Subset Of Nodes Research Articles

Branch and Price for the Stochastic Traveling Salesman Problem with Generalized Latency

We consider an extension of the symmetric traveling salesman problem with generalized latency that explicitly models uncertainty. The stochastic traveling salesman problem with generalized latency (STSP-GL) aims to choose a subset of nodes of an undirected graph and determines a Hamiltonian tour among those nodes, minimizing an objective function that is a weighted combination of route design and passenger routing costs. These nodes are selected to ensure that a predefined percentage of uncertain passenger demand is served with a given probability. We formulate the STSP-GL as a stochastic program and propose a branch-and-price algorithm for solving its deterministic equivalent. We also develop a local search approach with which we improve the performance of the branch-and-price approach. We assess the efficiency of the proposed methods on a set of instances from the literature. We demonstrate that the proposed methods outperform a known benchmark, improving upper bounds by up to 85% and lower bounds by up to 55%. Finally, we show that solutions of the stochastic model are both more cost-effective and robust than those of the deterministic model. History: This paper has been accepted for the Transportation Science Special Issue on TSL Conference 2023. Funding: This work was supported by the Bundesministerium für Bildung und Forschung [Grant 03ZU1105FA]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.0417 .

Sublinear message bounds of authenticated implicit Byzantine agreement

This paper studies the message complexity of authenticated Byzantine agreement (BA) in synchronous, fully-connected distributed networks under an honest majority. We focus on the so-called implicit Byzantine agreement problem where each node starts with an input value and at the end a non-empty subset of the honest nodes should agree on a common input value by satisfying the BA properties (i.e., there can be undecided nodes)3. We show that a sublinear (in n, number of nodes) message complexity BA protocol under honest majority is possible in the standard PKI model when the nodes have access to an unbiased global coin and hash function. In particular, we present a randomized Byzantine agreement algorithm which, with high probability achieves implicit agreement, uses O˜(n) messages, and runs in O˜(1) rounds while tolerating (1/2−ϵ)n Byzantine nodes for any fixed ϵ>0, the notation O˜ hides a O(polylogn) factor4. The algorithm requires standard cryptographic setup PKI and hash function with a static Byzantine adversary. The algorithm works in the CONGEST model and each node does not need to know the identity of its neighbors, i.e., works in the KT0 model. The message complexity (and also the time complexity) of our algorithm is optimal up to a polylog n factor, as we show a Ω(n) lower bound on the message complexity. We further extend the result to Byzantine subset agreement, where a non-empty subset of nodes should agree on a common value. Lastly, we analyze several relevant results that follow from the construction of the main result.To the best of our knowledge, this is the first sublinear message complexity result of Byzantine agreement. A quadratic message lower bound is known for any deterministic BA protocol (due to Dolev-Reischuk [JACM 1985]). The existing randomized BA protocols have at least quadratic message complexity in the honest majority setting. Our result shows the power of a global coin in achieving significant improvement over the existing results. It can be viewed as a step towards understanding the message complexity of randomized Byzantine agreement in distributed networks with PKI.

Improving community detection in blockmodel by distance-based observation selection

Community detection is an important research topic in complex systems and has plenty of applications in real-world networks. Probabilistic methods, such as the Expectation–Maximization (EM), are developed to classify nodes that have similar connection patterns in a network based on blockmodels. However, the detection procedures in these models are typically started from randomly generated initial community distributions without prior knowledge. In biological and social networks, there are practical measures to obtain prior knowledge for a subset of nodes, such as local observations. These facts lead us to question how we can select a subset of nodes with known community labels to enhance the accuracy of the EM method. The current selection methods lack the relationship between detection accuracy and structural characteristics and most approaches consider the nodes as the center of communities, which is not suitable for block models. In this paper, we first study the relationships between the structural distance and detection accuracy without prior knowledge. Then we propose a distance-based indicator to describe the performance of the observation node set in the EM method. Finally, we introduce a scoring method based on the indicator to select a partial observation set, improving the accuracy of community detection using the EM method. Empirical results from synthetic and real-world networks corroborate that the proposed indicator could contribute to a better performance in kinds of scenarios.

