and exploits the close relationship between the DHCP and the Assignment Problem (AP) and utilizes a technique based on Boolean satisfiability (SAT). By combining effective algorithms for the AP and SAT, our algorithm significantly outperforms previous exact DHCP algorithms, including an algorithm based on the award-winning Concorde TSP algorithm. The second result of the current study is an experimental analysis of phase transitions of the DHCP, verifying and refining a known phase transition of the DHCP.

MOTIVATION: Inference of haplotypes from genotype data is crucial and challenging for many vitally important studies. The first, and most critical step, is the ascertainment of a biologically sound model to be optimized. Many models that have been proposed rely partially or entirely on reducing the number of unique haplotypes in the solution. RESULTS: This article examines the parsimony of haplotypes using known haplotypes as well as genotypes from the HapMap project. Our study reveals that there are relatively few unique haplotypes, but not always the least possible, for the datasets with known solutions. Furthermore, we show that there are frequently very large numbers of parsimonious solutions, and the number increases exponentially with increasing cardinality. Moreover, these solutions are quite varied, most of which are not consistent with the true solutions. These results quantify the limitations of the Pure Parsimony model and demonstrate the imperative need to consider additional properties for haplotype inference models. At a higher level, and with broad applicability, this article illustrates the power of combinatorial methods to tease out imperfections in a given biological model.

UNLABELLED: MicroRNA (miRNAs) play essential roles in post-transcriptional gene regulation in animals and plants. Several existing computational approaches have been developed to complement experimental methods in discovery of miRNAs that express restrictively in specific environmental conditions or cell types. These computational methods require a sufficient number of characterized miRNAs as training samples, and rely on genome annotation to reduce the number of predicted putative miRNAs. However, most sequenced genomes have not been well annotated and many of them have a very few experimentally characterized miRNAs. As a result, the existing methods are not effective or even feasible for identifying miRNAs in these genomes. Aiming at identifying miRNAs from genomes with a few known miRNA and/or little annotation, we propose and develop a novel miRNA prediction method, miRank, based on our new random walks- based ranking algorithm. We first tested our method on Homo sapiens genome; using a very few known human miRNAs as samples, our method achieved a prediction accuracy greater than 95%. We then applied our method to predict 200 miRNAs in Anopheles gambiae, which is the most important vector of malaria in Africa. Our further study showed that 78 out of the 200 putative miRNA precursors encode mature miRNAs that are conserved in at least one other animal species. These conserved putative miRNAs are good candidates for further experimental study to understand malaria infection. AVAILABILITY: MiRank is programmed in Matlab on Windows platform. The source code is available upon request.

Lung transplantation is the treatment of choice for end-stage pulmonary diseases. A limited donor supply has resulted in 4000 patients on the waiting list. Currently, 10-20% of donor organs are deemed suitable under the selection criteria, of which 15-25% fails due to primary graft dysfunction (PGD). In this study, we attempt to further our understanding of PGD by observing the changes in gene expression across donor lungs that developed PGD versus those that did not. Our second goal is to use a machine learning tool - support vector machine (SVM), to distinguish unsuitable donor lungs from suitable donor lungs, based on the gene expression data. Classification results for distinguishing suitable and unsuitable lungs for transplantation using a SVM were promising. This is the first such attempt to use human lungs used for transplantation and combine the identification of a molecular signature for PGD, with machine learning methods for donor lung prediction.

Automatic discovery of community structures in complex networks is a fundamental task in many disciplines, including social science, engineering, and biology. A quantitative measure called modularity (Q) has been proposed to effectively assess the quality of community structures. Several community discovery algorithms have since been developed based on the optimization of Q. However, this optimization problem is NP-hard, and the existing algorithms have a low accuracy or are computationally expensive. In this paper, we present an efficient spectral algorithm for modularity optimization. When tested on a large number of synthetic or real-world networks, and compared to the existing algorithms, our method is efficient and and has a high accuracy. In addition, we have successfully applied our algorithm to detect interesting and meaningful community structures from real-world networks in different domains, including biology, medicine and social science. Due to space limitation, results of these applications are presented in a complete version of the paper available on our Website (http://cse .wustl.edu/~jruan/).

