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In automata networks, it is well known that the way entities update their states over time has a major impact on their dynamics. In particular, depending on the chosen update schedule, the underlying dynamical systems may exhibit more or less asymptotic dynamical behaviours such as fixed points or limit cycles. Since such mathematical models have been used in the framework of biological networks modelling, the question of choosing appropriate update schedules has arised soon. In this note, focusing on Boolean networks, our aim is to emphasise that the adequate way of thinking regulations and genetic expression over time is certainly not to consider a wall segregating synchronicity from asynchronicity because they actually complement rather well. In particular, we highlight that specific update schedules, namely block-parallel update schedules, whose intrinsic features are still not known from a theoretical point of view, admit realistic and pertinent properties in the context of biological modelling and deserve certainly more attention from the community. [ABSTRACT FROM AUTHOR]

Analyzing protein–protein interaction (PPI) networks using machine learning and deep learning algorithms, alongside centrality measures, holds paramount importance in understanding complex biological systems. These advanced computational techniques enable the extraction of valuable insights from intricate network structures, shedding light on the functional relationships between proteins. By leveraging AI-driven approaches, researchers can uncover key regulatory mechanisms, identify critical nodes within the network and predict novel protein interactions with high accuracy. Ultimately, this integration of computational methodologies enhances our ability to comprehend the dynamic behavior of biological systems at a molecular level, paving the way for advancements in drug discovery, disease understanding and personalized medicine. This review paper starts by outlining various popular available PPI network databases and network centrality calculation tools. A thorough classification of various centrality measures has been identified. It primarily delves into the centrality-driven discoveries within PPI networks in biological systems and suggests using edge centrality measures and a hybrid version of node and edge centrality measures in machine learning algorithms and deep learning algorithms to predict hidden knowledge much more effectively. The review paper begins by outlining various popular available PPI network databases and network centrality calculation tools. A thorough classification of various centrality measures has been identified. A detailed view of various findings of different types of centrality measures in PPI networks is presented. [ABSTRACT FROM AUTHOR]

TEX file as is needed for processing, selecting the file designation of TeX/LaTeX Suppl File. Graph Professor Waterman is one of the founders of the field of computational biology and has made many fundamental contributions to the field. [Extracted from the article]

One of the key problems the brain faces is inferring the state of the world from a sequence of dynamically changing stimuli, and it is not yet clear how the sensory system achieves this task. A well-established computational framework for describing perceptual processes in the brain is provided by the theory of predictive coding. Although the original proposals of predictive coding have discussed temporal prediction, later work developing this theory mostly focused on static stimuli, and key questions on neural implementation and computational properties of temporal predictive coding networks remain open. Here, we address these questions and present a formulation of the temporal predictive coding model that can be naturally implemented in recurrent networks, in which activity dynamics rely only on local inputs to the neurons, and learning only utilises local Hebbian plasticity. Additionally, we show that temporal predictive coding networks can approximate the performance of the Kalman filter in predicting behaviour of linear systems, and behave as a variant of a Kalman filter which does not track its own subjective posterior variance. Importantly, temporal predictive coding networks can achieve similar accuracy as the Kalman filter without performing complex mathematical operations, but just employing simple computations that can be implemented by biological networks. Moreover, when trained with natural dynamic inputs, we found that temporal predictive coding can produce Gabor-like, motion-sensitive receptive fields resembling those observed in real neurons in visual areas. In addition, we demonstrate how the model can be effectively generalized to nonlinear systems. Overall, models presented in this paper show how biologically plausible circuits can predict future stimuli and may guide research on understanding specific neural circuits in brain areas involved in temporal prediction. Author summary: While significant advances have been made in the neuroscience of how the brain processes static stimuli, the time dimension has often been relatively neglected. However, time is crucial since the stimuli perceived by our senses typically dynamically vary in time, and the cortex needs to make sense of these changing inputs. This paper describes a computational model of cortical networks processing temporal stimuli. This model is able to infer and track the state of the environment based on noisy inputs, and predict future sensory stimuli. By ensuring that these predictions match the incoming stimuli, the model is able to learn the structure and statistics of its temporal inputs and produces responses of neurons resembling those in the brain. The model may help in further understanding neural circuits in sensory cortical areas. [ABSTRACT FROM AUTHOR]

Circular RNA (CircRNA)–microRNA (miRNA) interaction (CMI) is an important model for the regulation of biological processes by non-coding RNA (ncRNA), which provides a new perspective for the study of human complex diseases. However, the existing CMI prediction models mainly rely on the nearest neighbor structure in the biological network, ignoring the molecular network topology, so it is difficult to improve the prediction performance. In this paper, we proposed a new CMI prediction method, BEROLECMI, which uses molecular sequence attributes, molecular self-similarity, and biological network topology to define the specific role feature representation for molecules to infer the new CMI. BEROLECMI effectively makes up for the lack of network topology in the CMI prediction model and achieves the highest prediction performance in three commonly used data sets. In the case study, 14 of the 15 pairs of unknown CMIs were correctly predicted. [ABSTRACT FROM AUTHOR]

Background: In bioinformatics, interactions are modelled as networks, based on graph models. Generally, these support a single-layer structure which incorporates a specific entity (i.e., node) and only one type of link (i.e., edge). However, real-world biological systems consisting of biological objects belonging to heterogeneous entities, and these operate and influence each other in multiple contexts, simultaneously. Usually, node similarities are investigated to assess the relatedness between biological objects in a network of interest, and node embeddings are widely used for studying novel interaction from a topological point of view. About that, the state-of-the-art presents several methods for evaluating the node similarity inside a given network, but methodologies able to evaluate similarities between pairs of nodes belonging to different networks are missing. The latter are crucial for studies that relate different biological networks, e.g., for Network Alignment or to evaluate the possible evolution of the interactions of a little-known network on the basis of a well-known one. Existing methods are ineffective in evaluating nodes outside their structure, even more so in the context of multilayer networks, in which the topic still exploits approaches adapted from static networks. In this paper, we presented pyMulSim, a novel method for computing the pairwise similarities between nodes belonging to different multilayer networks. It uses a Graph Isomorphism Network (GIN) for the representative learning of node features, that uses for processing the embeddings and computing the similarities between the pairs of nodes of different multilayer networks. Results: Our experimentation investigated the performance of our method. Results show that our method effectively evaluates the similarities between the biological objects of a source multilayer network to a target one, based on the analysis of the node embeddings. Results have been also assessed for different noise levels, also through statistical significance analyses properly performed for this purpose. Conclusions: PyMulSim is a novel method for computing the pairwise similarities between nodes belonging to different multilayer networks, by using a GIN for learning node embeddings. It has been evaluated both in terms of performance and validity, reporting a high degree of reliability. [ABSTRACT FROM AUTHOR]

