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Many networks can be characterised by the presence of communities, which are groups of units that are closely linked and can be relevant in understanding the system's overall function. Recently, hypergraphs have emerged as a fundamental tool for modelling systems where interactions are not limited to pairs but may involve an arbitrary number of nodes. Using a dual approach to community detection, in this study we extend the concept of link communities to hypergraphs, allowing us to extract informative clusters of highly related hyperedges. We analyze the dendrograms obtained by applying hierarchical clustering to distance matrices among hyperedges on a variety of real-world data, showing that hyperlink communities naturally highlight the hierarchical and multiscale structure of higher-order networks. Moreover, by using hyperlink communities, we are able to extract overlapping memberships from nodes, overcoming limitations of traditional hard clustering methods. Finally, we introduce higher-order network cartography as a practical tool for categorizing nodes into different structural roles based on their interaction patterns and community participation. This approach helps identify different types of individuals in a variety of real-world social systems. Our work contributes to a better understanding of the structural organization of real-world higher-order systems.

Scale-free networks are prevalently observed in a great variety of complex systems, which triggers various researches relevant to networked models of such type. In this work, we propose a family of growth tree networks $\mathcal{T}_{t}$, which turn out to be scale-free, in an iterative manner. As opposed to most of published tree models with scale-free feature, our tree networks have the power-law exponent $\gamma=1+\ln5/\ln2$ that is obviously larger than $3$. At the same time, "small-world" property can not be found particularly because models $\mathcal{T}_{t}$ have an ultra-large diameter $D_{t}$ (i.e., $D_{t}\sim|\mathcal{T}_{t}|^{\ln3/\ln5}$) and a greater average shortest path length $\langle\mathcal{W}_{t}\rangle$ (namely, $\langle\mathcal{W}_{t}\rangle\sim|\mathcal{T}_{t}|^{\ln3/\ln5}$) where $|\mathcal{T}_{t}|$ represents vertex number. Next, we determine Pearson correlation coefficient and verify that networks $\mathcal{T}_{t}$ display disassortative mixing structure. In addition, we study random walks on tree networks $\mathcal{T}_{t}$ and derive exact solution to mean hitting time $\langle\mathcal{H}_{t}\rangle$. The results suggest that the analytic formula for quantity $\langle\mathcal{H}_{t}\rangle$ as a function of vertex number $|\mathcal{T}_{t}|$ shows a power-law form, i.e., $\langle\mathcal{H}_{t}\rangle\sim|\mathcal{T}_{t}|^{1+\ln3/\ln5}$. Accordingly, we execute extensive experimental simulations, and demonstrate that empirical analysis is in strong agreement with theoretical results. Lastly, we provide a guide to extend the proposed iterative manner in order to generate more general scale-free tree networks with large diameter.

Within network data analysis, bipartite networks represent a particular type of network where relationships occur between two disjoint sets of nodes, formally called sending and receiving nodes. In this context, sending nodes may be organized into layers on the basis of some defined characteristics, resulting in a special case of multilayer bipartite network, where each layer includes a specific set of sending nodes. To perform a clustering of sending nodes in multi-layer bipartite network, we extend the Mixture of Latent Trait Analyzers (MLTA), also taking into account the influence of concomitant variables on clustering formation and the multi-layer structure of the data. To this aim, a multilevel approach offers a useful methodological tool to properly account for the hierarchical structure of the data and for the unobserved sources of heterogeneity at multiple levels. A simulation study is conducted to test the performance of the proposal in terms of parameters' and clustering recovery. Furthermore, the model is applied to the European Social Survey data (ESS) to i) perform a clustering of individuals (sending nodes) based on their digital skills (receiving nodes); ii) understand how socio-economic and demographic characteristics influence the individual digitalization level; iii) account for the multilevel structure of the data; iv) obtain a clustering of countries in terms of the base-line attitude to digital technologies of their residents.

Percolation theory investigates systems of interconnected units, their resilience to damage and their propensity to propagation. For random networks we can solve the percolation problems analytically using the generating function formalism. Yet, with the introduction of higher order networks, the generating function calculations are becoming difficult to perform and harder to validate. Here, I illustrate the mapping of percolation in higher order networks to percolation in chygraphs. Chygraphs are defined as a set of complexes where complexes are hypergraphs with vertex sets in the set of complexes. In a previous work I reported the generating function formalism to percolation in chygraphs and obtained an analytical equation for the order parameter. Taking advantage of this result, I recapitulate analytical results for percolation problems in higher order networks and report extensions to more complex scenarios using symbolic calculations. The code for symbolic calculations can be found at //github.com/av2atgh/chygraph.

Sensor network localization (SNL) problems require determining the physical coordinates of all sensors in a network. This process relies on the global coordinates of anchors and the available measurements between non-anchor and anchor nodes. Attributed to the intrinsic non-convexity, obtaining a globally optimal solution to SNL is challenging, as well as implementing corresponding algorithms. In this paper, we formulate a non-convex multi-player potential game for a generic SNL problem to investigate the identification condition of the global Nash equilibrium (NE) therein, where the global NE represents the global solution of SNL. We employ canonical duality theory to transform the non-convex game into a complementary dual problem. Then we develop a conjugation-based algorithm to compute the stationary points of the complementary dual problem. On this basis, we show an identification condition of the global NE: the stationary point of the proposed algorithm satisfies a duality relation. Finally, simulation results are provided to validate the effectiveness of the theoretical results.

