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DE
Im vorliegenden Aufsatz wird die Frage nach der potentiellen Implementierung der rekursiven AnBn--Strukturen durch den Mechanismus der Satzverarbeitung behandelt. Es wird darauf hingewiesen, dass die einfachste Verarbeitungsstrategie, wo die adjazenten Sequenzen von zwei Kategorien A und B aufgezählt und verglichen werden, wegen der asymmetrischen Struktur der zentral-eingebetteten syntaktischen Abhängigkeiten keine Anwendung bei der kognitiven Verarbeitung finden kann.
EN
This article is devoted to the issue of the potential implementation of recursive AnBn structures by the sentence-processing mechanism. Worth noting is the fact that the simplest processing strategy, whereby categories A and B are listed and compared, cannot be applied to the cognitive processing of asymmetric structures of centrally embedded syntactic dependencies.
EN
The article investigates the problems of the investment management digital transformations at the enterprise, where the instrumental basis based on the system economic theory and integrated IT risk management theory are allocated. The purpose of the study is to develop a recursive and convergence methodology of the investment management of the enterprise digitalization processes. The components of the process of investment digitalization of enterprises are structurally reflected and a deterministic 5-component model of developing a recursive and convergence management methodology based on the digital economy is formed. It is determined that the recursive and conversion methodology is based on the understanding of investment management digital transformations at an enterprise as a complex system, characterized primarily by the diversity and heterogeneity of the constituent elements, numerous internal and external connections, which causes a variety of their interaction, changes in the composition and state of the system. The recursive model provides management of the investment of digitalization in the enterprise as a sequential transition between processes of one level only after all the cycles provided for the current process are implemented. However, such a coherent sequence is possible at the expense of effective information support of each process, which should be implemented on a convergence basis. The precondition for its implementation in the field of digital technologies is civilizational development, consequences of globalization and digitalization.
EN
The article is  a  reconnaissance. The  author of  the  paper aims at  providing a  comparison of  mathematical and empirical results of  research on the  evolution of  language. The  content of  the  paper focuses on issues relating to the emergence of  language. The author seeks to answer the question: What differentiates human and animal communication?
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Content available remote Continued fractions and polynomials related to hyperbinary representations
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EN
Schinzel recently showed that the nth Stern polynomial of Klavžar et al. is the numerator of a certain finite continued fraction. This was subsequently extended by Mansour to q-Stern polynomials. We extend these results further to a 2-parameter bivariate analogue of the sequence of Stern polynomials which arise naturally in the characterization of hyperbinary representations of a given integer. In the process we define a class of companion polynomials with which we can determine the denominators of the continued fractions in question.
EN
We model infinite regress structures — not arguments — by means of ungrounded recursively defined functions in order to show that no such structure can perform the task of providing determination to the items composing it, that is, that no determination process containing an infinite regress structure is successful.
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Content available remote Some Undecidable Statements of Quite Simple Mathematics
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EN
There are well known problems which are not decidable: halting problem, provability in PA, being a first order tautology, and others. Since all these problem deal with notions like computability and provability, they are beyond the scope of “usual” mathematics - mathematical analysis, for instance. Here, we will show a bunch of examples of simple undecidable statements of such mathematics.
EN
The paper applies an interdisciplinary perspective to a fictional text showing that fractals as mathematical models are a powerful tool for conceptualizing life experience in biographical narratives. The multilevel construction of Chatterton by Peter Ackroyd is explored on the basis of fractal metaphor theory. This research focuses on the LIFE IS A STORY conceptual fractal metaphor which is built up on analogical mappings, mental space connections, and blends. The fractal model of metaphor in biographical narrative, which is assigned to the formula LIFE IS A STORY f (1) + f (2) + f (3) + … + f (n), contains the mental space of the intentional source domain story, which provides a way to structure the understanding of the limiting target domain of the concept life. Fractal metaphors aim at making the conceptual metaphor flexible and dynamic, renewing its ability of self-development and self-perfection, transforming itself into one of the means of changeable conceptualization of reality.
