To quantify network structure using FRACTAL DIMENSION: please I need suggestions on how best to introduce the topic, description of network structure and fractal dimension application to network.
FRACTAL DIMENSION
Today the method of determining the dimension is being applied to many kinds of observations, especially to time series in physics, engineering, and in fields as far apart as meteorology and neurophysiology. A fractal dimension of a set is a number that tells us how densely the set occupies the metric space in which it lies. It is invariant under various stretching and squeezing of the underlying space.This makes the fractal dimension meaningful as an experimental observable, it possesses a certain robustness and independent of the measurement units.
Complex networks are important since they describe efficiently many social, biological and communication systems .There exist many types of networks and characterizing their topology is very important for a wide range of static and dynamic properties.
Complex networks have been studied extensively in interdisciplinary fields including mathematic, statistical physics, computer science, sociology, economics, biology, etc. Complex networks are ubiquitous in the real world, e.g., there are technological networks such as the power grid, biological networks such as the protein interaction networks,and social networks such as scientific collaboration networks,and human communication networks, to name a few.
Many real complex networks share distinctive characteristic properties that differ in many ways from the random and regular networks. One such property is the “small-world effect”, which means that the average shortest path length between vertices in network is short, usually scaling logarithmically with the size N of network, while maintaining high clustering coefficient. A famous example is the so-called “six degrees of separa- tion” in social networks.
Many real networks have two fundamental properties, scale-free property and small-world property. If the degree distribution of the network follows a power-law, the network is scale-free; if any two arbitrary nodes in a network can be connected in a very small number of steps, the network is said to be small-world.
The small-world properties can be mathematically expressed by the slow increase of the average diameter of the network, with the total number of nodes .
To investigate self-similarity in networks, we use the box-counting method and renormalization.
Application
Many natural phenomena are better described using a fractional dimension, and fractals are thus used as descriptive models for the growth of plants, particle aggregation, river cartography, realistic images, and similar phenomena. Their fractal dimension characterizes most of these fractal models. In physical systems, the fractal dimension reflects some properties of the system. The physical characteristics of some bodies are related to the fractal dimension of their surfaces.
In analytical chemistry, the fractal dimension is used as a tool to characterize chemical patterns and problems of sample homogeneity. A given fractal dimension makes it possible to simulate a variety of systems: fluid extraction or contaminant mitigation techniques, the hybrid orbital model of proteins, or the growth of conflict rate in aircraft flight schedules.
Fractal dimension provides an objective meaning for comparing fractals and they can be attached to clouds, trees, coastlines, feathers, networks of neurons in the body, dust in the air at an instant in time, the clothes we are wearing, the distribution of frequencies of the light reflected by a flower, the colors emitted by the sun, and the wrinkled surface of the sea during a storm.
To quantify network structure using FRACTAL DIMENSION: please I need suggestions on how best to introduce...
Please submit your paper topic so that I can review it and make any necessary suggestions or corrections. Your submission should include a brief description of the vulnerable population you will be researching and a brief explanation of what type of risk this population faces. When considering a topic for your paper, make sure that you can find an adequate number of scholarly resources.
How to solve Label Fell Off as an operation management question? I need 3 suggestions for that. Please writes as detailed as you can.
My employer has me creating a system and tasked me to select network and access security controls. I need suggestions and real life examples on which network security controls that I should use and some access control technology for my company which is a local electric company outside of Jackson, MS.
I need to know how to dimension the inductor and the capacitor of a Boost convertor in discontinuos mode. I would be glad if that is some explanation.
Please I need a paragraph about any ANIMAL using the PIE structure please helpp P. I. E. Please follow these instructions for writing paragraphs in all your written assignments. P-Point - Communicate your purpose to the reader by writing a topic sentence that addresses the issue with an opinion based on facts. -A point is an opinion based on facts, not merely a fact. -A point is a topic sentence for a body paragraph. -A topic sentence has two functions:...
Subject : Dell in Artificial Intelligent (AI) I need help for Introduce the process is analyzing – take a bigger perspective. This description should tell a reader how the selected process fits into overall ‘big’ picture for the whole organization.
I need this ASAP please Choose the data structure from the list at right that best represents the description at left. Last item added is the first to be removed java.util collections calls this a Map [Choose ] Priority Queue Bag SortedArrayList ArrayList Stack Expression Tree Queue Iterator Binary Search Tree Heap Hash Table Dictionary First item added is the first to be removed Your computer operating system uses one manage processes and job requests when resources are tight. Combines...
For each compound (a-e) i need to know whether the lewis structure or vespr structure works Which works best using either the VESPR or Lewis structure. Show work: a) AlCl b) C032- c) SO42 d) H3o* e) CO2 Which works best using either the VESPR or Lewis structure. Show work: a) AlCl b) C032- c) SO42 d) H3o* e) CO2
WHAT ARE THE KEY CONCEPTS YOU NEED TO KNOW ABOUT THE IT NETWORK ENGINEERING? PLEASE EXPLAIN THE GENERAL CONCEPTS TO BEGIN WITH PLEASE GIVE SOME GOOD REFERENCES AND BOOKS TO LOOK INTO FOR THE EXAMS FOR COMPTIA SECURITY + EXAM THE CompTIA CySA+ (CompTIA IT Certifications) CONSISTS OF - IT FUNDEMENTALS EXAM - A+ EXAM - Network+ EXAM - Security+ EXAM , etc. PLEASE GIVE THE BOOKS OR REFERENCES OR LINKS I COULD USE FOR THE GOOD REFERENCES FOR PREPARING...
good Companies to work with the instructions below. only need company suggestions please Project Presentation: The final presentation should reflect an in-depth analysis of the organization you choose. It should be about 10-15 slides. Please refer to the following guidelines when you prepare the presentation: 1). Structure of the presentation. The structure of a presentation is very important. Having discernible sections, with titles and subtitles, and connections between different parts of the presentation helps you organize your thoughts effectively. Below...