Opinion dynamics in financial markets via random networks.

We investigate financial market dynamics by introducing a heterogeneous agent-based opinion formation model. In this work, we organize individuals in a financial market according to their trading strategy, namely, whether they are noise traders or fundamentalists. The opinion of a local majority compels the market exchanging behavior of noise traders, whereas the global behavior of the market influences the decisions of fundamentalist agents. We introduce a noise parameter, q, to represent the level of anxiety and perceived uncertainty regarding market behavior, enabling the possibility of adrift financial action. We place individuals as nodes in an Erdös-Rényi random graph, where the links represent their social interactions. At any given time, individuals assume one of two possible opinion states ±1 regarding buying or selling an asset. The model exhibits fundamental qualitative and quantitative real-world market features such as the distribution of logarithmic returns with fat tails, clustered volatility, and the long-term correlation of returns. We use Student's t distributions to fit the histograms of logarithmic returns, showing a gradual shift from a leptokurtic to a mesokurtic regime depending on the fraction of fundamentalist agents. Furthermore, we compare our results with those concerning the distribution of the logarithmic returns of several real-world financial indices.

Most influential countries in the international medical device trade: Network-based analysis.

Since the outbreak of the coronavirus disease 2019 (COVID-19) pandemic, the international medical device trade has received extensive attention. To maintain the domestic supply of medical devices, some countries have sought multilateral trade cooperation or simply implemented export restrictions, which has exacerbated the instability and fragility of the global medical device market. It is crucial for government policymakers to identify the most influential countries in the international medical device trade and nip exports in the bud. However, few efforts have been made in previous studies to explore various countries' influence on the international medical device trade in light of their intricate trade relationships. To fill these research gaps, this study constructs a global medical device trade network (GMDTN) and explores the criticality of various countries from a network-based perspective. The evolution patterns and geographical distribution of influence among countries in the GMDTN are revealed. Details on the ways in which the influence of some crucial countries has formed are provided. The results show that the global medical device trade market is export oriented. The formation of some countries' strong influence may be due to their large number of trading partners or the deep dependence of some of those trading partners on that country (namely, breadth- or depth-based patterns). It is worth noting that the US has a dominant position in the international medical device trade in terms of both breadth and depth. In addition, some countries play a critical role as intermediate points in the influence formation process of other countries, although these countries are not critical direct trading partners. The findings of this study provide implications for policymakers seeking to understand the influence of countries on the international medical device trade and to proactively prepare responses to unexpected changes in this trade.

Network resilience of non-hub nodes failure under memory and non-memory based attacks with limited information.

Previous studies on network robustness mainly concentrated on hub node failures with fully known network structure information. However, hub nodes are often well protected and not accessible to damage or malfunction in a real-world networked system. In addition, one can only gain insight into limited network connectivity knowledge due to large-scale properties and dynamic changes of the network itself. In particular, two different aggression patterns are present in a network attack: memory based attack, in which failed nodes are not attacked again, or non-memory based attack; that is, nodes can be repeatedly attacked. Inspired by these motivations, we propose an attack pattern with and without memory based on randomly choosing n non-hub nodes with known connectivity information. We use a network system with the Poisson and power-law degree distribution to study the network robustness after applying two failure strategies of non-hub nodes. Additionally, the critical threshold 1 - p and the size of the giant component S are determined for a network configuration model with an arbitrary degree distribution. The results indicate that the system undergoes a continuous second-order phase transition subject to the above attack strategies. We find that 1 - p gradually tends to be stable after increasing rapidly with n. Moreover, the failure of non-hub nodes with a higher degree is more destructive to the network system and makes it more vulnerable. Furthermore, from comparing the attack strategies with and without memory, the results highlight that the system shows better robustness under a non-memory based attack relative to memory based attacks for n > 1. Attacks with memory can block the system's connectivity more efficiently, which has potential applications in real-world systems. Our model sheds light on network resilience under memory and non-memory based attacks with limited information attacks and provides valuable insights into designing robust real-world systems.

Three-state majority-vote model on small-world networks.

In this work, we study the opinion dynamics of the three-state majority-vote model on small-world networks of social interactions. In the majority-vote dynamics, an individual adopts the opinion of the majority of its neighbors with probability 1-q, and a different opinion with chance q, where q stands for the noise parameter. The noise q acts as a social temperature, inducing dissent among individual opinions. With probability p, we rewire the connections of the two-dimensional square lattice network, allowing long-range interactions in the society, thus yielding the small-world property present in many different real-world systems. We investigate the degree distribution, average clustering coefficient and average shortest path length to characterize the topology of the rewired networks of social interactions. By employing Monte Carlo simulations, we investigate the second-order phase transition of the three-state majority-vote dynamics, and obtain the critical noise [Formula: see text], as well as the standard critical exponents [Formula: see text], [Formula: see text], and [Formula: see text] for several values of the rewiring probability p. We conclude that the rewiring of the lattice enhances the social order in the system and drives the model to different universality classes from that of the three-state majority-vote model in two-dimensional square lattices.

