Robust methods for stock market data analysis

Abstract We consider the problem of extraction of trend and chaotic components from irregular stock market time series. The proposed methods also permit to extract a part of chaotic component, the so-called anomalous term, caused by the transient short-time surges with high amplitudes. This provides more accurate determination of the trend component. The methods are based on the M-evaluation with decision functions of Huber and Tukey type. The iterative numerical schemes for determination of trend and chaotic components are brie y presented, resulting in an acceptable solution within a ÿnite number of iterations. The optimal level for extraction of the chaotic component is determined by a new numerical scheme based on the fractal dimension of the chaotic component of the analyzed series. Forecasting from the realized part of the analyzed series and a priori expert information is also discussed

Challenges in QCD matter physics - The Compressed Baryonic Matter experiment at FAIR

Substantial experimental and theoretical efforts worldwide are devoted to explore the phase diagram of strongly interacting matter. At LHC and top RHIC energies, QCD matter is studied at very high temperatures and nearly vanishing net-baryon densities. There is evidence that a Quark-Gluon-Plasma (QGP) was created at experiments at RHIC and LHC. The transition from the QGP back to the hadron gas is found to be a smooth cross over. For larger net-baryon densities and lower temperatures, it is expected that the QCD phase diagram exhibits a rich structure, such as a first-order phase transition between hadronic and partonic matter which terminates in a critical point, or exotic phases like quarkyonic matter. The discovery of these landmarks would be a breakthrough in our understanding of the strong interaction and is therefore in the focus of various high-energy heavy-ion research programs. The Compressed Baryonic Matter (CBM) experiment at FAIR will play a unique role in the exploration of the QCD phase diagram in the region of high net-baryon densities, because it is designed to run at unprecedented interaction rates. High-rate operation is the key prerequisite for high-precision measurements of multi-differential observables and of rare diagnostic probes which are sensitive to the dense phase of the nuclear fireball. The goal of the CBM experiment at SIS100 (sqrt(s_NN) = 2.7 - 4.9 GeV) is to discover fundamental properties of QCD matter: the phase structure at large baryon-chemical potentials (mu_B > 500 MeV), effects of chiral symmetry, and the equation-of-state at high density as it is expected to occur in the core of neutron stars. In this article, we review the motivation for and the physics programme of CBM, including activities before the start of data taking in 2022, in the context of the worldwide efforts to explore high-density QCD matter.Comment: 15 pages, 11 figures. Published in European Physical Journal

Metric analysis as a tool for interpolating multivariate functions in the case of an information lack

In report the ill-posed problems in view arising at the solution of applied problems by means of the metric analysis are considered. In the report new schemes and algorithms for smoothing and restoration based on the metric analysis were presented. These schemes and algorithms have demonstrated a high accuracy of smoothing and retrieving the values of functions of one or many variables. Examples of such problems are problems of interpolation, filtration and forecasting of values of functions of one and many variables claimed at the solution of applied problems physicists, technicians, economy and other areas of researches. © Springer International Publishing AG 2016

Metric analysis as a tool for interpolating multivariate functions in the case of an information lack

In report the ill-posed problems in view arising at the solution of applied problems by means of the metric analysis are considered. In the report new schemes and algorithms for smoothing and restoration based on the metric analysis were presented. These schemes and algorithms have demonstrated a high accuracy of smoothing and retrieving the values of functions of one or many variables. Examples of such problems are problems of interpolation, filtration and forecasting of values of functions of one and many variables claimed at the solution of applied problems physicists, technicians, economy and other areas of researches. © Springer International Publishing AG 2016

Extrapolation of Functions of Many Variables by Means of Metric Analysis

The paper considers a problem of extrapolating functions of several variables. It is assumed that the values of the function of m variables at a finite number of points in some domain D of the m-dimensional space are given. It is required to restore the value of the function at points outside the domain D. The paper proposes a fundamentally new method for functions of several variables extrapolation. In the presented paper, the method of extrapolating a function of many variables developed by us uses the interpolation scheme of metric analysis. To solve the extrapolation problem, a scheme based on metric analysis methods is proposed. This scheme consists of two stages. In the first stage, using the metric analysis, the function is interpolated to the points of the domain D belonging to the segment of the straight line connecting the center of the domain D with the point M, in which it is necessary to restore the value of the function. In the second stage, based on the auto regression model and metric analysis, the function values are predicted along the above straight-line segment beyond the domain D up to the point M. The presented numerical example demonstrates the efficiency of the method under consideration. © 2018 The Authors, published by EDP Sciences

Phenomenon of Education: Philosophical and Methodological Aspects of Research

The purpose of the work is to identify in the study of education, as a socio-cultural phenomenon, its functional and structural-organizational features at different historical stages of development and to analyze the relation of the concepts of "education", "science" and "intelligence". Methodology and research methods used in the study are the following: comparative analysis method, systematic approach, functional and cultural approaches and philosophical reflection. Key findings are the following: strategy of introducing new standards in the educational process in connection with the transition to digital reality requires changing the educational methodology and creating a new format for the development of teaching methods. The relation between the concepts of "methodology", "education" and "science" are ambiguous, their use is contextual. The main method of analysis of the study of functionality is philosophical reflection, which reveals their meaning and purpose. As a result of the study of the functional, structural and organizational features of education, the necessary object (material or spiritual) of research is created, where the relation between science and education is revealed. The question of the relation of research methodology and methods of the educational process becomes a question of the interactions of spirituality and science, values and knowledge

Extrapolation of Functions of Many Variables by Means of Metric Analysis

The paper considers a problem of extrapolating functions of several variables. It is assumed that the values of the function of m variables at a finite number of points in some domain D of the m-dimensional space are given. It is required to restore the value of the function at points outside the domain D. The paper proposes a fundamentally new method for functions of several variables extrapolation. In the presented paper, the method of extrapolating a function of many variables developed by us uses the interpolation scheme of metric analysis. To solve the extrapolation problem, a scheme based on metric analysis methods is proposed. This scheme consists of two stages. In the first stage, using the metric analysis, the function is interpolated to the points of the domain D belonging to the segment of the straight line connecting the center of the domain D with the point M, in which it is necessary to restore the value of the function. In the second stage, based on the auto regression model and metric analysis, the function values are predicted along the above straight-line segment beyond the domain D up to the point M. The presented numerical example demonstrates the efficiency of the method under consideration. © 2018 The Authors, published by EDP Sciences