Feedback Loops in Opinion Dynamics of Agent-Based Models with Multiplicative Noise

We introduce an agent-based model for co-evolving opinions and social dynamics, under the influence of multiplicative noise. In this model, every agent is characterized by a position in a social space and a continuous opinion state variable. Agents’ movements are governed by the positions and opinions of other agents and similarly, the opinion dynamics are influenced by agents’ spatial proximity and their opinion similarity. Using numerical simulations and formal analyses, we study this feedback loop between opinion dynamics and the mobility of agents in a social space. We investigate the behaviour of this ABM in different regimes and explore the influence of various factors on the appearance of emerging phenomena such as group formation and opinion consensus. We study the empirical distribution, and, in the limit of infinite number of agents, we derive a corresponding reduced model given by a partial differential equation (PDE). Finally, using numerical examples, we show that a resulting PDE model is a good approximation of the original ABM.     

Fear and its implications for stock markets

The value of stocks, indices and other assets, are examples of stochastic processes with unpredictable dynamics. In this paper, we discuss asymmetries in short term price movements that can not be associated with a long term positive trend. These empirical asymmetries predict that stock index drops are more common on a relatively short time scale than the corresponding raises. We present several empirical examples of such asymmetries. Furthermore, a simple model featuring occasional short periods of synchronized dropping prices for all stocks constituting the index is introduced with the aim of explaining these facts. The collective negative price movements are imagined triggered by external factors in our society, as well as internal to the economy, that create fear of the future among investors. This is parameterized by a “fear factor” defining the frequency of synchronized events. It is demonstrated that such a simple fear factor model can reproduce several empirical facts concerning index asymmetries. It is also pointed out that in its simplest form, the model has certain shortcomings.     

Weblog patterns and human dynamics with decreasing interest

In order to describe the phenomenon that people’s interest in doing something always keep high in the beginning while gradually decreases until reaching the balance, a model which describes the attenuation of interest is proposed to reflect the fact that people’s interest becomes more stable after a long time. We give a rigorous analysis on this model by non-homogeneous Poisson processes. Our analysis indicates that the interval distribution of arrival-time is a mixed distribution with exponential and power-law feature, which is a power law with an exponential cutoff. After that, we collect blogs in ScienceNet.cn and carry on empirical study on the interarrival time distribution. The empirical results agree well with the theoretical analysis, obeying a special power law with the exponential cutoff, that is, a special kind of Gamma distribution. These empirical results verify the model by providing an evidence for a new class of phenomena in human dynamics. It can be concluded that besides power-law distributions, there are other distributions in human dynamics. These findings demonstrate the variety of human behavior dynamics.     

Modelling price dynamics: A hybrid truncated Lévy Flight–GARCH approach

ARCH and GARCH stochastic processes are widely used in finance and are generally accepted as good approximations when modelling the price dynamics with Gaussian conditional probability. It can be seen that certain aspects of the empirical data for asset price changes seems to more closely fit a Truncated Lévy Flight or GARCH model, but each with individual shortfalls. In this paper therefore, we combine the GARCH process with a conditional truncated Lévy distribution in order to build a hybrid model that most notably describes the price change and associated volatility probability density distributions and scaling behaviour over different time horizons.     

Human dynamics scaling characteristics for aerial inbound logistics operation

In recent years, the study of power-law scaling characteristics of real-life networks has attracted much interest from scholars; it deviates from the Poisson process. In this paper, we take the whole process of aerial inbound operation in a logistics company as the empirical object. The main aim of this work is to study the statistical scaling characteristics of the task-restricted work patterns. We found that the statistical variables have the scaling characteristics of unimodal distribution with a power-law tail in five statistical distributions — that is to say, there obviously exists a peak in each distribution, the shape of the left part closes to a Poisson distribution, and the right part has a heavy-tailed scaling statistics. Furthermore, to our surprise, there is only one distribution where the right parts can be approximated by the power-law form with exponent α=1.50. Others are bigger than 1.50 (three of four are about 2.50, one of four is about 3.00). We then obtain two inferences based on these empirical results: first, the human behaviors probably both close to the Poisson statistics and power-law distributions on certain levels, and the human-computer interaction behaviors may be the most common in the logistics operational areas, even in the whole task-restricted work pattern areas. Second, the hypothesis in Vázquez et al. (2006) [A. Vázquez, J. G. Oliveira, Z. Dezsö, K.-I. Goh, I. Kondor, A.-L. Barabási. Modeling burst and heavy tails in human dynamics, Phys. Rev. E 73 (2006) 036127] is probably not sufficient; it claimed that human dynamics can be classified as two discrete university classes. There may be a new human dynamics mechanism that is different from the classical Barabási models.     