Node and relevant data selection in distributed predictive analytics: A query-centric approach

Distributed Predictive Analytics (DPA) refers to constructing predictive models based on data distributed across nodes. DPA reduces the need for data centralization, thus, alleviating concerns about data privacy, decreasing the load on central servers, and minimizing communication overhead. However, data collected by nodes are inherently different; each node can have different distributions, volumes, access patterns, and features space. This heterogeneity hinders the development of accurate models in a distributed fashion. Many state-of-the-art methods adopt random node selection as a straightforward approach. Such method is particularly ineffective when dealing with data and access pattern heterogeneity, as it increases the likelihood of selecting nodes with low-quality or irrelevant data for DPA. Consequently, it is only after training models over randomly selected nodes that the most suitable ones can be identified based on the predictive performance. This results in more time and resource consumption, and increased network load. In this work, holistic knowledge of nodes’ data characteristics and access patterns is crucial. Such knowledge enables the successful selection of a subset of suitable nodes for each DPA task (query) before model training. Our method engages the most suitable nodes by predicting their relevant distributed data and learning predictive models per query. We introduce a novel DPA query-centric mechanism for node and relevant data selection. We contribute with (i) predictive selection mechanisms based on the availability and relevance of data per DPA query and (ii) various distributed machine learning mechanisms that engage the most suitable nodes for model training. We evaluate the efficiency of our mechanism and provide a comparative assessment with other methods found in the literature. Our experiments showcase that our mechanism significantly outperforms other approaches being applicable in DPA.

Navigating the Intersection of Glycemic Control and Fertility: A Network Perspective.

The rising incidence of metabolic diseases is linked to elevated blood glucose levels, contributing to conditions such as diabetes and promoting the accumulation of advanced glycation end products (AGEs). AGEs, formed by non-enzymatic reactions between sugars and proteins, build up in tissues and are implicated in various diseases. This article explores the relationship between glycemic control and AGE accumulation, focusing on fertility implications. A computational model using network theory was developed, featuring a molecular database and a network with 145 nodes and 262 links, categorized as a Barabasi-Albert scale-free network. Three main subsets of nodes emerged, centered on glycemic control, fertility, and immunity, with AGEs playing a critical role. The transient receptor potential vanilloid 1 (TRPV1), a receptor expressed in several tissues including sperm, was identified as a key hub, suggesting that the modulation of TRPV1 in sperm by AGEs may influence fertility. Additionally, a novel link between glycemic control and immunity was found, indicating that immune cells may play a role in endocytosing specific AGEs. This discovery underscores the complex interplay between glycemic control and immune function, with significant implications for metabolic, immune health, and fertility.

Multiagent learning for competitive opinion optimization

From a perspective of designing or engineering for opinion formation games in social networks, the opinion maximization (or minimization) problem has been studied mainly for designing seeding algorithms that aim at selecting a subset of nodes to control their opinions. We first define a two-player zero-sum Stackelberg game of competitive opinion optimization by letting the player under study as the leader minimize the sum of expressed opinions by doing so-called “internal opinion design”, knowing that the other adversarial player as the follower is to maximize the same objective by also conducting her own internal opinion design. We furthermore consider multiagent learning, specifically using the Optimistic Gradient Descent Ascent, and analyze its convergence to equilibria in the simultaneous-game version of competitive opinion optimization.

Differentiation of intrathoracic lymph node histopathology by volumetric dual energy CT radiomic analysis

PurposeTo determine the performance of volumetric dual energy low kV and iodine radiomic features for the differentiation of intrathoracic lymph node histopathology, and influence of contrast protocol. Materials and methodsIntrathoracic lymph nodes with histopathologic correlation (neoplastic, granulomatous sarcoid, benign) within 90 days of DECT chest imaging were volumetrically segmented. 1691 volumetric radiomic features were extracted from iodine maps and low-kV images, totaling 3382 features. Univariate analysis was performed using 2-sample t-test and filtered for false discoveries. Multivariable analysis was used to compute AUCs for lymph node classification tasks. Results129 lymph nodes from 72 individuals (mean age 61 ± 15 years) were included, 52 neoplastic, 51 benign, and 26 granulomatous-sarcoid. Among all contrast enhanced DECT protocol exams (routine, PE and CTA), univariable analysis demonstrated no significant differences in iodine and low kV features between neoplastic and non-neoplastic lymph nodes; in the subset of neoplastic versus benign lymph nodes with routine DECT protocol, 199 features differed (p = .01- < 0.05).Multivariable analysis using both iodine and low kV features yielded AUCs >0.8 for differentiating neoplastic from non-neoplastic lymph nodes (AUC 0.86), including subsets of neoplastic from granulomatous (AUC 0.86) and neoplastic from benign (AUC 0.9) lymph nodes, among all contrast protocols. ConclusionsVolumetric DECT radiomic features demonstrate strong collective performance in differentiation of neoplastic from non-neoplastic intrathoracic lymph nodes, and are influenced by contrast protocol.