MicroRNAs are short, noncoding RNAs that play important roles in post-transcriptional gene regulation. Although many functions of microRNAs in plants and animals have been revealed in recent years, the transcriptional mechanism of microRNA genes is not well-understood. To elucidate the transcriptional regulation of microRNA genes, we study and characterize, in a genome scale, the promoters of intergenic microRNA genes in Caenorhabditis elegans, Homo sapiens, Arabidopsis thaliana, and Oryza sativa. We show that most known microRNA genes in these four species have the same type of promoters as protein-coding genes have. To further characterize the promoters of microRNA genes, we developed a novel promoter prediction method, called common query voting (CoVote), which is more effective than available promoter prediction methods. Using this new method, we identify putative core promoters of most known microRNA genes in the four model species. Moreover, we characterize the promoters of microRNA genes in these four species. We discover many significant, characteristic sequence motifs in these core promoters, several of which match or resemble the known cis-acting elements for transcription initiation. Among these motifs, some are conserved across different species while some are specific to microRNA genes of individual species.

This paper demonstrates machine learning and data mining methods that can be developed and applied to analyzing large quantities of genomic information and gene expression data for characterizing and modeling gene expression regulation. In particular, there will be a discussion on some of the methods that have been developed for modeling gene expression regulation underlying abiotic stress (e.g., drought, low temperature and salinity) tolerance, for identifying gene responsive to particular environmental stress conditions, and for characterizing the functions of microRNA genes for stress regulation in model plant Arabidopsis thaliana.

MOTIVATION: The transcriptional regulation of a gene depends on the binding of cis-regulatory elements on its promoter to some transcription factors and the expression levels of the transcription factors. Most existing approaches to studying transcriptional regulation model these dependencies separately, i.e. either from promoters to gene expression or from the expression levels of transcription factors to the expression levels of genes. Little effort has been devoted to a single model for integrating both dependencies. RESULTS: We propose a novel method to model gene expression using both promoter sequences and the expression levels of putative regulators. The proposed method, called bi-dimensional regression tree (BDTree), extends a multivariate regression tree approach by applying it simultaneously to both genes and conditions of an expression matrix. The method produces hypotheses about the condition-specific binding motifs and regulators for each gene. As a side-product, the method also partitions the expression matrix into small submatrices in a way similar to bi-clustering. We propose and compare several splitting functions for building the tree. When applied to two microarray datasets of the yeast Saccharomyces cerevisiae, BDTree successfully identifies most motifs and regulators that are known to regulate the biological processes underlying the datasets. Comparing with an existing algorithm, BDTree provides a higher prediction accuracy in cross-validations.

Given a matrix of values in which the rows correspond to objects and the columns correspond to features of the objects, rearrangement clustering is the problem of rearranging the rows of the matrix such that the sum of the similarities between adjacent rows is maximized. Referred to by various names and reinvented several times, this clustering technique has been extensively used in many fields over the last three decades. In this paper, we point out two critical pitfalls that have been previously overlooked. The first pitfall is deleterious when rearrangement clustering is applied to objects that form natural clusters. The second concerns a similarity metric that is commonly used. We present an algorithm that overcomes these pitfalls. This algorithm is based on a variation of the Traveling Salesman Problem. It offers an extra benefit as it automatically determines cluster boundaries. Using this algorithm, we optimally solve four benchmark problems and a 2,467-gene expression data clustering problem. As expected, our new algorithm identifies better clusters than those found by previous approaches in all five cases. Overall, our results demonstrate the benefits of rectifying the pitfalls and exemplify the usefulness of this clustering technique. Our code is available at our websites.

