RESEARCH ON THE INFORMATION GLOBULAR RADIATION

MODEL IN CYBERSPACE

Niannian Jia, Jiannan Yu and Yunfan Xia

School of Science, Harbin Engineering University, Harbin, China

Keywords: Cyberspace, Information diffusion, Globular radiation, Measure distribution of information.

Abstract: According to advantage of information diffusion in cyberspace, the process of information diffusion can be

simulated a compound process of time-variation and space spreading. On basis of Network Dimension-force

theory, this paper builds the information globular radiation model in cyberspace. Starting with the ideal

cyberspace and reality cyberspace, the model simulates the process of information diffusion with time as the

diffuse radius and the amount of information as the diffuse volume. Using physics properties and rigorous

mathematical reasoning, the paper proved existence and rationality of the model, which provided new

directions for network information diffusion.

1 INTRODUCTION

With the rapid development of network, the world

enters into the information age charactered by high

efficiency. Owing to network, the superiorities of

information diffusion is mainly about small time

difference but large quantity. From the point of view

of information science, information diffusion in

cyberspace is a process of information diffusing

from one node to the whole space .In other words, it

is a compound process of time-variation and space

spreading (Zhao, 2006). From the perspective of the

cyberspace, complicated network is abstracted into

nodes and paths (Deng, 2008). The nodes represent

the location of the information, and the paths

represent the area of flow of information. The paper

advances a completely new model of information

diffusion in cyberspace on the basis of the above-

mentioned two views, namely globular radiation

model of information in cyberspace.

2 THE THEORETICAL

RESEARCH ON THE

GLOBULAR RADIATION

MODEL OF INFORMATION

IN CYBERSPACE

2.1 The Definition of Cyberspace

The three elements of cyberspace are information,

information nodes and paths between nodes.

Therefore cyberspace is defined as three-

dimensional vector

1

{,,}

M

PL .

12

,,,

n

M

mm m

represents a set of flowing information in

cyberspace, where

i

m flowing in connecting paths

and existing on the network nodes is a set of

information. Considering information with

properties of sets, therefore

i

mM . Otherwise

i

m

is called fake information of

M

(Chen, 2004).

12

{, , , }

n

Ppp p represents a set of nodes in

cyberspace. In the theory of Network Dimension-

force, information source nodes are divided into two

types: shining point and vanishing point. A shining

point represents the node being able to send out

information, while a vanishing point represents the

opposite. Information sink nodes can be classified as

reachable points and unreachable points. A

reachable point is the node being able to receive

information, while an unreachable point is the

418

Jia N., Yu J. and Xia Y..

RESEARCH ON THE INFORMATION GLOBULAR RADIATION MODEL IN CYBERSPACE.

DOI: 10.5220/0003569804180422

In Proceedings of the 13th International Conference on Enterprise Information Systems (NMI-2011), pages 418-422

ISBN: 978-989-8425-53-9

Copyright

c

2011 SCITEPRESS (Science and Technology Publications, Lda.)

opposite.

11

{, ,, , }

ij nn

L

lll represents the set of

paths of network space.

ij

l

represents the path

between

i

p and

j

p .When

i

p and

j

p are both

shining points or reachable points,

ij

l is called access

.When at least one of

i

p and

j

p

is vanishing point

or unreachable point,

ij

l is considered as a broken

path or inexistent.

2.2 The Mode of Information Diffusion

in Ideal Cyberspace

In cyberspace, the information diffusion is a process

of information transmitted from one point to another

(Deng, 2008). In ideal cyberspace, the information

dissemination is not affected by any restraints of

objective and subjective conditions .In such a

circumstance all the information source nodes are

shining points, and all the information sink nodes are

reachable points .All the paths

ij

l

are connected.

Therefore, in ideal cyberspace the information on

the information source node is transmitted to the

numerous information sink nodes in diffuse way

during

(0)tt . As Fig. 1 showed, the numerous

nodes formed a spherical surface with

t as the

radius. The surface is formed by the information

transmitted to all the information sink nodes after

t . During the next t , all the information sink

nodes become information source nodes, then the

information on the nodes is transmitted to the

numerous new information sink nodes in diffuse

way. Obviously, a new spherical surface is formed

by each node. Because

0t

, a new spherical

surface is formed out of the previous one with the

same sphere’s center, but the radius of the new

spherical surface is 2

t . So when the number of t

approaches infinite, numerous spherical surfaces,

with

(1,2,...)ntn as their individual radius

and the same center, are formed. Thus, a sphere with

tnt as the radius is formed after nt

.The

formation of the sphere with

t is the process of the

information diffusion in the ideal cyberspace. This

diffusion way is there-dimensional from point to

plane. The information transmission mode is

constructed as globular radiation model of

information in ideal cyberspace (Cai, 2010). The

model can fully reflect that information diffusion is

a complex process of time variation and space

spreading. This section must be in one column.

