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Cross-modal retrieval has become a topic of popularity, since multi-data is heterogeneous and the similarities between different forms of information are worthy of attention. Traditional single-modal methods reconstruct the original information and lack of considering the semantic similarity between different data. In this work, a cross-modal semantic autoencoder with embedding consensus (CSAEC) is proposed, mapping the original data to a low-dimensional shared space to retain semantic information. Considering the similarity between the modalities, an automatic encoder is utilized to associate the feature projection to the semantic code vector. In addition, regularization and sparse constraints are applied to low-dimensional matrices to balance reconstruction errors. The high dimensional data is transformed into semantic code vector. Different models are constrained by parameters to achieve denoising. The experiments on four multi-modal data sets show that the query results are improved and effective cross-modal retrieval is achieved. Further, CSAEC can also be applied to fields related to computer and network such as deep and subspace learning. The model breaks through the obstacles in traditional methods, using deep learning methods innovatively to convert multi-modal data into abstract expression, which can get better accuracy and achieve better results in recognition.

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Structures of genetic regulatory networks are not fixed. These structural perturbations can cause changes to the reachability of systems' state spaces. As system structures are related to genotypes and state spaces are related to phenotypes, it is important to study the relationship between structures and state spaces. However, there is still no method can quantitively describe the reachability differences of two state spaces caused by structural perturbations. Therefore, Difference in Reachability between State Spaces (DReSS) is proposed. DReSS index family can quantitively describe differences of reachability, attractor sets between two state spaces and can help find the key structure in a system, which may influence system's state space significantly. First, basic properties of DReSS including non-negativity, symmetry and subadditivity are proved. Then, typical examples are shown to explain the meaning of DReSS and the differences between DReSS and traditional graph distance. Finally, differences of DReSS distribution between real biological regulatory networks and random networks are compared. Results show most structural perturbations in biological networks tend to affect reachability inside and between attractor basins rather than to affect attractor set itself when compared with random networks, which illustrates that most genotype differences tend to influence the proportion of different phenotypes and only a few ones can create new phenotypes. DReSS can provide researchers with a new insight to study the relation between genotypes and phenotypes.

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BACKGROUND: Classification of diseases based on genetic information is of great significance as the basis for precision medicine, increasing the understanding of disease etiology and revolutionizing personalized medicine. Much effort has been directed at understanding disease associations by constructing disease networks, and classifying patient samples according to gene expression data. Integrating human gene networks overcomes limited coverage of genes. Incorporating pathway information into disease classification procedure addresses the challenge of cellular heterogeneity across patients. RESULTS: In this work, we propose a disease classification model LAMP, which concentrates on the layered assessment on modules and pathways. Directed human gene interactions are the foundation of constructing the human gene network, where the significant roles of disease and pathway genes are recognized. The fast unfolding algorithm identifies 11 modules in the largest connected component. Then layered networks are introduced to distinguish positions of genes in propagating information from sources to targets. After gene screening, hierarchical clustering and refined process, 1726 diseases from KEGG are classified into 18 categories. Also, it is expounded that diseases with overlapping genes may not belong to the same category in LAMP. Within each category, entropy is applied to measure the compositional complexity, and to evaluate the prospects for combination diagnosis and gene-targeted therapy for diseases. CONCLUSION: In this work, by collecting data from BioGRID and KEGG, we develop a disease classification model LAMP, to support people to view diseases from the perspective of commonalities in etiology and pathology. Comprehensive research on existing diseases can help meet the challenges of unknown diseases. The results provide suggestions for combination diagnosis and gene-targeted therapy, which motivates clinicians and researchers to reposition the understanding of diseases and explore diagnosis and therapy strategies.