EN
The focus of the authors’ interest is recursion, serving as one of the principles of de-sign and existence of hierarchical systems. Its features are among others the infinite self-transformation associated with the return and playback based on the algorithm of its own unfolding, by analogy, which ensures the movement inward, on the basis of which complication of the system takes place. This method is quite common in cultural space, giving rise to a situation of multiplicity of values and interpretations.
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EN
It is a fairly hard task TO design hardware that implements recursive computations using a repetitive style, which is supported in mast hardware description languages suck as VHDL and Verilog. In this paper we show how one can very elegant and rapidly yield hardware models that implement recursive computations. The hardware model is expressed in the most popular hardware description language VHDL As a case study, we implement the Karatsuba-Ofman's divide-and-conquer multiplication algorithm. The generated hardware is efficient in terms of response time and compact in terms of hardware area.
EN
This study explores the amount of lexical innovation (hapax legomena or non repeated words) during a question-led (i.e. semi spontaneous) spoken word production task. Native adult non-impaired Spanish speakers (n = 8) were asked the same question 8 times with an interval of one day each; 4 participants answered the stimulus question in L1 and 4 did so in English. Participants were also given specific instructions to avoid conscious verbal monitoring, specially trying to evade or emphasise word repetition. Their responses were not time controlled. Quantitative word analysis reveals all subjects have recourse to an increased percentage of lexical recycling (vocabulary repetition), idiomatic and phraseology recurrence, as well as a limited percentage of lexical innovation or hapax. These findings are of interest to foreign language acquisition research, curricula design and idiolect re-encoding because they suggest that thematic-bound unities of thought elicited in word production are stable and comprise a major portion of all verbal content. These results may call into question the pertinence and efficacy of traditional syllabi focusing on linguistic points rather than on the role of recycling thematic-dependent learners’ verbal repertoire.
EN
There are two major theories about the origin of human syntax: evolutionary and catastrophic, the latter appears more probable on theoretical and empirical grounds, the most serious reason being the problem with imagining the intermediate stages between protosyntax and full-blown syntax (Bickerton 1998). The “missing link” is recently often associated with recursion, a sole element of human syntax considered specifically human and specifically linguistic. Some accounts associate this trigger with a subpart of recursion, either operation Merge or a subpart of Merge, operation Label (Hornstein 2009) which by breaking the initial symmetry provides a sine qua non condition for asymmetric syntax in terms of endocentricity, phrase structure and, consequently, recursive embedding. My hypothesis is that assuming the catastrophic scenario, more than one catastrophic event must have happened in a very short time. Given that human vocal tract and human phonetics and phonology have several unique features compared with Great Apes (hierarchical but non-recursive structure, speech imitation skills, abundant use of formants, lack of laryngeal air sacks in the vocal tract) and given that the phonological form constitutes the interface of the human syntax, the mere addition of Label to the already existing operations of the protolanguage is insufficient, since (1) it does not account for the emergence of the phonologically interfaced syntax, (2) it fails to explain the indisociability of non-syntactic elements of language in terms of phonology, semantics and syntax as evidenced in Jackendoff (2011). Consequently, I assume that human language emerged as a result of at least two catastrophic processes: catastrophic emergence of phonetics and catastrophic emergence of syntax accompanied by the rapid expansion of the lexicon, the latter possibly as a result of a quantitative rather than qualitative development. The emergence of human phonology might have occurred gradually, but as a result of the catastrophic emergence of phonetics.
EN
One of the main problems in mobile robotics is obtaining knowledge about the surroundings from sensor data. This article describes attempts of fast 3D observed scene feature extraction based on information from a two-camera stereovision system. The additional assumption is that the robot vision system, dedicated to the navigation purpose, should be able to work with low quality images. The power of recursive techniques in the implementation of real-time working algorithms is presented in regard to standard area-based stereo matching but mainly focused on the new recursive algorithm for characteristic object segmentation in low quality images.
