Wyniki wyszukiwania - Biblioteka Nauki

1

Structural reliability - fuzzy sets theory approach

100%

Szeliga E.

Journal of Theoretical and Applied Mechanics

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2004

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tom Vol. 42 nr 3

651-666

EN

In the paper two kinds of uncertainty: randomness and imprecision are proposed to be considered in a structure description. Imprecise experts' opinions can be described using fuzzy numbers. As a results, the reliability analysis of a structure can be based on the limit state function with fuzzy parameters. As a consequence, the structural failure or survival can be treated as fuzzy events. The probabilities of these fuzzy events can be the upper and the lower estimations of the structural reliability. They can be achieved using well-known reliability methods (e.g. Hasofer-Lind index and Monte Carlo simulations). They can be used as a base for the calibration of partial safety factors in desing codes.

PL

W niniejszej pracy proponuje się uwzględnić w opisie konstrukcji dwa rodzaje niepewności: losowość i nieprecyzyjność. Nieprecyzyjne oceny ekspertów dotyczące konstrukcji proponuje się opisywać za pomocą liczb rozmytych. W rezultacie, niezawodność konstrukcji określać się będzie w oparciu o funkcję stanu granicznego z rozmytymi parametrami. W konsekwencji, awarię konstrukcji lub jej brak traktować się będzie jako rozmyte zdarzenia losowe. Prawdopodobieństwa tych zdarzeń stanowić będą dolne i górne oszacowanie niezawodności konstrukcji. Można je wyznaczać za pomocą metod stosowanych już w niezawodności (np. wskaźnik Hasofera-Linda lub metody Monte Carlo). Mogą one służyć jako podstawa kalibrowania częściowych współczynników bezpieczeństwa w normach projektowych.

2

On the completeness of some Lp-spaces of operator-valued functions

100%

Klotz L.

Probability and Mathematical Statistics

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1999

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tom Vol. 19, Fasc. 2

463--468

EN

In [3] there were studied Banach spaces of (equivalence classes of) functions Φ whose values are unbounded operators, in general, and which are p-integrable with respect to operator-valued measures having an operator density N with respect to some non-negative scalar measure μ. In the present short note it is shown that the values of all functions Φ are even bounded linear operators if and only if there is not any set A of positive finite measure μ such that the values of N on A have non-closed ranges. The result is used to answer a question raised by Górniak et al. [2].

3

In memoriam : Czesław Ryll-Nardzewski's contributions to probability theory

100%

Rolski T. , Woyczyński W. A.

Probability and Mathematical Statistics

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2017

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tom Vol. 37, Fasc. 1

1--20

EN

In this paper we review contributions of late Czesław Ryll-Nardzewski to probability theory. In particular, we discuss his papers on point processes, random power series, random series in infinite-dimensional spaces, ergodic theory, de Finetti’s exchangeable sequences, conditional distributions and applications of the Kuratowski-Ryll-Nardzewski theorem on selectors.

4

Nonelementary Notes on Elementary Events

100%

Frič R.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2003

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tom Vol. 9

137--141

EN

Our goal is to present simple examples illustrating the nature and role of elementary events and random variables in probability theory, both classical and operational (fuzzy). As stated in Płocki [10], in teaching probability we should concentrate on the construction of probability spaces and their properties, and not on the calculation of probability of various strange events (like hitting a bear if we can shoot three times, etc.). On a rather advanced level, Łoś [8] analyzed the constructions of probability spaces in the classical probability. J. Loś explained the nature and underscored the role of elementary events. Roughly, the events form a Boolean algebra, but some probability properties of the algebra depend on its representation via subsets and this is done via the choice of some fundamental subset of events and the choice of elementary events. Remember, choice! There are situations in which the classical probability model is not quite suitable (quantum physics, fuzzy models, c.f. Dvurečenskij and Pulmannová [3], Frič [5]), and I would like to present simple examples and simple models of such situations. In order to understand the generalizations, let me start with a well-known example of throwing two dice.

5

Modelling Progressive Filtering

100%

Armano G.