The network alignment problem refers to how to find the node correspondence across different networks in multiplex networks. This study has significant implications in various disciplinary fields. However, current network alignment work focuses on simple networks. These methods based on simple networks are doomed to fail to capture high-order relationships. In order to fill the gap in this area, this paper will introduce a prediction method of inter-layer connectivity based on multi hypernetwork structure attributes. Among them, the hyperedge similarity index of nodes is specially designed for higher-order relationships in hypernetworks, and a degree punishment mechanism is designed to reasonably evaluate the similarity of higher-order relationships between nodes in different environments. This method further considers the quantity and strength information of the similarity of higher-order relations, which helps to further increase the accuracy rate on the hypernetwork. We compare this method with other advanced methods on different real-world hypernetworks and artificial hypernetworks. Experiments show that the method has good performance and robustness. In the biological metabolic network, the accuracy of this method can even be improved by 29.8% compared with the comparison method. In the 38 groups of data we tested, the accuracy rate was 78.9% when it was stably higher than other methods, 15.9% when it was not lower than the comparison method, and only 5.2% when the method performed poorly. [ABSTRACT FROM AUTHOR]

Motivation The rapid increase of bio-medical literature makes it harder and harder for scientists to keep pace with the discoveries on which they build their studies. Therefore, computational tools have become more widespread, among which network analysis plays a crucial role in several life-science contexts. Nevertheless, building correct and complete networks about some user-defined biomedical topics on top of the available literature is still challenging. Results We introduce NetMe 2.0, a web-based platform that automatically extracts relevant biomedical entities and their relations from a set of input texts—i.e. in the form of full-text or abstract of PubMed Central's papers, free texts, or PDFs uploaded by users—and models them as a BioMedical Knowledge Graph (BKG). NetMe 2.0 also implements an innovative Retrieval Augmented Generation module (Graph-RAG) that works on top of the relationships modeled by the BKG and allows the distilling of well-formed sentences that explain their content. The experimental results show that NetMe 2.0 can infer comprehensive and reliable biological networks with significant Precision–Recall metrics when compared to state-of-the-art approaches. Availability and implementation https://netme.click/. [ABSTRACT FROM AUTHOR]

Community detection is a well-known area of research that yields essential results in various fields such as social media, biological networks, pandemic spread, recommendation systems, etc. There are two important areas for improvement in existing community detection algorithms: quality of community formed should be improved and a parallel approach to community detection is needed to handle massive data. In this paper, we have proposed a three-step parallel algorithm, Par-Com, using the concept of k Clique and modularity optimization to address both of the above issues. The proposed algorithm increases the execution speed and also improves the quality of the community formed by optimizing modularity. Par-Com uses dynamic load balancing on the multicore architecture of Supercomputer ParamShivay. We have also evaluated Par-Com's performance against nine sequential and three parallel community detection algorithms on varying size datasets, i.e. karate, macaque, email, immuno, soc-epinions, facebook, and com-Friendster. The experiment result shows that Par-Com outperforms other algorithms under consideration with up to 45% increase in modularity and up to 84% increase in execution speed. Par-Com is also capable of detecting overlapping communities, fuzzy membership of each node, most influential node in each community formed, and outlier nodes. Nodes within a community that have the highest influence are deemed as experts. The choices made by an expert in a particular community are served as recommendations to other users within that community. [ABSTRACT FROM AUTHOR]

The potential role of bottom-up Synthetic Cells (SCs) in the Internet of Bio-Nano Things (IoBNT) is discussed. In particular, this perspective paper focuses on the growing interest in networks of biological and/or artificial objects at the micro- and nanoscale (cells and subcellular parts, microelectrodes, microvessels, etc.), whereby communication takes place in an unconventional manner, i.e., via chemical signaling. The resulting "molecular communication" (MC) scenario paves the way to the development of innovative technologies that have the potential to impact biotechnology, nanomedicine, and related fields. The scenario that relies on the interconnection of natural and artificial entities is briefly introduced, highlighting how Synthetic Biology (SB) plays a central role. SB allows the construction of various types of SCs that can be designed, tailored, and programmed according to specific predefined requirements. In particular, "bottom-up" SCs are briefly described by commenting on the principles of their design and fabrication and their features (in particular, the capacity to exchange chemicals with other SCs or with natural biological cells). Although bottom-up SCs still have low complexity and thus basic functionalities, here, we introduce their potential role in the IoBNT. This perspective paper aims to stimulate interest in and discussion on the presented topics. The article also includes commentaries on MC, semantic information, minimal cognition, wetware neuromorphic engineering, and chemical social robotics, with the specific potential they can bring to the IoBNT. [ABSTRACT FROM AUTHOR]

Centrality measurement plays an important role to identify important/influential vertices and edges in a network or graph from different points of view. It also provide invaluable insights into the structure and functioning of interconnected systems, enabling researchers to identify critical nodes for targeted interventions, predict network behaviors, and optimize network performance. Though there are different centrality measurements in graphs theory, yet closeness centrality is widely used to analyze biological networks, social networks, fuzzy social network, transportation networks, etc. The closeness centrality of a node x in a network/graph is the unit fraction whose denominator is the sum of the distances from x to other nodes. This paper presents theoretical development to compute the closeness centrality of each node/vertex of different corona product graphs between well known graph (path graph, complete graph, cycle graph, wheel graph, star graph and complete bipartite graph) and general graph. Corona graph has lots of applications in signed networks, biotechnology, chemistry, small-world network, etc. We also present a suitable real application of our proposed results by which we can identify the influential nodes in small-world network. [ABSTRACT FROM AUTHOR]

