scholarly journals Abstract Description of Internet Traffic of Generalized Cauchy Type

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Ming Li ◽  
Wei Zhao
Keyword(s):  
Fractal Dimension ◽  
Fundamental Problem ◽  
Internet Traffic ◽  
Similar Process ◽  
Hurst Parameter ◽  
Cauchy Type ◽  
Self Similarity ◽  
Abstract Description ◽  
The One ◽  
Traffic Theory

Self-similar process with long-range dependence (LRD), that is, fractional Gaussian noise (fGn) with LRD is a widely used model of Internet traffic. It is indexed by its Hurst parameterHfGnthat linearly relates to its fractal dimensionDfGn. Note that, on the one hand, the fractal dimensionDof traffic measures local self-similarity. On the other hand, LRD is a global property of traffic, which is characterized by its Hurst parameterH. However, by using fGn, both the self-similarity and the LRD of traffic are measured byHfGn. Therefore, there is a limitation for fGn to accurately model traffic. Recently, the generalized Cauchy (GC) process was introduced to model traffic with the flexibility to separately measure the fractal dimensionDGCand the Hurst parameterHGCof traffic. However, there is a fundamental problem whether or not there exists the generality that the GC model is more conformable with real traffic than single parameter models, such as fGn,irrelevant of traffic traces used in experimental verification. The solution to that problem remains unknown but is desired for model evaluation in traffic theory or for model selection against specific issues, such as queuing analysis relating to the autocorrelation function (ACF) of arrival traffic. The key contribution of this paper is our solution to that fundamental problem (see Theorem 3.17) with the following features in analysis. (i) Set-valued analysis of the traffic of the fGn type. (ii) Set-valued analysis of the traffic of the GC type. (iii) Revealing the generality previously mentioned by comparing metrics of the traffic of the fGn type to that of the GC type.

scholarly journals Self-Similar Markovian Sources

2020 ◽  
Vol 10 (11) ◽  
pp. 3727 ◽  
Author(s):  
Adam Domański ◽  
Joanna Domańska ◽  
Katarzyna Filus ◽  
Jakub Szyguła ◽  
Tadeusz Czachórski
Keyword(s):  
Long Range ◽  
Computer Networks ◽  
Markov Models ◽  
Internet Traffic ◽  
Similar Process ◽  
Queueing Models ◽  
Network Structures ◽  
Self Similarity ◽  
Self Similar

Markov queueing models are a powerful tool to evaluate the performance of computer networks and have been used in telecommunication studies for over 100 years. To apply them to the evaluation of the modern Internet, we should not only adapt them to the contemporary network structures but also include a description of the complex stochastic patterns (self-similarity and long-range dependance) of transmitted flows. We examine the features of two Markov models of an almost self-similar process, keeping in mind the modeling of Internet traffic. We have found that the obtained results are comparable with those achieved using a well-known generator of self-similar traffic.

scholarly journals Supramolecular Fractal Growth of Self-Assembled Fibrillar Networks

Gels ◽  
2021 ◽  
Vol 7 (2) ◽  
pp. 46
Author(s):  
Pedram Nasr ◽  
Hannah Leung ◽  
France-Isabelle Auzanneau ◽  
Michael A. Rogers
Keyword(s):  
Fractal Dimension ◽  
Crystallization Temperature ◽  
Cayley Tree ◽  
Fractal Dimensions ◽  
Self Similarity ◽  
Avrami Model ◽  
Cluster Aggregation ◽  
Box Counting ◽  
Self Assembled ◽  
Limited Diffusion

Complex morphologies, as is the case in self-assembled fibrillar networks (SAFiNs) of 1,3:2,4-Dibenzylidene sorbitol (DBS), are often characterized by their Fractal dimension and not Euclidean. Self-similarity presents for DBS-polyethylene glycol (PEG) SAFiNs in the Cayley Tree branching pattern, similar box-counting fractal dimensions across length scales, and fractals derived from the Avrami model. Irrespective of the crystallization temperature, fractal values corresponded to limited diffusion aggregation and not ballistic particle–cluster aggregation. Additionally, the fractal dimension of the SAFiN was affected more by changes in solvent viscosity (e.g., PEG200 compared to PEG600) than crystallization temperature. Most surprising was the evidence of Cayley branching not only for the radial fibers within the spherulitic but also on the fiber surfaces.

scholarly journals A Neural Network-Based Approach for Approximating Arbitrary Roots of Polynomials