Figure 1: The picture of the process of the information

diffusion.

2.3 The Mode of Information Diffusion

in Reality Cyberspace

Unlike in the ideal cyberspace, however,

information can not spread to every information

node in the reality cyberspace .Due to various

reasons, a few information nodes related to the

information of information source are not able to

receive information .Such information node is called

vanishing point of information. According to

different kinds of information, the number of the

vanishing points of information is different. A

vanishing point can lead to a number of unreachable

points. Figure 2 is a schematic illustration of

vanishing point of information.

Figure 2: The picture of vanishing points of information

diffusion.

2.4 The Globular Radiation Model of

Information in Cyberspace

Described as the globular radiation model of

information in ideal cyberspace, it is the amount of

information of diffusing that formed infinitely many

spherical surfaces with

(1,2,,)ntn

as their

radius and the same center. The amount of

information of diffusing formed a sphere with

tnt

as the radius. Let

2

() 4 ( )

s

tt

, where

()

s

t is the surface area of the sphere at time t and

RESEARCH ON THE INFORMATION GLOBULAR RADIATION MODEL IN CYBERSPACE

419

is time-intensity parameter. Because ()

s

t is an

integrable function on interval

[0, )

,

()qt = ()Vt =

2

0

4()

t

rtdt

=

3

4

()

3

t

()t . ()qt , the total number of information at

time

t in an ideal state, accord with the variation

rule of the volume of the sphere with

t

as the

radius.

In the reality cyberspace, under the influence of

various subjective and objective conditions,

information nodes that can not transmit information

with time are existent. In other words,

12

{, , , }

n

Ppp p ,the set of nodes, has vanishing

point or unreachable point

i

p . As figure 2 shows,

more new vanishing points and unreachable points

are caused by these vanishing points and

unreachable points. Information transmission would

produce the losses of the amount of information with

an obvious randomness in the reality cyberspace,

namely

3

4

() () ( )

3

RI

qt qt t

, where

()

I

qt

represents the total information of the ideal

cyberspace and

()

R

qt represents the total

information of the reality cyberspace.

3 THE PROOF OF GLOBULAR

RADIATION MODEL OF

INFORMATION IN

CYBERSPACE

When describing the cyberspace, there is an

important measure, network measure distribution

function

()k

, the definition of which is the

probability of the node randomly selected with

k

connecting paths. In the globular radiation model

of information in cyberspace, the shorter the

connecting time

t among points, the more the

paths

k from point to point. Therefore there are a

certain inverse relationship between time t and

connecting path

k , namely

1

k

t

.According to the

study in recent years, the network measure

distribution function shows power exponent law,

namely

()kk

, so

()kt

, where

is

power exponent

(Wang, 2004). The basic

constitution of the globular radiation model of

information in cyberspace is as follows. Starting

with

0t , there are at least

(0)( (0) 1)

information originating nodes. ()t

represents the number of nodes in cyberspace at time

t . After that the following four processes would

happen during every

t

time step.

1) Some information source nodes are vanishing

points in cyberspace, and information source nodes

becoming vanishing points are stochastic. Let the

number of the nodes without information sent out

is c .

2) Stochastic selection of diffusion, information

sink nodes receive information transmitted by

information source in the reality cyberspace on the

basis of competitive selection .The number of

information sink nodes is several ,therefore

information source nodes and information sink

nodes would produce

e connecting paths

ij

l between

nodes .The preferential probability that information

source node

0

p reaches information sink node

i

p ,

i

i

j

j

k

k

(1)

3)

r connecting paths of information nodes in

cyberspace as

ij

l :a connecting path is the path from

shining points to reachable points, the preferential

probability of the information source node

determined by (1).

4)

n broken paths of information nodes in

cyberspace as

ij

l : when information sink nodes are

unreachable points, information sent to space can

not be received ,which would cause broken paths.

Meanwhile information source node

0

p are selected

in anti-preferential probability (Jia, 2009)

'

1

() 1

i

i

t

(2)

Consequently,

() (1 )tcte

. ()t

represents the

total measure of the nodes in cyberspace at time

t

,namely

()

j

j

tk

.Therefore

()

()

()

t

kt

t

at

time

t ,where ()kt represents the average measure of

information nodes at time

t .