Influence Maximization Based on Adaptive Graph Convolution Neural Network in Social Networks

The influence maximization problem is a hot issue in the research on social networks due to its wide application. The problem aims to find a small subset of influential nodes to maximize the influence spread. To tackle the challenge of striking a balance between efficiency and effectiveness in traditional influence maximization algorithms, deep learning-based influence maximization algorithms have been introduced and have achieved advancement. However, these algorithms still encounter two key problems: (1) Traditional deep learning models are not well-equipped to capture the latent topological information of networks with varying sizes and structures. (2) Many deep learning-based methods use the influence spread of individual nodes as labels to train a model, which can result in an overlap of influence among the seed nodes selected by the model. In this paper, we reframe the influence maximization problem as a regression task and introduce an innovative approach to influence maximization. The method adopts an adaptive graph convolution neural network which can explore the latent topology information of the network and can greatly improve the performance of the algorithm. In our approach, firstly, we integrate several network-level attributes and some centrality metrics into a vector as the presentation vector of nodes in the social network. Next, we propose a new label generation method to measure the influence of nodes by neighborhood discount strategy, which takes full account of the influence overlapping problem. Subsequently, labels and presentation vectors are fed into an adaptive graph convolution neural network model. Finally, we use the well-trained model to predict the importance of nodes and select top-K nodes as a seed set. Abundant experiments conducted on various real-world datasets have confirmed that the performance of our proposed algorithm surpasses that of several current state-of-the-art algorithms.

Target control of linear directed networks based on the path cover problem

Securing complete control of complex systems comprised of tens of thousands of interconnected nodes holds immense significance across various fields, spanning from cell biology and brain science to human-engineered systems. However, depending on specific functional requirements, it can be more practical and efficient to focus on a pre-defined subset of nodes for control, a concept known as target control. While some methods have been proposed to find the smallest driver node set for target control, they either rely on heuristic approaches based on k-walk theory, lacking a guarantee of optimal solutions, or they are overly complex and challenging to implement in real-world networks. To address this challenge, we introduce a simple and elegant algorithm, inspired by the path cover problem, which efficiently identifies the nodes required to control a target node set within polynomial time. To practically apply the algorithm in real-world systems, we have selected several networks in which a specific set of nodes with functional significance can be designated as a target control set. The analysed systems include the complete connectome of the nematode worm C. elegans, the recently disclosed connectome of the Drosophila larval brain, as well as dozens of genome-wide metabolic networks spanning major plant lineages. The target control analysis shed light on distinctions between neural systems in nematode worms and larval brain insects, particularly concerning the number of nodes necessary to regulate specific functional systems. Furthermore, our analysis uncovers evolutionary trends within plant lineages, notably when examining the proportion of nodes required to control functional pathways.

FICOM: an effective and scalable active learning framework for GNNs on semi-supervised node classification

Active learning for graph neural networks (GNNs) aims to select B nodes to label for the best possible GNN performance. Carefully selected labeled nodes can help improve GNN performance and hence motivates a line of research works. Unfortunately, existing methods still provide inferior GNN performance or cannot scale to large networks.Motivated by these limitations, in this paper, we present FICOM, an effective and scalable GNN active learning framework. Firstly, we formulate the node selection as an optimization problem where we consider the importance of a node from (i) the importance of a node during the feature propagation with a connection to the personalized PageRank (PPR), and (ii) the diversity of a node brings in the embedding space generated by feature propagation. We show that the defined problem is submodular, and a greedy solution can provide a (1-1/e)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(1-1/e)$$\\end{document}-approximate solution.However, a standard greedy solution requires getting the node with the maximum marginal gain of the objective score in each iteration, which incurs a prohibitive running cost and cannot scale to large datasets. As our main contribution, we present FICOM, an efficient and scalable solution that provides (1-1/e)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(1-1/e)$$\\end{document}-approximation guarantee and scales to graphs with millions of nodes on a single machine. The main idea is that we adaptively maintain the lower- and upper-bound of the marginal gain for each node v. In each iteration, we can first derive a small subset of candidate nodes and then compute the exact score for this subset of candidate nodes so that we can find the node with the maximum marginal gain efficiently. Extensive experiments on six benchmark datasets using four GNNs, including GCN, SGC, APPNP, and GCNII, show that our FICOM consistently outperforms existing active learning approaches on semi-supervised node classification tasks using different GNNs. Moreover, our solution can finish within 5 h on a million-node graph.

