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The robustness of metro networks with the rich-core structure

2024-11-01
Z. Liu , Wei Li , Yuxiang Yang

Step-Video-T2V Technical Report: The Practice, Challenges, and Future of Video Foundation Model

2025-02-14
Guoqing Ma , Haoyang Huang , Kun Yan +7 more
We present Step-Video-T2V, a state-of-the-art text-to-video pre-trained model with 30B parameters and the ability to generate videos up to 204 frames in length. A deep compression Variational Autoencoder, Video-VAE, is ā€¦ We present Step-Video-T2V, a state-of-the-art text-to-video pre-trained model with 30B parameters and the ability to generate videos up to 204 frames in length. A deep compression Variational Autoencoder, Video-VAE, is designed for video generation tasks, achieving 16x16 spatial and 8x temporal compression ratios, while maintaining exceptional video reconstruction quality. User prompts are encoded using two bilingual text encoders to handle both English and Chinese. A DiT with 3D full attention is trained using Flow Matching and is employed to denoise input noise into latent frames. A video-based DPO approach, Video-DPO, is applied to reduce artifacts and improve the visual quality of the generated videos. We also detail our training strategies and share key observations and insights. Step-Video-T2V's performance is evaluated on a novel video generation benchmark, Step-Video-T2V-Eval, demonstrating its state-of-the-art text-to-video quality when compared with both open-source and commercial engines. Additionally, we discuss the limitations of current diffusion-based model paradigm and outline future directions for video foundation models. We make both Step-Video-T2V and Step-Video-T2V-Eval available at https://github.com/stepfun-ai/Step-Video-T2V. The online version can be accessed from https://yuewen.cn/videos as well. Our goal is to accelerate the innovation of video foundation models and empower video content creators.
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A Generalization of Chebyshev--Markov Type Inequality

2025-05-01
Li Zhu , Feng Wu , Yongliang Zhao +2 more

An adaptive high-order stochastic perturbation collocation method for uncertainty quantification and propagation

2025-05-01
Ke Zhao , Feng Wu , Xin Wu +2 more

Fluorescent Magnetic Periodic Mesoporous Organosilicas for Gambogic Acid Loading, Controlled Release, and Targeted Delivery To VX2 Tumor Cells

2025-05-21
Yan Huang , Asma Khalid , Yufei Xie +4 more

Fluorescent Magnetic Periodic Mesoporous Organosilicas for Gambogic Acid Loading, Controlled Release, and Targeted Delivery To VX2 Tumor Cells

2025-05-21
Yan Huang , Asma Khalid , Yufei Xie +4 more

A Generalization of Chebyshev--Markov Type Inequality

2025-05-01
Li Zhu , Feng Wu , Yongliang Zhao +2 more

An adaptive high-order stochastic perturbation collocation method for uncertainty quantification and propagation

2025-05-01
Ke Zhao , Feng Wu , Xin Wu +2 more

Step-Video-T2V Technical Report: The Practice, Challenges, and Future of Video Foundation Model

2025-02-14
Guoqing Ma , Haoyang Huang , Kun Yan +7 more
We present Step-Video-T2V, a state-of-the-art text-to-video pre-trained model with 30B parameters and the ability to generate videos up to 204 frames in length. A deep compression Variational Autoencoder, Video-VAE, is ā€¦ We present Step-Video-T2V, a state-of-the-art text-to-video pre-trained model with 30B parameters and the ability to generate videos up to 204 frames in length. A deep compression Variational Autoencoder, Video-VAE, is designed for video generation tasks, achieving 16x16 spatial and 8x temporal compression ratios, while maintaining exceptional video reconstruction quality. User prompts are encoded using two bilingual text encoders to handle both English and Chinese. A DiT with 3D full attention is trained using Flow Matching and is employed to denoise input noise into latent frames. A video-based DPO approach, Video-DPO, is applied to reduce artifacts and improve the visual quality of the generated videos. We also detail our training strategies and share key observations and insights. Step-Video-T2V's performance is evaluated on a novel video generation benchmark, Step-Video-T2V-Eval, demonstrating its state-of-the-art text-to-video quality when compared with both open-source and commercial engines. Additionally, we discuss the limitations of current diffusion-based model paradigm and outline future directions for video foundation models. We make both Step-Video-T2V and Step-Video-T2V-Eval available at https://github.com/stepfun-ai/Step-Video-T2V. The online version can be accessed from https://yuewen.cn/videos as well. Our goal is to accelerate the innovation of video foundation models and empower video content creators.
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The robustness of metro networks with the rich-core structure

