Stability and Controllability of a class of 2D linear systems with Dynamic Boundary Conditions

Discrete linear repetitive processes are a distinct class of 2D linear systems with applications in areas ranging from long-wall coal cutting through to iterative learning control schemes. The feature which makes them distinct from other classes of 2D linear systems is that information propagation in one of the two independent directions only occurs over a finite duration. This, in turn, means that a distinct systems theory must be developed for them. In this paper a complete characterization of stability and so-called pass controllability (and several resulting features), essential building blocks for a rigorous systems theory, under a general set of initial, or boundary, conditions is developed. Finally, some significant new results on the problem of stabilization by choice of the pass state initial vector sequence are developed

Lagrangian modeling of reactive transport in heterogeneous porous media with an automatic locally adaptive particle support volume

The particle support volume is crucial for simulating reactive transport with Lagrangian methods as it dictates the interaction among particles. Assuming that it is constant in space, the particle support volume can be selected by means of kernel density estimation theory, an approach that has been shown to provide accurate estimates in simple setups. However, the particle support volume should intuitively vary with the particle position and evolve with time so as to mimic the local behavior of the solute plume. In this paper, we present a new approach to select a locally optimal particle support volume in reactive transport simulations. We consider that each particle has a different support volume that can locally adapt its shape and size with time based on the nearby particle distribution. By introducing a new optimality criterion, closed-form expressions of the particle support volume are presented under certain assumptions. In advection-dominated transport, we propose to orient the support volume along the local velocities. Numerical simulations of solute transport in a randomly heterogeneous porous medium demonstrate that the new approach can substantially increase accuracy with a more rapid convergence to the true solution with the number of particles. The error reduction seen in local approaches is particularly important in regions with extreme (high and low) density of particles. The method is shown to be computationally efficient, displaying better results than traditional histogram or global kernel methods for the same computational effort.Peer ReviewedPostprint (published version

Entity-Attribute-Value approach in databases

W artykule omówiono pewien specyficzny sposób reprezentacji danych, który w pewnych sytuacjach może być stosowany w miejsce klasycznego podejścia relacyjnego. Jest on stosunkowo mało znany i choć zakres jego stosowalności jest ograniczony a pewne niekorzystne właściwości znaczne, to warto go poznać, gdyż istnieją obszary, gdzie jego stosowanie może przynieść wymierne korzyści. Mowa tu o tzw. podejściu Entity-Attribute-Value, w skrócie EAV. Jest ono całkowicie różne od podejścia relacyjnego. W pracy pokazano główne założenia EAV wraz z przykładami oraz omówiono jego podstawowe zalety i wady. Krótko omówiono również pewne alternatywne rozwiązanie do EAV, które posiada niektóre cechy EAV, a jednocześnie nie burzy tak bardzo podejścia relacyjnego.In the paper a specific kind of data representation is presented. In some situations it can be used in place of classical relational approach. This data representation, although not new, is not widely known, and in spite of some serious limitations, can be used in many specific database areas. We describe the Entity-Attribute-Value (EAV) approach. This approach is totally different to the relational one. In the paper we give an overview of the EAV as well as we show the main advantages and disadvantages. Also, we show an alternative approach to EAV which does not suffer the EAV limitations

Higher order discretisations methods for a class of 2D continuous-discrete linear systems

Differential linear repetitive processes are a distinct class of two-dimensional linear systems which can be used, for example, to model industrial processes such as long-wall coal cutting operations. Also they can be used to study key properties of classes of linear iterative learning schemes. The key feature of interest in this paper is the fact that information propagation in one of the two separate directions in such processes evolves continuously over a finite fixed duration and in the other direction it is, in effect, discrete. The paper develops discrete approximations for the dynamics of these processes and examines the effects of the approximation techniques used on two key systems-related properties. These are stability and the structure of the resulting discrete state-space models. Some ongoing work and areas for further development are also briefly noted

Nonparametric estimation of selected parameters of steam and gas power plant

W pracy pokazano przykład użycia nieparametrycznej estymacji danych. Z pomocą tej techniki dokonano oszacowania emisji tlenków azotu (NOx) na podstawie danych eksploatacyjnych zbieranych podczas normalnej pracy Elektrociepłowni w Zielonej Górze. Na wstępnie dokonano krótkiego przeglądu najbardziej popularnych technik estymacji parametrycznej i porównano je z technikami nieparametrycznymi. Następnie na prostym przykładzie pokazano istotę działania estymacji nieparametrycznej. Pracę kończy rozdział, w którym krótko omówiono uzyskane wyniki symulacyjne.In the paper there are shown some practical examples of using nonparametric estimation. Using this technique there were estimated the nitrogen oxides (NOx) emissions based on the data taken from a real industry plant (gas and steam combined heat and power (CHP) plant in Zielona Góra, Poland). This work can be treated as a continuation of the paper [2]. In the first section there is given a short overview of estimation methods, including the linear and nonlinear regression, and comparison of them with nonparametric ones. In the second section there is briefly presented the nonparametric estimation technique and there is given a simple illustrative example. The third paragraph is dedicated to presenting the experimental results. Basing on the data from the CHP plant, the NOx emission was estimated and the satisfactory results (in comparison, for example, with the results obtained from the linear regression estimator) were obtained. All calculations were carried out using np package for R-project environment which implements a variety of nonparametric (and also semiparametric) kernel-based estimators