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 317
Author(s):  
Diogo Freitas ◽  
Luiz Guerreiro Lopes ◽  
Fernando Morgado-Dias
Keyword(s):  
Iterative Methods ◽  
Fundamental Problem ◽  
Iterative Algorithms ◽  
Rounding Errors ◽  
Suggested Approach ◽  
Simultaneous Iterative Methods ◽  
Complex Roots ◽  
Roots Of Polynomials ◽  
Comparative Results ◽  
The One

Finding arbitrary roots of polynomials is a fundamental problem in various areas of science and engineering. A myriad of methods was suggested to address this problem, such as the sequential Newton’s method and the Durand–Kerner (D–K) simultaneous iterative method. The sequential iterative methods, on the one hand, need to use a deflation procedure in order to compute approximations to all the roots of a given polynomial, which can produce inaccurate results due to the accumulation of rounding errors. On the other hand, the simultaneous iterative methods require good initial guesses to converge. However, Artificial Neural Networks (ANNs) are widely known by their capacity to find complex mappings between the dependent and independent variables. In view of this, this paper aims to determine, based on comparative results, whether ANNs can be used to compute approximations to the real and complex roots of a given polynomial, as an alternative to simultaneous iterative algorithms like the D–K method. Although the results are very encouraging and demonstrate the viability and potentiality of the suggested approach, the ANNs were not able to surpass the accuracy of the D–K method. The results indicated, however, that the use of the approximations computed by the ANNs as the initial guesses for the D–K method can be beneficial to the accuracy of this method.

scholarly journals A Community-Structure-Based Method for Estimating the Fractal Dimension, and its Application to Water Networks for the Assessment of Vulnerability to Disasters

2021 ◽  
Vol 35 (4) ◽  
pp. 1197-1210
Author(s):  
C. Giudicianni ◽  
A. Di Nardo ◽  
R. Greco ◽  
A. Scala
Keyword(s):  
Fractal Dimension ◽  
Community Structure ◽  
Distribution Systems ◽  
Water Distribution ◽  
Scaling Law ◽  
Vulnerability Index ◽  
The Self ◽  
Node Degree ◽  
Specific Response ◽  
Self Similarity

AbstractMost real-world networks, from the World-Wide-Web to biological systems, are known to have common structural properties. A remarkable point is fractality, which suggests the self-similarity across scales of the network structure of these complex systems. Managing the computational complexity for detecting the self-similarity of big-sized systems represents a crucial problem. In this paper, a novel algorithm for revealing the fractality, that exploits the community structure principle, is proposed and then applied to several water distribution systems (WDSs) of different size, unveiling a self-similar feature of their layouts. A scaling-law relationship, linking the number of clusters necessary for covering the network and their average size is defined, the exponent of which represents the fractal dimension. The self-similarity is then investigated as a proxy of recurrent and specific response to multiple random pipe failures – like during natural disasters – pointing out a specific global vulnerability for each WDS. A novel vulnerability index, called Cut-Vulnerability is introduced as the ratio between the fractal dimension and the average node degree, and its relationships with the number of randomly removed pipes necessary to disconnect the network and with some topological metrics are investigated. The analysis shows the effectiveness of the novel index in describing the global vulnerability of WDSs.

Runoff Fractal Dimension of Songhua River Basin in Harbin Station Based on Db4 Wavelet

2012 ◽  
Vol 550-553 ◽  
pp. 2537-2540
Author(s):  
Hai Yan Gu ◽  
Yong Wang ◽  
Lei Yu
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
River Basin ◽  
Fractal Theory ◽  
Measurement Methods ◽  
Self Similarity ◽  
Songhua River ◽  
Songhua River Basin ◽  
The Songhua River Basin ◽  
The Songhua River

The wavelet analysis and fractal theory into the analysis of hydrological time series, fluctuations in hydrological runoff sequence given the complexity of the measurement methods--- fractal dimension. The real monthly runoffs of 28 years from Songhua River basin in Harbin station are selected as research target. Wavelet transform combined with spectrum method is used to calculate the fractal dimension of runoff. Moreover, the result demonstrates that the runoff in Songhua River basin has the characteristic of self-similarity, and the complexity of runoff in the Songhua River basin in Harbin station is described quantificationally.

