How to plug out of the networks in jeopardy of ASF, Covid-19, social media or markets toxicity

Aim: In our research, we examine universal properties of the global network whose structure represents a real-world network that might be later extended to social media, commodity market or countries under the infl uence of diseases like Covid-19 or ASF.Methods: We propose quasi-epidemiological agent-based model of virus spread on a network. Firstly, we consider countries represented by subnetworks that have a scale-free structure achieved by the preferential attachment construction with a node hierarchy and binary edges. The global network of countries is a complete, directed, weighted network of thesesubnetworks connected by their capitals and divided into cultural and geographical proximity. Viruses with a defi ned strength or aggressiveness occur independently at one of the nodes of a selected subnetwork and correspond to a piece of products or messages or diseases.Results and conclusion: We analyse dynamics set by varying parameter values and observe a variety of phenomena including local and global pandemics and the existence of an epidemic threshold in the subnetworks. These phenomena have been also shown fromindividual users points of view because the node removal from the network might have impact on its nearest neighbours differently. The selective participation in global network is proposed here to avoid side effects when the global network has been fully connected and no longer divided into clusters.

PREFERENTIAL ATTACHMENT WITH FITNESS DEPENDENT CHOICE

Исследуется асимптотическое поведение максимальной степени вершины в графе предпочтительного присоединения с выбором вершины, основанном как на ее степени, так и на дополнительном параметре (пригодности). Модели предпочтительного присоединения широко используются для моделирования сложных сетей (таких как нейронные сети и т.д.). Они строятся следующим образом. Мы начинаем с двух вершин и ребра между ними. Затем на каждом шаге мы рассматриваем выборку из уже существующих вершин, выбранных с вероятностями, пропорциональными их степеням плюс некоторый параметр β>- 1. Затем мы добавляем новую вершину и соединяем ее ребром с вершиной из выборки, на которой достигается максимум произведения ее степени на ее пригодность. Мы доказали, что в зависимости от параметров модели возможны три типа поведения максимальной степени вершины - сублинейное, линейное и порядка /ln , где n - число вершин в графе. We study the asymptotic behavior of the maximum degree in the preferential attachment tree model with a choice based on both the degree and fitness of a vertex. The preferential attachment models are natural models for complex networks (like neural networks, etc.) and constructed in the following recursive way. To each vertex is assigned a parameter that is called a fitness of a vertex. We start from two vertices and an edge between them. On each step, we consider a sample with repetition of d vertices, chosen with probabilities proportional to their degrees plus some parameter β>-1. Then we add a new vertex and draw an edge from it to the vertex from the sample with the highest product of fitness and degree. We prove that the maximum degree, dependent on parameters of the model, could exhibit three types of asymptotic behavior: sublinear, linear, and of /ln order, where n is the number of edges in the graph.

Knowledge Diffusion and the Dynamics of Citation Accrual

<p>The diffusion of knowledge through society proceeds like an invisible ripple that moves between agents through multiple information channels. However, some types of knowledge are recorded, systematised and digitised for the benefit of everyone. Patents and academic articles are examples of such codified knowledge. These documents also contain a common element that is utilised for linking new and established knowledge: citations. This thesis harnesses citations in patents and scientific articles as proxies for signifying the existence of knowledge flows between cited and citing documents, focusing primarily on the dynamics of citation accumulation and the mechanisms governing these dynamics. For this purpose, it is helpful to think of patents and their citations as nodes and links, respectively, in a network where new nodes join the network and distribute their citations among existing nodes. This mode of thinking leads directly to the question: How does the citation network grow? This thesis addresses that question both empirically and theoretically. Two mechanisms that can explain much of the observed citation dynamics are preferential attachment and node ageing. The former mechanism reflects the tendency for successful nodes (by citation count) to become even more successful, while the latter captures the propensity for knowledge to become obsolete over time. The independence of these phenomena is nontrivial, but has generally been assumed. We put this assumption to the test for both patent and scientific-article citation networks and found it to be generally true if precautions are taken to account for important context surrounding the meaning of citations. Achieving a clear separation of these mechanisms is found to be very useful both mathematically and empirically, as they can now be studied independently. Patents are particularly sophisticated documents, with various components holding specific legal meanings. Associating certain properties of these components with popularity in the form of citation accrual creates a rare opportunity to build a framework that can identify ex-ante node fitnesses and examine their effect on the growth of a citation network. We find that a significant portion of the preferential-attachment process observed in the patent-citation network can be attributed to basic properties of patents determined by their time of grant. Besides suggesting novel approaches towards estimating patent quality, the results of our work also provide a platform for gaining a deeper understanding of the various mechanisms that underpin the success-breeds-success dynamics ubiquitously observed in complex systems.</p>