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Non-coding RNAs are fundamental to the competing endogenous RNA (CeRNA) hypothesis in oncology. Previous work focused on static CeRNA networks. We construct and analyze CeRNA networks for four sequential stages of lung adenocarcinoma (LUAD) based on multi-omics data of long non-coding RNAs (lncRNAs), microRNAs and mRNAs. We find that the networks possess a two-level bipartite structure: common competing endogenous network (CCEN) composed of an invariant set of microRNAs over all the stages and stage-dependent, unique competing endogenous networks (UCENs). A systematic enrichment analysis of the pathways of the mRNAs in CCEN reveals that they are strongly associated with cancer development. We also find that the microRNA-linked mRNAs from UCENs have a higher enrichment efficiency. A key finding is six microRNAs from CCEN that impact patient survival at all stages, and four microRNAs that affect the survival from a specific stage. The ten microRNAs can then serve as potential biomarkers and prognostic tools for LUAD.

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Disease classification based on gene information has been of significance as the foundation for achieving precision medicine. Previous works focus on classifying diseases according to the gene expression data of patient samples, and constructing disease network based on the overlap of disease genes, as many genes have been confirmed to be associated with diseases. In this work, the effects of diseases on human biological functions are assessed from the perspective of gene network modules and pathways, and the distances between diseases are defined to carry out the classification models. In total, 1728 diseases are divided into 12 and 14 categories by the intensity and scope of effects on pathways, respectively. Each category is a mix of several types of diseases identified based on congenital and acquired factors as well as diseased tissues and organs. The disease classification models on the basis of gene network are parallel with traditional pathology classification based on anatomic and clinical manifestations, and enable us to look at diseases in the viewpoint of commonalities in etiology and pathology. Our models provide a foundation for exploring combination therapy of diseases, which in turn may inform strategies for future gene-targeted therapy.

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We analyze five big data sets from a variety of online social networking (OSN) systems and find that the growth dynamics of meme popularity exhibit characteristically different behaviors. For example, there is linear growth associated with online recommendation and sharing platforms, a plateaued (or an "S"-shape) type of growth behavior in a web service devoted to helping users to collect bookmarks, and an exponential increase on the largest and most popular microblogging website in China. Does a universal mechanism with a common set of dynamical rules exist, which can explain these empirically observed, distinct growth behaviors? We provide an affirmative answer in this paper. In particular, inspired by biomimicry to take advantage of cell population growth dynamics in microbial ecology, we construct a base growth model for meme popularity in OSNs. We then take into account human factors by incorporating a general model of human interest dynamics into the base model. The final hybrid model contains a small number of free parameters that can be estimated purely from data. We demonstrate that our model is universal in the sense that, with a few parameters estimated from data, it can successfully predict the distinct meme growth dynamics. Our study represents a successful effort to exploit principles in biology to understand online social behaviors by incorporating the traditional microbial growth model into meme popularity. Our model can be used to gain insights into critical issues such as classification, robustness, optimization, and control of OSN systems.

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The gene interaction network is one of the most important biological networks and has been studied by many researchers. The gene interaction network provides information about whether the genes in the network can cause or heal diseases. As gene-gene interaction relations are constantly explored, gene interaction networks are evolving. To describe how much a gene has been studied, an approach based on a logistic model for each gene called gene saturation has been proposed, which in most cases, satisfies non-decreasing, correlation and robustness principles. The average saturation of a group of genes can be used to assess the network constructed by these genes. Saturation reflects the distance between known gene interaction networks and the real gene interaction network in a cell. Furthermore, the saturation values of 546 disease gene networks that belong to 15 categories of diseases have been calculated. The disease gene networks' saturation for cancer is significantly higher than that of all other diseases, which means that the disease gene networks' structure for cancer has been more deeply studied than other disease. Gene saturation provides guidance for selecting an experimental subject gene, which may have a large number of unknown interactions.