PL
Artykuł opisuje próby ekstrakcji cech trójwymiarowych obserwowanej sceny na podstawie informacji, pochodzącej z dwukamerowego systemu stereowizyjnego robota mobilnego. Jako dodatkowe założenie przyjęto, że system wizyjny robota, przeznaczony do celów nawigacji, powinien działać bazując nawet na obrazach niskiej jakości, która często jest efektem braku sztywności układu kamer podczas ruchu robota. Tematem wiodącym jest ukazanie siły technik rekurencyjnych, pozwalających na implementację algorytmów pracujących w czasie rzeczywistym. Zaprezentowano zasadę stosowania rekurencji do eliminacji obliczeń Redundantnych w algorytmach stereoskopowego dopasowywania obszarami oraz nowy algorytm rekurencyjny opracowany w celu wychwytywania obiektów charakterrystycznych w obrazach niskiej jakości. Algorytm, po wykonanej filtracji LoG, pozwala na wykrywanie obiektów dużych oraz grup małych obiektów, zależnie od ustawionego progu. Ponadto, zastosowanie algorytmu nie wymaga użycia dodatkowych metod usuwania szumów z obrazu. Opracowana metoda, przeznaczona do przygotowania obrazów stereowizyjnych do dalszej analizy, pozwala zachować w postaci obiektów większą ilość charakterystycznych cech widocznych na obrazie. Wyodrębnione obiekty mają umożliwić dalszą rekonstrukcję sceny 3D.
15
Content available Matrix black box algorithms - a survey
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EN
The implementations of matrix multiplication on contemporary, vector-oriented, and multicore-oriented computer hardware are very carefully designed and optimized with respect to their efficiency, due to the essential significance of that operation in other science and engineering domains. Consequently, the available implementations are very fast and it is a natural desire to take advantage of the efficiency of those implementations in other problems, both matrix and nonmatrix. Such an approach is often called a black box matrix computation paradigm in the literature on the subject. In this article, we gathered a broad series of algorithms taking advantage of the efficiency of fast matrix multiplication algorithms in other mathematical and computer science operations.
EN
The known standard recursion methods of computing the full normalized associated Legendre functions do not give the necessary precision due to application of IEEE754-2008 standard, that creates a problems of underflow and overflow. The analysis of the problems of the calculation of the Legendre functions shows that the problem underflow is not dangerous by itself. The main problem that generates the gross errors in its calculations is the problem named the effect of “absolute zero”. Once appeared in a forward column recursion, “absolute zero” converts to zero all values which are multiplied by it, regardless of whether a zero result of multiplication is real or not. Three methods of calculating of the Legendre functions, that removed the effect of “absolute zero” from the calculations are discussed here. These methods are also of interest because they almost have no limit for the maximum degree of Legendre functions. It is shown that the numerical accuracy of these three methods is the same. But, the CPU calculation time of the Legendre functions with Fukushima method is minimal. Therefore, the Fukushima method is the best. Its main advantage is computational speed which is an important factor in calculation of such large amount of the Legendre functions as 2 401 336 for EGM2008.
PL
Celem artykułu jest przeprowadzenie analizy możliwości wykorzystania Warstwy Tranzycji Petriego w adaptacyjnych regulatorach neuronowo-rozmytych z rekurencjami zwiększającymi wymiar bazy reguł regulatora. Zastosowanie rekurencji prowadzi do zmiany funkcji sterującej regulatora, co przy odpowiednim doborze rekurencji oraz parametrów regulatora prowadzi do poprawy wskaźników jakości sterowania. Niestety w przypadku regulatorów N-F z rekurencjami od wyjścia do wejścia lub innymi rozwiązaniami powodującymi zwiększenie liczby wejść regulatora, a tym samym wymiaru bazy reguł znacząco wzrasta złożoność obliczeniowa rozważanych algorytmów. Zastosowanie WTP pozwala na obniżenie kosztu numerycznego algorytmu. Jednoczesne zastosowanie zarówno rekurencji jak i WTP pozwala na jednoczesną poprawę wskaźników jakości sterowania bez zwiększania, a nawet przy zmniejszeniu kosztu numerycznego algorytmu. Rozważania teoretyczne zostały poparte badaniami symulacyjnymi jak i eksperymentalnymi. Zaproponowano także metodologię doboru nastaw regulatora.