MOTIVATION: A fundamental problem of computational genomics is identifying the genes that respond to certain endogenous cues and environmental stimuli. This problem can be referred to as targeted gene finding. Since gene regulation is mainly determined by the binding of transcription factors and cis-regulatory DNA sequences, most existing gene annotation methods, which exploit the conservation of open reading frames, are not effective in finding target genes. RESULTS: A viable approach to targeted gene finding is to exploit the cis-regulatory elements that are known to be responsible for the transcription of target genes. Given such cis-elements, putative target genes whose promoters contain the elements can be identified. As a case study, we apply the above approach to predict the genes in model plant Arabidopsis thaliana which are inducible by a phytohormone, abscisic acid (ABA), and abiotic stress, such as drought, cold and salinity. We first construct and analyze two ABA specific cis-elements, ABA-responsive element (ABRE) and its coupling element (CE), in A.thaliana, based on their conservation in rice and other cereal plants. We then use the ABRE-CE module to identify putative ABA-responsive genes in A.thaliana. Based on RT-PCR verification and the results from literature, this method has an accuracy rate of 67.5% for the top 40 predictions. The cis-element based targeted gene finding approach is expected to be widely applicable since a large number of cis-elements in many species are available.

BACKGROUND: Many classification approaches have been applied to analyzing transcriptional regulation of gene expressions. These methods build models that can explain a gene's expression level from the regulatory elements (features) on its promoter sequence. Different types of features, such as experimentally verified binding motifs, motifs discovered by computer programs, or transcription factor binding data measured with Chromatin Immunoprecipitation (ChIP) assays, have been used towards this goal. Each type of features has been shown successful in modeling gene transcriptional regulation under certain conditions. However, no comparison has been made to evaluate the relative merit of these features. Furthermore, most publicly available classification tools were not designed specifically for modeling transcriptional regulation, and do not allow the user to combine different types of features. RESULTS: In this study, we use a specific classification method, decision trees, to model transcriptional regulation in yeast with features based on predefined motifs, automatically identified motifs, ChlP-chip data, or their combinations. We compare the accuracies and stability of these models, and analyze their capabilities in identifying functionally related genes. Furthermore, we design and implement a user-friendly web server called CAGER (Classification Analysis of Gene Expression Regulation) that integrates several software components for automated analysis of transcriptional regulation using decision trees. Finally, we use CAGER to study the transcriptional regulation of Arabidopsis genes in response to abscisic acid, and report some interesting new results. CONCLUSION: Models built with ChlP-chip data suffer from low accuracies when the condition under which gene expressions are measured is significantly different from the condition under which the ChIP experiment is conducted. Models built with automatically identified motifs can sometimes discover new features, but their modeling accuracies may have been over-estimated in previous studies. Furthermore, models built with automatically identified motifs are not stable with respect to noises. A combination of ChlP-chip data and predefined motifs can substantially improve modeling accuracies, and is effective in identifying true regulons. The CAGER web server, which is freely available at http://cic.cs.wustl.edu/CAGER/, allows the user to select combinations of different feature types for building decision trees, and interact with the models graphically. We believe that it will be a useful tool to facilitate the discovery of gene transcriptional regulatory networks.

The critical resource that limits the application of best-first search is memory. We present a new class of best-first search algorithms that reduce the space complexity. The key idea is to store only the Open list of generated nodes, but not the Closed list of expanded nodes. The solution path can be recovered by a divide-and-conquer technique, either as a bidirectional or unidirectional search. For many problems, frontier search dramatically reduces the memory required by best-first search. We apply frontier search to breadth-first search of sliding-tile puzzles and the 4-peg Towers of Hanoi problem, Dijkstra's algorithm on a grid with random edge costs, and the A* algorithm on the Fifteen Puzzle, the four-peg Towers of Hanoi Problem, and optimal sequence alignment in computational biology.