Neural discovery of balance-aware polarized communities

Signed graphs are a model to depict friendly (positive) or antagonistic (negative) interactions (edges) among users (nodes). 2-Polarized-Communities (2pc) is a well-established combinatorial-optimization problem whose goal is to find two polarized communities from a signed graph, i.e., two subsets of nodes (disjoint, but not necessarily covering the entire node set) which exhibit a high number of both intra-community positive edges and negative inter-community edges. The state of the art in 2pc suffers from the limitations that (i) existing methods rely on a single (optimal) solution to a continuous relaxation of the problem in order to produce the ultimate discrete solution via rounding, and (ii) 2pc objective function comes with no control on size balance among communities. In this paper, we provide advances to the 2pc problem by addressing both these limitations, with a twofold contribution. First, we devise a novel neural approach that allows for soundly and elegantly explore a variety of suboptimal solutions to the relaxed 2pc problem, so as to pick the one that leads to the best discrete solution after rounding. Second, we introduce a generalization of 2pc objective function – termed γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document}-polarity – which fosters size balance among communities, and we incorporate it into the proposed machine-learning framework. Extensive experiments attest high accuracy of our approach, its superiority over the state of the art, and capability of function γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document}-polarity to discover high-quality size-balanced communities.

Expectation-Maximization enables Phylogenetic Dating under a Categorical Rate Model.

Dating phylogenetic trees to obtain branch lengths in time unit is essential for many downstream applications but has remained challenging. Dating requires inferring substitution rates that can change across the tree. While we can assume to have information about a small subset of nodes from the fossil record or sampling times (for fast-evolving organisms), inferring the ages of the other nodes essentially requires extrapolation and interpolation. Assuming a distribution of branch rates, we can formulate dating as a constrained maximum likelihood (ML) estimation problem. While ML dating methods exist, their accuracy degrades in the face of model misspecification where the assumed parametric statistical distribution of branch rates vastly differs from the true distribution. Notably, most existing methods assume rigid, often unimodal, branch rate distributions. A second challenge is that the likelihood function involves an integral over the continuous domain of the rates and often leads to difficult non-convex optimization problems. To tackle these two challenges, we propose a new method called Molecular Dating using Categorical-models (MD-Cat). MD-Cat uses a categorical model of rates inspired by non-parametric statistics and can approximate a large family of models by discretizing the rate distribution into k categories. Under this model, we can use the Expectation- Maximization (EM) algorithm to co-estimate rate categories and branch lengths in time units. Our model has fewer assumptions about the true distribution of branch rates than parametric models such as Gamma or LogNormal distribution. Our results on two simulated and real datasets of Angiosperms and HIV and a wide selection of rate distributions show that MD-Cat is often more accurate than the alternatives, especially on datasets with exponential or multimodal rate distributions.

A network flow approach to a common generalization of Clar and Fries numbers

Clar number and Fries number are two thoroughly investigated parameters of plane graphs emerging from mathematical chemistry to measure stability of organic molecules. First, we introduce a common generalization of these two concepts for bipartite plane graphs, and then we extend it further to the notion of source-sink pairs of subsets of nodes in a general (not necessarily planar) directed graph. The main result is a min-max formula for the maximum weight of a source-sink pair. The proof is based on the recognition that the convex hull of source-sink pairs can be obtained as the projection of a network tension polyhedron. The construction makes it possible to apply any standard cheapest network flow algorithm to compute both a maximum weight source-sink pair and a minimizer of the dual optimization problem formulated in the min-max theorem. As a consequence, our approach gives rise to the first purely combinatorial, strongly polynomial algorithm to compute a largest (or even a maximum weight) Fries-set of a perfectly matchable plane bipartite graph and an optimal solution to the dual minimization problem.

