Modeling random and non-random decision uncertainty in ratings data: a fuzzy beta model

Modeling human ratings data subject to raters’ decision uncertainty is an attractive problem in applied statistics. In view of the complex interplay between emotion and decision making in rating processes, final raters’ choices seldom reflect the true underlying raters’ responses. Rather, they are imprecisely observed in the sense that they are subject to a non-random component of uncertainty, namely the decision uncertainty. The purpose of this article is to illustrate a statistical approach to analyse ratings data which integrates both random and non-random components of the rating process. In particular, beta fuzzy numbers are used to model raters’ non-random decision uncertainty and a variable dispersion beta linear model is instead adopted to model the random counterpart of rating responses. The main idea is to quantify characteristics of latent and non-fuzzy rating responses by means of random observations subject to fuzziness. To do so, a fuzzy version of the Expectation–Maximization algorithm is adopted to both estimate model’s parameters and compute their standard errors. Finally, the characteristics of the proposed fuzzy beta model are investigated by means of a simulation study as well as two case studies from behavioral and social contexts.

USING METHODS FOR ASSESSING ECONOMIC RISKS TO MAKE INVESTMENT DECISIONS

The article uses methods of quantitative evaluation of economic risks that allow in conditions of uncertainty to provide an industrial enterprise with information on a less risky investment project for the adoption of a managerial decision. Several methods for assessing the risk of investing are used: the size of the dispersion, the value of the coefficient variation, the size of the semivariation, the size of the coefficient of semivariation, the value of the coefficient of asymmetry. Dispersion is a statistical term that describes the value range values expected for a particular variable. Dispersion is used in studying the variability of profits from a specific trading strategy or investment portfolio. This is often interpreted as a degree of uncertainty and, therefore, the risk associated with a certain portfolio of securities or investments. Semiivariation is an indicator of data that can be used to assess potential investment risks. Semivarianity is calculated by measuring the dispersion of all observations that fall below the middle or target data set. Neoclassical theory goes out for understanding that risks are just unfavorable scenarios for an investor company. Therefore, it is necessary to take into account the unfavorable deviations. When the management subject is loyal to risk, then it is necessary to use the coefficient of semivariation, which can also be determined which of the projects. If the company wants to successfully investigate the project, it is important to identify situations where the probability and magnitude of a positive (or negative) result is much larger than the opposite result. Understanding asymmetric risk is crucial for making correct decisions. The ability to identify asymmetric risk helps to avoid potentially dangerous situations where there are not enough errors. It also allows you to use the opportunities for investments where there are several ways to win. The criterion of maximum asymmetry is the minimum risk criterion. The results of the quantitative assessment of economic risks enable to substantiate the economic efficiency of investment projects.

Dispersion measure variability for 36 millisecond pulsars at 150 MHz with LOFAR

Context. Radio pulses from pulsars are affected by plasma dispersion, which results in a frequency-dependent propagation delay. Variations in the magnitude of this effect lead to an additional source of red noise in pulsar timing experiments, including pulsar timing arrays (PTAs) that aim to detect nanohertz gravitational waves. Aims. We aim to quantify the time-variable dispersion with much improved precision and characterise the spectrum of these variations. Methods. We use the pulsar timing technique to obtain highly precise dispersion measure (DM) time series. Our dataset consists of observations of 36 millisecond pulsars, which were observed for up to 7.1 yr with the LOw Frequency ARray (LOFAR) telescope at a centre frequency of ~150 MHz. Seventeen of these sources were observed with a weekly cadence, while the rest were observed at monthly cadence. Results. We achieve a median DM precision of the order of 10−5 cm−3 pc for a significant fraction of our sources. We detect significant variations of the DM in all pulsars with a median DM uncertainty of less than 2 × 10−4 cm−3 pc. The noise contribution to pulsar timing experiments at higher frequencies is calculated to be at a level of 0.1–10 μs at 1.4 GHz over a timespan of a few years, which is in many cases larger than the typical timing precision of 1 μs or better that PTAs aim for. We found no evidence for a dependence of DM on radio frequency for any of the sources in our sample. Conclusions. The DM time series we obtained using LOFAR could in principle be used to correct higher-frequency data for the variations of the dispersive delay. However, there is currently the practical restriction that pulsars tend to provide either highly precise times of arrival (ToAs) at 1.4 GHz or a high DM precision at low frequencies, but not both, due to spectral properties. Combining the higher-frequency ToAs with those from LOFAR to measure the infinite-frequency ToA and DM would improve the result.

IMPACT OF HOUSING AFFORDABILITY AND OTHER SOCIOECONOMIC VARIABLES ON INTERNAL MIGRATION IN LITHUANIA

The way housing affordability/wages/unemployment influenced internal migration of the population in Lithuania within the period of 2005−2019 is being analyzed in the article. Correlation-regression analysis is used to determine the relationships between the analyzed social phenomena. First, the correlation between housing affordability/wages/unemployment (their changes) and internal migration indicators is calculated, and the impact of data delays is assessed. Later simple and multiple regression equations are constructed. The conditions under which and how strongly housing affordability/wages/unemployment can influence population migration decisions have been identified in the analysis. Higher affordability of housing/wages is positively related to the number of people who moved to a certain Lithuanian city from other places in Lithuania per year. On the contrary, negative dependence of the number of people who moved to a certain city from other places in Lithuania on the unemployment rate in the city where those people moved in have been recorded. Both, affordability of housing and the unemployment rate explain actually 73−88 percent of variable dispersion of the internal migration in Vilnius, Kaunas and Klaipėda.

