Modelling Negative Correlation in Complex Networks Via Anti-Transitivity

2021 ◽  
Author(s):  
Hari Prasad Pokhrel
Keyword(s):  
Social Networks ◽  
Stock Market ◽  
Complex Networks ◽  
Negative Correlation ◽  
Deterministic Model ◽  
Power Laws ◽  
High Density ◽  
Time Step ◽  
Constant Diameter ◽  
Local Clustering

Negative correlation appears often in complex networks. For example, in social networks, negative correlation corresponds to rivalry between agents in the network, while in stock market graphs, negative correlation corresponds stocks that move in opposite directions in price action. We present a simplified, deterministic model of negative correlation in networks based on the principle of anti-transitivity: a non-friend of a non-friend is a friend. In the Iterated Local Anti-Transitivity (ILAT) model, for every node u in a given time-step, we add an anti-clone node that is adjacent to the complement of the closed neighborhood of u. We prove that graphs generated by the ILAT model satisfy several properties observed in complex networks, such as high density and densification power laws, constant diameter, and high local clustering. We also prove that the domination and cop numbers of graphs generated by the ILAT model are bounded above by small, absolute constants as time increases.

scholarly journals Modelling Negative Correlation in Complex Networks Via Anti-Transitivity

2021 ◽  
Author(s):  
Hari Prasad Pokhrel
Keyword(s):  
Social Networks ◽  
Stock Market ◽  
Complex Networks ◽  
Negative Correlation ◽  
Deterministic Model ◽  
Power Laws ◽  
High Density ◽  
Time Step ◽  
Constant Diameter ◽  
Local Clustering

Negative correlation appears often in complex networks. For example, in social networks, negative correlation corresponds to rivalry between agents in the network, while in stock market graphs, negative correlation corresponds stocks that move in opposite directions in price action. We present a simplified, deterministic model of negative correlation in networks based on the principle of anti-transitivity: a non-friend of a non-friend is a friend. In the Iterated Local Anti-Transitivity (ILAT) model, for every node u in a given time-step, we add an anti-clone node that is adjacent to the complement of the closed neighborhood of u. We prove that graphs generated by the ILAT model satisfy several properties observed in complex networks, such as high density and densification power laws, constant diameter, and high local clustering. We also prove that the domination and cop numbers of graphs generated by the ILAT model are bounded above by small, absolute constants as time increases.

Dynamical evolution of trading behavior on anti-coordination game in complex networks

2016 ◽  
Vol 6 (4) ◽  
pp. 367-379 ◽  
Author(s):  
Yue-tang Bian ◽  
Lu Xu ◽  
Jin-Sheng Li ◽  
Xia-qun Liu
Keyword(s):  
Stock Market ◽  
Complex Networks ◽  
Dynamical Evolution ◽  
Coordination Game ◽  
Future Research ◽  
Trading Behavior ◽  
Time Step ◽  
Risk Dominance ◽  
Content Type ◽  
Market Networks

Purpose The purpose of this paper is to explore the evolvement of investors’ behavior in stock market dynamically on the basis of non-cooperative strategy applied by investors in complex networks. Design/methodology/approach Using modeling and simulation research method, this study designs and conducts a mathematical modeling and its simulation experiment of financial market behavior according to research’s basic norms of complex system theory and methods. Thus the authors acquire needed and credible experimental data. Findings The conclusions drawn in this paper are as follows. The dynamical evolution of investors’ trading behavior is not only affected by the stock market network structure, but also by the risk dominance degree of certain behavior. The dynamics equilibrium of trading behavior’s evolvement is directly influenced by the risk dominance degree of certain behavior, connectivity degree and the heterogeneity of the stock market networks. Research limitations/implications This paper focuses on the dynamical evolvement of investors’ behavior on the basis of the hypothesis that common investors prefer to mimic their network neighbors’ behavior through different analysis by the strategy of anti-coordination game in complex network. While the investors’ preference and the beliefs among them are not easy to quantify, that is deterministic or stochastic as the environment changes, and is heterogeneous definitely. Thus, these limitations should be broken through in the future research. Originality/value This paper aims to address the dynamical evolvement of investors’ behavior in stock market networks on the principle of non-cooperative represented by anti-coordination game in networks for the first time, considering that investors prefer to mimic their network neighbors’ behavior through different analysis by the strategy of differential choosing in every time step. The methodology designed and used in this study is a pioneering and exploratory experiment.

scholarly journals Power Laws in Economics: An Introduction

2016 ◽  
Vol 30 (1) ◽  
pp. 185-206 ◽  
Author(s):  
Xavier Gabaix
Keyword(s):  
Stock Market ◽  
Power Law ◽  
Power Laws ◽  
Economic Fluctuations ◽  
Formal Definition ◽  
Empirical Power

Many of the insights of economics seem to be qualitative, with many fewer reliable quantitative laws. However a series of power laws in economics do count as true and nontrivial quantitative laws—and they are not only established empirically, but also understood theoretically. I will start by providing several illustrations of empirical power laws having to do with patterns involving cities, firms, and the stock market. I summarize some of the theoretical explanations that have been proposed. I suggest that power laws help us explain many economic phenomena, including aggregate economic fluctuations. I hope to clarify why power laws are so special, and to demonstrate their utility. In conclusion, I list some power-law-related economic enigmas that demand further exploration. A formal definition may be useful.

scholarly journals Gated Recurrent Unit Networks and Discrete Wavelet Transforms Applied to Forecasting and Trading in the Stock Market

