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1
Content available remote Self-stabilisation of Cellular Automata on Tilings
Fatès Nazima, Marcovici Irèneb, Taati Siamak
Fundamenta Informaticae
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2022
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Vol. 185, nr 1
27--82
EN
Given a finite set of local constraints, we seek a cellular automaton (i.e., a local and uniform algorithm) that self-stabilises on the configurations that satisfy these constraints. More precisely, starting from a finite perturbation of a valid configuration, the cellular automaton must eventually fall back into the space of valid configurations where it remains still. We allow the cellular automaton to use extra symbols, but in that case, the extra symbols can also appear in the initial finite perturbation. For several classes of local constraints (e.g., k-colourings with k ≠ 3, and North-East deterministic constraints), we provide efficient self-stabilising cellular automata with or without additional symbols that wash out finite perturbations in linear or quadratic time, but also show that there are examples of local constraints for which the self-stabilisation problem is inherently hard. We note that the optimal self-stabilisation speed is the same for all local constraints that are isomorphic to one another. We also consider probabilistic cellular automata rules and show that in some cases, the use of randomness simplifies the problem. In the deterministic case, we show that if finite perturbations are corrected in linear time, then the cellular automaton self-stabilises even starting from a random perturbation of a valid configuration, that is, when errors in the initial configuration occur independently with a sufficiently low density.
2
Content available remote Periodic Orbits and Dynamical Complexity in Cellular Automata
Dennunzio A., Di Lena P., Formenti E., Margara L.
Fundamenta Informaticae
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2013
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Vol. 126, nr 2-3
183--199
EN
We investigate the relationships between dynamical complexity and the set of periodic configurations of surjective Cellular Automata. We focus on the set of strictly temporally periodic configurations, i.e., the set of those configurations which are temporally but not spatially periodic for a given surjective automaton. The cardinality of this set turns out to be inversely related to the dynamical complexity of the cellular automaton. In particular, we show that for surjective Cellular Automata, the set of strictly temporally periodic configurations has strictly positive measure if and only if the cellular automaton is equicontinuous. Furthermore, we show that the set of strictly temporally periodic configurations is dense for almost equicontinuous surjective cellular automata, while it is empty for the positively expansive ones. In the class of additive cellular automata, the set of strictly temporally periodic points can be either dense or empty. The latter happens if and only if the cellular automaton is topologically transitive. This is not true for general transitive Cellular Automata, where the set of of strictly temporally periodic points can be non-empty and non-dense.
3
Content available Metody dynamiki symbolicznej w ocenie aktywności baroreceptorów po zabiegach kriostymulacji ogólnoustrojowej
Buszko K., Weber P., Zalewski P., Tafil-Klawe M., Klawe J., Pepłowski P.
Acta Bio-Optica et Informatica Medica. Inżynieria Biomedyczna
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2013
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Vol. 19, nr 3
123--132
PL
Celem pracy jest przedstawienie zastosowania metod dynamiki symbolicznej do oceny aktywności baroreceptorów u zdrowych osób poddanych zabiegowi kriostymulacji ogólnoustrojowej. Ilościowa analiza odruchu z baroreceptorów możliwa była dzięki rejestracji sygnału elektrokardiograficznego (EKG) i ciśnienia systolicznego (sBP) w badaniu uczestników eksperymentu systemem Task Force Monitor. Zakodowane wartości odległości pomiędzy kolejnymi załamkami R w zapisie EKG (RRI) i wartości sBP wykorzystano do definicji aktywności baroreceptorów, a jej ilościowa ocenę przeprowadzono, uwzględniając częstości występowania sekwencji symboli mających odniesienie do aktywności baroreceptorów. Analiza wyznaczonych częstości przed i po zabiegu kriostymulacji ogólnoustrojowej pokazała, że częstość występowania sekwencji symboli związanych z odruchem z baroreceptorów jest istotnie mniejsza po zabiegu kriostymulacji. W pracy zaproponowano również modyfikację wprowadzonej definicji, która uwzględnia korekcję błędów pomiaru i pozwala na szacowanie czułości odruchu z baroreceptorów.
