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The shapes of distributions of personal incomes in USA have been investigated based on the data for 1993 to 2008. Comparisons between four models utilizing various number of parameters have been performed. The studies showed that the empirical data is described the best by the three-parameter Dagum model. Values of the models parameters indicate that the distribution of personal incomes can be regarded as zero-modal one. However, one-parameter exponential model shows a good agreement with data and can be treated as a good approximation of empirical distribution with the exception of the region with very high incomes. The high-income region is characterized by the relatively great number of events and is described much better by the Dagum distribution.
In recent years the issue of costly punishment in systems where free-riding occurs has been a subject of extensive research in the field of game theory. This issue is present in many areas of human activities like paying taxes, using public transport, wireless Internet or P2P networks. It is one of the most common dilemmas in modern societies. In this work we present a simple model of cooperation with three possible strategies (cooperate, defect or punish). In the model players explore the available strategies according to their interactions with other players. We introduce two groups of parameters. The first group is sociological-like and it describes the social acceptance for the free riding behavior. The other group of parameters describes the economical aspects of the system - the cost and efficiency of punishers. Using differential equations approach, as well as an agent based model, we look for equilibrium properties of the system.
Simulations are performed according to the Axelrod model of culture dissemination, with modified mechanism of repulsion. Previously, repulsion was considered by Radillo-Diaz et al. as dependent on a predefined threshold. Here the probabilities of attraction and repulsion are calculated from the number of cells in the same states. We also investigate the influence of some homogeneity, introduced to the initial state. As the result of the probabilistic definition of repulsion, the ordered state vanishes. A small cluster of a few percent of population is retained only if in the initial state a set of agents is prepared in the same state. We conclude that the modelled imitation is successful only with respect to agents, and not only their features.
Learning is a complex cognitive process that depends not only on an individual capability of knowledge absorption but it can be also influenced by various group interactions and by the structure of an academic curriculum. We have applied methods of statistical analyses and data mining (principal component analysis and maximal spanning tree) for anonymized students' scores at Faculty of Physics, Warsaw University of Technology. A slight negative linear correlation exists between mean and variance of course grades, i.e. courses with higher mean scores tend to possess a lower scores variance. There are courses playing a central role, e.g. their scores are highly correlated to other scores and they are in the centre of corresponding maximal spanning trees. Other courses contribute significantly to students' score variance as well to the first principal component and they are responsible for differentiation of students' scores. Correlations of the first principal component to courses' mean scores and scores variance suggest that this component can be used for assigning ECTS points to a given course. The analysis is independent of declared curricula of considered courses. The proposed methodology is universal and can be applied for analysis of students' scores and academic curriculum at any faculty.
A relationship between daily prices of Polish WIG index and trading volumes is investigated. By introducing variables related to a number of last prices and volumes, a history of values in a certain period of time (which could be regarded as an investor memory) is taken into account. Different characteristics of autocorrelations for prices and trading volumes are observed. By studying mutual correlations between the variables, a local maximum at about 100 trading days is discovered. The Granger causality test is performed, indicating very strong influence of prices on volumes. This property can be considered as a sign of markets maturity.
This paper presents an exactly solvable (by applying the fractional calculus) the rheological model of fractional dynamics of financial market conformed to the principle of no arbitrage present on financial market. The rheological model of fractional dynamics of financial market describes some singular, empirical, speculative daily peaks of stock market indices, which define crashes as a kind of phase transition. In the frame of the model the plastic market hypothesis and financial uncertainty principle were formulated, which proposed possible scenarios of some market crashes. The brief presentation of the model was made in our earlier work (and references therein). The rheological model of fractional dynamics of financial market is a deterministic model and it is complementary to already existing other ones; together with them it offers possibility for thorough and widespread technical analysis of crashes. The constitutive, fractional integral equation of the model is an analogy of the corresponding one, which defines the fractional Zener model of plastic material. The fractional Zener model is the canonical one for modern rheology, polymer physics and biophysics concerning non-Debye relaxation of viscoelastic biopolymers. The useful approximate solution of the constitutive equation of the rheological model of fractional dynamics of financial market consists of two parts: (i) the first one connected with long-term memory present in the system, which is proportional to the generalized exponential function defined by the Mittag-Leffler function and (ii) the second one describing oscillations (e.g. beats or oscillations having two slightly shifted frequences). The shape exponent leading the Mittag-Leffler function, defines here the order of the phase transition between bullish and bearish states of the financial market, in particular, for recent hossa and bessa on some small, middle and large stock markets. It happened that this solution also successfully estimated some long-term price dynamics on the hypothetical market in United States.