Mask the Unknown: Assessing Different Strategies to Handle Weak Annotations in the MICCAI2023 Mediastinal Lymph Node Quantification Challenge

Pathological lymph node delineation is crucial in cancer diagnosis, progression assessment, and treatment planning. The MICCAI 2023 Lymph Node Quantification Challenge published the first public dataset for pathological lymph node segmentation in the mediastinum. As lymph node annotations are expensive, the challenge was formed as a weakly supervised learning task, where only a subset of all lymph nodes in the training set have been annotated. For the challenge submission, multiple methods for training on these weakly supervised data were explored, including noisy label training, loss masking of unlabeled data, and an approach that integrated the TotalSegmentator toolbox as a form of pseudo labeling in order to reduce the number of unknown voxels. Furthermore, multiple public TCIA datasets were incorporated into the training to improve the performance of the deep learning model. Our submitted model achieved a Dice score of 0.628 and an average symmetric surface distance of 5.8~mm on the challenge test set. With our submitted model, we accomplished the third rank in the MICCAI2023 LNQ challenge. A finding of our analysis was that the integration of all visible, including non-pathological lymph nodes improved the overall segmentation performance on pathological lymph nodes of the test set. Furthermore, segmentation models trained only on clinically enlarged lymph nodes, as given in the challenge scenario, could not generalize to smaller pathological lymph nodes. The code and model for the challenge submission are available at &lt;a href='https://gitlab.lrz.de/compai/MediastinalLymphNodeSegmentation'&gt;https://gitlab.lrz.de/compai/MediastinalLymphNodeSegmentation&lt;/a&gt;

Competitive Influence Maximization in Trust-Based Social Networks With Deep Q-Learning

Social network analysis is a rapidly evolving research area having several real-life application areas, e.g. digital marketing, epidemiology, spread of misinformation. Influence maximization aims to select a subset of nodes in such manner that the information propagated over the network is maximized. Competitive influence maximization, which describes the phenomena of multiple actors competing for resources within the same infrastructure, can be solved with a greedy approach selecting the seed nodes utilizing the influence strength between nodes. Recently, deep reinforcement learning methods were applied for estimating the influence strength. We train a controller with reinforcement learning for selecting a node list of given length as the initial seed set for the information spread. Our experiments show that deep Q-learning methods are suitable to analyze the competitive influence maximization on trust and distrust based social networks. Keywords: influence maximization, reinforcement learning, Q-learning.

A Comprehensive Architecture for Federated Learning-Based Smart Advertising.

This paper introduces a cutting-edge data architecture designed for a smart advertising context, prioritizing efficient data flow and performance, robust security, while guaranteeing data privacy and integrity. At the core of this study lies the application of federated learning (FL) as the primary methodology, which emphasizes the authenticity and privacy of data while promptly discarding irrelevant or fraudulent information. Our innovative data model employs a semi-random role assignment strategy based on a variety of criteria to efficiently collect and amalgamate data. The architecture is composed of model nodes, data nodes, and validator nodes, where the role of each node is determined by factors such as computational capability, interconnection quality, and historical performance records. A key feature of our proposed system is the selective engagement of a subset of nodes for modeling and validation, optimizing resource use and minimizing data loss. The AROUND social network platform serves as a real-world case study, illustrating the efficacy of our data architecture in a practical setting. Both simulated and real implementations of our architecture showcase its potential to dramatically curtail network traffic and average CPU usage, while preserving the accuracy of the FL model. Remarkably, the system is capable of achieving over a 50% reduction in both network traffic and average CPU usage even when the user count escalates by twenty-fold. The click rate, user engagement, and other parameters have also been evaluated, proving that the proposed architecture's advantages do not affect the smart advertising accuracy. These findings highlight the proposed architecture's capacity to scale efficiently and maintain high performance in smart advertising environments, making it a valuable contribution to the evolving landscape of digital marketing and FL.

A Learnheuristic Algorithm Based on Thompson Sampling for the Heterogeneous and Dynamic Team Orienteering Problem

The team orienteering problem (TOP) is a well-studied optimization challenge in the field of Operations Research, where multiple vehicles aim to maximize the total collected rewards within a given time limit by visiting a subset of nodes in a network. With the goal of including dynamic and uncertain conditions inherent in real-world transportation scenarios, we introduce a novel dynamic variant of the TOP that considers real-time changes in environmental conditions affecting reward acquisition at each node. Specifically, we model the dynamic nature of environmental factors—such as traffic congestion, weather conditions, and battery level of each vehicle—to reflect their impact on the probability of obtaining the reward when visiting each type of node in a heterogeneous network. To address this problem, a learnheuristic optimization framework is proposed. It combines a metaheuristic algorithm with Thompson sampling to make informed decisions in dynamic environments. Furthermore, we conduct empirical experiments to assess the impact of varying reward probabilities on resource allocation and route planning within the context of this dynamic TOP, where nodes might offer a different reward behavior depending upon the environmental conditions. Our numerical results indicate that the proposed learnheuristic algorithm outperforms static approaches, achieving up to 25% better performance in highly dynamic scenarios. Our findings highlight the effectiveness of our approach in adapting to dynamic conditions and optimizing decision-making processes in transportation systems.