Markov switching of the electricity supply curve and power prices dynamics

Regime-switching models seem to well capture the main features of power prices behavior in deregulated markets. In a recent paper, we have proposed an equilibrium methodology to derive electricity prices dynamics from the interplay between supply and demand in a stochastic environment. In particular, assuming that the supply function is described by a power law where the exponent is a two-state strictly positive Markov process, we derived a regime switching dynamics of power prices in which regime switches are induced by transitions between Markov states.In this paper, we provide a dynamical model to describe the random behavior of power prices where the only non-Brownian component of the motion is endogenously introduced by Markov transitions in the exponent of the electricity supply curve. In this context, the stochastic process driving the switching mechanism becomes observable, and we will show that the non-Brownian component of the dynamics induced by transitions from Markov states is responsible for jumps and spikes of very high magnitude. The empirical analysis performed on three Australian markets confirms that the proposed approach seems quite flexible and capable of incorporating the main features of power prices time-series, thus reproducing the first four moments of log-returns empirical distributions in a satisfactory way.     

Individual and group dynamics in purchasing activity

As a major part of the daily operation in an enterprise, purchasing frequency is in constant change. Recent approaches on the human dynamics can provide some new insights into the economic behavior of companies in the supply chain. This paper captures the attributes of creation times of purchase orders to an individual vendor, as well as to all vendors, and further investigates whether they have some kind of dynamics by applying logarithmic binning to the construction of distribution plots. It’s found that the former displays a power-law distribution with approximate exponent 2.0, while the latter is fitted by a mixture distribution with both power-law and exponential characteristics. Obviously, two distinctive characteristics are presented for the interval time distribution from the perspective of individual dynamics and group dynamics. Actually, this mixing feature can be attributed to the fitting deviations as they are negligible for individual dynamics, but those of different vendors are cumulated and then lead to an exponential factor for group dynamics. To better describe the mechanism generating the heterogeneity of the purchase order assignment process from the objective company to all its vendors, a model driven by product life cycle is introduced, and then the analytical distribution and the simulation result are obtained, which are in good agreement with the empirical data.     

Testing the Goodwin growth-cycle macroeconomic dynamics in Brazil

This paper discusses the empirical validity of Goodwin’s (1967) macroeconomic model of growth with cycles by assuming that the individual income distribution of the Brazilian society is described by the Gompertz–Pareto distribution (GPD). This is formed by the combination of the Gompertz curve, representing the overwhelming majority of the population (∼99%), with the Pareto power law, representing the tiny richest part (∼1%). In line with Goodwin’s original model, we identify the Gompertzian part with the workers and the Paretian component with the class of capitalists. Since the GPD parameters are obtained for each year and the Goodwin macroeconomics is a time evolving model, we use previously determined, and further extended here, Brazilian GPD parameters, as well as unemployment data, to study the time evolution of these quantities in Brazil from 1981 to 2009 by means of the Goodwin dynamics. This is done in the original Goodwin model and an extension advanced by Desai et al. (2006). As far as Brazilian data is concerned, our results show partial qualitative and quantitative agreement with both models in the studied time period, although the original one provides better data fit. Nevertheless, both models fall short of a good empirical agreement as they predict single center cycles which were not found in the data. We discuss the specific points where the Goodwin dynamics must be improved in order to provide a more realistic representation of the dynamics of economic systems.     