Fundamenta Informaticae

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2015

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tom Vol. 138, nr 3

285--320

EN

Progressive filtering is a simple way to perform hierarchical classification, inspired by the behavior that most humans put into practice while attempting to categorize an item according to an underlying taxonomy. Each node of the taxonomy being associated with a different category, one may visualize the categorization process by looking at the item going downwards through all the nodes that accept it as belonging to the corresponding category. This paper is aimed at modeling the progressive filtering technique from a probabilistic perspective. As a result, the designer of a system based on progressive filtering should be facilitated in the task of devising, training, and testing it.

6

The infinite divisibility and orthogonal polynomials with a constant recursion formula in free probability theory

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Saitoh N. , Yoshida H.

Probability and Mathematical Statistics

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2001

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tom Vol. 21, Fasc. 1

159--170

EN

We calculate Voiculescu’s R-transform of the compactly supported probability measure on Rinduced from the orthogonal polynomials with a constant recursion formula, and investigate its infinite divisibility with respect to the additive free convolution. In the case of infinite divisibility, we give the Lévy-Hinčin measure explicitly for the integral representation of the R-transform of the free analogue of the Lévy-Hinčin formula.

7

Random stain

100%

Hensz-Chądzyńska E. , Jajte R. , Paszkiewicz A.

Probability and Mathematical Statistics

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1998

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tom Vol. 18, Fasc. 1

199--218

EN

A stochastic model of a stain of pollution is proposed. The asymptotic shape of the edges of a stain is examined. The description is kept at the elementary level of probability theory.

8

An extended problem to Bertrand's paradox

100%

Ardakani M. , Wulff S.

Discussiones Mathematicae Probability and Statistics

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2014

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tom 34

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nr 1-2

23-34

EN

Bertrand's paradox is a longstanding problem within the classical interpretation of probability theory. The solutions 1/2, 1/3, and 1/4 were proposed using three different approaches to model the problem. In this article, an extended problem, of which Bertrand's paradox is a special case, is proposed and solved. For the special case, it is shown that the corresponding solution is 1/3. Moreover, the reasons of inconsistency are discussed and a proper modeling approach is determined by careful examination of the probability space.

9

A few word about Daniel W. Stroock

100%

Zegarliński B.

Antiquitates Mathematicae

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2015

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tom 9

PL

10

An Analysis of Probabilistic Approximations for Rule Induction from Incomplete Data Sets

88%

Clark P. G. , Grzymala-Busse J. W. , Hippe Z. S.

Fundamenta Informaticae

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2014

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tom Vol. 132, nr 3

365--379

EN

The main objective of our research was to test whether the probabilistic approximations should be used in rule induction from incomplete data. For our research we designed experiments using six standard data sets. Four of the data sets were incomplete to begin with and two of the data sets had missing attribute values that were randomly inserted. In the six data sets, we used two interpretations of missing attribute values: lost values and “do not care” conditions. In addition we used three definitions of approximations: singleton, subset and concept. Among 36 combinations of a data set, type of missing attribute values and type of approximation, for five combinations the error rate (the result of ten-fold cross validation) was smaller than for ordinary (lower and upper) approximations; for other four combinations, the error rate was larger than for ordinary approximations. For the remaining 27 combinations, the difference between these error rates was not statistically significant.

11

Triangular structures and duality

75%

Frič R. , Papčo P.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2007

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tom Vol. 12

23-28

EN

We introduce and study the category AFD the objects of which are generalized convergence D-posets (with more than just one greatest element) of maps into a triangle object T and the morphisms of which are sequentially continuous D-homomorphisms. The category AFD can serve as a base category for antagonistic fuzzy probability theory. AFD-measurable maps can be considered as generalized random variables and ADF-morphisms, as their dual maps, can be considered as generalized observables.

12

Stochastic Cellular Automata: Correlations : Decidability and Simulations

75%

Arrighi P. , Schabanel N. , Theyssier G.