Identification of complex communities in biological networks is a critical and ongoing challenge since lots of network-related problems correspond to the subgraph isomorphism problem known in the literature as NP-hard. Several optimization algorithms have been dedicated and applied to solve this problem. The main challenge regarding the application of optimization algorithms, specifically to handle large-scale complex networks, is their relatively long execution time. Thus, this paper proposes a parallel extension of the PSO algorithm to detect communities in complex biological networks. The main contribution of this study is summarized in three- fold; Firstly, a modified PSO algorithm with a local search operator is proposed to detect complex biological communities with high quality. Secondly, the variability in the capability of PSO to extract community structure in biological networks is studied when different types of crossover operators are used. Finally, to reduce the computational time needed to solve this problem, especially when detecting complex communities in large-scale biological networks, we have implemented parallel computing to execute the algorithm. The performance of the proposed algorithm was tested and evaluated on two real biological networks. The experimental results showed the effective performance of the proposed algorithm when using single-point crossover operator, and its superiority over other counterpart algorithms. Moreover, the use of parallel computing in the proposed algorithm representation has greatly reduced the computational time required for its execution. [ABSTRACT FROM AUTHOR]

We present a rigorous and precise analysis of the maximum degree and the average degree in a dynamic duplication-divergence graph model introduced by Sol\'e et al. [Adv. Complex Syst., 5 (2002), pp. 43-54] in which the graph grows according to a duplication-divergence mechanism, i.e., by iteratively creating a copy of some node and then randomly alternating the neighborhood of a new node with probability p. This model captures the growth of some real-world processes, e.g., biological or social networks. In this paper, we prove that for some 0 < p < 1, the maximum degree and the average degree of a duplication-divergence graph on t vertices are asymptotically concentrated with high probability around tp and max\{ t2p-1, 1}, respectively, i.e., they are within at most a polylogarithmic factor from these values with probability at least 1-t-A for any constant A >0. [ABSTRACT FROM AUTHOR]

Cell fate decisions and transitions are common in almost all developmental processes. Therefore, it is important to identify the decision-making mechanisms and important individual molecules behind the fate decision processes. In this paper, we propose an interpretable strategy based on systematic perturbation, unsupervised hierarchical cluster analysis (HCA), machine learning (ML), and Shapley additive explanation (SHAP) analysis for inferring the contribution and importance of individual molecules in cell fate decision and transition processes. In order to verify feasibility of the approach, we apply it to the core epithelial to mesenchymal transition (EMT)-metastasis network. The key factors identified in EMT-metastasis are consistent with relevant experimental observations. The approach presented here can be applied to other biological networks to identify important factors related to cell fate decisions and transitions. [ABSTRACT FROM AUTHOR]

In this paper, we study the stability of an Ordinary Differential Equation (ODE) usually referred to as Cyclic Feedback Loop, which typically models a biological network of d molecules where each molecule regulates its successor in a cycle ( A 1 → A 2 → ⋯ → A d − 1 → A d → A 1 ). Regulations, which can be either positive or negative, are modelled by increasing or decreasing functions. We make an analysis of this model for a wide range of functions (including affine and Hill functions) by determining the parameters for which bistability and oscillatory behaviours arise. These results encompass previous theoretical studies of gene regulatory networks, which are particular cases of this model. [ABSTRACT FROM AUTHOR]

A family of results, referred to as inheritance results, tell us which enlargements of a chemical reaction network (CRN) preserve its capacity for nontrivial behaviours such as multistationarity and oscillation. In this paper, the following inheritance result is proved: under mild assumptions, splitting chemical reactions and inserting complexes involving some new chemical species preserves the capacity of a mass action CRN for multiple nondegenerate equilibria and/or periodic orbits. The claim has been proved previously for equilibria alone; however, the generalisation to include oscillation involves extensive development of rather different techniques. Several inheritance results for multistationarity and oscillation in mass action CRNs, including the main result of this paper, are gathered into a single theorem. Examples are presented showing how these results can be used together to make claims about reaction networks based on knowledge of their subnetworks. The examples include some networks of biological importance. [ABSTRACT FROM AUTHOR]

Link prediction in complex networks has recently attracted a great deal of attraction in diverse scientific domains, including social and biological sciences. Given a snapshot of a network, the goal is to predict links that are missing in the network or that are likely to occur in the near future. This problem has both theoretical and practical significance; it not only helps us to identify missing links in a network more efficiently by avoiding the expensive and time consuming experimental processes, but also allows us to study the evolution of a network with time. To address the problem of link prediction, numerous attempts have been made over the recent years that exploit the local and the global topological properties of the network to predict missing links in the network. In this paper, we use parametrised matrix forest index (PMFI) to predict missing links in a network. We show that, for small parameter values, this index is linked to a heat diffusion process on a graph and therefore encodes geometric properties of the network. We then develop a framework that combines the PMFI with a local similarity index to predict missing links in the network. The framework is applied to numerous networks obtained from diverse domains such as social network, biological network, and transport network. The results show that the proposed method can predict missing links with higher accuracy when compared to other state-of-the-art link prediction methods. [ABSTRACT FROM AUTHOR]

Single-cell RNA-sequencing (scRNA-seq) has emerged as a powerful technique for studying gene expression patterns at the single-cell level. Inferring gene regulatory networks (GRNs) from scRNA-seq data provides insight into cellular phenotypes from the genomic level. However, the high sparsity, noise and dropout events inherent in scRNA-seq data present challenges for GRN inference. In recent years, the dramatic increase in data on experimentally validated transcription factors binding to DNA has made it possible to infer GRNs by supervised methods. In this study, we address the problem of GRN inference by framing it as a graph link prediction task. In this paper, we propose a novel framework called GNNLink, which leverages known GRNs to deduce the potential regulatory interdependencies between genes. First, we preprocess the raw scRNA-seq data. Then, we introduce a graph convolutional network-based interaction graph encoder to effectively refine gene features by capturing interdependencies between nodes in the network. Finally, the inference of GRN is obtained by performing matrix completion operation on node features. The features obtained from model training can be applied to downstream tasks such as measuring similarity and inferring causality between gene pairs. To evaluate the performance of GNNLink, we compare it with six existing GRN reconstruction methods using seven scRNA-seq datasets. These datasets encompass diverse ground truth networks, including functional interaction networks, Loss of Function/Gain of Function data, non-specific ChIP-seq data and cell-type-specific ChIP-seq data. Our experimental results demonstrate that GNNLink achieves comparable or superior performance across these datasets, showcasing its robustness and accuracy. Furthermore, we observe consistent performance across datasets of varying scales. For reproducibility, we provide the data and source code of GNNLink on our GitHub repository: https://github.com/sdesignates/GNNLink. [ABSTRACT FROM AUTHOR]

