Principles of Information Science
Chapter 9
Information Organization
-- System Optimization Theory
§ 1.1 System Fundamentals -
Definitions
System,Definitions
System – integrity of elements that form a certain structure
internally and perform certain functions externally,
L,von Bertalanffy:,System -- set of interrelated elements”
Basic Features of Systems include,
(1) Integrity as an entirety;
(2) Interrelated among elements;
(3) Multilevel
(4) Relativity
(5) Goal-Keeping
(6) Dynamic
§ 1.2 System Fundamentals -
Features
§ 1.3 Organization & Information
Information and Stochastic System’s Organism
A stochastic system S = {(s1,p1),…,(s n,pn),…,(s N,pN)}
Uncertainty,H(S) = - ? pn log pn
n
0 = [H(S)]min ? H(S) ? [H(S)]max = H0 = logN
Organization,?? = H0 – H(S) H
0
= R
§ 1.4 Self-Organizing &
Information
Conditions Required for Self-Organizing
A system,S,under environment,E,is self-organizable iff
H(S) > H(E) ? 0 or dR dt > 0,
The latter means H(S) dH0 dt > H0 dH(S) dt,and this leads to
1) If N is given,dH0/dt = 0,then it must have dH(S) dt < 0;
2) If H(S) = Const and N is variable,then it must have
dH0
dt > 0,
§ 2.1 Information & Optimization
Mechanism for Optimization
Functions
Detected
System to be
Optimized
Observer
Structure
Information
Structure
§ 2.2 Optimization Algorithm
The structure of the System to be optimized,
S,c1,…,c n,…,c N
x1,…,x n,…,x N
t1,…,t n,…,t N
{ }
The utility of the system related to the structure,u1,…,u N,
Thus,the optimal structure of the system should be
Sopt = {S| I(?) = max I(?)}
{S}
§ 2.3 Examples
Optimization algorithm may be reduced to various cases,
-- Linear Programming
-- Non-Linear Programming
-- Networking (Minimum Route,Maximum Traffic,
Minimum Cost,etc)
-- Decision-Making Game (MIniMax,MaxMin,etc)
-- Dynamic Programming
§ 3.1 Systems and Order
Decreasing
A Natural trend in closed systems
From higher order to lower order (Maxwell Demon)
§ 3.2 Systems and Order
Increasing
Evolution,from lower order to higher order
§ 3.3 Dissipative Structure
Prigogine pointed out (1977) that whether the order of a
system decreases or increases depends on whether the
System is closed or open,
However,openness of a system is only a necessary condition
for its self-organizability,
Whether or not an open system is self-organizable depends
on how the open system exchange its matter,energy,and
information with its outer world (environment),
§ 3.4 Synergetic Theory
Haken noted that the order parameter of an open system
plays a dominate role in determining when and how the
system is self-organized,The order parameter is thus called
The master while other parameters the slavers,
When the order parameter reaches to a critical point,or a
region,the original stable state of the system enters into two
different states,one is the new stable state with higher order
and the other is an unstable state with lower order,This is
called the dichotomy,The latter forms chaotic process and
means losing information,
Example in Mechanics V(q)
q
V(q) = ? kq2 + ? k1q4
,
.,
q
V(q)
K<0
K>0
q = - kq - k1q3,
K is an order parameter
Example in Laser System,n = ng – nl
where ng = GNn,nl = 2?n,2? = 1/t0
N = N0 - ?N = N0 - ?n
n – number of photons,ng – number of its growth,nl – number
of its loss,N – number of excited atoms,G – gain cofficient,
t0 – the lifetime of photon,N0 – number of excited atom kept via
External source,? -- reduction coefficient of atoms,
Thus n = - kn – k1n2
where k = 2? - GN0 > < 0,k1 = ?G > 0
When external exciter strong enough N0 > 2?/G,then k < 0,the
Laser works; otherwise,it does not,
,
,