2020 ◽  
Author(s):  
Victor Biazon ◽  
Reinaldo Bianchi
Keyword(s):  
Stock Market ◽  
Wavelet Transforms ◽  
Stock Price ◽  
Discrete Wavelet ◽  
Discrete Wavelet Transforms ◽  
Time Step ◽  
Proposed Model ◽  
Gated Recurrent Unit ◽  
Novel Model ◽  
Unit Network

Trading in the stock market always comes with the challenge of deciding the best action to take on each time step. The problem is intensified by the theory that it is not possible to predict stock market time series as all information related to the stock price is already contained in it. In this work we propose a novel model called Discrete Wavelet Transform Gated Recurrent Unit Network (DWT-GRU). The model learns from the data to choose between buying, holding and selling, and when to execute them. The proposed model was compared to other recurrent neural networks, with and without wavelets preprocessing, and the buy and hold strategy. The results shown that the DWT-GRU outperformed all the set baselines in the analysed stocks of the Brazilian stock market.

scholarly journals A novel similarity measure for missing link prediction in social networks

2020 ◽  
Vol 19 (2) ◽  
pp. 1071
Author(s):  
Gogulamudi Naga Chandrika ◽  
E. Srinivasa Reddy
Keyword(s):  
Social Networks ◽  
Complex Networks ◽  
Similarity Measure ◽  
Network Theory ◽  
Link Prediction ◽  
Prediction Methods ◽  
Missing Link ◽  
The Social ◽  
Hidden Patterns ◽  
Over Time

<p><span>Social Networks progress over time by the addition of new nodes and links, form associations with one community to the other community. Over a few decades, the fast expansion of Social Networks has attracted many researchers to pay more attention towards complex networks, the collection of social data, understand the social behaviors of complex networks and predict future conflicts. Thus, Link prediction is imperative to do research with social networks and network theory. The objective of this research is to find the hidden patterns and uncovered missing links over complex networks. Here, we developed a new similarity measure to predict missing links over social networks. The new method is computed on common neighbors with node-to-node distance to get better accuracy of missing link prediction. </span><span>We tested the proposed measure on a variety of real-world linked datasets which are formed from various linked social networks. The proposed approach performance is compared with contemporary link prediction methods. Our measure makes very effective and intuitive in predicting disappeared links in linked social networks.</span></p>

scholarly journals RECIPROCITY AND THE EMERGENCE OF POWER LAWS IN SOCIAL NETWORKS

2006 ◽  
Vol 17 (07) ◽  
pp. 1067-1076 ◽  
Author(s):  
MICHAEL SCHNEGG
Keyword(s):  
Social Networks ◽  
Power Laws ◽  
Scaling Exponent ◽  
Policy Makers ◽  
Public Health Programs ◽  
Scale Free ◽  
The Past ◽  
Naturally Occurring ◽  
Growing Networks ◽  
Law Degree

Research in network science has shown that many naturally occurring and technologically constructed networks are scale free, that means a power law degree distribution emerges from a growth model in which each new node attaches to the existing network with a probability proportional to its number of links (= degree). Little is known about whether the same principles of local attachment and global properties apply to societies as well. Empirical evidence from six ethnographic case studies shows that complex social networks have significantly lower scaling exponents γ ~ 1 than have been assumed in the past. Apparently humans do not only look for the most prominent players to play with. Moreover cooperation in humans is characterized through reciprocity, the tendency to give to those from whom one has received in the past. Both variables — reciprocity and the scaling exponent — are negatively correlated (r = -0.767, sig = 0.075). If we include this effect in simulations of growing networks, degree distributions emerge that are much closer to those empirically observed. While the proportion of nodes with small degrees decreases drastically as we introduce reciprocity, the scaling exponent is more robust and changes only when a relatively large proportion of attachment decisions follow this rule. If social networks are less scale free than previously assumed this has far reaching implications for policy makers, public health programs and marketing alike.

scholarly journals Efficient Approximate Techniques for Integrating Stochastic Differential Equations

2006 ◽  
Vol 134 (10) ◽  
pp. 3006-3014 ◽  
Author(s):  
James A. Hansen ◽  
Cecile Penland
Keyword(s):  
Time Series ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Deterministic Model ◽  
Probability Distributions ◽  
Approximate Solutions ◽  
Integration Scheme ◽  
Time Step ◽  
Integration Schemes ◽  
Runge Kutta

Abstract The delicate (and computationally expensive) nature of stochastic numerical modeling naturally leads one to look for efficient and/or convenient methods for integrating stochastic differential equations. Concomitantly, one may wish to sensibly add stochastic terms to an existing deterministic model without having to rewrite that model. In this note, two possibilities in the context of the fourth-order Runge–Kutta (RK4) integration scheme are examined. The first approach entails a hybrid of deterministic and stochastic integration schemes. In these examples, the hybrid RK4 generates time series with the correct climatological probability distributions. However, it is doubtful that the resulting time series are approximate solutions to the stochastic equations at every time step. The second approach uses the standard RK4 integration method modified by appropriately scaling stochastic terms. This is shown to be a special case of the general stochastic Runge–Kutta schemes considered by Ruemelin and has global convergence of order one. Thus, it gives excellent results for cases in which real noise with small but finite correlation time is approximated as white. This restriction on the type of problems to which the stochastic RK4 can be applied is strongly compensated by its computational efficiency.

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