2024-11-01
Z. Liu , Wei Li , Yuxiang Yang
Coauthor Papers Together
Feng Wu 2
Ke Zhao 1
Biao Huang 1
Yan Huang 1
Shuchang Zhou 1
Yang Li 1
Xianfang Zeng 1
Guorong Yan 1
Yuehui Yin 1
Yuheng Feng 1
Weiwei Huan 1
Liguo Tan 1
Wei Zhong 1
Ge Yang 1
Na Wang 1
Haiyang Feng 1
Xinhao Zhang 1
Huixin Xiong 1
Yu Luo 1
Ray Ming 1
Qiaohui Chen 1
Zheng Ge 1
Yufei Xie 1
Xing Chen 1
Tiancheng Cao 1
Nan Duan 1
Weipeng Ming 1
Siqi Liu 1
Junzhe Lin 1
Binxing Jiao 1
Deyu Zhou 1
Brian Li 1
Haonan Jia 1
Qiuyan Liang 1
Jianchang Wu 1
Guangnan Huang 1
E. Liu 1
Rui Wang 1
Ze Zhang 1
Daxin Jiang 1
Jie Wu 1
Heungā€Yeung Shum 1
Jian Zhou 1
Hanpeng Hu 1
Qiling Wu 1
Hanqi Chen 1
Yanbo Yu 1
Shuli Gao 1
Liying Shi 1
Chaoying Ni 1

A multi-body dynamical evolution model for generating the point set with best uniformity

2022-06-22
Feng Wu , Yuelin Zhao , Ke Zhao +1 more

Identification of core-periphery structure in networks

2015-03-06
Xiao Zhang , Travis Martin , M. E. J. Newman
Many networks can be usefully decomposed into a dense core plus an outlying, loosely connected periphery. Here we propose an algorithm for performing such a decomposition on empirical network data ā€¦ Many networks can be usefully decomposed into a dense core plus an outlying, loosely connected periphery. Here we propose an algorithm for performing such a decomposition on empirical network data using methods of statistical inference. Our method fits a generative model of core-periphery structure to observed data using a combination of an expectation-maximization algorithm for calculating the parameters of the model and a belief propagation algorithm for calculating the decomposition itself. We find the method to be efficient, scaling easily to networks with a million or more nodes, and we test it on a range of networks, including real-world examples as well as computer-generated benchmarks, for which it successfully identifies known core-periphery structure with low error rate. We also demonstrate that the method is immune to the detectability transition observed in the related community detection problem, which prevents the detection of community structure when that structure is too weak. There is no such transition for core-periphery structure, which is detectable, albeit with some statistical error, no matter how weak it is.
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A Set of Measures of Centrality Based on Betweenness

1977-03-01
Linton C. Freeman
A family of new measures of point and graph centrality based on early intuitions of Bavelas (1948) is introduced. These measures define centrality in terms of the degree to which ā€¦ A family of new measures of point and graph centrality based on early intuitions of Bavelas (1948) is introduced. These measures define centrality in terms of the degree to which a point falls on the shortest path between others and there fore has a potential for control of communication. They may be used to index centrality in any large or small network of symmetrical relations, whether connected or unconnected.

Rich-Cores in Networks

2015-03-23
Athen Ma , RaĆŗl J. MondragĆ³n
A core comprises of a group of central and densely connected nodes which governs the overall behaviour of a network. It is recognised as one of the key meso-scale structures ā€¦ A core comprises of a group of central and densely connected nodes which governs the overall behaviour of a network. It is recognised as one of the key meso-scale structures in complex networks. Profiling this meso-scale structure currently relies on a limited number of methods which are often complex and parameter dependent or require a null model. As a result, scalability issues are likely to arise when dealing with very large networks together with the need for subjective adjustment of parameters. The notion of a rich-club describes nodes which are essentially the hub of a network, as they play a dominating role in structural and functional properties. The definition of a rich-club naturally emphasises high degree nodes and divides a network into two subgroups. Here, we develop a method to characterise a rich-core in networks by theoretically coupling the underlying principle of a rich-club with the escape time of a random walker. The method is fast, scalable to large networks and completely parameter free. In particular, we show that the evolution of the core in World Trade and C. elegans networks correspond to responses to historical events and key stages in their physical development, respectively.
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A generalization of Chebyshevā€™s inequality for Hilbert-space-valued random elements