In this paper, we develop a network-based methodology to investigate the problems related to matrix stability and bifurcations in nonlinear dynamical systems. By matching a matrix with a network, i.e., interaction graph, we propose a new network-based matrix analysis method by proving a theorem about matrix determinant under which matrix stability can be considered in terms of feedback loops. Especially, the approach can tell us how a node, a path, or a feedback loop in the interaction graph affects matrix stability. In addition, the roles played by a node, a path, or a feedback loop in determining bifurcations in nonlinear dynamical systems can also be revealed. Therefore, the approach can help us to screen optimal node or node combinations. By perturbing them, unstable matrices can be stabilized more efficiently or bifurcations can be induced more easily to realize desired state transitions. To illustrate feasibility and efficiency of the approach, some simple matrices are used to show how single or combinatorial perturbations affect matrix stability and induce bifurcations. In addition, the main idea is also illustrated through a biological problem related to T cell development with three nodes: TCF-1, GATA3, and PU.1, which can be considered to be a three-variable nonlinear dynamical system. The approach is especially helpful in understanding crucial roles of single or molecule combinations in biomolecular networks. The approach presented here can be expected to analyze other biological networks related to cell fate transitions and systematic perturbation strategy selection. [ABSTRACT FROM AUTHOR]

In this paper, we study the stability of an Ordinary Differential Equation (ODE) usually referred to as Cyclic Feedback Loop, which typically models a biological network of d molecules where each molecule regulates its successor in a cycle ( A 1 → A 2 → ⋯ → A d − 1 → A d → A 1 ). Regulations, which can be either positive or negative, are modelled by increasing or decreasing functions. We make an analysis of this model for a wide range of functions (including affine and Hill functions) by determining the parameters for which bistability and oscillatory behaviours arise. These results encompass previous theoretical studies of gene regulatory networks, which are particular cases of this model. [ABSTRACT FROM AUTHOR]

Link prediction in complex networks has recently attracted a great deal of attraction in diverse scientific domains, including social and biological sciences. Given a snapshot of a network, the goal is to predict links that are missing in the network or that are likely to occur in the near future. This problem has both theoretical and practical significance; it not only helps us to identify missing links in a network more efficiently by avoiding the expensive and time consuming experimental processes, but also allows us to study the evolution of a network with time. To address the problem of link prediction, numerous attempts have been made over the recent years that exploit the local and the global topological properties of the network to predict missing links in the network. In this paper, we use parametrised matrix forest index (PMFI) to predict missing links in a network. We show that, for small parameter values, this index is linked to a heat diffusion process on a graph and therefore encodes geometric properties of the network. We then develop a framework that combines the PMFI with a local similarity index to predict missing links in the network. The framework is applied to numerous networks obtained from diverse domains such as social network, biological network, and transport network. The results show that the proposed method can predict missing links with higher accuracy when compared to other state-of-the-art link prediction methods. [ABSTRACT FROM AUTHOR]

Previous studies have inferred robust stability of reaction networks by utilizing linear programs or iterative algorithms. Such algorithms become tedious or computationally infeasible for large networks. In addition, they operate like black boxes without offering intuition for the structures that are necessary to maintain stability. In this work, we provide several graphical criteria for constructing robust stability certificates, checking robust non-degeneracy, verifying persistence, and establishing global stability. By characterizing a set of stability-preserving graph modifications that includes the enzymatic modification motif, we show that the stability of arbitrarily large nonlinear networks can be examined by simple visual inspection. We show applications of this technique to ubiquitous motifs in systems biology such as post-translational modification (PTM) cycles, the ribosome flow model (RFM), T-cell kinetic proofreading, and others. The results of this paper are dedicated in honor of Eduardo D. Sontag's seventieth birthday and his pioneering work in nonlinear dynamical systems and mathematical systems biology. [ABSTRACT FROM AUTHOR]

Motivation: Recent advances in spatially resolved transcriptomics (ST) technologies enable the measurement of gene expression profiles while preserving cellular spatial context. Linking gene expression of cells with their spatial distribution is essential for better understanding of tissue microenvironment and biological progress. However, effectively combining gene expression data with spatial information to identify spatial domains remains challenging. Results: To deal with the above issue, in this paper, we propose a novel unsupervised learning framework named STMGCN for identifying spatial domains using multi-view graph convolution networks (MGCNs). Specifically, to fully exploit spatial information, we first construct multiple neighbor graphs (views) with different similarity measures based on the spatial coordinates. Then, STMGCN learns multiple view-specific embeddings by combining gene expressions with each neighbor graph through graph convolution networks. Finally, to capture the importance of different graphs, we further introduce an attention mechanism to adaptively fuse view-specific embeddings and thus derive the final spot embedding. STMGCN allows for the effective utilization of spatial context to enhance the expressive power of the latent embeddings with multiple graph convolutions. We apply STMGCN on two simulation datasets and five real spatial transcriptomics datasets with different resolutions across distinct platforms. The experimental results demonstrate that STMGCN obtains competitive results in spatial domain identification compared with five state-of-the-art methods, including spatial and non-spatial alternatives. Besides, STMGCN can detect spatially variable genes with enriched expression patterns in the identified domains. Overall, STMGCN is a powerful and efficient computational framework for identifying spatial domains in spatial transcriptomics data. [ABSTRACT FROM AUTHOR]