In this work we applied our original solution of the literal Rheological Model of Fractional Dynamics of Financial Market, i.e., the time-dependent solution proportional to the Mittag-Leffler function superposed with oscillations, not only to describe the singular dynamics of financial markets but also to study the singular dynamics of various macroeconomic sectors. The approach makes possible to sufficiently estimate (among others) the time of crash as well as its order. Thus we demonstrate, perhaps useful for stock market investors as well as for various macroeconomic agents, the technical analysis of bubble and crash, which is complementary to the famous one supplying power-law superposed with log-periodic oscillations.
The term "complexity" used frequently as a kind of "buzzword" has gained a specific role in the language of modern social sciences and social practice. A question is arising - how can we understand complexity of social systems/social phenomena which are characterized by limited possibility of explanation, unpredictability or low reliability of prediction? The aim of the paper is to provide a partial answer to this question. A survey of characteristics of complex systems and typology of various kinds of complexity, and of their sources is presented. It is also shown that broadly defined social systems (human systems) are affected by all kinds of complexity - they are "complexities of complexities". Using the typology of interpretations of complexity as an example, it is shown what are the limitations of transferring knowledge from physics, chemistry, information theory and biology to the studies of complexity of social systems. It is especially emphasized that mathematical models, which are treated as objective when applied in social sciences must be considered as an element of intersubjective discourse.
The phenomenon of epidemic spreading in a real social network is described and investigated numerically. On the basis of data concerning amount of time devoted daily to social interactions, the influence of human activity on spreading process is investigated in the frame of SIRS model. It was found that the activity of an individual is positively correlated with its connectivity and the relation has power law form. The influence of control measures on the spreading process is investigated as a function of initial conditions. The cost-effectiveness of mass immunizations campaigns and target vaccinations is compared. It was found that the form of activity distribution has significant influence on the spreading phenomena in the network.
In an emergency situation, imitation of strategies of neighbours can lead to an order-disorder phase transition, where spatial clusters of pedestrians adopt the same strategy. We assume that there are two strategies, cooperating and competitive, which correspond to a smaller or larger desired velocity. The results of our simulations within the Social Force Model indicate that the ordered phase can be detected as an increase of spatial order of positions of the pedestrians in the crowd.
We investigate the origin of the emergence of the plutonomy, an extreme form of hierarchy, where the top 1% of households account for more wealth than the bottom 99%. For a model fair society where individuals participate in a competition with equal right, we show that the plutonomy can be self-organized when individuals divided into several groups compete with those in the same group for a certain period (season) and they are regrouped at the end of every season. In the fair society, the wealth flows steadily from lower groups to the highest group, which is the origin of the plutonomy. Using mean-field analysis, we show that the fraction of winners decreases in proportion to the inverse of the number of groups.
Activity of users on Internet discussion forums is analyzed. The rank of users is shown to be approximated better by stretched-exponential function than by the Zipf law. Cumulative distribution function is found as an excellent tool in analysis of the dynamics of the collective social phenomena. We are able to approximate the number of blog comments with time by simple sigmoidal functions: probability of posting a comment is given by P(t)=P₀(t)/[1+P₀(t)], where P₀(t)=(t/t₀)^{β} and β is close to 1.
This article presents a network algorithm for identifying transactions which may constitute a violation of restricted periods, namely, making transactions in company shares by persons possessing inside information. The empirical research was performed on the basis of publicly available information on exchange trading, originating from the Warsaw Stock Exchange. The analysis is based on a numerical model which describes information spreading in a network with an information bottleneck. The applied method can confirm with high probability the use of inside information for carrying out unauthorized stock market transactions.