According to Dynamical Mean-Field Theory,

(Xu, 2010)measure distribution of node

i

p in

cyberspace can be obtained. If

i

k is successive,

i

k

satisfies

(1 )

()

ii

iiij

ij

kk

er r

tt

ICEIS 2011 - 13th International Conference on Enterprise Information Systems

420

''

(1 )

iij

ij

n

(3)

And average measure distribution of information

nodes in

t

time is

2[ ( ) ]

()

()

()

1

eckt rn

t

kt

t

c

(4)

Then

2( )

()

1

ern

kt

c

when

t .Insert

function

() (1 )tct

and

average measure

distribution of information nodes into

（4）,where

2( )(1 )

()

1

ern c

tt

c

(5)

Applying (3) with

()t

、 ()t

, we obtain

approximating linear differential equation

22 21

2( )(1 ) 1

ii

kk

ercecn n

ternct ct

(6)

Let

22

2( )(1 )

e r ce cn

x

ern c

，

2

1

n

y

c

， initial

condition is

()

i

kt e ，whence

() ( )( )

x

ii

i

yt y

kt e

x

tx

(7)

The solution of the inequality

()

ii

kt k

is

1

x

i

y

e

x

tt

y

k

x

(8)

Therefore

1

()( )

x

ii

y

e

x

kk tt

y

k

x

1

1( )

x

i

y

e

x

tt

y

k

x

(9)

If

i

t satisfying homogeneous distribution (Samuel,

2009), measure distribution function of information

nodes is

1

1

()

()

1

()

(0)

()

x

i

x

x

y

e

kk

t

x

k

kxt

y

k

x

(10)

So when time is

(1,2,...,)tntn , then

1

1

() ( )( )

x

y

y

ke k

x

xx

(11)

While

12( )(1)

11

()(1)2

ern c

x

er c cn

(12)

We have on the basis of (11) that information nodes

measure distribution function

()k

have parameter

exponent and power exponent, and power exponent

is to correspond with

1

1

x

. Since

1

k

t

and (1,2,...,)tntn

, therefore

()kt

,thus, ()qt t

. In the information

globular radiation model in network, time

t

be a

continuous increasing variable, clearly the

parameters show that

0, 0 1, 0, 0,ecrnern

. Inserting this

parameters into (12), the power exponent

is to

correspond with

13

. Firstly, while 1

, it

indicates the information is being transmitted and

received from the source nodes. While

01

,

there is no source node or the source point transmit

nothing in the cyberspace. While

13

, there are

vanishing and unreachable points in the cyberspace.

Only when

3

, the cyberspace is ideal, where all

the source nodes are shining points and all the sink

nodes are reachable points. Therefore the quantity of

information function can be illustrated as

3

4

() ( )

3

qt t

(0 )t

. This equation meets

suppose of information diffusion spherical radiated

model in ideal cyberspace.

4 CONCLUSIONS

Network Dimension-force discovered that network

provided the superiority in time and space to

information diffusion. This paper based on this

superiority build the information globular radiation

model in network space, to show the process of

information diffusion is the complex process of

network information with time variation and space

spreading. And the model of existence and

rationality has proved though the physics nature of

network, for this reason, the information globular

radiation model in network space is able to describe

information diffusion in cyberspace. Thereby this

model is suitable in research on information

diffusion in cyberspace and analysis of the problems

of network information.

RESEARCH ON THE INFORMATION GLOBULAR RADIATION MODEL IN CYBERSPACE

421

ACKNOWLEDGEMENTS

This work supported by The Fundamental Research

Funds for the Central Universities (Grant

HEUCF20111135).

REFERENCES

Zhao J. L., 2006. Network Dimension-force Based on

Original Philosophy and Management Innovations.

Harbin: Harbin Engineering University Doctor Paper.

Deng Y. R., 2008. Research on Information Diffusion

Based on Network Dimension-force.

Harbin: Harbin

Engineering University Doctor Paper.

Chen J., 2004.

The Research on Free Degree of Network

Information Transmission Based on Internet.

Wuhan:

HuaZhong Normal University.

Deng Y. R., 2008. Research on the Dynamic Mechanism

of Information Diffusion in Network Environment.

Library and Information Service.

Cai C., 2010. Research of Models and Integration for 3D

Spatial Data.

Geospatial Information.

Wang W. N., 2004. On the Topology of Complex

Networks in the Information Networks. Nanjing:

Journal of Nanjing Institute of Posts and

Telecommunications (Natural Science).

Jia X. L., 2009.A Dynamic Scale-free Network Model.

Sichuan:

Journal of Sichuan Normal University

(Natural Science).

Xu S. H., 2010. Analysis of Knowledge Transfer Network

Characteristics Based on Small-world Network Model.

Journal of the China Society for Scientific and

Technical Information.

Samuel Karlin, 2009. Howard M. Taylor.

A Second

Course in Stochastic Processes

. Beijing Posts &

Telecom Press.

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