204
A. CRISTEA
x (t), Q is a variational principle for "ii, whose optimum establishment may
simply be approximated by the equation of a general extremum regulator
dii
bQ
_=,12_d t
b"it (I)
(2)
The current value of Q, indicating "biological quality", represents a
criterion in dependence on errors and dispersions around the optimum and
is maximal for the extremum. Q increases with the ratios
or
rp+, rp-: terms for
stabilizing flows
meaning a signal to noise ratio or the ratio of order imposing to degrading
forces. The C-space here reflects the stability against disturbances.
It may be assumed that an adaptive (or evolutionary) transition exists
such that on the S-space
aN
-
2
-+-+
(-v~_ a Q __ )
--=D(S,N,t)V_N+ v V_N+KN
- 3S
3 t
s
s
'
(3)
Here the dynamics N (5, t) of a population in the domain D is reflecting
(a) diffusive (i.e. variant) effects (= isotropic part of the transition) (b)
drift towards the extremum v of the "optimum quality" Q (= anisotropic
part of the transition) and (c) autocatalytic rate KN. Self-improvement
occurs by reinforcement of diffusion for small v and enhancement of the
transition rate toward larger v. The upper level uses the information from
environment (M) and interior to select reactions of optimal decision (R) [3].
By anchoring this decision device into the input-output relation a certain
amount of memory originates. If v depends mainly on its own generation
rate along with a trend towards still higher maxima an autocatalytic process
representing the general process of biological evolution can be imagined.
References
1. BARLETT, M.: An introduction to stochastic processes. Cambridge: Univ.
Press 1955.
2. BELLMAN, R. : Adaptive processes. A guided tour. Princeton N. J.: Princeton
Univ. Press 1961.
3. BUSH, R. R., and F. MOSTELLER: Stochastic models for learning. New York:
John Wiley and Sons 1955.
4. FEYNMAN, R.: Rev. Mod. Phys. 20, 367 (1948).
5. WALD, A.: Decision processes. Cambridge: Univ. Press 1955.
6. WIENER, N.: Cybernetics. New York: John Wiley and Sons 1948.
A. CRISTEA
x (t), Q is a variational principle for "ii, whose optimum establishment may
simply be approximated by the equation of a general extremum regulator
dii
bQ
_=,12_d t
b"it (I)
(2)
The current value of Q, indicating "biological quality", represents a
criterion in dependence on errors and dispersions around the optimum and
is maximal for the extremum. Q increases with the ratios
or
rp+, rp-: terms for
stabilizing flows
meaning a signal to noise ratio or the ratio of order imposing to degrading
forces. The C-space here reflects the stability against disturbances.
It may be assumed that an adaptive (or evolutionary) transition exists
such that on the S-space
aN
-
2
-+-+
(-v~_ a Q __ )
--=D(S,N,t)V_N+ v V_N+KN
- 3S
3 t
s
s
'
(3)
Here the dynamics N (5, t) of a population in the domain D is reflecting
(a) diffusive (i.e. variant) effects (= isotropic part of the transition) (b)
drift towards the extremum v of the "optimum quality" Q (= anisotropic
part of the transition) and (c) autocatalytic rate KN. Self-improvement
occurs by reinforcement of diffusion for small v and enhancement of the
transition rate toward larger v. The upper level uses the information from
environment (M) and interior to select reactions of optimal decision (R) [3].
By anchoring this decision device into the input-output relation a certain
amount of memory originates. If v depends mainly on its own generation
rate along with a trend towards still higher maxima an autocatalytic process
representing the general process of biological evolution can be imagined.
References
1. BARLETT, M.: An introduction to stochastic processes. Cambridge: Univ.
Press 1955.
2. BELLMAN, R. : Adaptive processes. A guided tour. Princeton N. J.: Princeton
Univ. Press 1961.
3. BUSH, R. R., and F. MOSTELLER: Stochastic models for learning. New York:
John Wiley and Sons 1955.
4. FEYNMAN, R.: Rev. Mod. Phys. 20, 367 (1948).
5. WALD, A.: Decision processes. Cambridge: Univ. Press 1955.
6. WIENER, N.: Cybernetics. New York: John Wiley and Sons 1948.