Strong global correlations in the systems of coupled chaotic map lattices based on a modified logistic map are investigated. It is shown that, in the parameter range close to the edge of chaos as defined for an individual map, the systems exhibit off-diagonal long-range order and single-particle reduced density matrices defined in a natural way possess one strongly dominant eigenvalue. In addition, pattern formation [13] in the above systems has been investigated.
Interaction of argon clusters with intense laser pulses is studied theoretically. Free electrons energy distribution is studied. Differences between infrared and vacuum ultraviolet frequency regimes are pointed out. Clear physical interpretation of the obtained results is given.
Anderson localization of electromagnetic waves in random arrays of dielectric cylinders confined within a planar metallic waveguide is studied. The disordered dielectric medium is modeled by a system of randomly distributed 2D electric dipoles. An effective theoretical approach based on the method of images is developed. A clear distinction between isolated localized waves (which exist in finite media) and the band of localized waves (which appears only in the limit of the infinite medium) is presented. The Anderson transition emerging in the limit of an infinite medium is observed both in finite size scaling analysis of transmission and in the properties of the spectra of some random matrices. The sound physical interpretation of the obtained results suggests deeper insight into the existing experimental and theoretical work.
In this study we compare the income distributions for men and women in Poland in 2014. To examine the differences in the entire range of income values we utilize the hazard function approach. A flexible hazard-function based estimator in the presence of covariates (education, age, etc.) is used to construct conditional density and cumulative distribution functions. Then, we decompose the differences between two distributions using the counterfactual distribution. We estimate also the Lorenz curves for incomes and decompose the differences between the values of the Gini coefficients.
The explosion of rare-gas atomic clusters induced by short, intense X-ray pulses generated by a free-electron laser is studied. A numerical approach for an explicitly time-dependent description of small to medium size clusters in 3D is developed within the Thomas-Fermi model. Such an approach, though strongly simplified in comparison to fully quantum-mechanical schemes, is nevertheless expected to yield a qualitatively correct description of the electronic and ionic dynamics of these systems, at a much lower computational cost.
Modified Kaldor-Kalecki-type model of business cycles with delays are considered. Unidirectional and bidirectional couplings are introduced to investigate relationships between three "global" markets and two "local" markets. Selected results of an extensive numerical analysis are presented.
The dynamics of small (<55 atoms) argon clusters ionized by an intense, infrared, femtosecond laser pulse is studied using a Bloch-like hydrodynamic model. Evolution of both free electrons and ions formed in the cluster explosion process is examined. Oscillations of the electron cloud in a rare-gas atomic cluster are described as a motion of a fluid obeying Bloch-like hydrodynamic equations. Our theoretical approach includes all possible ionization mechanisms: tunnel (or field) ionization both by an external laser field, and by an internal field due to the space-charge distribution inside the cluster, as well as electron-impact (or collisional) ionization. The results of our simulations are compared both with experimental findings and with predictions of other theoretical models.
We investigate numerically the problem of optimization of directional characteristics of dipole antennas located inside, or in the vicinity of, photonic crystals or more general artificial dielectrics, made of very thin perfectly conducting wires. We concentrate on two-dimensional propagation. Simulated annealing is used to find the distribution of wires which optimizes the directional pattern. It is demonstrated that high directivity can be obtained for systems containing a very small number of elements provided that the size and shape of the unit cell as well as the position of the radiating source with respect to the crystal are optimized. Building up of the radiation pattern is also illustrated with the help of the wave-optical rays.
In this work we analyze empirically customer churn problem from a physical point of view to provide objective, data driven and significant answers to support decision making process in business application. In particular, we explore different entropy measures applied to decision trees and assess their performance from the business perspective using set of model quality measures often used in business practice. Additionally, the decision trees are compared with logistic regression and two machine learning methods - neural networks and support vector machines.
In this study we compared incomes distributions in the USA for two subgroups (defined according to sex or race). We utilized the quantile decomposition method to describe differences between the two distributions as a function of their quantiles. The analyzed objects are characterized by the set of attributes (education, age, etc.). We evaluate strength of the influence of the attributes onto the various parts of the incomes distributions. In such a way we evaluate income inequalities and their causes in two subgroups of people.
In this paper we study the relations between personal incomes and incomes of families with two adults in USA. We describe family income distributions using the simple two-parametric model. Assuming incomes of spouses are statistically independent of each other we obtain theoretical exponential income distributions for males and females. We show that these distributions are not coincident with distributions constructed based on the personal data. Obtained results indicate on statistical dependence between incomes of males and females in the families. We track changes and trends in data for years from 2001 to 2016.
Identification of patterns in stock markets has been an important subject for many years. In the past, numerous techniques, both technical and econometric, were used to predict changes in stock markets, but dependences among all the companies listed on a stock market were considered in a limited extent. Numerous studies confirm that larger stocks items appear to influence smaller ones and that, on a global level, most of the world's stock markets are integrated. Therefore, this study implements the association rules using a data mining approach to explore the co-movement between stock items listed on the Warsaw Stock Exchange. We believe that in order to describe and to understand market's behavior, data mining techniques are more flexible in use than for instance pricing models based on a finance theory. The former seems to be more effective for explaining market behavior without making particular assumptions.
We studied the spectral properties of the matrices describing multiple scattering of electromagnetic waves from randomly distributed point-like magneto-optically active scatterers under an external magnetic field B. We showed that the complex eigenvalues of these matrices exhibit some universal properties such as the self-averaging behavior of their real parts, as in the case of scatterers without magneto-optical activity. However, the presence of magneto-optically active scatterers is responsible for a striking particularity in the spectra of these matrices: the splitting of the values of the imaginary part of their eigenvalues. This splitting is proportional to the strength of the magnetic field and can be interpreted as a consequence of the Zeeman splitting of the energy levels of a single scatterer.
Credit risk models used in banks are based on probability models for occurrence of default. A vast class of the models used in practice (e.g., Credit Metrics) is based on the notion of intensity. In 1997 Jarrow applied Markov chain approach to analyze intensities. The key problem that arises is the selection of appropriate estimators. Within the Markov approach among the most frequently used estimators of a migration matrix are cohort and duration estimators. Migration matrices can also be obtained with help of statistical longitudinal models (GLMM) in which states (rating classes) in discrete time points are regarded as matched pairs. In this paper we compare Markov chain models and GLMM models and the influence of their application on bank portfolio evaluation.
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.
Localized waves in disordered left-handed materials are studied using a generalized coupled-dipole model. Resonances in an open system consisting of randomly distributed electric and magnetic dipoles are investigated. A new type of long-lived resonance modes localized at the boundary of the system is found. They resemble evanescent waves responsible for a superfocusing phenomenon by a left-handed lens.
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 is concerned with two coupled Kaldor-Kalecki models of business cycles with delays in both the gross product and the capital stock. We consider two types of investment functions that lead to different behavior of the system. We introduce the model with unidirectional coupling to investigate the influence of a global economy (like the European Union) on a local economy (like Poland). We present detailed results of numerical analysis.
Indices of selected financial markets from various parts of world, different sizes and levels of development are investigated. The local Hurst exponent is globally compared to log-prices. Periodic changes in correlation coefficient are quantified via discrete Fourier transform. Local Hurst exponents spectra are discussed for investigated markets.
Dynamics of a number of new users registering for the first time to a Polish internet-base social network http://Grono.net is investigated via various regression models. Trends are estimated and the statistical significance of their forecasting is tested.
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