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Achlioptas processes, a class of percolation models which can lead to rich critical phenomena, including the well-known explosive percolation, have attracted much attention in recent years. In this paper, we show that, in a three-vertex Achlioptas process, two giant clusters emerge after the percolation transition with size fluctuations in different realizations, and the choice of the connecting vertex in the smaller cluster depends on a probability parameter p, the increase of which can make the transition sharper. Using finite-size scaling analysis, we can determine the critical point r(c) and critical exponents η, 1/ν, and ß through Monte Carlo simulations. Comparison of such exponents for different giant clusters indicates that their critical nature is always the same. However, when link choice is strongly biased, it is surprising that the scaling relation η=ß/ν is violated, and the data collapse for scaling function diverges. Furthermore, by inspecting the variance of exponents with p, three distinct scaling phases are classified for different parameter intervals according to the divergence scaling function, which suggests an inconsistent scaling form in the critical window with the supercritical region. The study on the criticality and scaling behavior of multiple giant clusters in an Achlioptas process, in particular, the discovery of three scaling phases that depend on the parameter p, may help us in finding a complete scaling theory for the Achlioptas-process percolation and give insight into understanding the accelerating nature of the phase transition for Achlioptas processes once reaching criticality.

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Percolation is one of the most widely studied models in which a unique giant cluster emerges after the phase transition. Recently, a new phenomenon, where multiple giant clusters are observed in the so called Bohman-Frieze-Wormald (BFW) model, has attracted much attention, and how multiple giant clusters could emerge in generic percolation processes on random networks will be discussed in this paper. By introducing the merging probability and inspecting the distinct mechanisms which contribute to the growth of largest clusters, a sufficient condition to generate multiple stable giant clusters is given. Based on the above results, the BFW model and a multi-Erdös-Rényi (ER) model given by us are analyzed, and the mechanism of multiple giant clusters of these two models is revealed. Furthermore, large fluctuations are observed in the size of multiple giant clusters in many models, but the sum size of all giant clusters exhibits self-averaging as that in the size of unique giant cluster in ordinary percolation. Besides, the growth modes of different giant clusters are discussed, and we find that the large fluctuations observed are mainly due to the stochastic behavior of the evolution in the critical window. For all the discussion above, numerical simulations on the BFW model and the multi-ER model are done, which strongly support our analysis. The investigation of merging probability and the growth mechanisms of largest clusters provides insight for the essence of multiple giant clusters in the percolation processes and can be instructive for modeling or analyzing real-world networks consisting of many large clusters.

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To solve the combinatorial optimization problems, especially the minimal Vertex-cover problem with high efficiency, is a significant task in theoretical computer science and many other subjects. Aiming at detecting the solution space of Vertex-cover, a new structure named mutual-determination is defined and discovered for Vertex-cover on general graphs, which results in the emergence of strong correlations among the unfrozen nodes. Based on the backbones and mutual-determinations with node ranks by leaf removal, we propose a Mutual-determination and Backbone Evolution Algorithm to achieve the reduced solution graph, which provides a graphical expression of the solution space of Vertex-cover. By this algorithm, the whole solution space and detailed structures such as backbones can be obtained strictly when there is no leaf-removal core on the given graph. Compared with the current algorithms, the Mutual-determination and Backbone Evolution Algorithm performs as well as the replica symmetry one in a certain interval but has a small gap higher than the replica symmetric breaking one and has a relatively small error for the exact results. The algorithm with the mutual-determination provides a new viewpoint to solve Vertex-cover and understand the organizations of the solution spaces, and the reduced solution graph gives an alternative way to catch detailed information of the ground/steady states.

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The satisfiability of a class of random Boolean equations named massive algebraic system septated to linear and nonlinear subproblems is studied in this paper. On one hand, the correlation between the magnetization of generators and the clustering of solutions of the linear subproblem is investigated by analyzing the Gaussian elimination process. On the other hand, the characteristics of maximal elements of solutions of the nonlinear subproblem are studied by introducing the partial order among solutions. Based on the algebraic characteristics of these two subproblems, the upper and lower bounds of satisfiability threshold of massive algebraic system are obtained by unit-clause propagation and leaf-removal process, and coincide as the ratio of nonlinear equations q>0.739 in which analytical values of the satisfiability threshold can be derived. Furthermore, a complete algorithm with heuristic decimation is proposed to observe the approximation of the satisfiability threshold, which performs more efficiently than the classical ones.

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