Cluster analysis is a fundamental problem and technique in many areas related to machine learning. In this paper, we consider rearrangement clustering, which is the problem of finding sets of objects that share common or similar features by arranging the rows (objects) of a matrix (specifying object features) in such a way that adjacent objects are similar to each other (based on a similarity measure of the features) so as to maximize the overall similarity. Based on formulating this problem as the Traveling Salesman Problem (TSP), we develop a new TSP-based optimal clustering algorithm called TSPCluster. We overcome a flaw that is inherent in previous approaches by relaxing restrictions on dissimilarities between clusters. Our new algorithm has three important features: finding the optimal k clusters for a given k, automatically detecting cluster borders, and ascertaining a set of most viable clustering results that make good balances among maximizing the overall similarity within clusters and dissimilarity between clusters. We apply TSPCluster to cluster and display ~500 genes of flowering plant Arabidopsis which are regulated under various abiotic stress conditions. We compare TSPCluster to the bond energy algorithm and two existing clustering algorithms. Our TSPCluster code is available at (Climer & Zhang, 2004).

MOTIVATION: Pseudoknots have generally been excluded from the prediction of RNA secondary structures due to its difficulty in modeling. Although, several dynamic programming algorithms exist for the prediction of pseudoknots using thermodynamic approaches, they are neither reliable nor efficient. On the other hand, comparative methods are more reliable, but are often done in an ad hoc manner and require expert intervention. Maximum weighted matching, an algorithm for pseudoknot prediction with comparative analysis, suffers from low-prediction accuracy in many cases. RESULTS: Here we present an algorithm, iterated loop matching, for reliably and efficiently predicting RNA secondary structures including pseudoknots. The method can utilize either thermodynamic or comparative information or both, thus is able to predict pseudoknots for both aligned and individual sequences. We have tested the algorithm on a number of RNA families. Using 8-12 homologous sequences, the algorithm correctly identifies more than 90% of base-pairs for short sequences and 80% overall. It correctly predicts nearly all pseudoknots and produces very few spurious base-pairs for sequences without pseudoknots. Comparisons show that our algorithm is both more sensitive and more specific than the maximum weighted matching method. In addition, our algorithm has high-prediction accuracy on individual sequences, comparable with the PKNOTS algorithm, while using much less computational resources. AVAILABILITY: The program has been implemented in ANSI C and is freely available for academic use at http://www.cse.wustl.edu/~zhang/projects/rna/ilm/ SUPPLEMENTARY INFORMATION: http://www.cse.wustl.edu/~zhang/projects/rna/ilm/

In recent years, there has been much interest in phase transitions of combinatorial problems. Phase transitions have been successfully used to analyze combinatorial optimization problems, characterize their typical-case features and locate the hardest problem instances. In this paper, we study phase transitions of the asymmetric Traveling Salesman Problem (ATSP), an NP-hard combinatorial optimization problem that has many real-world applications. Using random instances of up to 1,500 cities in which intercity distances are uniformly distributed, we empirically show that many properties of the problem, including the optimal tour cost and backbone size, experience sharp transitions as the precision of intercity distances increases across a critical value. Our experimental results on the costs of the ATSP tours and assignment problem agree with the theoretical result that the asymptotic cost of assignment problem is pi ^2 /6 the number of cities goes to infinity. In addition, we show that the average computational cost of the well-known branch-and-bound subtour elimination algorithm for the problem also exhibits a thrashing behavior, transitioning from easy to difficult as the distance precision increases. These results answer positively an open question regarding the existence of phase transitions in the ATSP, and provide guidance on how difficult ATSP problem instances should be generated.

The author proposes an approach to represent assembly by Petri nets and presents an algorithm of automatic robot assembly planning based on the Petri-net model. The Petri-net model of assembly is configured by the goal structures and initial constraints, both in the Petri-net formalism. Due to the Petri-net representation of assembly, the plan generation is quite straightforward and the planning algorithm can be easily and efficiently implemented with simple matrix manipulation. An example of how to plan an assembly by the Petri net model is presented.>