Current deep neural networks (DNNs) for autonomous driving computer vision are typically trained on specific datasets that only involve a single type of data and urban scenes. Consequently, these models struggle to handle new objects, noise, nighttime conditions, and diverse scenarios, which is essential for safety-critical applications. Despite ongoing efforts to enhance the resilience of computer vision DNNs, progress has been sluggish, partly due to the absence of benchmarks featuring multiple modalities. We introduce a novel and versatile dataset named InfraParis that supports multiple tasks across three modalities: RGB, depth, and infrared. We assess various state-of-the-art baseline techniques, encompassing models for the tasks of semantic segmentation, object detection, and depth estimation. More visualizations and the download link for InfraParis are available at \href{//ensta-u2is.github.io/infraParis/}{//ensta-u2is.github.io/infraParis/}.

The paper tackles the problem of clustering multiple networks, directed or not, that do not share the same set of vertices, into groups of networks with similar topology. A statistical model-based approach based on a finite mixture of stochastic block models is proposed. A clustering is obtained by maximizing the integrated classification likelihood criterion. This is done by a hierarchical agglomerative algorithm, that starts from singleton clusters and successively merges clusters of networks. As such, a sequence of nested clusterings is computed that can be represented by a dendrogram providing valuable insights on the collection of networks. Using a Bayesian framework, model selection is performed in an automated way since the algorithm stops when the best number of clusters is attained. The algorithm is computationally efficient, when carefully implemented. The aggregation of clusters requires a means to overcome the label-switching problem of the stochastic block model and to match the block labels of the networks. To address this problem, a new tool is proposed based on a comparison of the graphons of the associated stochastic block models. The clustering approach is assessed on synthetic data. An application to a set of ecological networks illustrates the interpretability of the obtained results.

Crowd simulations play a pivotal role in building design, influencing both user experience and public safety. While traditional knowledge-driven models have their merits, data-driven crowd simulation models promise to bring a new dimension of realism to these simulations. However, most of the existing data-driven models are designed for specific geometries, leading to poor adaptability and applicability. A promising strategy for enhancing the adaptability and realism of data-driven crowd simulation models is to incorporate visual information, including the scenario geometry and pedestrian locomotion. Consequently, this paper proposes a novel visual-information-driven (VID) crowd simulation model. The VID model predicts the pedestrian velocity at the next time step based on the prior social-visual information and motion data of an individual. A radar-geometry-locomotion method is established to extract the visual information of pedestrians. Moreover, a temporal convolutional network (TCN)-based deep learning model, named social-visual TCN, is developed for velocity prediction. The VID model is tested on three public pedestrian motion datasets with distinct geometries, i.e., corridor, corner, and T-junction. Both qualitative and quantitative metrics are employed to evaluate the VID model, and the results highlight the improved adaptability of the model across all three geometric scenarios. Overall, the proposed method demonstrates effectiveness in enhancing the adaptability of data-driven crowd models.

The synthesis of information deriving from complex networks is a topic receiving increasing relevance in ecology and environmental sciences. In particular, the aggregation of multilayer networks, i.e. network structures formed by multiple interacting networks (the layers), constitutes a fast-growing field. In several environmental applications, the layers of a multilayer network are modelled as a collection of similarity matrices describing how similar pairs of biological entities are, based on different types of features (e.g. biological traits). The present paper first discusses two main techniques for combining the multi-layered information into a single network (the so-called monoplex), i.e. Similarity Network Fusion (SNF) and Similarity Matrix Average (SMA). Then, the effectiveness of the two methods is tested on a real-world dataset of the relative abundance of microbial species in the ecosystems of nine glaciers (four glaciers in the Alps and five in the Andes). A preliminary clustering analysis on the monoplexes obtained with different methods shows the emergence of a tightly connected community formed by species that are typical of cryoconite holes worldwide. Moreover, the weights assigned to different layers by the SMA algorithm suggest that two large South American glaciers (Exploradores and Perito Moreno) are structurally different from the smaller glaciers in both Europe and South America. Overall, these results highlight the importance of integration methods in the discovery of the underlying organizational structure of biological entities in multilayer ecological networks.

Recent advances in 3D fully convolutional networks (FCN) have made it feasible to produce dense voxel-wise predictions of volumetric images. In this work, we show that a multi-class 3D FCN trained on manually labeled CT scans of several anatomical structures (ranging from the large organs to thin vessels) can achieve competitive segmentation results, while avoiding the need for handcrafting features or training class-specific models. To this end, we propose a two-stage, coarse-to-fine approach that will first use a 3D FCN to roughly define a candidate region, which will then be used as input to a second 3D FCN. This reduces the number of voxels the second FCN has to classify to ~10% and allows it to focus on more detailed segmentation of the organs and vessels. We utilize training and validation sets consisting of 331 clinical CT images and test our models on a completely unseen data collection acquired at a different hospital that includes 150 CT scans, targeting three anatomical organs (liver, spleen, and pancreas). In challenging organs such as the pancreas, our cascaded approach improves the mean Dice score from 68.5 to 82.2%, achieving the highest reported average score on this dataset. We compare with a 2D FCN method on a separate dataset of 240 CT scans with 18 classes and achieve a significantly higher performance in small organs and vessels. Furthermore, we explore fine-tuning our models to different datasets. Our experiments illustrate the promise and robustness of current 3D FCN based semantic segmentation of medical images, achieving state-of-the-art results. Our code and trained models are available for download: //github.com/holgerroth/3Dunet_abdomen_cascade.