Dynamics of bloggers’ communities: Bipartite networks from empirical data and agent-based modeling

We present an analysis of the empirical data and the agent-based modeling of the emotional behavior of users on the Web portals where the user interaction is mediated by posted comments, like Blogs and Diggs. We consider the dataset of discussion-driven popular Diggs, in which all comments are screened by machine-learning emotion detection in the text, to determine positive and negative valence (attractiveness and aversiveness) of each comment. By mapping the data onto a suitable bipartite network, we perform an analysis of the network topology and the related time-series of the emotional comments. The agent-based model is then introduced to simulate the dynamics and to capture the emergence of the emotional behaviors and communities. The agents are linked to posts on a bipartite network, whose structure evolves through their actions on the posts. The emotional states (arousal and valence) of each agent fluctuate in time, subject to the current contents of the posts to which the agent is exposed. By an agent’s action on a post its current emotions are transferred to the post. The model rules and the key parameters are inferred from the considered empirical data to ensure their realistic values and mutual consistency. The model assumes that the emotional arousal over posts drives the agent’s action. The simulations are preformed for the case of constant flux of agents and the results are analyzed in full analogy with the empirical data. The main conclusions are that the emotion-driven dynamics leads to long-range temporal correlations and emergent networks with community structure, that are comparable with the ones in the empirical system of popular posts. In view of pure emotion-driven agents actions, this type of comparisons provide a quantitative measure for the role of emotions in the dynamics on real blogs. Furthermore, the model reveals the underlying mechanisms which relate the post popularity with the emotion dynamics and the prevalence of negative emotions (critique). We also demonstrate how the community structure is tuned by varying a relevant parameter in the model. All data used in these works are fully anonymized.     

A general evolving model for growing bipartite networks

In this Letter, we propose and study an inner evolving bipartite network model. Significantly, we prove that the degree distribution of two different kinds of nodes both obey power-law form with adjustable exponents. Furthermore, the joint degree distribution of any two nodes for bipartite networks model is calculated analytically by the mean-field method. The result displays that such bipartite networks are nearly uncorrelated networks, which is different from one-mode networks. Numerical simulations and empirical results are given to verify the theoretical results.     

一个描述合作网络顶点度分布的模型

讨论一类社会合作网络以及一些与其拓扑结构相似的技术网络的度分布.建议一个最简化模型，通过解析的方法说明这些网络演化的共同动力学机理，而且说明顶点的度分布和项目度分布之间具有密切的一致关系，而项目所含的顶点数分布对度分布的影响较小；对模型的更一般情况进行数值模拟，说明上述结论具有一定的普遍性.这个模型显示这类广义的合作网络一般具有处于幂函数和指数函数这两种极端情况之间的度分布.简要介绍对一些实际合作网络做统计研究的结果，说明本模型的合理性. 关键词： 合作网络 度分布 项目度分布 项目含顶点数     

Social network based microblog user behavior analysis

The influence of microblog on information transmission is becoming more and more obvious. By characterizing the behavior of following and being followed as out-degree and in-degree respectively, a microblog social network was built in this paper. It was found to have short diameter of connected graph, short average path length and high average clustering coefficient. The distributions of out-degree, in-degree and total number of microblogs posted present power-law characters. The exponent of total number distribution of microblogs is negatively correlated with the degree of each user. With the increase of degree, the exponent decreases much slower. Based on empirical analysis, we proposed a social network based human dynamics model in this paper, and pointed out that inducing drive and spontaneous drive lead to the behavior of posting microblogs. The simulation results of our model match well with practical situation.     

Bounded rational expectations and the stability of interest rate policy

The New Keynesian model has recently been subject to two serious criticisms: the model cannot produce plausible inflation and output dynamics following a monetary shock, and the stability of its dynamics suffers from indeterminacy. The procedures that have been proposed to eliminate these two shortcomings fall into two categories: the introduction of some sort of backward price indexation into the standard model and/or other forms of stickiness (like sticky information); and the adoption of some form of policy rule that completely offsets the effects of forward looking dynamics in the optimization process. In this paper we do not eradicate forward looking behavior from the dynamics of the New Keynesian model, neither do we impose some form of backward price indexation. We assume that private economic agents have forward looking behavior and that they do try to optimize with all available information; the only novelty is that they are allowed to make small mistakes near the rational expectations equilibrium, in a fully deterministic setup. These “near rational” or “bounded rational” expectations show that the dynamics of the model with active interest rate rules is much richer than the simple problem of local indeterminacy as is usually found in the literature.     