Knowledge Diffusion and the Dynamics of Citation Accrual

<p>The diffusion of knowledge through society proceeds like an invisible ripple that moves between agents through multiple information channels. However, some types of knowledge are recorded, systematised and digitised for the benefit of everyone. Patents and academic articles are examples of such codified knowledge. These documents also contain a common element that is utilised for linking new and established knowledge: citations. This thesis harnesses citations in patents and scientific articles as proxies for signifying the existence of knowledge flows between cited and citing documents, focusing primarily on the dynamics of citation accumulation and the mechanisms governing these dynamics. For this purpose, it is helpful to think of patents and their citations as nodes and links, respectively, in a network where new nodes join the network and distribute their citations among existing nodes. This mode of thinking leads directly to the question: How does the citation network grow? This thesis addresses that question both empirically and theoretically. Two mechanisms that can explain much of the observed citation dynamics are preferential attachment and node ageing. The former mechanism reflects the tendency for successful nodes (by citation count) to become even more successful, while the latter captures the propensity for knowledge to become obsolete over time. The independence of these phenomena is nontrivial, but has generally been assumed. We put this assumption to the test for both patent and scientific-article citation networks and found it to be generally true if precautions are taken to account for important context surrounding the meaning of citations. Achieving a clear separation of these mechanisms is found to be very useful both mathematically and empirically, as they can now be studied independently. Patents are particularly sophisticated documents, with various components holding specific legal meanings. Associating certain properties of these components with popularity in the form of citation accrual creates a rare opportunity to build a framework that can identify ex-ante node fitnesses and examine their effect on the growth of a citation network. We find that a significant portion of the preferential-attachment process observed in the patent-citation network can be attributed to basic properties of patents determined by their time of grant. Besides suggesting novel approaches towards estimating patent quality, the results of our work also provide a platform for gaining a deeper understanding of the various mechanisms that underpin the success-breeds-success dynamics ubiquitously observed in complex systems.</p>

Preferential Attachment and Fitness in the Evolution of the Brazilian Film Network

This study analyzes the network evolution, specifically that of the Brazilian film network. It examines two generative mechanisms that lie behind the network evolution: preferential attachment and fitness. The starting point is that preferential attachment and fitness may compete to shape the network evolution. We built a novel dataset with 974 Brazilian feature films released between 1995 and 2017 and used PAFit, a brand-new statistical method, to estimate the joint effects of preferential attachment and fitness on the evolution of the Brazilian film network. This study concludes that the network evolution is shaped by both preferential attachment and fitness. However, in the presence of fitness, the effects of preferential attachment on the network evolution become weaker. This means that the node ability to form ties in the Brazilian film network is mainly explained by its fitness. Besides, the preferential attachment assumes a sub-linear form. Costs, communication and managerial capabilities, and node age explain why nodes are unable to accumulate ties at rates proportional to their degree. Finally, preferential attachment and fitness manifest themselves heterogeneously, depending on either the type or the duration of the network. Preferential attachment drives the cast network evolution, whereas fitness is the main generative mechanism of the crew network. Actors and actresses rely on their status, privilege, and power to obtain future contracts (preferential attachment), whereas technical members are selected on the basis of their talent, skills, and knowledge (fitness). Due to node age or exit, preferential attachment becomes stronger in shorter networks.