EN
This article aims to analyze the possibility of using Petri Transition Layer in the adaptive neuro-fuzzy controllers with recursions increasing number of controllers rules. The use of recursion leads to a change of control function, and an appropriate selection of recursion and controller parameters leads to improved control quality indicators. Unfortunately, in the case of NF controllers with output to input recursion or other solutions that cause an increase in the number of controller inputs, the dimension of the controllers rules base significantly increases the computational complexity of the algorithm. At the same time the use of PTL reduces the numerical cost of the algorithm. Simultaneous use of both recursion and PTL enables simultaneous improvements in quality control without increasing, and even while reducing the cost of numerical algorithm. Theoretical considerations have been supported by studies and experimental simulation. Also methodology of tuning of controller parameters was proposed.
EN
This paper addresses the problem of using functional programming (FP) languages for research and educational purposes. In order to identify the problems associated with the use of FP languages such as Erlang, an experiment consisting of two surveys was performed. The first survey was anonymous and aimed at establishing whether the participants prefer object-oriented or functional coding. The second one was a survey made after the students finished an Erlang course. The results of these two surveys demonstrate that functional programming is underrated with no apparent reasons. Possible steps to address this problem are suggested.
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PL
Od kilkunastu lat na łamach zagranicznych czasopism toczy się debata wokół rekursywności ludzkich procesów umysłowych. Jej inicjator i główny propagator terminu „rekursja” (recursion) to Noam Chomsky. Ogranicza on jej występowanie do płaszczyzny ludzkiego języka i przypisuje cechę rekursywności (recursive property) składni tzw. języka umysłu. Wywołało to mocny sprzeciw badaczy upatrujących przejawów rekursji także na innych płaszczyznach ludzkiego funkcjonowania, jak komunikacja, teoria umysłu, składnia dopełnieniowa czy pragmatyka. Tekst przedstawia argumenty przemawiające za możliwością rozpatrywania rekursji jako mechanizmu wspólnego wszystkim wspomnianym płaszczyznom, pod warunkiem przyjęcia rozwojowej perspektywy, uwzględniającej dynamikę i sekwencyjność zachodzących w nich procesów i zmian.
EN
For nearly twenty years there has been an ongoing debate in international journals concerning the recursiveness of human mental processes. The main instigator of the debate and at the same time the main exponent of the term “recursion” is Noam Chomsky. According to him, recursion is an exclusive property of the syntax of the so-called “internal language of mind” (I-language). This conclusion has been contested by researchers claiming that recursion can also be observed in: communication, theory of mind, the syntax of complementation, or pragmatics. The article presents some arguments in favor of understanding recursion as a common ground of all the above phenomena as long as they are analyzed from a developmental perspective, with the dynamics and sequentiality of the constantly occurring processes and changes taken into account.