2014-01-29
Katarzyna Budny

Optimal traffic networks

2006-07-24
Marc BarthƩlemy , Alessandro Flammini
Inspired by studies on the airports' network and the physical Internet, we propose a general model of weighted networks via an optimization principle. The topology of the optimal network turns ā€¦ Inspired by studies on the airports' network and the physical Internet, we propose a general model of weighted networks via an optimization principle. The topology of the optimal network turns out to be a spanning tree that minimizes a combination of topological and metric quantities. It is characterized by strongly heterogeneous traffic, non-trivial correlations between distance and traffic and a broadly distributed centrality. A clear spatial hierarchical organization, with local hubs distributing traffic in smaller regions, emerges as a result of the optimization. Varying the parameters of the cost function, different classes of trees are recovered, including in particular the minimum spanning tree and the shortest path tree. These results suggest that a variational approach represents an alternative and possibly very meaningful path to the study of the structure of complex weighted networks.
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Likelihood approximation by numerical integration on sparse grids

2008-01-15
Florian HeiƟ , Viktor Winschel
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A very simple proof of the multivariate Chebyshev's inequality

2013-12-13
Jorge Navarro
In this short note, a very simple proof of the Chebyshev's inequality for random vectors is given. This inequality provides a lower bound for the percentage of the population of ā€¦ In this short note, a very simple proof of the Chebyshev's inequality for random vectors is given. This inequality provides a lower bound for the percentage of the population of an arbitrary random vector X with finite mean Ī¼ = E(X) and a positive definite covariance matrix V = Cov(X) whose Mahalanobis distance with respect to V to the mean Ī¼ is less than a fixed value. The main advantage of the proof is that it is a simple exercise for a first year probability course. An alternative proof based on principal components is also provided. This proof can be used to study the case of a singular covariance matrix V.

Networked analysis of the Shanghai subway network, in China

2011-06-27
Jianhua Zhang , Xiaoming Xu , Hong Liu +2 more

Prominence and Control: The Weighted Rich-Club Effect

2008-10-17
Tore Opsahl , Vittoria Colizza , Pietro Panzarasa +1 more
Complex systems are often characterized by large-scale hierarchical organizations. Whether the prominent elements, at the top of the hierarchy, share and control resources or avoid one another lies at the ā€¦ Complex systems are often characterized by large-scale hierarchical organizations. Whether the prominent elements, at the top of the hierarchy, share and control resources or avoid one another lies at the heart of a system's global organization and functioning. Inspired by network perspectives, we propose a new general framework for studying the tendency of prominent elements to form clubs with exclusive control over the majority of a system's resources. We explore associations between prominence and control in the fields of transportation, scientific collaboration, and online communication.
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ON GENERALISED TCHEBYCHEFF THEOREMS IN THE MATHEMATICAL THEORY OF STATISTICS

1919-01-01
Karl Pearson
Journal Article ON GENERALISED TCHEBYCHEFF THEOREMS IN THE MATHEMATICAL THEORY OF STATISTICS Get access KARL PEARSON, F.R.S. KARL PEARSON, F.R.S. Search for other works by this author on: Oxford Academic ā€¦ Journal Article ON GENERALISED TCHEBYCHEFF THEOREMS IN THE MATHEMATICAL THEORY OF STATISTICS Get access KARL PEARSON, F.R.S. KARL PEARSON, F.R.S. Search for other works by this author on: Oxford Academic Google Scholar Biometrika, Volume 12, Issue 3-4, November 1919, Pages 284ā€“296, https://doi.org/10.1093/biomet/12.3-4.284 Published: 01 November 1919
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Rich-club phenomenon across complex network hierarchies