Finite dynamical systems are used to model problems from different branches of sciences such as biological networks, computer process, physics, and engineered control systems. An important combinatorial tool for studying limit cycles of a finite dynamical system is dependency graph. In Veliz-Cuba and Laubenbacher (2019) , cycle structure of semilattice networks has completely been characterized when the dependency graph is strongly connected. This characterization is in terms of the loop number of the dependency graph. In this paper, we use the methods developed in Jarrah et al. (2010) ; Veliz-Cuba and Laubenbacher (2019) and we study cycle structure of a semilattice network with an arbitrary dependency graph. We show that the period of any limit cycle divides the loop number. Next, we prove that all periodic points of a semilattice network are fixed points if and only if the loop number of dependency graph is 1. We also find some sufficient conditions under which system has periodic points of any period that divides the loop number. Then, using the same idea as Chen et al. (2020) , we give a reduction process in studying cycle structure of a semilattice networks. Finally, we completely characterized the set of fixed points of a semilattice networks in terms of the set of isotone maps between two certain partially ordered sets. Using this characterization, we give a sharp lower bound for the number of fixed points. The results in this paper apply to certain types of Boolean networks and diffusion models, and in particular extends and recovers some of the results of Chen et al. (2020) ; Jarrah et al. (2010). [ABSTRACT FROM AUTHOR]

Simple Summary: The growing evidence suggested that competing endogenous RNAs (ceRNAs) have significant associations with tumor occurrence and progression, yet the regulatory mechanism of them in lung adenocarcinoma remains unclear. Identification of the regulatory modules for lung adenocarcinoma is a critical and fundamental step towards understanding the regulatory mechanisms during carcinogenesis. Deep neural network (DNN) models have become a powerful tool to intelligently recognize the sophisticated relationships of ceRNAs appropriately. In this paper, multiple deep neural network models were constructed using the expression data to identify regulatory modules for lung adenocarcinoma in biological networks. Three identified regulatory modules association with lung adenocarcinoma were validated from three aspects, i.e., literature review, functional enrichment analysis, and an independent dataset. The regulatory relationships between RNAs were validated in various datasets, including CPTAC, TCGA and an expression profile from the GEO database. Our study will contribute to improving the understanding of regulatory mechanisms in the carcinogenesis of lung adenocarcinoma and provide schemes for identifying novel regulatory modules of other cancers. Lung adenocarcinoma is the most common type of primary lung cancer, but the regulatory mechanisms during carcinogenesis remain unclear. The identification of regulatory modules for lung adenocarcinoma has become one of the hotspots of bioinformatics. In this paper, multiple deep neural network (DNN) models were constructed using the expression data to identify regulatory modules for lung adenocarcinoma in biological networks. First, the mRNAs, lncRNAs and miRNAs with significant differences in the expression levels between tumor and non-tumor tissues were obtained. MRNA DNN models were established and optimized to mine candidate mRNAs that significantly contributed to the DNN models and were in the center of an interaction network. Another DNN model was then constructed and potential ceRNAs were screened out based on the contribution of each RNA to the model. Finally, three modules comprised of miRNAs and their regulated mRNAs and lncRNAs with the same regulation direction were identified as regulatory modules that regulated the initiation of lung adenocarcinoma through ceRNAs relationships. They were validated by literature and functional enrichment analysis. The effectiveness of these regulatory modules was evaluated in an independent lung adenocarcinoma dataset. Regulatory modules for lung adenocarcinoma identified in this study provided a reference for regulatory mechanisms during carcinogenesis. [ABSTRACT FROM AUTHOR]

In this paper we study the regularity of weak solutions to an elliptic-parabolic system modeling natural network formation. The system is singular and involves cubic nonlinearity. Our investigation reveals that weak solutions are Hölder continuous when the space dimension N is 2. This is achieved via an inequality associated with the Stummel-Kato class of functions and refinement of a lemma originally due to S. Campanato and C.B. Morrey ([5] , p. 86). [ABSTRACT FROM AUTHOR]

The popularity of social networks is growing and offering promising opportunities for practical applications, such as computer networks, social systems, physical systems, and biological networks. The use of networks provides valuable insights into the patterns, relationships, and behavior of various entities and their interactions. Healthcare service systems are critical social systems that can be analyzed using network-based methodologies, one of which is influence maximization (IM). It is a network analysis technique that identifies a small subset of suppliers in a network that has the most influence on the overall behavior of the healthcare system. By utilizing network analysis techniques, data scientists can identify the most crucial healthcare providers in a network and better understand the system's operation. The paper uses a network global structure-based centrality (ngsc) approach that combines conventional k-shell and the sum of neighbors' degree methods with information about the network's global structural features to identify significant providers in the provider-interacting network. The experimental outcomes on five real-world networks reveal that the proposed NGSC technique outperforms earlier benchmark methods in identifying significant providers under a spreading dynamic when using the IC model. [ABSTRACT FROM AUTHOR]

A wealth of causal relationships exists in biological systems, both causal brain networks and causal protein signaling networks are very classical causal biological networks (CBNs). Learning CBNs from biological signal data reliably is a critical problem today. However, most of the existing methods are not excellent enough in terms of accuracy and time performance, and tend to fall into local optima because they do not take full advantage of global information. In this paper, we propose a parallel ant colony optimization algorithm to learn causal biological networks from biological signal data, called PACO. Specifically, PACO first maps the construction of CBNs to ants, then searches for CBNs in parallel by simulating multiple groups of ants foraging, and finally obtains the optimal CBN through pheromone fusion and CBNs fusion between different ant colonies. Extensive experimental results on simulation data sets as well as two real-world data sets, the fMRI signal data set and the Single-cell data set, show that PACO can accurately and efficiently learn CBNs from biological signal data. [ABSTRACT FROM AUTHOR]

In this paper, based on the feedback mechanism from the perspective of network groups, the evolutionary characteristics and laws of group networks under information dissemination are studied. First, the network is divided into groups of different sizes, and each group is given a dynamically changing group activity and a positive degree of response to different categories of information. Second, a feedback-based model of information dissemination in group networks is developed, which takes into account the differences between same-group and cross-group dissemination of information. Next, the model is applied to a scale-free network and a small-world network for simulation experiments. The experimental results show that, under the feedback mechanism, the main factor affecting the final evolutionary results of each group size in the small-world network is group positivity, which has little relationship with the initial size; similarly, the main factor affecting the average degree of each group in the scale-free network is also group positivity, which has nothing to do with the initial average degree. Finally, the method is applied to a real network to verify the rationality and effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