Fundamenta Informaticae

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2013

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tom Vol. 126, nr 2-3

121--156

EN

This paper introduces a simple formalism for dealing with deterministic, non-deterministic and stochastic cellular automata in an unified and composable manner. This formalism allows for local probabilistic correlations, a feature which is not present in usual definitions. We show that this feature allows for strictly more behaviors (for instance, number conserving stochastic cellular automata require these local probabilistic correlations). We also show that several problems which are deceptively simple in the usual definitions, become undecidable when we allow for local probabilistic correlations, even in dimension one. Armed with this formalism, we extend the notion of intrinsic simulation between deterministic cellular automata, to the non-deterministic and stochastic settings. Although the intrinsic simulation relation is shown to become undecidable in dimension two and higher, we provide explicit tools to prove or disprove the existence of such a simulation between any two given stochastic cellular automata. Those tools rely upon a characterization of equality of stochastic global maps, shown to be equivalent to the existence of a stochastic coupling between the random sources. We apply them to prove that there is no universal stochastic cellular automaton. Yet we provide stochastic cellular automata achieving optimal partial universality, as well as a universal non-deterministic cellular automaton.

13

Should we use a uniform prior in probabilistic decision making?

75%

Piegat A. , Landowsky M.

Foundations of Computing and Decision Sciences

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2010

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tom Vol. 35, No. 1

43--61

EN

In probabilistic decision-making and diagnostics problems solved with the use of Bayes' theorem and in Bayes' networks if a priori distribution of probability density is not known the uniform distribution is assumed to determine the working, approximate solution of the problem. However, in many practical problems experts possess some qualitative knowledge about a priori distribution, e.g. the distribution is unimodal (one maximum) or it is unimodal right-asymmetric one, etc. It was explained in the paper that in such cases we need not unconditionally use the uniform distribution but we may use other types of distributions which better correspond to our qualitative knowledge and to the reality. However, to determine a priori distribution compatible with our qualitative knowledge we have to calculate the approximate, average, limit distribution the AAL- distribution of an infinitely large number of all possible distributions that possess the given qualitative feature, e.g., which are unimodal and right-asymmetrical ones. Is it possible at all? In the paper it was shown that it is possible if a special method conceived by one of the authors, the method of event-granulation diminution (GD-method) is applied. With this method the Readers themselves can determine their own limit distribution of all possible distributions which possess required qualitative features. The paper gives 3 such distributions determined by one of the authors that can directly be used in problems. It was also shown that the uniform distribution itself is the average, limit distribution of an infinite number of all possible distributions. According to the authors' knowledge the presented concept of the average, safe distribution is new in the scientific literature.

14

Probabilistic Constructions of Computable Objects and a Computable Version of Lovász Local Lemma

75%

Rumyantsev A. , Shen A.

Fundamenta Informaticae

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2014

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tom Vol. 132, nr 1

1--14

EN

A nonconstructive proof can be used to prove the existence of an object with some properties without providing an explicit example of such an object. A special case is a probabilistic proof where we show that an object with required properties appears with some positive probability in some random process. Can we use such arguments to prove the existence of a computable infinite object? Sometimes yes: following [8], we show how the notion of a layerwise computable mapping can be used to prove a computable version of Lovász local lemma.

15

From Constructivism to Logic Programming : an Homage to Mario Ornaghi

75%

Ferrari M. , Fiorentini C. , Momigliano A.

Fundamenta Informaticae

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2018

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tom Vol. 161, nr 1/2

1--7

EN

In this brief note, we outline Mario Ornaghi’s contributions to the field of computational logic to celebrate his 70th birthday.

16

Logic-based Verification of the Distributed Dining Philosophers Protocol

75%

Delzanno G.

Fundamenta Informaticae

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2018

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tom Vol. 161, nr 1/2

113--133

EN

We present a logic-based framework for the specification and validation of distributed protocols. Our specification language is a logic-based presentation of update rules for arbitrary graphs. Update rules are specified via conditional rewriting rules defined over a relational language. We focus our attention on unary and binary relations as a way to specify predicates over nodes and edges of a graph. For the considered language, we define assertions that can be applied to specify correctness properties for arbitrary configurations. We apply the language to model the distributed version of the Dining Philosopher Protocol. The protocol is defined for asynchronous processes distributed over a graph with arbitrary topology. We propose then validation methods based on source to source transformations and deductive reasoning. We apply the resulting method to provide a succint correctness proof of the considered case-study.