2007-08-20
Julian McAuley , Luciano da Fontoura Costa , TibƩrio S. Caetano
The ā€œrich-club phenomenonā€ in complex networks is characterized when nodes of higher degree are more interconnected than nodes with lower degree. The presence of this phenomenon may indicate several interesting ā€¦ The ā€œrich-club phenomenonā€ in complex networks is characterized when nodes of higher degree are more interconnected than nodes with lower degree. The presence of this phenomenon may indicate several interesting high-level network properties, such as tolerance to hub failures. Here, the authors investigate the existence of this phenomenon across the hierarchies of several real-world networks. Their simulations reveal that the presence or absence of this phenomenon in a network does not imply its presence or absence in the networkā€™s successive hierarchies, and that this behavior is even nonmonotonic in some cases.
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Efficient Behavior of Small-World Networks

2001-10-17
Vito Latora , Massimo Marchiori
We introduce the concept of efficiency of a network as a measure of how efficiently it exchanges information. By using this simple measure, small-world networks are seen as systems that ā€¦ We introduce the concept of efficiency of a network as a measure of how efficiently it exchanges information. By using this simple measure, small-world networks are seen as systems that are both globally and locally efficient. This gives a clear physical meaning to the concept of "small world," and also a precise quantitative analysis of both weighted and unweighted networks. We study neural networks and man-made communication and transportation systems and we show that the underlying general principle of their construction is in fact a small-world principle of high efficiency.
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A long-time limit for world subway networks

2012-05-16
Camille Roth , Soong Moon Kang , Michael Batty +1 more
We study the temporal evolution of the structure of the world's largest subway networks in an exploratory manner. We show that, remarkably, all these networks converge to a shape that ā€¦ We study the temporal evolution of the structure of the world's largest subway networks in an exploratory manner. We show that, remarkably, all these networks converge to a shape that shares similar generic features despite their geographical and economic differences. This limiting shape is made of a core with branches radiating from it. For most of these networks, the average degree of a node (station) within the core has a value of order 2.5 and the proportion of k = 2 nodes in the core is larger than 60 per cent. The number of branches scales roughly as the square root of the number of stations, the current proportion of branches represents about half of the total number of stations, and the average diameter of branches is about twice the average radial extension of the core. Spatial measures such as the number of stations at a given distance to the barycentre display a first regime which grows as r 2 followed by another regime with different exponents, and eventually saturates. These resultsā€”difficult to interpret in the framework of fractal geometryā€”confirm and yield a natural explanation in the geometric picture of this core and their branches: the first regime corresponds to a uniform core, while the second regime is controlled by the interstation spacing on branches. The apparent convergence towards a unique network shape in the temporal limit suggests the existence of dominant, universal mechanisms governing the evolution of these structures.
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Detecting rich-club ordering in complex networks

2006-01-15
Vittoria Colizza , Alessandro Flammini , M. Ɓngeles Serrano +1 more
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The Rich-Club Phenomenon in the Internet Topology

2004-03-01
Shi Zhou , RaĆŗl J. MondragĆ³n
We show that the Internet topology at the autonomous system (AS) level has a rich-club phenomenon. The rich nodes, which are a small number of nodes with large numbers of ā€¦ We show that the Internet topology at the autonomous system (AS) level has a rich-club phenomenon. The rich nodes, which are a small number of nodes with large numbers of links, are very well connected to each other. The rich-club is a core tier that we measured using the rich-club connectivity and the node-node link distribution. We obtained this core tier without any heuristic assumption between the ASs. The rich-club phenomenon is a simple qualitative way to differentiate between power law topologies and provides a criterion for new network models. To show this, we compared the measured rich-club of the AS graph with networks obtained using the Baraba/spl acute/si-Albert (BA) scale-free network model, the Fitness BA model and the Inet-3.0 model.
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A modified stochastic perturbation method for stochastic hyperbolic heat conduction problems

2016-03-28
Feng Wu , Wei Zhong

Clustering coefficients of large networks

2016-12-15
Yusheng Li , Yilun Shang , Yiting Yang
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Rich-club ordering and the dyadic effect: Two interrelated phenomena

2017-09-21
Matteo Cinelli , Giovanna Ferraro , Antonio Iovanella
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Chebyshevā€™s inequality for Banach-space-valued random elements