Percolation on coupled networks with multiple effective dependency links.

The ubiquitous coupled relationship between network systems has become an essential paradigm to depict complex systems. A remarkable property in the coupled complex systems is that a functional node should have multiple external support associations in addition to maintaining the connectivity of the local network. In this paper, we develop a theoretical framework to study the structural robustness of the coupled network with multiple useful dependency links. It is defined that a functional node has the broadest connectivity within the internal network and requires at least M support link of the other network to function. In this model, we present exact analytical expressions for the process of cascading failures, the fraction of functional nodes in the stable state, and provide a calculation method of the critical threshold. The results indicate that the system undergoes an abrupt phase transition behavior after initial failure. Moreover, the minimum inner and inter-connectivity density to maintain system survival is graphically presented at different multiple effective dependency links. Furthermore, we find that the system needs more internal connection densities to avoid collapse when it requires more effective support links. These findings allow us to reveal the details of a more realistic coupled complex system and develop efficient approaches for designing resilient infrastructure.

Three-State Majority-vote Model on Scale-Free Networks and the Unitary Relation for Critical Exponents.

We investigate the three-state majority-vote model for opinion dynamics on scale-free and regular networks. In this model, an individual selects an opinion equal to the opinion of the majority of its neighbors with probability 1 - q, and different to it with probability q. The parameter q is called the noise parameter of the model. We build a network of interactions where z neighbors are selected by each added site in the system, a preferential attachment network with degree distribution k-λ, where λ = 3 for a large number of nodes N. In this work, z is called the growth parameter. Using finite-size scaling analysis, we obtain that the critical exponents [Formula: see text] and [Formula: see text] associated with the magnetization and the susceptibility, respectively. Using Monte Carlo simulations, we calculate the critical noise parameter qc as a function of z for the scale-free networks and obtain the phase diagram of the model. We find that the critical exponents add up to unity when using a special volumetric scaling, regardless of the dimension of the network of interactions. We verify this result by obtaining the critical noise and the critical exponents for the two and three-state majority-vote model on cubic lattice networks.

Effect of Strong Opinions on the Dynamics of the Majority-Vote Model.

We study how the presence of individuals with strong opinions affects a square lattice majority-vote model with noise. In a square lattice network we perform Monte-Carlo simulations and replace regular actors σ with strong actors µ in a random distribution. We find that the value of the critical noise parameter q c is a decreasing function of the concentration r of strong actors in the social interaction network. We calculate the critical exponents ß/ν, γ/ν, and 1/ν and find that the presence of strong actors does not change the Ising universality class of the isotropic majority-vote model.

Topological properties of the limited penetrable horizontal visibility graph family.

The limited penetrable horizontal visibility graph algorithm was recently introduced to map time series in complex networks. In this work, we extend this algorithm to create a directed-limited penetrable horizontal visibility graph and an image-limited penetrable horizontal visibility graph. We define two algorithms and provide theoretical results on the topological properties of these graphs associated with different types of real-value series. We perform several numerical simulations to check the accuracy of our theoretical results. Finally, we present an application of the directed-limited penetrable horizontal visibility graph to measure real-value time series irreversibility and an application of the image-limited penetrable horizontal visibility graph that discriminates noise from chaos. We also propose a method to measure the systematic risk using the image-limited penetrable horizontal visibility graph, and the empirical results show the effectiveness of our proposed algorithms.

Exact results of the limited penetrable horizontal visibility graph associated to random time series and its application.

The limited penetrable horizontal visibility algorithm is an analysis tool that maps time series into complex networks and is a further development of the horizontal visibility algorithm. This paper presents exact results on the topological properties of the limited penetrable horizontal visibility graph associated with independent and identically distributed (i:i:d:) random series. We show that the i.i.d: random series maps on a limited penetrable horizontal visibility graph with exponential degree distribution, independent of the probability distribution from which the series was generated. We deduce the exact expressions of mean degree and clustering coefficient, demonstrate the long distance visibility property of the graph and perform numerical simulations to test the accuracy of our theoretical results. We then use the algorithm in several deterministic chaotic series, such as the logistic map, H´enon map, Lorenz system, energy price chaotic system and the real crude oil price. Our results show that the limited penetrable horizontal visibility algorithm is efficient to discriminate chaos from uncorrelated randomness and is able to measure the global evolution characteristics of the real time series.