17

Ryzyko wdarć wody w kopalniach węgla kamiennego

75%

Rogoż M. , Frolik A.

Przegląd Górniczy

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1999

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tom T. 55, nr 12

5-11

PL

Analiza rynku uaktywnienia zagrożenia wodnego w podziemnej kopalni węgla kamiennego została przeprowadzona w warunkach stosowanej w polskim górnictwie węglowym prewencji, dotyczy ona zatem ryzyka resztkowego istniejącego pomimo prewencji. Przedstawiono propozycję dotyczącą sposobu obliczania prawdopowdobieństwa wdarć wody do kopalń i na podstawie danych dotyczących wdarć zistniałych w ostatnim 25-leciu określono prawdopodobieństwo wystąpienia wdarć w okresie najbliższych pięciu lat. Ustalono cztery kategorie skutków wdarć wody do kopalń, przypisując im odpowiednie wartości wyrażone w złotych i obliczono prawdopodobieństwa wdarć o skutkach zaliczonych do poszczególnych kategorii. Określono maksymalną wartość prawdopodobieństwa wdarcia w przeliczeniu na jednego pracownika dołowego i stwierdzono ,że mieści się ono w granicach ryzyka akceptowalnego.

EN

Analysis of activation of water hazard in an uderground hard coal mine has been carried out under circumstances of prevention applied in Polish coal mining so it refers to the residual risk existing in spite of prevention. A proposal reffering to water inrush probability calculation way is presented and probability of water inrushes occurence in coming five years is determined basing on the data on water inrushes ahich occurred i nthe last 25 years. Four categories of results of water inrushes into mines have been set assigning to them appropriate values expressed in zlotys (PLN-the Polish currency) and probabilities of water inrushes with results numbered among particular categories have been calculated. The maximal probability value of inrush counted per one underground worker has been determined nd it is stated that it was within the limit of the acceptable risk.

18

Ocena czasu oczekiwania na przystankach dla losowych zgłoszeń pasażerów

75%

Horbachov P. , Chyghyk V.

Zeszyty Naukowo-Techniczne Stowarzyszenia Inżynierów i Techników Komunikacji w Krakowie. Seria: Materiały Konferencyjne

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2014

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tom Nr 1(103)

87--98

PL

W artykule zdefiniowano problem i przedstawiono ujęcie analityczne modelowania obliczeń czasu oczekiwania na przystanku, gdy zgłoszenie pasażera na przystanek na charakter losowy. Rozważany jest szeroki zakres zmienności przebiegów tras linii – poczynając od przyjęcia pełnej zgodności interwałów kursowania linii w rozkładach jazdy do całkowicie losowych odjazdów pojazdów z przystanków pośrednich. Zostały również porównane doświadczalne i teoretyczne oszacowania czasów oczekiwania na przystankach dla podstawowych linii.

EN

The paper presents the problem definition and analytical modeling for waiting time calculation in urban transit system when passengers arrive at a transit stop randomly. The wide range of variants of the urban transit routes operation services is considered – from full implementation of the identical headways schedule to the completely random departure time of transport units from a terminal. Also, experimental and theoretical estimates of a passenger waiting time for a certain route are compared.

19

Geneza prawdopodobieństwa

75%

Heller M.

Zagadnienia Filozoficzne w Nauce

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2006

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nr 38

61-75

PL

After briefly reviewing classical and quantum aspects of probability, basic concepts of the noncommutative calculus of probability (called also free calculus of probability) and its possible application to model the fundamental level of physics are presented. It is shown that the pair (M, *), where M is a (noncommutative) von Neumann algebra, and a state on it, is both a dynamical object and a probabilistic object. In this way, dynamics and probability can be unified in noncommutative geometry. Some philosophical consequences of such an approach are indicated.

20

Applying the idea of fusionism in the probability theory

75%

Major M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2007

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tom Vol. 12

69-76

EN

The solutions presented in this paper may serve as an illustration of the principle of internal integration, know as the idea of fusionism. In the paper we consider some problem. From an urn containing b white balls and c black ones are selected simultaneously some balls. If the balls are of the same colours one of the players wins, otherwise the other player is the winner. For which values of b and c is the game fair?