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PL
W ostatnich dziesięcioleciach słowo fraktal na dobre weszło do naszego leksykonu i popkultury. Zapewne każdy słyszał o bardzo skomplikowanych wzorach geometrycznych, przyciągających wzrok misternymi kształtami oraz pełną paletą zmieniających się kolorów. Walory estetyczne fraktali niewątpliwie przykuwają uwagę nie tylko projektantów mody czy artystów, ale również osób, które nie są bezpośrednio związane ani z matematyką, ani z grafiką komputerową. Estetyka i piękno skomplikowania tych obiektów geometrycznych, których tworzenie opiera się na bardzo prostych wzorach rekurencyjnych, to nie wszystko, co one potrafią zaoferować. Przez swoją stosunkowo krótką historię fraktale zdążyły zaistnieć w wielu dziedzinach nauki i techniki, co więcej, stać się niezastąpionymi narzędziami w tych dziedzinach i uruchomić całe mnóstwo nowych możliwości.
EN
In recent decades the word fractal has entered our lexicon and pop culture for good. Everyone has probably heard about the highly complicated geometric patterns that catch the eye with their masterful shapes and a full palette of changing colours. The aesthetic values of fractals undoubtedly attract the attention not only of fashion designers and artists, but also of people who are not directly involved in either mathematics or computer graphics. The aesthetics and beauty of the complexity of these geometric objects, whose creation is based on very simple recursive patterns, is not all they can offer. Throughout their relatively short history, fractals have managed to appear in many fields of science and technology and, what is more, to become indispensable tools in these fields and to set in motion a whole host of new possibilities.
EN
This paper is devoted to simulations the networks with self-similar traffic. The self-similarity in the stochastic process is identified by calculation of the herst parameter value. Based on the results, received from the experimental research of network perfomance, we may conclude that the observed traffic in real-time mode is self-similar by its nature. Given results may be used for the further investigation of network traffic and work on the existing models of network traffic (particularly for new networks concepts like IoT, WSN, BYOD etc) from viewpoint of its cybersecurity. Furthermore, the adequacy of the description of real is achieved by complexifying the models, combining several models and integration of new parameters. Accordingly, for more complex models, there are higher computing abilities needed or longer time for the generation of traffic realization.
EN
The implementation of wireless data transmission technology and, in turn, increasing the efficiency of the functioning of the automatic control systems of the aviation gas turbine engines by determining their self-similarity of operating modes will ensure the mobility of control and diagnostics by the nodes of the gas turbine engine (GTE), the definition of resources and their use, as well as the reduction of the cost of their maintenance. The paper deals with the issue of the appropriate location of the wireless module operation of the electronic control system within the fractal and multifractal wavelet models of the individual components of the telecommunication IEEE 802.15.4 traffic and the transmission of information through the switch node of the packet switching, which allows conducting the research with the methods involving choice of parameters of telecommunication networks under the conditions of precisely and approximate given input data. The studies on the influence of mono and multifractality of network traffic for the characteristics of queuing on an overloaded mobile communication system server were conducted and the recommendations for IEEE 802.15.4 communication channels electronic turbo propeller fan engine control system was proposed.
4
Content available Variance-to-mean ratio in ICT traffic
EN
In this paper the ICT network traffic analysis from the point of view of the varianceto- mean ratio is presented and discussed. The analysis is based on the real traffic captured at the West Pomeranian University of Technology. The results of averaged traffic analysis over different time scales shows the relation between variance-to-mean ratio and the level of self-similarity, which in turn affects the quality of service in ICT networks.
EN
Self-similarity analysis and anomaly detection in networks are interesting fields of research and scientific work of scientists around the world. Simulation studies have demonstrated that the Hurst parameter estimation can be used to detect traffic anomaly. The actual network traffic is self-similar or long-range dependent. The dramatic expansion of applications on modern networks gives rise to a fundamental challenge to network security. The Hurst values are compared with confidence intervals of normal values to detect anomaly in VoIP.
EN
The earthquake inter-event time distribution is studied, using catalogs for different recent aftershock sequences. For aftershock sequences following the Modified Omori’s Formula (MOF) it seems clear that the inter-event distribution is a power law. The parameters of this law are defined and they prove to be higher than the calculated value (2 – 1/p). Based on the analysis of the catalogs, it is determined that the probability densities of the inter-event time distribution collapse into a single master curve when the data is rescaled with instantaneous intensity, R(t; Mth), defined by MOF. The curve is approximated by a gamma distribution. The collapse of the data provides a clear view of aftershock-occurrence self-similarity.