Mathematical modeling of the emergent dynamics of gene regulatory networks (GRN) faces a double challenge of (a) dependence of model dynamics on parameters, and (b) lack of reliable experimentally determined parameters. In this paper we compare two complementary approaches for describing GRN dynamics across unknown parameters: (1) parameter sampling and resulting ensemble statistics used by RACIPE (RAndom CIrcuit PErturbation), and (2) use of rigorous analysis of combinatorial approximation of the ODE models by DSGRN (Dynamic Signatures Generated by Regulatory Networks). We find a very good agreement between RACIPE simulation and DSGRN predictions for four different 2- and 3-node networks typically observed in cellular decision making. This observation is remarkable since the DSGRN approach assumes that the Hill coefficients of the models are very high while RACIPE assumes the values in the range 1-6. Thus DSGRN parameter domains, explicitly defined by inequalities between systems parameters, are highly predictive of ODE model dynamics within a biologically reasonable range of parameters. [ABSTRACT FROM AUTHOR]

Community detection is a prominent research topic in Complex Network Analysis, and it constitutes an important research field on all those areas where complex networks represent a powerful interpretation tool for describing and understanding systems involved in neuroscience, biology, social science, economy, and many others. A challenging approach to uncover the community structure in complex network, and then revealing the internal organization of nodes, is Modularity optimization. In this research paper, we present an immune optimization algorithm (opt-IA) developed to detect community structures, with the main aim to maximize the modularity produced by the discovered communities. In order to assess the performance of opt-IA, we compared it with an overall of 20 heuristics and metaheuristics, among which one Hyper-Heuristic method, using social and biological complex networks as data set. Unlike these algorithms, opt-IA is entirely based on a fully random search process, which in turn is combined with purely stochastic operators. According to the obtained outcomes, opt-IA shows strictly better performances than almost all heuristics and metaheuristics to which it was compared; whilst it turns out to be comparable with the Hyper-Heuristic method. Overall, it can be claimed that opt-IA, even if driven by a purely random process, proves to be reliable and with efficient performance. Furthermore, to prove the latter claim, a sensitivity analysis of the functionality was conducted, using the classic metrics NMI, ARI and NVI. [ABSTRACT FROM AUTHOR]

The paper is focused on the analysis of effect of coupling strength and time delay for a pair of connected neurons on the dynamics of the system. The FitzHugh–Nagumo model is used as a neuron model. The article contains analytical conditions for Hopf bifurcations in the system. A numerical verification of the results is given. Several examples of global bifurcation in the system were analyzed. [ABSTRACT FROM AUTHOR]

A large number of complex biochemical reaction networks are included in the gene expression, cell development, and cell differentiation of in vivo cells, among other processes. Biochemical reaction-underlying processes are the ones transmitting information from cellular internal or external signaling. However, how this information is measured remains an open question. In this paper, we apply the method of information length, based on the combination of Fisher information and information geometry, to study linear and nonlinear biochemical reaction chains, respectively. Through a lot of random simulations, we find that the amount of information does not always increase with the length of the linear reaction chain; instead, the amount of information varies significantly when this length is not very large. When the length of the linear reaction chain reaches a certain value, the amount of information hardly changes. For nonlinear reaction chains, the amount of information changes not only with the length of this chain, but also with reaction coefficients and rates, and this amount also increases with the length of the nonlinear reaction chain. Our results will help to understand the role of the biochemical reaction networks in cells. [ABSTRACT FROM AUTHOR]

How to explain the emergence of cooperative behavior remains a significant problem. As players may hold diverse perceptions on a particular dilemma, the concept of multigames has been introduced. Therefore, a multigame is studied within various binary networks. Since group structures are common in human society and a person can participate in multiple groups, this paper studies an evolutionary multigame with high-order interaction properties. For this purpose, a uniform random hypergraph is adopted as the network structure, allowing players to interact with all nodes in the same hyperedge. First, we investigate the effect of the multigame payoff matrix differences on the evolution of cooperation and find that increasing the differences in the payoff matrix promotes cooperation on the hypergraph network. Second, we discover that an increase in the average hyperdegree of the hypergraph network promotes network reciprocity, wherein high-hyperdegree nodes influence surrounding nodes to form a cooperator cluster. Conversely, groups with a low hyperdegree are more susceptible to betrayal, leading to a decline in cooperation. [ABSTRACT FROM AUTHOR]

Rich club is a special phenomenon in complex networks. It refers to the nodes with high degrees (i.e., rich nodes) that tend to connect with each other to form a "rich club". This phenomenon exists in many real networks, especially in social networks. However, there are also some networks not having this phenomenon, for example, in many biological networks. Thus, a natural question comes up: do these rich nodes contact with each other through an "agent"? Two rich nodes do not connect directly, but they can establish a connection by an "agent", i.e., they can connect with each other within two steps. If the rich nodes tend to connect with each other within two steps, we say that they form a "2-step rich club". The traditional rich club is then called "1-step rich club". In this paper, we aim to design one method to detect the "2-step rich club" phenomenon in real networks and check whether this new "2-step rich club" phenomenon commonly exists in real networks. We find that most networks with "1-step rich club" will also have "2-step rich club". However, there also exist few networks having "2-step rich club" structure while not having "1-step rich club" structure. In particular, either 1-step rich-club phenomenon or 2-step rich-club phenomenon exists in most social networks. [ABSTRACT FROM AUTHOR]

Individual-specific networks, defined as networks of nodes and connecting edges that are specific to an individual, are promising tools for precision medicine. When such networks are biological, interpretation of functional modules at an individual level becomes possible. An under-investigated problem is relevance or "significance" assessment of each individual-specific network. This paper proposes novel edge and module significance assessment procedures for weighted and unweighted individual-specific networks. Specifically, we propose a modular Cook's distance using a method that involves iterative modeling of one edge versus all the others within a module. Two procedures assessing changes between using all individuals and using all individuals but leaving one individual out (LOO) are proposed as well (LOO-ISN, MultiLOO-ISN), relying on empirically derived edges. We compare our proposals to competitors, including adaptions of OPTICS, kNN, and Spoutlier methods, by an extensive simulation study, templated on real-life scenarios for gene co-expression and microbial interaction networks. Results show the advantages of performing modular versus edge-wise significance assessments for individual-specific networks. Furthermore, modular Cook's distance is among the top performers across all considered simulation settings. Finally, the identification of outlying individuals regarding their individual-specific networks, is meaningful for precision medicine purposes, as confirmed by network analysis of microbiome abundance profiles. [ABSTRACT FROM AUTHOR]