Blockchian Based Hybrid Consensus Algorithm for Data Security in Edge Computing

Abstract: Edge computing has emerged as a paradigm to process data closer to its source, enabling low-latency and real-time applications. However, the distributed and heterogeneous nature of edge environments poses significant challenges for ensuring data security and integrity. Blockchain technology offers a promising solution by providing a decentralized and immutable ledger for recording transactions. This abstract proposes a consensus algorithm tailored for securing data in edge computing environments using blockchain technology. The proposed consensus algorithm leverages a hybrid approach combining Proof of Authority (PoA) and Practical Byzantine Fault Tolerance (PBFT). PoA ensures that only trusted nodes within the edge network are eligible to participate in the consensus process, mitigating the risk of malicious attacks. PBFT enhances the efficiency and scalability of the consensus algorithm by allowing fast decision-making among a subset of nodes, thereby reducing latency in data validation and verification. Furthermore, smart contracts are employed to enforce data access control and execute predefined rules for data processing and sharing. These smart contracts facilitate secure and transparent interactions among edge devices, ensuring that only authorized parties can access and manipulate sensitive data. The integration of blockchain technology with edge computing offers several benefits, including enhanced data security, traceability, and accountability. By employing a tailored consensus algorithm, edge computing environments can effectively mitigate security threats while maintaining low-latency data processing capabilities. Future research directions may explore optimization techniques to further improve the performance and scalability of the proposed solution in large-scale edge networks.

IMNE: Maximizing influence through deep learning-based node embedding in social network

Influence Maximization (IM) is a critical problem in social network analysis and marketing. It involves identifying a subset of nodes in a social network whose activation or influence can lead to the maximal spread of information, ideas, or behaviors within the network. Although many approaches have been developed in the literature to deal with this problem, most of these approaches are ineffective in dealing with large-scale social networks due to free parameters and computational complexity. Embeddings are used to learn low-dimensional representations of nodes in a social network. These embeddings capture the structural and semantic information of nodes and their relationships within the network. By training deep learning models on graph-structured data, node embeddings can capture complex patterns and dependencies in social networks, enabling more effective downstream tasks such as IM. Accordingly, this paper proposes an efficient algorithm to address the IM problem in social networks using deep learning-based Node Embedding (IMNE), which includes shell decomposition, graph/node embedding, and search space reduction as well as the use of local structural features. Our approach combines the power of deep learning for representation learning with the rich structural information present in social networks to address the challenge of IM in complex and dynamic social networks. IMNE uses the Independent Cascade (IC) information diffusion model to determine the labels needed to train the model by calculating the influence of nodes. Experimental results on several real-world networks considering different performance metrics show that IMNE performs better compared to existing baseline and state-of-the-art methods.

An encompassed representation of timescale hierarchies in first-order reaction network

Complex networks are pervasive in various fields such as chemistry, biology, and sociology. In chemistry, first-order reaction networks are represented by a set of first-order differential equations, which can be constructed from the underlying energy landscape. However, as the number of nodes increases, it becomes more challenging to understand complex kinetics across different timescales. Hence, how to construct an interpretable, coarse-graining scheme that preserves the underlying timescales of overall reactions is of crucial importance. Here, we develop a scheme to capture the underlying hierarchical subsets of nodes, and a series of coarse-grained (reduced-dimensional) rate equations between the subsets as a function of time resolution from the original reaction network. Each of the coarse-grained representations guarantees to preserve the underlying slow characteristic timescales in the original network. The crux is the construction of a lumping scheme incorporating a similarity measure in deciphering the underlying timescale hierarchy, which does not rely on the assumption of equilibrium. As an illustrative example, we apply the scheme to four-state Markovian models and Claisen rearrangement of allyl vinyl ether (AVE), and demonstrate that the reduced-dimensional representation accurately reproduces not only the slowest but also the faster timescales of overall reactions although other reduction schemes based on equilibrium assumption well reproduce the slowest timescale but fail to reproduce the second-to-fourth slowest timescales with the same accuracy. Our scheme can be applied not only to the reaction networks but also to networks in other fields, which helps us encompass their hierarchical structures of the complex kinetics over timescales.