7
Content available remote Analiza statyczna pracy sieci komputerowej w środowisku LabVIEW
PL
Analiza ruchu sieciowego oraz metod wykrywania nieprawidłowości pracy urządzeń sieciowych stanowi ciekawy problem dla analityków badających sieci komputerowe. Poprawna interpretacja anomalii oraz odpowiednia reakcja na nie może poprawić jakość działania sieci, zapobiec awarii lub skrócić jej czas. W artykule przedstawiono oryginalną aplikację utworzoną w środowisku LabVIEW, z zaimplementowanymi algorytmami do wyznaczania współczynnika Hursta, będącego miarą samopodobieństwa i określenia zależności długoterminowych oraz multifraktalności ruchu sieciowego. Celem aplikacji było zaimplementowanie znanych metod wyznaczania współczynnika Hursta m.in. metody statystyki R/S, metody wartości bezwzględnej oraz zagregowanej wariancji - jako aparatu statystycznego do określenia cech ruchu sieciowego. W badaniach wykorzystano wirtualną sieć testową, której model utworzono w środowisku OPNET Modeler. Przeprowadzona w programie analiza statystyczna wskazała, że poziom samopodobieństwa ruchu sieciowego zawiera się w przedziale od 0,5 do 1, zaś jego wartość przybiera wyższe wartości wraz z rosnącym wypełnieniem pasma sieci. Nieprzerwany ruch sieciowy o małym natężeniu (np. ruch typu VoIP) posiada samopodobieństwo porównywalne do szumu białego równe 0,5 co zaprezentowano w artykule.
EN
Network traffic analysis and the network devices working anomaly detection methods is an interesting problem for analysts researching computer networks. Proper interpretation of the anomalies and appropriate response to it can improve the quality of the network, to prevent a failure or shorten. The paper presents an original application created in the LabVIEW environment, with implemented algorithms to determine the Hurst coefficient, which is a measure of self-similarity and determine the long-range dependencies and multifractal traffic. The aim of the application was to implement known methods of determining the Hurst coefficient, e.g. the R/S statistics method, the absolute value method and the aggregate variance method, as a statistical apparatus to determine the characteristics of network traffic. The study used a virtual test network which model was created in the OPNET Modeler environment. Carried out in the application the statistical analysis indicated that the level of network traffic self-similarity is in the range from 0.5 to 1, and it’s value becomes higher with increasing fulfillment of the network bandwidth. Uninterrupted network traffic with a low intensity (e.g. VoIP traffic type) has a self-similarity comparable to the white noise equal to 0.5 which is presented in the article.
PL
Analiza samopodobieństwa i wykrywania nieprawidłowości działania sieci stanowi interesujący problem dla naukowców na całym świecie. W artykule pokazano wykorzystanie współczynnika Hursta, jako parametru na podstawie którego można wykryć wszelkie anomalia pracy sieci. Odchylenia od wartości bazowej parametru Hursta w czasie pracy mogą sygnalizować nieprawidłowości działania. Badania mogą obejmować dowolny typ ruchu np. usługi HTTP.
EN
Self-similarity analysis and anomaly detection in networks are interesting field of research and scientific work of scientists around the world. Simulation studies have demonstrated that the Hurst parameter estimation can be used to detect traffic anomaly – the Hurst values are compared with confidence intervals of normal values to detect anomaly in few kinds of traffic: HTTP protocol, email, SSL.
9
Content available remote Long-range dependencies in quick-sort algorithm
PL
Sortowanie jest jednym z najczęstszych wykorzystywanych typów przetwarzania w systemach komputerowych. W prezentowanym podejściu sortowanie będzie rozważane jako wprowadzenie porządku w przetwarzanym zadaniu wejściowym oraz algorytm jako fizyczny system (odpowiedzialny za obliczenia). Zazwyczaj analiza zachowania dowolnego algorytmu jest realizowana w kontekście klasycznej złożoności obliczeniowej. W niniejszej pracy istnienie zależności długoterminowych w dynamice przetwarzania jest wyznaczane w oparciu o współczynnik Hurst’a.
EN
Sorting is one of the most frequently used types of processing in computer systems. In presented approach sorting will be considered as an introduction of order into processed input task and algorithm as a physical system (responsible for computations). This analysis shows how the dependencies in processed tasks can influence the behavior of algorithm (or equivalently Turing machine). Normally, analysis of any algorithm behavior is done in terms of classical computational complexity. In this paper the rate of existence of long-term correlations in processing dynamics is calculated basing on Hurst coefficient.