EN
The paper presents application of symbolic dynamics methods to evaluate baroreflex activity in healthy men undergoing whole-body cryotherapy. A quantitative analysis was performed by using electrocardiogram signal (ECG) and systolic blood pressure signal (sBP). Both signals have been recorded by Task Force Monitor experimental system. The values of successive R-R intervals in ECG signal (RRI) and sBP values were used to define the baroreceptors activity. Quantitative evaluation of baroreceptors activity was carried out by introducing the frequencies of symbols sequences in both signals. Analysis of the designated frequencies before and after the treatment of whole-body cryostimulation showed that the incidence of the sequences of symbols associated with the baroreceptor reflex is significantly lower after whole-body cryostimulation. The paper also proposes a modified definition of baroreceptors activity that considers a measurement error and allows the estimation of baroreflex sensitivity.
4
Content available remote From One-dimensional to Two-dimensional Cellular Automata
Dennunzio A.
Fundamenta Informaticae
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2012
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Vol. 115, nr 1
87-105
EN
We enlighten the differences between one-dimensional and two-dimensional cellular automata by considering both the dynamical and decidability aspects. We also show a canonical representation theorem for the slicing constructions, a tool allowing to give the 2D version of important 1D CA notions as closing and positive expansivity and lift 1D results to the 2D settings.
5
Content available remote Algorithmic Approach to Devaney Chaos in Shift Spaces
Oprocha P.
Fundamenta Informaticae
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2008
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Vol. 87, nr 3-4
435-446
EN
Among the class of sofic shifts Devaney chaos is equivalent to topological transitivity. The aim of this paper is to study possibilities of detection of this phenomena when a right-resolving graph presentation of a sofic shift is given. We show that Devaney chaos detection is co-NP-hard problem and point out some possible improvements of algorithms known from the literature.
6
Content available Mieszanie topologiczne w dyskretnych układach dynamicznych - krótkie wprowadzenie
Oprocha P.
Automatyka / Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie
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2008
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T. 12, z. 1
77-88
PL
Badając dynamikę procesów zmieniających się w czasie, zazwyczaj mamy do czynienia z dwoma głównymi kierunkami badań: poszukujemy regularności (stabilność) oraz staramy się zrozumieć zachowania nieregularne (chaos). Intuicyjnie, nieprzewidywalność wiąże się z pewnym rodzajem "mieszania" w przestrzeni stanów. Celem artykułu jest prezentacja możliwości opisu tego zjawiska w oparciu o pojęcia topologiczne.
EN
When we study processes evolving in time, we usually consider two directions of research: we look for regularity (stability) of dynamics and we try to understand irregular behavior (chaos) which is present in the system. Intuitively, unpredictability of dynamics is related to some kind of "mixing" in the phase space. The aim of this article is to present notions which try to describe this phenomena on a basis of topological approach.
7
Content available remote A numerical view on topological transitivity and mixing for symbolic dynamics
Jabłoński D., Oprocha P.
Demonstratio Mathematica
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2007
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Vol. 40, nr 1
229-238
EN
The aim of this paper is to give some algorithms detecting topological transitivity, mixing and other properties of subshifts of finite type.
8
Content available remote Computing forbidden words of regular languages
Béal M-P., Crochemore M., Mignosi F., Restivo A., Sciortino M.
Fundamenta Informaticae
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2003
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Vol. 56, nr 1,2
121-135
EN
We give a quadratic-time algorithm to compute the set of minimal forbidden words of a factorial regular language. We give a linear-time algorithm to compute the minimal forbidden words of a finite set of words. This extends a previous result given for the case of a single word only. We also give quadratic-time algorithms to check whether a regular language is factorial or anti-factorial.
9
On the topological entropy of green interval maps
Bobok J.
Journal of Applied Analysis
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2001
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Vol. 7, nr 1
107-112
EN
We investigate the topological entropy of a green interval map. Defining the complexity we estimate from above the topological entropy of a green interval map with a given complexity. The main result of the paper — stated in Theorem 0.2 — should be regarded as a completion of results of [4].
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