2012-02-07
Ling Zhou , Ze-Chun Hu
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Resilience of Core-Periphery Networks in the Case of Rich-Club

2017-01-01
Matteo Cinelli , Giovanna Ferraro , Antonio Iovanella
Core-periphery networks are structures that present a set of central and densely connected nodes, namely, the core, and a set of noncentral and sparsely connected nodes, namely, the periphery. The ā€¦ Core-periphery networks are structures that present a set of central and densely connected nodes, namely, the core, and a set of noncentral and sparsely connected nodes, namely, the periphery. The rich-club refers to a set in which the highest degree nodes show a high density of connections. Thus, a network that displays a rich-club can be interpreted as a core-periphery network in which the core is made up of a number of hubs. In this paper, we test the resilience of networks showing a progressively denser rich-club and we observe how this structure is able to affect the network measures in terms of both cohesion and efficiency in information flow. Additionally, we consider the case in which, instead of making the core denser, we add links to the periphery. These two procedures of core and periphery thickening delineate a decision process in the placement of new links and allow us to conduct a scenario analysis that can be helpful in the comprehension and supervision of complex networks under the resilience perspective. The advantages of the two procedures, as well as their implications, are discussed in relation to both network efficiency and node heterogeneity.
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Attack robustness and stability of generalized k-cores

2019-09-01
Yilun Shang
Abstract Earlier studies on network robustness have mainly focused on the integrity of functional components such as the giant connected component in a network. Generalized k -core ( Gk -core) ā€¦ Abstract Earlier studies on network robustness have mainly focused on the integrity of functional components such as the giant connected component in a network. Generalized k -core ( Gk -core) has been recently investigated as a core structure obtained via a k -leaf removal procedure extending the well-known leaf removal algorithm. Here, we study analytically and numerically the network robustness in terms of the numbers of nodes and edges in Gk -core against random attacks (RA), localized attacks (LA) and targeted attacks (TA), respectively. In addition, we introduce the concept of Gk -core stability to quantify the extent to which the Gk -core of a network contains the same nodes under independent multiple RA, LA and TA, respectively. The relationship between Gk -core robustness and stability has been studied under our developed percolation framework, which is of significance in better understanding and design of resilient networks.
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Quantifying efficient information exchange in real network flows

2021-06-09
Giulia Bertagnolli , Riccardo Gallotti , Manlio De Domenico
Abstract Network science enables the effective analysis of real interconnected systems, characterized by a complex interplay between topology and network flows. It is well-known that the topology of a network ā€¦ Abstract Network science enables the effective analysis of real interconnected systems, characterized by a complex interplay between topology and network flows. It is well-known that the topology of a network affects its resilience to failures or attacks, as well as its functions. Many real systemsā€”such as the Internet, transportation networks and the brainā€”exchange information, so it is crucial to quantify how efficiently systemā€™s units communicate. Measures of parallel communication efficiency for weighted networks rely on the identification of an ideal version of the system, which currently lacks a universal definition. Consequently, an inattentive choice might hinder a rigorous comparison of network flows across scales or might lead to a descriptor not robust to fluctuations in the topology or the flows. We propose a physically-grounded estimator of flow efficiency valid for any weighted network, regardless of scale, nature of weights and (missing) metadata, allowing for comparison across disparate systems. Our estimator captures the effect of flows heterogeneity along with topological differences of both synthetic and empirical systems. We also show that cutting the heaviest connections may increase the average efficiency of the system and hence, counterintuively, a sparser network is not necessarily less efficient.
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Generalized k-core percolation on correlated and uncorrelated multiplex networks