Ligação Preferencial e Aptidão na Evolução da Rede de Filmes Brasileiros

This study analyzes the network evolution, specifically that of the Brazilian film network. It examines two generative mechanisms that lie behind the network evolution: preferential attachment and fitness. The starting point is that preferential attachment and fitness may compete to shape the network evolution. We built a novel dataset with 974 Brazilian feature films released between 1995 and 2017 and used PAFit, a brand-new statistical method, to estimate the joint effects of preferential attachment and fitness on the evolution of the Brazilian film network. This study concludes that the network evolution is shaped by both preferential attachment and fitness. However, in the presence of fitness, the effects of preferential attachment on the network evolution become weaker. This means that the node ability to form ties in the Brazilian film network is mainly explained by its fitness. Besides, the preferential attachment assumes a sub-linear form. Costs, communication and managerial capabilities, and node age explain why nodes are unable to accumulate ties at rates proportional to their degree. Finally, preferential attachment and fitness manifest themselves heterogeneously, depending on either the type or the duration of the network. Preferential attachment drives the cast network evolution, whereas fitness is the main generative mechanism of the crew network. Actors and actresses rely on their status, privilege, and power to obtain future contracts (preferential attachment), whereas technical members are selected on the basis of their talent, skills, and knowledge (fitness). Due to node age or exit, preferential attachment becomes stronger in shorter networks.

A computational exploration of resilience and evolvability of protein–protein interaction networks

Protein–protein interaction (PPI) networks represent complex intra-cellular protein interactions, and the presence or absence of such interactions can lead to biological changes in an organism. Recent network-based approaches have shown that a phenotype’s PPI network’s resilience to environmental perturbations is related to its placement in the tree of life; though we still do not know how or why certain intra-cellular factors can bring about this resilience. Here, we explore the influence of gene expression and network properties on PPI networks’ resilience. We use publicly available data of PPIs for E. coli, S. cerevisiae, and H. sapiens, where we compute changes in network resilience as new nodes (proteins) are added to the networks under three node addition mechanisms—random, degree-based, and gene-expression-based attachments. By calculating the resilience of the resulting networks, we estimate the effectiveness of these node addition mechanisms. We demonstrate that adding nodes with gene-expression-based preferential attachment (as opposed to random or degree-based) preserves and can increase the original resilience of PPI network in all three species, regardless of gene expression distribution or network structure. These findings introduce a general notion of prospective resilience, which highlights the key role of network structures in understanding the evolvability of phenotypic traits.

A meritocratic network formation model for the rise of social media influencers

Many of today’s most used online social networks such as Instagram, YouTube, Twitter, or Twitch are based on User-Generated Content (UGC). Thanks to the integrated search engines, users of these platforms can discover and follow their peers based on the UGC and its quality. Here, we propose an untouched meritocratic approach for directed network formation, inspired by empirical evidence on Twitter data: actors continuously search for the best UGC provider. We theoretically and numerically analyze the network equilibria properties under different meeting probabilities: while featuring common real-world networks properties, e.g., scaling law or small-world effect, our model predicts that the expected in-degree follows a Zipf’s law with respect to the quality ranking. Notably, the results are robust against the effect of recommendation systems mimicked through preferential attachment based meeting approaches. Our theoretical results are empirically validated against large data sets collected from Twitch, a fast-growing platform for online gamers.

Percolation phase transition in weight-dependent random connection models

We investigate spatial random graphs defined on the points of a Poisson process in d-dimensional space, which combine scale-free degree distributions and long-range effects. Every Poisson point is assigned an independent weight. Given the weight and position of the points, we form an edge between any pair of points independently with a probability depending on the two weights of the points and their distance. Preference is given to short edges and connections to vertices with large weights. We characterize the parameter regime where there is a non-trivial percolation phase transition and show that it depends not only on the power-law exponent of the degree distribution but also on a geometric model parameter. We apply this result to characterize robustness of age-based spatial preferential attachment networks.