Bivariate time-periodic Fokker-Planck model for freeway traffic

Recorded data of the density of cars and their speed from a German motorway are modeled by a bivariate Fokker-Planck equation. In order to cope with the evident diurnal variation, we assume a 24 h-periodicity in the drift and diffusion coefficients of this equation. After fitting these and smoothing them by polynomials, we validate the model by comparison of the empirical densities and densities generated by the model dynamics. We show that the time dependence of the drift field is related to a saddle-node bifurcation due to which the congested traffic state becomes stable. The separatrix between the basins of attraction is used to define flowing and jamming traffic during rush hours and characterizes the traffic dynamics together with the fixed points and the centre manifold.     

Ehrlich-Schwoebel barrier controlled slope selection in epitaxial growth

We examine the step dynamics in a 1+1-dimensional model of epitaxial growth based on the BCF-theory. The model takes analytically into account the diffusion of adatoms, an incorporation mechanism and an Ehrlich-Schwoebel barrier at step edges. We find that the formation of mounds with a stable slope is closely related to the presence of an incorporation mechanism. We confirm this finding using a solid-on-solid model in 2+1 dimensions. In the case of an infinite step edge barrier we are able to calculate the saturation profile analytically. Without incorporation but with inclusion of desorption and detachment we find a critical flux for instable growth but no slope selection. In particular, we show that the temperature dependence of the selected slope is solely determined by the Ehrlich-Schwoebel barrier which opens a new possibility in order to measure this fundamental barrier in experiments. Received 11 May 1999 and Received in final form 6 November 1999     

Forecasting volatility of SSEC in Chinese stock market using multifractal analysis

In this paper, taking about 7 years’ high-frequency data of the Shanghai Stock Exchange Composite Index (SSEC) as an example, we propose a daily volatility measure based on the multifractal spectrum of the high-frequency price variability within a trading day. An ARFIMA model is used to depict the dynamics of this multifractal volatility (MFV) measures. The one-day ahead volatility forecasting performances of the MFV model and some other existing volatility models, such as the realized volatility model, stochastic volatility model and GARCH, are evaluated by the superior prediction ability (SPA) test. The empirical results show that under several loss functions, the MFV model obtains the best forecasting accuracy.     

Price dynamics from a simple multiplicative random process model

The existence of stylized facts suggests that there might be `universal' mechanism which drives price evolution on financial markets in general. Based on empirical estimates of 10 major indices, we propose a stylized model of endogenous price formation on an aggregate level whose key issue is that price evolution is driven by the `market's' expectations about future growth rates of investment. The model is a multiplicative random process with a stochastic, state-dependent growth rate which establishes a negative feedback component in the price dynamics which admits some far reaching formal analysis. Generated return trails exhibit statistical properties such as 'volatility clustering', multi scaling, and a non-Gaussian distribution which is in quantitative in agreement with stylized facts from empirical asset returns. Additionally non-equilibrium entropies are also considered. These results suggests that the structure of the model mimicks a mechanism which is essential in driving price dynamics of financial markets in general.     

Randomness in denoised stock returns: The case of Moroccan family business companies

In this paper, we scrutinize entropy in family business stocks listed on Casablanca stock exchange and market index to assess randomness in their returns. For this purpose, we adopt a novel approach based on combination of stationary wavelet transform and Tsallis entropy for empirical analysis of the return series. The obtained empirical results show strong evidence that their respective entropy functions are characterized by opposite dynamics. Indeed, the information contents of their respective dynamics are statistically and significantly different. Obviously, information on regular events carried by family business returns is more certain, whilst that carried by market returns is uncertain. Such results are definitively useful to understand the nonlinear dynamics on returns on family business companies and those of the market. Without a doubt, they could be helpful for quantitative portfolio managers and investors.     

Comparative studies of open qubit via Bloch equation and master equation of Redfield form

In this paper, we investigate the dynamics of an open qubit model by solving two sets of its reduced dynamical equations. One set of the equations is the well-known Bloch equations and the other is the widely investigated master equations of Redfield form. Both of them are obtained from the perturbation approximation which demands the system of interest weakly coupled to its environment. It is shown that the qubit has a longer decoherence and relaxiation time as the dynamics is described by the Redfield equantions.