scholarly journals THE DYNAMICS OF INTERNET TRAFFIC: SELF-SIMILARITY, SELF-ORGANIZATION, AND COMPLEX PHENOMENA

2011 ◽  
Vol 14 (06) ◽  
pp. 905-949 ◽  
Author(s):  
REGINALD D. SMITH
Keyword(s):  
Information Exchange ◽  
Complex Dynamics ◽  
Internet Traffic ◽  
Self Organization ◽  
The Internet ◽  
Biological Models ◽  
Self Similarity ◽  
Exchange Networks ◽  
Traffic Oscillations ◽  
Complex Phenomena

The Internet is one of the largest and most complex communication and information exchange networks ever created. Therefore, its dynamics and traffic unsurprisingly take on a rich variety of complex dynamics, self-organization, and other phenomena that have been researched for years. This paper is a review of the complex dynamics of Internet traffic. Departing from normal treatises, we will take a view from both the network engineering and physics perspectives showing the strengths and weaknesses as well as insights of both. In addition, many less covered phenomena such as traffic oscillations, BGP storms, and comparisons of the Internet and biological models will be covered.

scholarly journals RELIGION IN THOUGHT MURTADHA MUTHAHHARI

Tsaqofah ◽  
2020 ◽  
Vol 18 (02) ◽  
pp. 99
Author(s):  
Didin Komarudin Komarudin
Keyword(s):  
Content Analysis ◽  
Fundamental Problem ◽  
Religious Practice ◽  
Sociological Analysis ◽  
Religion And Science ◽  
Daily Lives ◽  
The One ◽  
And Behavior ◽  
The Relationship ◽  
Religious Actors

This writing is based on the background that religious formalism is increasingly becoming a fundamental problem. This is marked by the patterns and behavior of people who claim to be religious but there is no concrete implementation in their daily lives. This research was conducted to determine the concept of religion as a fitrah for humans as well as how religious beliefs are to the level of the relationship between religion and science according to Murtadha Motahhari. This research is a qualitative study that uses a sociological analysis approach, while the data in this study come from content analysis collected from various sources. , the level of religious belief, until people know God, the criticisms of Murtadha muthahhari which are an integral part of the life of the above figures to practice true religious values. Religion as human nature gives birth to the belief that religion is the only way to fulfill all needs, so that religion is not only a label or social formality but is able to become a guide in life and life. All religions teach goodness and peace, and no religion teaches violence. But sometimes there is violence in the name of religion because of a lack of understanding or a distortion of the source of religion itself. So that religion is sometimes used, and it seems that religion and religious practice are the opposite. So what is blamed on the concept of religion itself is actually the one who is wrong for religious actors.

scholarly journals Studying and evaluating the performance of pedestrian crossing facilities in Babil governorate

2019 ◽  
Vol 28 (3) ◽  
pp. 417-431
Author(s):  
Ali Dakhil ◽  
Dheyaa Alobaidi ◽  
Saba Shaheed
Keyword(s):  
Fundamental Problem ◽  
Health Department ◽  
Positive Effects ◽  
Pedestrian Bridges ◽  
Traffic Volumes ◽  
Interview Survey ◽  
The One ◽  
Questionnaire Method ◽  
Pedestrian Crossing ◽  
In Transit

Walking is one of the oldest means of mobility. It is an indispensable necessity to reach destinations despite the fact that walking or walking is one of everyday activities of man, which have positive effects on health, and activity on the one hand; vehicles cannot reach destinations only required by often walking from the other. The main problem address by the research is the random passage of the sieve and uncontrolled when it is most designs for the city’s road network have not addressed. This fundamental problem as well as the lack of a city to the safe facilities to cross the pedestrian. Therefore, this paper is a trial to study and analyze the current reality of crossing the sap then find solutions and treatments that reduce or limit the overlap between different traffic events and events crossing the pedestrian. Field data on the syllabic traffic volumes collected in all areas of the study (peak hour volume) and the photographic technique method. The study chose four areas to study the sap (60th Street, 40th Street, Al-Hussein, intersection circle at Babel Health Department), which are residential, commercial and educational zones, representing diversity in land use and scheme sidewalk and the design of the city of Hilla. The study attempted to show the state of lateral walks. The study also used the questionnaire method (interview survey) to determine the suitability of pedestrian bridges in transit and land transit. The study concluded that the area of Al-Hussein represents the highest traffic volumes of the sieve in addition to the lack of it the sidewalks in terms of absorption and quality and abuses. As well as the reluctance to use pedestrian bridges in transit in the area of 60th Street through high ground transit time, which necessitates the establishment of dual-step (fixed and mobile) – legislation and education through all means.

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