Suppression of nonlinear noise in a high-speed optical channel with variable dispersion compensation

The numerical modeling of short optical pulses propagation in the communication link is carried out. The combination of high chirp and variable dispersion compensation is proposed to suppress the nonlinear noise. The variable dispersion decreases the bit error rate by 10 times. Calculations for 25 ps pulses propagating by 1000 km with 8-level amplitude-phase modulation and two polarization states confirm that the chirp and compensation decrease the nonlinearity effects and improve the quality of detection radically. The results can be useful when choosing a high-speed communication line design.

Transformation of Eigenvalues of the Zakharov–Shabat Problem under the Effect of Soliton Collision

Background and Objectives: The Zakharov–Shabat spectral problem allows to find soliton solutions of the nonlinear Schrodinger equation. Solving the Zakharov–Shabat problem gives both a discrete set of eigenvalues λj and a continuous one. Each discrete eigenvalue corresponds to an individual soliton with the real part Re(λj) providing the soliton velocity and the imaginary part Im(λj) determining the soliton amplitude. Solitons can be used in optical communication lines to compensate both non-linearity and dispersion. However, a direct use of solitons in return-to-zero signal encoding is inhibited. The interaction between solitions leads to the loss of transmitted data. The problem of soliton interaction can be solved using eigenvalues. The latter do not change when the solitons obey the nonlinear Schrodinger equation. Eigenvalue communication was realized recently using electronic signal processing. To increase the transmission speed the all-optical method for controlling eigenvalues should be developed. The presented research is useful to develop optical methods for the transformation of the eigenvalues. The purpose of the current paper is twofold. First, we intend to clarify the issue of whether the dispersion perturbation can not only split a bound soliton state but join solitons into a short oscillating period breather. The second goal of the paper is to describe the complicated dynamics and mutual interaction of complex eigenvalues of the Zakharov–Shabat spectral problem. Materials and Methods: Pulse propagation in single-mode optical fibers with a variable core diameter can be described using the nonlinear Schrödinger equation (NLSE) which coefficients depends on the evolution coordinate. The NLSE with the variable dispersion coefficient was considered. The dispersion coefficient was described using a hyperbolic tangent function. The NLSE and the Zakharov– Shabat spectral problem were solved using the split-step method and the layer-peeling method, respectively. Results: The results of numerical analysis of the modification of soliton pulses under the effect of variable dispersion coefficient are presented. The main attention is paid to the process of transformation of eigenvalues of the Zakharov–Shabat problem. Collision of two in-phase solitons, which are characterized by two complex eigenvalues is considered. When the coefficients of the nonlinear Schrodinger equation change, the collision of the solitons becomes inelastic. The inelastic collision is characterized by the change of the eigenvalues. It is shown that the variation of the coefficients of the NLSE allows to control both real and imaginary parts of the eigenvalues. Two scenarios for the change of the eigenvalues were identified. The first scenario is characterized by preserving the zero real part of the eigenvalues. The second one is characterized by the equality of their imaginary parts. The transformation of eigenvalues is most effective at the distance where the field spectrum possesses a two-lobe shape. Variation of the NLSE coefficient can introduce splitting or joining of colliding soliton pulses. Conclusion: The presented results show that the eigenvalues can be changed only with a small variation of the NLSE coefficients. On the one hand, a change in the eigenvalues under the effect of inelastic soliton collision is an undesirable effect since the inelastic collision of solitons will lead to unaccounted modulation in soliton optical communication links. On the other hand, the dependence of the eigenvalues on the parameters of the colliding solitons allows to modulate the eigenvalues using all-fiber optical devices. Currently, the modulation of the eigenvalues is organized using electronic devices. Therefore, the transmission of information is limited to nanosecond pulses. For picosecond pulse communication, the development of all-optical modulation methods is required. The presented results will be useful in the development of methods for controlling optical solitons and soliton states of the Bose–Einstein condensate.

Discrete Stochastic Regulator on a Manifold, Minimizing Dispersion of the Output Macrovariable

A theoretical result is presented in the form of a new algorithm for the synthesis of a control system over a non-linear object, whose mathematical model represents a stochastic matrix difference equation having noise with a zero mean and finite dispersion in the righthand part. The new algorithm for synthesizing stochastic control for such an object is based on a three-stage procedure. In the first stage, the structure of the control system is formed in accordance with the classical method of analytical design of aggregated regulators (ADAR) in a fixed-noise assumption. In the second stage, the conditional mathematical expectation of the resulting expression for the first-stage control is determined. In the third stage, the control model is refined by excluding the noise variable from the control formula based on decomposing the initial control system affected by the new control. It is shown that the proposed control strategies minimize the target macro variable dispersion and ensure a stable, on average, achievement of the target manifold. A detailed example of an application of the algorithm for synthesizing control over the motion of an immobile center of mass is given, whose analog is represented by the objects such as by robot-manipulators, is given. The results of numerical modeling are presented, which confirm the operability of the constructed controller. Numerical simulations of the designed control system was performed using the authentic working equipment data.