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1

Ślęzak D., Synak P., Wojna A., Wróblewski J.

Fundamenta Informaticae

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2013

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Vol. 127, nr 1-4

445--459

EN

We present analytic data processing technology derived from the principles of rough sets and granular computing. We show how the idea of approximate computations on granulated data has evolved toward complete product supporting standard analytic database operations and their extensions. We refer to our previous works where our query execution algorithms were described in terms of iteratively computed rough approximations. We explain how to interpret our data organization methods in terms of classical rough set notions such as reducts and generalized decisions.

2

Metastability exchange optical pumping low field polarizer for lung magnetic resonance imaging

Collier G., Suchanek M., Wojna A., Cieslar K., Palasz T., Glowacz B., Olejniczak Z., Dohnalik T.

Optica Applicata

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2012

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Vol. 42, nr 1

223-239

EN

An extensive improvement of our low field polarizer is described. It produces 3He gas polarized up to 40% in a 6 h decay time storage cell. Production rate was raised by a factor of 10 to 4-5 scc/min thanks to the implementation of a new 10 W laser and a new design of a peristaltic compressor, easier to handle. Some applications of polarized gas are also presented: dynamic images of gas inhalation in the rat as well as a static image of human lungs using hyperpolarized gas were obtained.

3

Wielowymiarowe modele sterowania zapasami i ich zastosowanie

Wojna A., Kłodzińska A.

Badania Operacyjne i Decyzje

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2005

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nr 2

83-90

PL

W artykule przeprowadzono matematyczną formalizację wielowymiarowych modeli sterowania zapasami z wykorzystaniem procesów sum zmiennych losowych określonych na łańcuchu Markowa. Na podstawie tej formalizacji określono funkcję ryzyka funkcjonowania wielowymiarowych modeli sterowania zapasami. Rozpatrzono również zagadnienie analizy niezawodności funkcjonowania oraz ustalenia optymalnej struktury specjalnego systemu obsługi Markowa za pomocą określenia jego funkcji ryzyka.

EN

The multidimensional stock control that functions in a random Markov environment is considered. The mathematical formalization of this model was considered with the use of sums of the random variables de-fmed on the Markov chains. The authors introduce a definition of risk function of the type of downside risk measures and find the explicit formulas for its determinations. The example of the application of these formulas is provided: the tasks of the reliability and optimal configuration for the queueing problem are regarded. The formulas defining the function by the system parameters were obtained

4

Center-Based Indexing in Vector and Metric Spaces

Wojna A.

Fundamenta Informaticae

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2003

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Vol. 56, nr 3

285-310

EN

The paper addresses the problem of indexing data for k nearest neighbors (k-nn) search. Given a collection of data objects and a similarity measure the searching goal is to find quickly the k most similar objects to a given query object. We present a top-down indexing method that employs a widely used scheme of indexing algorithms. It starts with the whole set of objects at the root of an indexing tree and iteratively splits data at each level of indexing hierarchy. In the paper two different data models are considered. In the first, objects are represented by vectors from a multi-dimensional vector space. The second, more general, is based on an assumption that objects satisfy only the axioms of a metric space. We propose an iterative k-means algorithm for tree node splitting in case of a vector space and an iterative k-approximate-centers algorithm in case when only a metric space is provided. The experiments show that the iterative k-means splitting procedure accelerates significantly k-nn searching over the one-step procedure used in other indexing structures such as GNAT, SS-tree and M-tree and that the relevant representation of a tree node is an important issue for the performance of the search process. We also combine different search pruning criteria used in BST, GHT nad GNAT structures into one and show that such a combination outperforms significantly each single pruning criterion. The experiments are performed for benchmark data sets of the size up to several hundreds of thousands of objects. The indexing tree with the k-means splitting procedure and the combined search criteria is particularly effective for the largest tested data sets for which this tree accelerates searching up to several thousands times

5

Funkcja użyteczności w modelach sterowania ryzykiem

Wojna A.

Badania Operacyjne i Decyzje

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2003

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nr 2

77-87

PL

W artykule rozpatrywane jest pojęcie ryzyka, zwłaszcza ryzyka ekonomicznego. Przeanalizowano relację pomiędzy nieokreślonością a ryzykiem oraz zbadano zagadnienia matematycznej formalizacji ryzyka ekonomicznego i jego elementów. Wymieniono kilka przykładów systemów w warunkach nieokreśloności oraz przedstawiono ich matematyczny opis. Na przykładzie problemu optymalnego wyboru portfela papierów wartościowych wyjaśniono, w jaki sposób można ocenić ilościowo ryzyko operacji finansowych. Szczegółowo zbadano rolę funkcji użyteczności przy formalizacji matematycznej ryzyka, jej własności, sposoby określania oraz możliwości zastosowania w ekonomicznych modelach sterowania ryzykiem.

EN

In the article, the concept of risk, especially the economical risk, is regarded. The relation between the concepts of indetermination and risk is analyzed and the problem of the mathematical formalization of economical risk and its elements is investigated. Some examples of the systems under conditions of indetermination and their mathematical description are given. The quantitative estimations of the risk in financial operations, in particular the example of portfolio selection problem, are considered. The utility function is introduced, its properties and definitions are given, and its usefulness for the mathematical formalization and control of economical risk is investigated. Some examples of applications of the utility function for the optimal control in problems of financial mathematics are given.

6

RIONA: A New Classification System Combining Rule Induction and Instance-Based Learning

Góra G., Wojna A.

Fundamenta Informaticae

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2002

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Vol. 51, nr 4

369-390

EN

The article describes a method combining two widely-used empirical approaches to learning from examples: rule induction and instance-based learning. In our algorithm (RIONA) decision is predicted not on the basis of the whole support set of all rules matching a test case, but the support set restricted to a neighbourhood of a test case. The size of the optimal neighbourhood is automatically induced during the learning phase. The empirical study shows the interesting fact that it is enough to consider a small neighbourhood to achieve classification accuracy comparable to an algorithm considering the whole learning set. The combination of k-NN and a rule-based algorithm results in a significant acceleration of the algorithm using all minimal rules. Moreover, the presented classifier has high accuracy for both kinds of domains: more suitable for k-NN classifiers and more suitable for rule based classifiers.