The aim of this article is to examine the possibility of implementing the rules of prosumption in the public administration sector in Poland. The level of development of the Polish e-Government system is far from satisfactory, taking into consideration comparatively narrow (regarding both type and range) set of public services provided on-line. A comprehensive method of public administration sector evaluation has not been worked out yet on the level of communes, though it is very useful because of the greatest innovative potential which has not been used so far. An assessment of a relatively deteriorating indicator of innovation in the public administration sector in Poland is impossible without going to the local level and analysing the situation in certain voivodeships, especially in the communes which are the main units of the local government. Prosumption is the main idea of a new economic school called wikinomics, it means blurring the difference between the producer or a service provider and the customer by including the latter to the processes of production of goods or supplying services. According to the article, prosumption in the public administration sector can be used in two ways. Firstly, it should be known to what extent internet sites of commune offices can be transformed into social innovative platforms which could show natural creativity of customers. Secondly, it is important to determine whether the main principles of prosumption, such as getting rid of control, peering and sharing the results, can be used in practical work of commune offices. This article is focused on the research of web pages issued by the local authorities. The possibility to use web pages as platforms to provide public service on-line is evaluated. Besides, the correspondence analysis was introduced, which helped to identify the innovative potential in the public administration sector and evaluate it paying special attention to the processes of prosumption. A rational expectations hypothesis allowed to explain the process of the appearance of systematic errors in interaction between a citizen and an official. It appeared that systematic errors result in perception gaps. Prosumption is the most successful mechanism for reduction of perception gaps.
A popular method for network analysis of financial markets is a notable part of econophysics research. The networks created in such efforts are focused exclusively on linear correlations between stocks. While Pearson's correlation is the obvious starting point, it would be useful to look at its alternatives as to whether they provide improvements to this methodology, particularly given Pearson's correlation coefficient considers only a limited class of association patterns. We propose to use mutual information-based hierarchical networks, as mutual information is a natural generalisation of Pearson's correlation. We estimate mutual information using naive plug-in estimator as consistent bias is not harmful to this application, however other methods may also be used. We then transform the mutual information into an Euclidean metric and create minimal spanning trees and maximally filtered planar graphs. We apply this methodology to Warsaw Stock Exchange for years between 2000 and 2013, and comment on the differences with the standard methodology, as well as the structural changes on Warsaw Stock Exchange which the study reveals.
A new model is formulated of the sociological effect of the spiral of silence, introduced by Elisabeth Noelle-Neumann in 1974. The probability that a new opinion is openly expressed decreases with the difference between this new opinion and the perceived opinion of the majority. We also assume that the system is open, i.e. some people enter and some leave during the process of the opinion formation. An influence of a leader is simulated by a comparison of two runs of the simulation, where the leader has different opinion in each run. The difference of the mean expressed opinions in these two runs persists long after the leader's leave.
The Belief Propagation algorithm is a popular technique of solving inference problems for different graph-like structures. We present a discussion of the dynamics of that algorithm for the Ising model on the square lattice. Our main goal was to describe limit fixed points for that algorithm, which are strictly connected with the marginal probabilities and stationary points of the Bethe Free Energy. Analytical considerations provide an exact analysis of a class of symmetrical points while numerical simulations confirm that for small lattices there are no non-symmetrical points. Notwithstanding the prevalent use of the Belief Propagation as an inference tool we present a sociophysical interpretation of its dynamics. In that case our considerations may be viewed as an investigation of the possible fixed points of the social dynamics.
Two models of a queue are proposed: a human queue and two lines of vehicles before a narrowing. In both models, a queuer tries to evaluate his waiting time, taking into account the delay caused by intruders who jump to the queue front. As the collected statistics of such events is very limited, the evaluation can give very long times. The results provide an example, when direct observations should be supplemented by an inference from the context.
We extend the well-known Cont-Bouchaud model to include a hierarchical topology of agent's interactions. The influence of hierarchy on system dynamics is investigated by two models. The first one is based on a multi-level, nested Erdős-Rényi random graph and individual decisions by agents according to Potts dynamics. This approach does not lead to a broad return distribution outside a parameter regime close to the original Cont-Bouchaud model. In the second model we introduce a limited hierarchical Erdős-Rényi graph, where merging of clusters at a level h+1 involves only clusters that have merged at the previous level h and we use the original Cont-Bouchaud agent dynamics on resulting clusters. The second model leads to a heavy-tail distribution of cluster sizes and relative price changes in a wide range of connection densities, not only close to the percolation threshold.
In this paper, we investigate the statistical features of the weighted international-trade network. By finding the maximum weight spanning trees for this network we make the extraction of the truly relevant connections forming the network's backbone. We discuss the role of large-sized countries (strongest economies) in the tree. Finally, we compare the topological properties of this backbone to the maximum weight spanning trees obtained from the gravity model of trade. We show that the model correctly reproduces the backbone of the real-world economy.
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