EN
Economic systems as complex systems are the source of many unconventional researches. The actual phenomena in complex systems have the non-scalability features and non-scalability does not exist without the power laws. This paper presents the occurrence of power series of rights and self-similarity in the distribution of national income in 2010, in terms of countries, the European Union and the Polish subregions. This means that one can study economic systems using tools of complex systems theory. This applies especially to the study of the mechanisms governing the system at the local level that generate global action.
EN
The advent and wide usage of computer networks as well as an increasing number of various network services have resulted in the fact that the network traffic has become more complex and unpredictable. These properties have become especially apparent with the appearance of high-speed data transmission technology. It is connected with the fact that one of the main quality indeces (QoS) of operation of packet transmission networks is the number of lost packets. The loss of packets results to additional network traffic and, finally, “congestions”. At high speeds of data transmission packet losses, expressed in portions of a per-cent, lead to considerable information losses. It has been shown in numerous papers devoted to the research of network traffic that the abovementioned phenomena are related to the properties of the traffic self–similarity which is mainly caused by the TCP protocol behaviour. However to date models have not been offered which adequately describe the behaviour of the communication networks of information systems and which allow to apply the whole arsenal of classic methods of analyzing nonlinear dynamic systems.
EN
Algorithms of queue management in IP routers determine which packet should be deleted when necessary. The article investigates the influence of the self-similarity on the optimal packet rejection probability function in a special case of NLRED queues. This paper describes another approach to the non-linear packet dropping function. We propose to use the solutions based on the polynomials with degree equals to 3. The process of obtaining the optimal dropping packets function has been presented. Our researches were carried out using the Discrete Event Simulator OMNET++. The AQM model was early verified using the discrete-time Markov chain. The obtained results show that the traffic characteristic has the great impact on the network node behavior, but self-similarity of network traffic has no influence on the choosing of the optimal dropping packet function.
EN
The article presents research on the nature of the traffic in wireless local area networks (WLAN). There are presented conditions for assuming the traffic as self-similar. Then undertaken experiments are shown — for the traffic collected in five WLANs, three methods has been used: IDC (index of dispersion) and CV (coefficient of variation) indices, R=S method and method of variance time analysis. The article ends with final conclusions regarding observed dependence.
EN
A big impact of self-similar nature of network traffic on queueing performance and Quality of Service in computer networks involves new modeling techniques to provide low computational complexity and better approximation of the real traffic. A discrete-time Markov modulated Bernoulli process is one of the traffic models that captures fractal behavior and can be used in performance testing of queueing systems such as routers or switches. In this paper the model is presented and evaluated from the point of view of the desired self-similarity level. New parameter values that give better results for estimation of Hurst exponent has been proposed. Simulation results are compared with the literature data.
PL
Duży wpływ samopodobnego charakteru natężenia ruchu w sieciach komputerowych na efektywność pracy i poziom usług (Quality of Service) w sieci powoduje powstawanie nowych technik modelowania ruchu o niskiej złożoności obliczeniowej, lepiej dopasowanych do rzeczywistego ruchu. Proces Bernoulliego modulowany łańcuchem Markova będący dyskretnym procesem stochastycznym, ma właściwości które powodują, że przy odpowiednim doborze parametrów może on stanowić dobry model natężenia ruchu w sieci uwzględniający zjawisko samopodobieństwa, a co za tym idzie, może być z powodzeniem stosowany do testowania systemów kolejkowych zarówno teoretycznych jak i rzeczywistych takich jak routery czy switche. W artykule zaprezentowano i sprawdzono model pod kątem możliwości osiągnięcia założonego poziomu samopodobieństwa. Zaproponowano nowe wartości parametrów modelu dające lepsze rezultaty estymacji wykładnika Hursta. Wyniki symulacji porównano z danymi literaturowymi.
15
Content available remote Zastosowanie mikroskopii sił atomowych (AFM) w diagnostyce warstwy wierzchniej
PL
W niniejszej pracy przedstawiono mikroskopię sił atomowych jako zaawansowaną metodę inżynierską, dającą szerokie możliwości w nowoczesnej kontroli jakości wysokiej klasy elementów optyki, fotoniki czy półprzewodników. Ponadto silnie zaakcentowano konieczność opisu morfologii warstwy wierzchniej poprzez podanie wymiaru fraktalnego oraz długości korelacji jako zasadniczych parametrów opisujących samopodobieństwo oraz samoafiniczność powierzchni elementów technicznych. Przytaczaną metodykę poparto badaniami eksperymentalnymi, w ramach których przeprowadzono analizę fraktalną topografii powierzchni cienkiej folii stopu Heuslera typu Ni-Mn-Ga z zastosowaniem metody RMS (Root Mean Square).