Background: There is an increasing interest in the use of Deep Learning (DL) based methods as a supporting analytical framework in oncology. However, most direct applications of DL will deliver models with limited transparency and explainability, which constrain their deployment in biomedical settings. Methods: This systematic review discusses DL models used to support inference in cancer biology with a particular emphasis on multi-omics analysis. It focuses on how existing models address the need for better dialogue with prior knowledge, biological plausibility and interpretability, fundamental properties in the biomedical domain. For this, we retrieved and analyzed 42 studies focusing on emerging architectural and methodological advances, the encoding of biological domain knowledge and the integration of explainability methods. Results: We discuss the recent evolutionary arch of DL models in the direction of integrating prior biological relational and network knowledge to support better generalisation (e.g. pathways or Protein-Protein-Interaction networks) and interpretability. This represents a fundamental functional shift towards models which can integrate mechanistic and statistical inference aspects. We introduce a concept of bio-centric interpretability and according to its taxonomy, we discuss representational methodologies for the integration of domain prior knowledge in such models. Conclusions: The paper provides a critical outlook into contemporary methods for explainability and interpretability used in DL for cancer. The analysis points in the direction of a convergence between encoding prior knowledge and improved interpretability. We introduce bio-centric interpretability which is an important step towards formalisation of biological interpretability of DL models and developing methods that are less problem- or application-specific. [ABSTRACT FROM AUTHOR]

Cancer prognosis prediction and analysis can help patients understand expected life and help clinicians provide correct therapeutic guidance. Thanks to the development of sequencing technology, multi-omics data, and biological networks have been used for cancer prognosis prediction. Besides, graph neural networks can simultaneously consider multi-omics features and molecular interactions in biological networks, becoming mainstream in cancer prognosis prediction and analysis. However, the limited number of neighboring genes in biological networks restricts the accuracy of graph neural networks. To solve this problem, a local augmented graph convolutional network named LAGProg is proposed in this paper for cancer prognosis prediction and analysis. The process follows: first, given a patient's multi-omics data features and biological network, the corresponding augmented conditional variational autoencoder generates features. Then, the generated augmented features and the original features are fed into a cancer prognosis prediction model to complete the cancer prognosis prediction task. The conditional variational autoencoder consists of two parts: encoder-decoder. In the encoding phase, an encoder learns the conditional distribution of the multi-omics data. As a generative model, a decoder takes the conditional distribution and the original feature as inputs to generate the enhanced features. The cancer prognosis prediction model consists of a two-layer graph convolutional neural network and a Cox proportional risk network. The Cox proportional risk network consists of fully connected layers. Extensive experiments on 15 real-world datasets from TCGA demonstrated the effectiveness and efficiency of the proposed method in predicting cancer prognosis. LAGProg improved the C-index values by an average of 8.5% over the state-of-the-art graph neural network method. Moreover, we confirmed that the local augmentation technique could enhance the model's ability to represent multi-omics features, improve the model's robustness to missing multi-omics features, and prevent the model's over-smoothing during training. Finally, based on genes identified through differential expression analysis, we discovered 13 prognostic markers highly associated with breast cancer, among which ten genes have been proved by literature review. • Prediction cancer prognosis based on graph neural network. • Adopting a local augmentation strategy to represent genes' features. • Outperforming the competing methods and mining novel prognostic biomarkers for breast cancer. [ABSTRACT FROM AUTHOR]

Background: The identification of disease-related genes is of great significance for the diagnosis and treatment of human disease. Most studies have focused on developing efficient and accurate computational methods to predict disease-causing genes. Due to the sparsity and complexity of biomedical data, it is still a challenge to develop an effective multi-feature fusion model to identify disease genes. Results: This paper proposes an approach to predict the pathogenic gene based on multi-head attention fusion (MHAGP). Firstly, the heterogeneous biological information networks of disease genes are constructed by integrating multiple biomedical knowledge databases. Secondly, two graph representation learning algorithms are used to capture the feature vectors of gene-disease pairs from the network, and the features are fused by introducing multi-head attention. Finally, multi-layer perceptron model is used to predict the gene-disease association. Conclusions: The MHAGP model outperforms all of other methods in comparative experiments. Case studies also show that MHAGP is able to predict genes potentially associated with diseases. In the future, more biological entity association data, such as gene-drug, disease phenotype-gene ontology and so on, can be added to expand the information in heterogeneous biological networks and achieve more accurate predictions. In addition, MHAGP with strong expansibility can be used for potential tasks such as gene-drug association and drug-disease association prediction. [ABSTRACT FROM AUTHOR]

The article presents a response from the authors of the article "Proper evaluation of alignment-free network comparison methods" to a letter to the editor published in the previous issue criticizing the article.

Cell localization in medical image analysis is a challenging task due to the significant variation in cell shape, size and color. Existing localization methods continue to tackle these challenges separately, frequently facing complications where these difficulties intersect and adversely impact model performance. In this paper, these challenges are first reframed as issues of feature misalignment between cell images and location maps, which are then collectively addressed. Specifically, we propose a feature alignment model based on a multi-scale hypergraph attention network. The model considers local regions in the feature map as nodes and utilizes a learnable similarity metric to construct hypergraphs at various scales. We then utilize a hypergraph convolutional network to aggregate the features associated with the nodes and achieve feature alignment between the cell images and location maps. Furthermore, we introduce a stepwise adaptive fusion module to fuse features at different levels effectively and adaptively. The comprehensive experimental results demonstrate the effectiveness of our proposed multi-scale hypergraph attention module in addressing the issue of feature misalignment, and our model achieves state-of-the-art performance across various cell localization datasets. • This paper innovatively addresses the challenges stemming from significant variations in cell shape, scale, and color by reframing them as a feature misalignment problem between cell images and location maps, thereby presenting a unified solution to these complexities. • We propose an innovative multi-scale hypergraph attention module that achieves feature alignment through the adaptive aggregation of features across various scale ranges. • The proposed model achieves state-of-the-art performance on multiple cell localization datasets and reveals great potential. [ABSTRACT FROM AUTHOR]