2020-04-23
Yilun Shang
It has been recognized that multiplexes and interlayer degree correlations can play a crucial role in the resilience of many real-world complex systems. Here we introduce a multiplex pruning process ā€¦ It has been recognized that multiplexes and interlayer degree correlations can play a crucial role in the resilience of many real-world complex systems. Here we introduce a multiplex pruning process that removes nodes of degree less than ${k}_{i}$ and their nearest neighbors in layer $i$ for $i=1,...,m$, and establish a generic framework of generalized $\mathbf{k}$-core ($G\mathbf{k}$-core) percolation over interlayer uncorrelated and correlated multiplex networks of $m$ layers, where $\mathbf{k}=({k}_{1},...,{k}_{m})$ and $m$ is the total number of layers. $G\mathbf{k}$-core exhibits a discontinuous phase transition for all $\mathbf{k}$ owing to cascading failures. We have unraveled the existence of a tipping point of the number of layers, above which the $G\mathbf{k}$-core collapses abruptly. This dismantling effect of multiplexity on $G\mathbf{k}$-core percolation shows a diminishing marginal utility in homogeneous networks when the number of layers increases. Moreover, we have found the assortative mixing for interlayer degrees strengthens the $G\mathbf{k}$-core but still gives rise to discontinuous phase transitions as compared to the uncorrelated counterparts. Interlayer disassortativity on the other hand weakens the $G\mathbf{k}$-core structure. The impact of correlation effect on $G\mathbf{k}$-core tends to be more salient systematically over $\mathbf{k}$ for heterogenous networks than homogeneous ones.
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Resilience or robustness: identifying topological vulnerabilities in rail networks

2019-02-01
Alessio Pagani , Guillem Mosquera , Aseel Alturki +5 more
Many critical infrastructure systems have network structures and are under stress. Despite their national importance, the complexity of large-scale transport networks means that we do not fully understand their vulnerabilities ā€¦ Many critical infrastructure systems have network structures and are under stress. Despite their national importance, the complexity of large-scale transport networks means that we do not fully understand their vulnerabilities to cascade failures. The research conducted through this paper examines the interdependent rail networks in Greater London and surrounding commuter area. We focus on the morning commuter hours, where the system is under the most demand stress. There is increasing evidence that the topological shape of the network plays an important role in dynamic cascades. Here, we examine whether the different topological measures of resilience (stability) or robustness (failure) are more appropriate for understanding poor railway performance. The results show that resilience, not robustness, has a strong correlation with the consumer experience statistics. Our results are a way of describing the complexity of cascade dynamics on networks without the involvement of detailed agent-based models, showing that cascade effects are more responsible for poor performance than failures. The network science analysis hints at pathways towards making the network structure more resilient by reducing feedback loops.
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A clarified typology of core-periphery structure in networks

2021-03-17
Ryan J. Gallagher , Jean-Gabriel Young , Brooke Foucault Welles
Core-periphery structure, the arrangement of a network into a dense core and sparse periphery, is a versatile descriptor of various social, biological, and technological networks. In practice, different core-periphery algorithms ā€¦ Core-periphery structure, the arrangement of a network into a dense core and sparse periphery, is a versatile descriptor of various social, biological, and technological networks. In practice, different core-periphery algorithms are often applied interchangeably, despite the fact that they can yield inconsistent descriptions of core-periphery structure. For example, two of the most widely used algorithms, the k-cores decomposition and the classic two-block model of Borgatti and Everett, extract fundamentally different structures: the latter partitions a network into a binary hub-and-spoke layout, while the former divides it into a layered hierarchy. We introduce a core-periphery typology to clarify these differences, along with Bayesian stochastic block modeling techniques to classify networks in accordance with this typology. Empirically, we find a rich diversity of core-periphery structure among networks. Through a detailed case study, we demonstrate the importance of acknowledging this diversity and situating networks within the core-periphery typology when conducting domain-specific analyses.
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The temporal rich club phenomenon

2022-06-13
Nicola Pedreschi , Demian Battaglia , Alain Barrat
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Feature-enriched core percolation in multiplex networks

2022-11-29
Yilun Shang
Percolation models have long served as a paradigm for unraveling the structure and resilience of complex systems comprising interconnected nodes. In many real networks, nodes are identified by not only ā€¦ Percolation models have long served as a paradigm for unraveling the structure and resilience of complex systems comprising interconnected nodes. In many real networks, nodes are identified by not only their connections but nontopological metadata such as age and gender in social systems, geographical location in infrastructure networks, and component contents in biochemical networks. However, there is little known regarding how the nontopological features influence network structures under percolation processes. In this paper we introduce a feature-enriched core percolation framework using a generic multiplex network approach. We thereby analytically determine the corona cluster, size, and number of edges of the feature-enriched cores. We find a hybrid percolation transition combining a jump and a square root singularity at the critical points in both the network connectivity and the feature space. Integrating the degree-feature distribution with the Farlie-Gumbel-Morgenstern copula, we show the existence of continuous and discrete percolation transitions for feature-enriched cores at critical correlation levels. The inner and outer cores are found to undergo distinct phase transitions under the feature-enriched percolation, all limited by a characteristic curve of the feature distribution.
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Deep capsule encoderā€“decoder network for surrogate modeling and uncertainty quantification

