The paper presents the basic theory of wave probabilistic models together with their features. By introduction of the complementarity's principle between x-representation and k-representation the probability theory is completed for "structural" parameter which carries information about the changes of time series or random processes. The next feature of wave probabilistic models is the quantization principle or definition of probabilistic inclusion-exclusion rules.
The paper continues with the theory of wave probabilistic models and uses the inclusion-exclusion rule to describe quantum entanglement as a wave probabilities resonance principle. The achieved results are mathematically described and an illustrative example is shown to demonstrate the possible applications of the presented theory.
This paper presents the results of the application of wavelet decomposition to processing data from the GGP sites (The Global Geodynamics Project). The GGP is an international project within which the Earth's gravity field changes are recorded with high accuracy at a number of stations worldwide using superconducting gravimeters. Data with a 5-second sampling interval from Wettzell and Bad Homburg were used for the research. The wavelet transform enables the investigation of the temporal changes of the oscillation amplitudes or the decomposition of the time series for the analysis of the required frequencies. The wavelet decomposition was performed using the regular orthogonal symmetric Meyer wavelet. The research concerned data from an earthquake period recorded at various locations and a quiet period when the gravimeters worked without any disturbances. The decomposition was followed by the Fast Fourier Transform for signal frequency components and then by correlation analyses of corresponding frequency components (for periods from 10 to 60 000 seconds) for all sensor combinations, for the quiet and the earthquake periods separately. Frequency components defining long term changes for all sensor combinations, as well as combinations between two sensors at the same site for the quiet days are characterised by high correlation coefficients. For the time of the earthquake, the Wettzell site data proved strong correlation for all frequency components, while the Bad Homburg site data showed an unexpected decrease of correlation for the majority of frequency components. The authors also showed that wavelet decomposition can be a good method of data interpolation, especially from the time of earthquakes. Moreover, it is a very useful tool for filtering the data and removing the noises., Janusz Bogusz, Anna Klos and Wieslaw Kosek., and Obsahuje bibliografii
The paper presents a multi-output wavelet neural network (WNN) which, taking benefit of wavelets and neural networks, is able to accomplish data feature extraction and modeling. In this work, WNN is implemented with a feedforward one-hidden layer architecture, whose activation functions in its hidden layer neurons are wavelet functions, in our case, the first derivative of a Gaussian function. The network training is performed using a backpropagation algorithm, adjusting the connection weights along with the network parameters. This principle is applied to the simultaneous quantification of heavy metals present in liquid media, taking the cyclic voltammogram obtained with a modified epoxy-graphite composite sensor as departure information. The combination between processing tools and electrochemical sensors is already known as an electronic tongue.
Texture can be defined as a local statistical pattern of texture primitives in observer's domain of interest. Texture analysis such as segmentation plays a critical role in machine vision and pattern recognition applications. The widely applied areas are industrial automation, biomedical image processing and remote sensing. This paper describes a novel system for texture segmentation. We call this system Wavelet Oscillator Neural Networks (WONN). The proposed system is composed of two parts. A second-order statistical wavelet co-occurrence features are the first part of the proposed system and an oscillator neural network is in the second part of the system. The performance of the proposed system is tested on various texture mosaic images. The results of the proposed system are found to be satisfactory.
A new approach based on the implementation of probabilistic neural network (PNN) is presented for classification of electrocardiogram (ECG) beats. Four types of ECG beats (normal beat, congestive heart failure beat, ventricular tachyarrhythmia beat, atrial fibrillation beat) obtained from the Physiobank database were analyzed. The ECG signals were decomposed into time-frequency representations using discrete wavelet transform (DWT) and wavelet coefficients were calculated to represent the signals. The aim of the study is classification of the ECG beats by the combination of wavelet coefficients and PNN. The purpose is to determine an optimum classification scheme for this problem and also to infer clues about the extracted features. The present research demonstrated that the wavelet coefficients are the features which well represent the ECG signals and the PNN trained on these features achieved high classification accuracies.
In the paper we deal with weak Boolean products of bounded dually residuated l-monoids (DRl-monoids). Since bounded DRl-monoids are a generalization of pseudo MValgebras and pseudo BL-algebras, the results can be immediately applied to these algebras.
In this paper the notion of weak chain-completeness is introduced for pseudo-ordered sets as an extension of the notion of chain-completeness of posets (see [3]) and it is shown that every isotone map of a weakly chain-complete pseudo-ordered set into itself has a least fixed point.