A topological index is a number that is connected to a chemical composition in order to correlate a substance's chemical makeup with different physical characteristics, chemical reactivity, or biological activity. It is common to model drugs and other chemical substances as different forms, trees, and graphs. Certain physico-chemical features of chemical substances correlate better with degree-based topological invariants. Predictions concerning the dynamics of the continuing pandemic may be made with the use of the graphic theoretical approaches given here. In Networks, the degree entropy of the epidemic and related trees was computed. It highlights the essay's originality while also implying that this piece has improved upon prior literature-based realizations. In this paper, we study an important degree-based invariant known as the inverse sum indeg invariant for a variety of graphs of biological interest networks, including the corona product of some interesting classes of graphs and the pandemic tree network, curtain tree network, and Cayley tree network. We also examine the inverse sum indeg invariant features for the molecular graphs that represent the molecules in the bicyclic chemical graphs. [ABSTRACT FROM AUTHOR]

The high separation of crude oil supply and demand markets has led to the formation of a global crude oil trading system. This paper constructs global crude oil trade networks, integrates macro, meso, and micro network analysis methods, combines geospatial visualization techniques, and then portrays the spatiotemporal patterns and topological evolution of the global crude oil trade networks. Thus, it attempts to dig deeper into the world crude oil competition and cooperation links and evolution laws and provides a scientific reference for a comprehensive understanding of the global crude oil market dynamics. The results show that: (1) After three fluctuations of increase and decrease since 2000, the global crude oil trade volume is entering the adjustment period, and the scale of the crude oil market is rising slowly. (2) The international crude oil trade has formed trade network patterns with complex structures, clear hierarchy and unbalanced distribution. The "rich club" phenomenon is significant, with large trading countries dominating the trade network. (3) The scale and density of the global crude oil trade network show a trend of increasing and then decreasing, the network agglomeration pattern becoming more obvious, the inter-nodal links continuously strengthening, and the network connectivity improving. (4) The global crude oil trade networks are characterized by core–periphery structures, and the polarization effect is significant. The US, Russia, China, Japan, the Netherlands, and South Korea hold the core positions in the crude oil trade network, and the major importing countries have become the dominant forces in the trade network. In addition, we present policy suggestions for different types of countries for energy transformation and security in the global trade market system, which can be used as a reference for policymakers. [ABSTRACT FROM AUTHOR]

[Display omitted] • Convective and diffusive transport into the lymphatic system is modeled by a hybrid discrete-continuum vessel network. • Various physiological conditions on the lymphatic vessel wall affects absorption rate. • Evolution of concentration boundary layer is dominated by diffusion across the explicit vessels. • Injection depth shows negligible effect on drug absorption in the multi-layered tissue. • Binding of drug molecules to the extracellular matrix slows down the drug absorption. Subcutaneous administration is a common approach for the delivery of biotherapeutics, which is achieved mainly through the absorption across lymphatic vessels. In this paper, the drug transport and lymphatic uptake through a three-dimensional hybrid discrete-continuum vessel network in the skin tissue are investigated through high-fidelity numerical simulations. We find that the local lymphatic uptake through the explicit vessels significantly affects macroscopic drug absorption. The diffusion of drug solute through the explicit vessel network affects the lymphatic uptake after the injection. This effect, however, cannot be captured using previously developed continuum models. The lymphatic uptake is dominated by the convection due to lymphatic drainage driven by the pressure difference, which is rarely studied in experiments and simulations. Furthermore, the effects of injection volume and depth on the lymphatic uptake are investigated in a multi-layered domain. We find that the injection volume significantly affects the rate of lymphatic uptake through the heterogeneous vessel network, while the injection depth has little influence, which is consistent with the experimental results. At last, the binding and metabolism of drug molecules are studied to bridge the simulations to the drug clearance experients. We provide a new approach to study the diffusion and convection of drug molecules into the lymphatic system through the hybrid vessel network. [ABSTRACT FROM AUTHOR]

With the recent success of computer vision and deep learning, remarkable progress has been achieved on automatic personal recognition using vein biometrics. However, collecting large-scale real-world training data for palm vein recognition has turned out to be challenging, mainly due to the noise and irregular variations included at the time of acquisition. Meanwhile, existing palm vein recognition datasets are usually collected under near-infrared light, lacking detailed annotations on attributes (e.g., pose), so the influences of different attributes on vein recognition have been poorly investigated. Therefore, this paper examines the suitability of synthetic vein images generated to compensate for the urgent lack of publicly available large-scale datasets. Firstly, we present an overview of recent research progress of palm vein recognition, from the basic background knowledge to vein anatomical structure, data acquisition, public database, and quality assessment procedures. Then, we focus on the state-of-the-art methods that have allowed the generation of vascular structures for biometric purposes and the modeling of biological networks with their respective application domains. In addition, we review the existing research on the generation of style transfer and biological nature-based synthetic palm vein images algorithms. Afterward, we formalize a general flowchart for the creation of a synthetic database comparing real palm vein images and generated synthetic samples to obtain some understanding into the development of the realistic vein imaging system. Ultimately, we conclude by discussing the challenges, insights, and future perspectives in generating synthetic palm vein images for further works. • Factors that affect the visualization of vascular structures on palm vein images. • Generation of vascular structures for biometric purposes. • Modeling of biological networks with their respective application domains. • Generation of style transfer and biological nature-based synthetic palm vein images. • Challenges, insights, and future perspectives to generate synthetic palm vein images. [ABSTRACT FROM AUTHOR]

Leader–follower consensus control is a kind of consensus control, where some special agents, called the leaders, have relatively high flexibility in changing their states, and the other agents, called the followers, follow the leaders. One of the important issues for leader–follower consensus control is a leader selection problem, i.e. determining leaders to achieve a desired performance. On the other hand, the notion of a feedback vertex set is well-known in graph theory. Feedback vertex sets are known to play an important role in various problems, e.g. deadlock avoidance and sensing node selection of biological networks. Thus, they are expected to be closely related to leader–follower consensus control. However, their relationship has never been studied so far. This paper discloses the relationship between leader selection and feedback vertex sets. We deal with a problem of finding a minimum leader set to achieve the fastest convergence to consensus and show that a solution to the leader selection problem is given by a feedback vertex set. [ABSTRACT FROM AUTHOR]