EN
This paper introduces the Atomic Force Microscopy as an advanced engineering method that offers great potential in the modern, high-class quality control of optic, photonic, and semiconductor elements. Furthermore, what has been strongly emphasized is a real need to describe the morphology of a surface layer using the fractal parameter and the correlation length as fundamental parameters that describe self-similarity and self-affinity of surfaces of technical elements. The methodology shown in the paper is supported with some effects of experimental work, including fractal analysis of the topography of the surface of thin Ni-Mn-Ga type Heusler alloy with the Root Mean Square (RMS) method.
EN
Fractal nature of computer network traffic involves a big impact on performance of queueing systems (routers, switches, etc.), increasing delay values and packet losses. In this article, methods of measurement of network traffic as well as estimation methods of the self-similarity degree are presented and discussed. The most popular time-domain estimation techniques are evaluated from the point of view of reliability: R/S, variance-time and IDC analysis.
PL
Fraktalny charakter natężenia ruchu w sieciach komputerowych wywiera duży wpływ na wydajność systemów kolejkowych (rutery, przełączniki sieciowe, itd.), zwiększając wartości opóźnień oraz poziom strat pakietów. W niniejszym artykule zostanie podjęta dyskusja dotycząca zarówno metod pomiaru natężenia ruchu jak i metod późniejszej estymacji poziomu samopodobieństwa. Najbardziej popularne techniki estymacji w dziedzinie czasu (analiza R/S. variance-time oraz IDC) zostały ocenione z punktu widzenia wiarygodności dostarczanych przez nie wyników.
17
Content available remote Self-similar solution of a shock propagation in a non-ideal gas
EN
Similarity solutions for one-dimensional unsteady self-similar flow behind a strong shock driven out by a cylindricaI (or spherical) piston in a medium which is assumed to be a non-ideaI gas obeying a simplified van der Waals equation of state are obtained. Both the cases, when the flow between the shock and the piston is isothermal or adiabatic, are considered. It is observed that the assumption of zero temperature gradient brings a profound change in the density distribution as compared to that of the adiabatic flow; whereas the pressure and velocity distributions are little affected. Effects of the non-idealness of the gas on the flow-field between the shock and the piston are investigated. It is found that there is a decrease in the shock strength due to non-ideaIness of the gas. This decrease in the shock strength is interpreted as a result of a decrease in the compressibility of the gas.
EN
This paper investigates the influence of different SRD structures on a maximum delay value for queued LRD traffic with the usage of an envelope analysis. A FARIMA process is used as a traffic model since it can model both SRD and LRD structures independently. A FGN process is used as a reference of LRD traffic due to its relative simplicity. A drop probability is computed as a function of a buffer size that, in turn, is determined as a maximum delay function. All computations are performed with a support of an envelope process theory. A similarity between theoretical and simulations trends has been shown. The influence of an SRD structure for two different FARIMA models has been analysed for different network parameters.
EN
In this paper, we presented an analysis of VoIP traffic on both call and burst levels. The analysed traces were based on a real connection statistics and ON/OFF characteristics of VoIP coders equipped with voice activity detector (VAD). We stated that an exponential distribution is not valid for an approximation of connection duration times as well as for an approximation of the ON/OFF characteristics of voice coders regardless of their type. We also generated synthetic multiplexed VoIP trace and we computed its second order statistics - autocorrelation and Hurst parameter which showed that the trace reveals long-range dependence and self-similarity.
PL
Termin "samopodobieństwo" oznacza pewną właściwość, która zwykle kojarzy się z fraktalami: obiekt odniesienia zostaje powielony na wielu skalach - skalach geometrycznych w geometrii fraktalnej, skalach czasu w przypadku samopodobnych szeregów czasowych (jak np. samopodobny ruch telekomunikacyjny) - lecz obraz obiektu pozostaje niezmieniony. W artykule została przedstawiona analiza samopodobieństwa ruchu wideo MPEG-4. Wyniki pokazują, że samopodobieństwo ruchu generowanego na podstawie sekwencji filmowych kodowanych w standardzie MPEG-4 zależy zarówno od zawartości materiału filmowego, jak i od jakości obrazu oryginalnego.
EN
The term "selfsimilarity" denotes a certain property, which usually is associated with fractals: the reference object is repeated over many scales - geometrical scales in fractal geometry, temporal scales in case of selfsimilar time series (e.g. selfsimilar teletraffic) - but the object structure stays unchanged. In the paper, an analysis of selfsimilar properties of MPEG-4 video traffic is presented. Results shows, that selfsimilarity of an MPEG-encoded sequence depends both on video content and the picture quality.
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