2023-02-27
Akshay Thakur , Souvik Chakraborty
Abstract We propose a novel capsule ā€based deep encoderā€“decoder model for surrogate modeling and uncertainty quantification of systems in mechanics from sparse data. The proposed framework is developed by adapting ā€¦ Abstract We propose a novel capsule ā€based deep encoderā€“decoder model for surrogate modeling and uncertainty quantification of systems in mechanics from sparse data. The proposed framework is developed by adapting Capsule Network (CapsNet) architecture into an imageā€toā€image regression encoderā€“decoder network. Specifically, the aim is to exploit the benefits of CapsNet over convolution neural network (CNN) ā€“ retaining pose and position information related to an entity to name a few. The performance of the proposed approach is illustrated by solving two different variants of elliptic partial differential equations (PDE): a stochastic version without a source term having an input dimensionality of 1024 and a deterministic pressure Poisson equation for flow past a cylinder. The first PDE, that is, the stochastic PDE (SPDE), also governs systems in mechanics such as steady heat conduction, groundwater flow, or other diffusion processes. In this article, the problem definition for this SPDE is such that it does not restrict the random diffusion field to a particular covariance structure, and the more strenuous task of response prediction for an arbitrary diffusion field is solved. Finally, we also evaluate the performance of our model on the uncertainty propagation problem based on this equation. The obtained results from the performance evaluation of the developed model on the mentioned problems indicate that the proposed approach is accurate, data efficient, and robust.
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Core-periphery structure in networks: A statistical exposition

2023-01-01
Eric Yanchenko , Srijan Sengupta
Many real-world networks are theorized to have core-periphery structure consisting of a densely-connected core and a loosely-connected periphery. While this phenomenon has been extensively studied in a range of scientific ā€¦ Many real-world networks are theorized to have core-periphery structure consisting of a densely-connected core and a loosely-connected periphery. While this phenomenon has been extensively studied in a range of scientific disciplines, it has not received sufficient attention in the statistics community. In this expository article, our goal is to raise awareness about this topic and encourage statisticians to address the many open inference problems in this area. To this end, we first summarize the current research landscape by reviewing the metrics and models that have been used for quantitative studies on core-periphery structure. Next, we formulate and explore various inferential problems in this context, such as estimation, hypothesis testing, and Bayesian inference, and discuss related computational techniques. We also outline the multidisciplinary scientific impact of core-periphery structure in a number of real-world networks. Throughout the article, we provide our own interpretation of the literature from a statistical perspective, with the goal of prioritizing open problems where contribution from the statistics community will be most effective and important.
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Application of high-credible statistical results calculation scheme based on least squares Quasi-Monte Carlo method in multimodal stochastic problems

2023-11-05
Dongwei Huang , Feng Wu , Yuelin Zhao +2 more

The behavior of rich-club coefficient in scale-free networks

2024-09-01
Zhihang Liu , Wei Li , Yuxiang Yang

An importance quantification technique in uncertainty analysis for computer models

2002-12-04
Tsutomu Ishigami , Toshimitsu Homma
The authors have developed a technique to numerically quantify importance of input variables including uncertainties to the output uncertainty. The technique makes it practically possible to estimate the importance measure, ā€¦ The authors have developed a technique to numerically quantify importance of input variables including uncertainties to the output uncertainty. The technique makes it practically possible to estimate the importance measure, proposed by Hora and Iman (1986), which is based on the concept of uncertainty reduction. The technique required a limited number of calculations based on the original model using the Monte Carlo or the Latin hypercube sampling. Effectiveness of the technique is demonstrated in a comparative study by applying the technique and a conventional regression method to two computer models, an analytical model and the TERFOC model.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A new discrepancy for sample generation in stochastic response analyses of aerospace problems with uncertain parameters

2024-10-01
Feng WU , Yuelin Zhao , Yuxiang YANG +2 more