Two-dimensional (2D) positive systems are 2D state-space models whose state, input and output variables take only nonnegative values. In the paper we explore how linear matrix inequalities (LMIs) can be used to address the stability problem for 2D positive systems. Necessary and sufficient conditions for the stability of positive systems have been provided. The results have been obtained for most popular models of 2D positive systems, that is: Roesser model, both Fornasini-Marchesini models (FF-MM and SF-MM) and for the general model.

Extraction of the foetal electrocardiogram from single-channel maternal abdominal signals without disturbing its morphology is difficult. We propose to solve the problem by application of projective filtering of time-aligned ECG beats. The method performs synchronization of the beats and then employs the rules of principal component analysis to the desired ECG reconstruction. In the first stage, the method is applied to the composite abdominal signals, containing maternal ECG, foetal ECG, and various types of noise. The operation leads to maternal ECG enhancement and to suppression of the other components. In the next stage, the enhanced maternal ECG is subtracted from the composite signal, and this way the foetal ECG is extracted. Finally, the extracted signal is also enhanced by application of projective filtering. The influence of the developed method parameters on its operation is presented.

We present a novel quantum algorithm for the classification of images. The algorithm is constructed using principal component analysis and von Neuman quantum measurements. In order to apply the algorithm we present a new quantum representation of grayscale images.

Forecasting yield curves with regime switches is important in academia and financial industry. As the number of interest rate maturities increases, it poses difficulties in estimating parameters due to the curse of dimensionality. To deal with such a feature, factor models have been developed. However, the existing approaches are restrictive and largely based on the stationarity assumption of the factors. This inaccuracy creates non-ignorable financial risks, especially when the market is volatile. In this paper, a new methodology is proposed to adaptively forecast yield curves. Specifically, functional principal component analysis (FPCA) is used to extract factors capable of representing the features of yield curves. The local AR(1) model with time-dependent parameters is used to forecast each factor. Simulation and empirical studies reveal the superiority of this method over its natural competitor, the dynamic Nelson-Siegel (DNS) model. For the yield curves of the U.S. and China, the adaptive method provides more accurate 6- and 12-month ahead forecasts.

The aim of this article is to evaluate the quality of the Danube River in its course through Serbia as well as to demonstrate the possibilities for using three statistical methods: Principal Component Analysis (PCA), Factor Analysis (FA) and Cluster Analysis (CA) in the surface water quality management. Given that the Danube is an important trans-boundary river, thorough water quality monitoring by sampling at different distances during shorter and longer periods of time is not only ecological, but also a political issue. Monitoring was carried out at monthly intervals from January to December 2011, at 17 sampling sites. The obtained data set was treated by multivariate techniques in order, firstly, to identify the similarities and differences between sampling periods and locations, secondly, to recognize variables that affect the temporal and spatial water quality changes and thirdly, to present the anthropogenic impact on water quality parameters.

Multidimensional exploratory techniques, such as the Principal Component Analysis (PCA), have been used to analyze long-term changes in the flow regime and quality of water of the lowland dam reservoir Turawa (south-west Poland) in the catchment of the Mała Panew river (a tributary of the Odra). The paper proves that during the period of 1998–2016 the Turawa reservoir was equalizing the river’s water flow. Moreover, various physicochemical water quality indicators were analyzed at three measurement points (at the tributary’s mouth into the reservoir, in the reservoir itself and at the outflow from the reservoir). The water quality assessment was performed by analyzing physicochemical indicators such as water temperature, TSS, pH, dissolved oxygen, BOD₅, NH₄⁺, NO₃^-, NO₂^-, N, PO₄^3-, P, electrolytic conductivity, DS, SO₄^2- and Cl^- . Furthermore, the correlations between all these water quality indicators were analyzed statistically at each measurement point, at the statistical signifi cance level of p ≤ 0.05. PCA was used to determine the structures between these water quality variables at each measurement point. As a result, a theoretical model was obtained that describes the regularities in the relationships between the indicators. PCA has shown that biogenic indicators have the strongest influence on the water quality in the Mała Panew. Lastly, the differences between the averages of the water quality indicators of the inflowing and of the outflowing water were considered and their significance was analyzed. PCA unveiled structure and complexity of interconnections between river flow and water quality. The paper shows that such statistical methods can be valuable tools for developing suitable water management strategies for the catchment and the reservoir itself.

The petrographic composition of coal has a significant impact on its technological and sorption properties. That composition is most frequently determined by means of microscope quantitative analyses. Thus, aside from the purely scientific aspect, such measurements have an important practical application in the industrial usage of coal, as well as in issues related to the safety in underground mining facilities. The article discusses research aiming at analyzing the usefulness of selected parameters of a digital image description in the process of automatic identification of macerals of the inertinite group using neural networks. The description of the investigated images was based on statistical parameters determined on the basis of a histogram and co-occurrence matrix (Haralick parameters). Each of the studied macerals was described by means of a 20-element feature vector. An analysis of its principal components (PCA) was conducted, along with establishing the relationship between the number of the applied components and the effectiveness of the MLP network. Based on that, the optimum number of input variables for the investigated classification task was chosen, which resulted in reduction of the size of the network’s hidden layer. As part of the discussed research, the authors also analyzed the process of classification of macerals of the inertinite group using an algorithm based on a group of MLP networks, where each network possessed one output. As a result, average recognition effectiveness of 80.9% was obtained for a single MLP network, and of 93.6% for a group of neural networks. The obtained results indicate that it is possible to use the proposed methodology as a tool supporting microscopic analyses of coal.

To investigate the effect of different proximate index on minimum ignition temperature(MIT) of coal dust cloud, 30 types of coal specimens with different characteristics were chosen. A two-furnace automatic coal proximate analyzer was employed to determine the indexes for moisture content, ash content, volatile matter, fixed carbon and MIT of different types of coal specimens. As the calculated results showed that these indexes exhibited high correlation, a principal component analysis (PCA) was adopted to extract principal components for multiple factors affecting MIT of coal dust, and then, the effect of the indexes for each type of coal on MIT of coal dust was analyzed. Based on experimental data, support vector machine (SVM) regression model was constructed to predicate the MIT of coal dust, having a predicating error below 10%. This method can be applied in the predication of the MIT for coal dust, which is beneficial to the assessment of the risk induced by coal dust explosion (CDE).

Securing the certainty of supplies of the necessary minimum energy in each country is a basic condition for the energy security of the state and its citizens. The concept of energy security combines several aspects at the same time, as it can be considered in terms of the availability of own energy resources, it concerns technical aspects related to technical infrastructure, as well as political aspects related to the management and diversification of energy supplies. Another aspect of the issue of energy security is the environmental perspective, which is now becoming a priority in the light of the adopted objectives of the European Union’s energy policy. The restrictive requirements for reducing greenhouse gas emissions and increasing the required level of renewable energy sources in the energy balance of the Member States is becoming a challenge for economies that use fossil fuels to a large extent in the raw material structure, including Poland. Poland is the largest producer of hard coal in the European Union and hard coal is a strategic raw material as it satisfies about 50% of the country’s energy demand. In this context, the main goal of the article was to determine the future sale of hard coal by 2030 in relation to environmental regulations introduced in the energy sector. For this purpose, a mathematical model with a 95% confidence interval was developed using artificial LSTM neural networks, which belong to deep learning machine learning techniques, which reflects the key relationships between hard coal mining and the assumptions adopted in the National Energy and Climate Plan for the years 2021–2030 (NECP).