Estimation of nitrogen oxides NOx emission based on data from real industry plant

W pracy podjęto próbę szacowania emisji tlenków azotu (NOx,) na podstawie danych eksploatacyjnych zbieranych podczas normalnej pracy Elektrociepłowni w Zielonej Górze. Pomimo że zanieczyszczenia te monitorowane są z użyciem specjalistycznych czujników, to wydaje się, że dodatkowa ich kontrola może być bardzo pożądana. Zwłaszcza, że ilość emitowanych zanieczyszczeń (w tym NOx) jest ściśle limitowana i kontrolowana. Wspomniane szacowanie wykonano wykorzystując technikę statystyczną zwaną regresją liniową.In the paper there is analysed the possibility of estimating nitrogen oxides NOx emissions based on the data taken from an industry plant (gas-based combined heat and power (CHP) plant in Zielona Góra, Poland). Even though the emission of NOx is monitored on-line by dedicated sensors installed on the plant, we believe that some additional monitoring would be desirable. This is especially important because emission of different kind of air-pollutants (including NOx) is strictly limited and monitored. The above mentioned estimation is performed by the statistical technique known as linear regression. In Section 2 the gas-based combined heat and power plant in Zielona Góra is briefly described. A simplified chart of the plant is shown in Fig. 1. The list of measurement points taken from the DCS system (distributed control system) of the greatest influence on the NOx emission is also given. In Section 3 there is shown the way how the raw data should be prepared, especially in the context of removing unwanted disturbances as well as the points which were selected for the final regression analysis. The results obtained are presented in Section 4. The best regression solution (row 3 in Table 3) is shown in Fig. 4. The accuracy is quite satisfactory and we believe that it is sufficient for the purpose of additional monitoring the main NOx sensors installed on the plant

Automatic text summarization using algebraic approach

Duża liczba zwracanych (na przykład przez różnego rodzaju wyszukiwarki internetowe) dokumentów oznacza, że często zmuszeni jesteśmy do czasochłonnego ich przeglądania, celem weryfikacji trafności zwracanych wyników. Gdy dokumenty są długie, czas ich przeglądania znacznie się wydłuża. Można by go wydatnie skrócić, gdyby istniała możliwość automatycznego generowania sensownych podsumowań (streszczeń). W artykule omawiamy wybrane algebraiczne metody służące automatycznemu wydobywaniu z tekstu jego najistotniejszych słów kluczowych oraz najistotniejszych zdań.Text summarization is a real practical problem due to explosion of the volume of textual information available nowadays. In order to solve this problem, text summarization systems which extract brief information from a given text are created. The end user, by looking only at the summary, may decide whether the document is or is not of interest to him/her. Built summaries can have 2 fundamental forms. Firstly, extractive summarization may collect important sentences from the input text to constitute the summary. Secondly, abstractive summarization tries to capture main concepts of the text and then some new sentences, summarizing the input text, are generated. Nowadays, however, it seems that the latter approach still needs extensive works to be really useful. A summary can be extracted from a single document or multiple documents. In the paper the authors build summaries of one document only. The extension into multi-document summaries is the straightforward task in the case when a set of semantically uniform texts is summarized. Summaries may also be categorized as generic and query-based summaries. In the first case, there are generated summaries con-taining main topics of a document. In the second case, summaries contain the sentences that are related to the given queries. In the paper there are built generic summaries. Summarization systems use different approaches to determine important sentences. Here there is used semantic oriented approach based on a method known as Latent Semantic Analysis (LSA). LSA is an algebraic method that extracts meaning of words and similarity of sentences using the information about usage of the words in the context. It uses Singular Value Decomposition (SVD) for finding semantically similar words and sentences. Using the results of SVD the authors try to select best sentences (which constitute the best summary of the text). The paper is organized as follows. In Section 2 there is formulated the problem. In Section 3 there is shown how a docu-ment may be represented in a useful algebraic format. The so called Term-Sentence matrix (TSM) is used. The authors also point at some preliminary tasks necessary to be performed for successful further analysis. In Subsection 3.2 there is shortly presented an idea of LSA as based on SVD decomposition. In the last section 4 two examples of text summarizations build for both Polish and English texts are given. The two methods used differ slightly from each other. The authors' extracting key words and key sentences seems to be proper content-related summaries of the input texts

Graphics processing units in acceleration of bandwidth selection for kernel density estimation

The Probability Density Function (PDF) is a key concept in statistics. Constructing the most adequate PDF from the observed data is still an important and interesting scientific problem, especially for large datasets. PDFs are often estimated using nonparametric data-driven methods. One of the most popular nonparametric method is the Kernel Density Estimator (KDE). However, a very serious drawback of using KDEs is the large number of calculations required to compute them, especially to find the optimal bandwidth parameter. In this paper we investigate the possibility of utilizing Graphics Processing Units (GPUs) to accelerate the finding of the bandwidth. The contribution of this paper is threefold: (a) we propose algorithmic optimization to one of bandwidth finding algorithms, (b) we propose efficient GPU versions of three bandwidth finding algorithms and (c) we experimentally compare three of our GPU implementations with the ones which utilize only CPUs. Our experiments show orders of magnitude improvements over CPU implementations of classical algorithms