20
Content available Entropy paradigm in the theory of hierarchical
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EN
It is proposed a variant of the theory of active hierarchical systems. The variant is based upon the subjective entropy maximum principle [3, 4], which, from the formally-mathematical point of view, coincides with the principle of Jaynes-Gibbs [1, 2]. The mentioned principle rests upon the notion of subjective entropy, the principle of an „individual bearer”, and scheme of preferences aggregation; and, in this sense, the principle is an independent one. A model of preferences hierarchy is built for the distributions of objects and ratings preferences. It is used a property of the hierarchical additivity of entropy in the Shannon’s form. The theory of conflicts, as conflicts of preferences distributions, is developed on the basis of this model. It is proposed a classification of conflicts that reflects to a significant degree the existing knowledge in this field. A conflict transformation from one phase into another is connected with the overcoming of some certain entropy thresholds. It is considered the dynamics of conflicts, intrapersonal and interpersonal conflicts. The given theory, in our opinion, is an actual one at the study of the active systems safety problems including the problem of flight safety since an aviation transportation system, as a whole, and the system of „Aircraft-Pilot-Environment”, in particular, are active systems. The formalization developed here is the effective means of the problems solutions where the active system is in the situation of a choice from a certain set of alternatives. If we look closer, we will find that practically at each aviation incident that or another conflict takes place. We will try to disclose the term „active system” later [6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 18]. Here we will just refer to the statement by the philosopher Berdiayev N.A. [15] „The source and sense of Russian communism”: „The source of motion is inside, but not in the outside thick, coming from the outer space, as it is thought by the mechanical materialism, real freedom is intrinsic to the matter, there is a source of activity in the matter’s entrails/depth, the source changes the environment”. This point of view unisons with that authors think of. The task, in the given case, is to interpret it in the terms of the entropy paradigm, meaning the subjective entropy.
PL
W publikacji zaproponowano pewien wariant teorii hierarchicznych aktywnych systemów. Wariant ten oparty jest na zasadzie maksymalnej subiektywnej entropii [3, 4], która z punktu formalnie matematycznego, zbiega się z zasadą Jaynes-Gibbsa [1, 2].Wspomniana tu zasada opiera się na pojęciu subiektywnej entropii, na zasadzie „indywidualnym posiadaniu” i schemacie agregacji preferencji; i, w tym sensie, zasady te są niezależne. Model hierarchii preferencji jest zbudowany na rozkładzie przedmiotów i ocen preferencji. Stosowana jest zasada hierarchicznej addytywności entropii w postaci Shannona. Teoria konfliktów, konflikty rozkładów preferencji, jest opracowana na podstawie tego modelu. Zaproponowano klasyfikację konfliktów, które w znacznym stopniu odzwierciedlają istniejącą wiedzę w tej dziedzinie. Transformacja konfliktu z jednej fazy do drugiej jest związana z przezwyciężaniem pewnych określonych progów entropii. W pracy zauważono, że dynamika konfliktów zewnętrznych – niepersonalnych zależy od konfliktów personalnych – międzyludzkich. W przedłożonej teorii, zdaniem autorów, jest aktualnym problem wpływ na badania bezpieczeństwa aktywnych systemów oraz problemów bezpieczeństwa lotu od systemu transportu lotniczego, jako całość, oraz systemu „samolot-Pilot-środowisko”, w szczególności. Formalizacja opracowana w pracy jest skutecznym środkiem do rozwiązania problemów, w których system aktywny znajduje się w sytuacji wyboru decyzji z pewnego zbioru alternatyw. Jeśli przyjrzymy się bliżej, okaże się że ma to miejsce praktycznie w każdym wypadku lotniczym lub w innym konflikcie. Postaramy się wyjaśnić termin „system aktywny” w oparciu o [6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 18] w kolejnych pracach. Tutaj przytoczymy tylko terminy odnoszące się do pracy filozofa Berdiayev N. A. [15] „Źródło i sens rosyjskiego komunizmu”: „Źródło ruchu jest w środku, a nie na zewnątrz, nie pochodzi z kosmosu, jak myśl, przez materializm mechaniczny, prawdziwa wolność jest nierozerwalnie związana z materią, jest źródłem aktywności w tej sprawie z wnętrza zmienia środowisko”. Ten punkt widzenia jest jednolity z twórcą myśli. Zadanie w danym przypadku jest takie, aby interpretować je w warunkach paradygmatu entropii, czyli subiektywnej entropii.
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