The Front Structure of Growing Fungus Colonies truecm
Fungus grown on agar plates show interesting and complex patterns
where the colony gets trapped at some places finally showing
up as a cellular structure described by a specific characteristic length scale
in the front. We believe that this cellular structure is determined by
the production of waste products in an optimal growth zone at the interface.
In this zone the cells double on a specific time scale and the produced
waste slowly diffuses in the growth zone. We model this using
an analogy to solidification fronts where diffusing impurities
determines the wavelength of the cellular behavior. We plan to simulate
the corresponding diffusion equation and hope to be able to predict the wave
length of the growing colony.
M. H. Jensen, T. Sams, K. Sneppen, (B. E. Christensen)
1/f Noise in Sea-level Elevations
M. H. Jensen, T. Sams, K. Sneppen, (B. E. Christensen) truecm
1/f Noise in Sea-level Elevations truecm
We have analyzed a 101 year record of sea-level elevations. The data
consist of hourly recordings of sea-level elevations from
1889 to 1990 for the port of Esbjerg in Denmark. The power spectrum shows
three distinct regimes.
In the frequency range from 1/2 hour to 1/3 day the
spectrum shows 1/f behavior (plus the tidal components).
This is followed at lower frequencies by a two-decade region of 1/f noise,
finally crossing over to white noise at a frequency of 1/3 year.
This is one of the rare examples where a lower cutoff to 1/f noise is found.
We believe the 1/f noise is simply the result a diffusive process
observed in a particular way, possibly crossing over to a wave-equation at
shorter time-scales. In addition, intermittent behavior is suggested by
stretched exponential probability density distributions. By using methods based
on the correlation integral both the 1/f noise and the high frequency
part of the spectrum have been checked for low-dimensionality.
(H. Svensmark), (J.D. Pietrzak) and P. Dimon
From Macro- to Microeconomy: A Cascade Picture
(H. Svensmark), (J.D. Pietrzak) and P. Dimon truecm
From Macro- to Microeconomy: A Cascade Picture truecm
We study the flow of values from the macro-scale of the economy to the
micro-scale. Using a cascade picture we formulate a dynamical model
from the flow of values through the steps of the economy. The model has
the structure of a shell model where the scales are separated
Using the sum of values at all scales as a conserved quantity we
study the fluctuations of the values at the different scales and
hope to be able to reproduce the observed distribution functions
for various indexes in the economy.
M.H. Jensen and K. Sneppen
Self-Adaptive Neural Networks
M.H. Jensen and K. Sneppen truecm
Self-Adaptive Neural Networks truecm
We have undertaken neural network studies with particular emphasis on reinforcement learning and behavior (conditioning problems etc.). Models are developed that are feature focusing, dynamical, and able to function in an changeable environment. The research takes place on different levels. On the macroscopic level, we study the scientific descriptions of behavioral processes, and their `translations' into neural network problems. On the microscopic level, we investigate numerically and mathematically the dynamical rules underlying the models.
Our basic research has invoked a surprisingly
large interest from various industries. The interest concerns
customer information, resource allocation, process control,
and data acquisition.
P. AlstrÝm, P. Andresťn, K. N. Berntsen, M. Krogh, J. Nordfalk,
N. K. Petersen and A. Vallespin Gomez
Biological Evolution: Fitness Optimization and the Decay in Extinction Rate
P. AlstrÝm, P. Andresťn, K. N. Berntsen, M. Krogh, J. Nordfalk, N. K. Petersen and A. Vallespin Gomez truecm
Biological Evolution: Fitness Optimization and the Decay in Extinction Rate truecm
Fossil records indicate that the background extinction rate
has decreased since Cambrian time. As pointed out by
Raup and Sepkoski, this observation may be a natural
consequence of fitness optimization leading to prolonged
survival of species through evolutionary time.
Based on this view, we have investigated simple
mechanisms that lead to fitness optimization and a related
decay in extinction rate. In our model,
species evolve through punctuated equilibria.
We consider two different rules for extinction. The first
assumes that a fixed fraction of evolutionary jumps leads to
extinctions. The second specifically introduces a competition rule
acting among neighbors in a suitably defined ecology.
We have numerically determined some of the evolutionary measures
defined in biological evolution theory, and compared them with
data from fossil records. Our simple model displays a behavior
strikingly similar to the vastly more complex biological world.
(M. R. Schmidt), (P. Sibani) and P. AlstrÝm
Self-Organized Criticality, Stochastic Cellular Automata and the Game of Life
(M. R. Schmidt), (P. Sibani) and P. AlstrÝm truecm
Self-Organized Criticality, Stochastic Cellular Automata and the Game of Life truecm
The question of self-organized criticality in Conway's game of life
is studied in the broader context of stochastic cellular automata.
A main question is to what extent the probing underlying the claimed
criticality can be seen as a limit case of a system with probabilities
approaching 0 (or 1), i.e. the deterministic limit. We have carried
out extensive numerical studies of a selected stochastic cellular
automaton with a phase transitions line ending near the deterministic
limit describing Conway's game of life. Static as well as dynamical
exponents are determined and compared to those obtained in
directed percolation and other related models.
P. AlstrÝm, J. Nordfalk and N. K. Petersen
P. AlstrÝm, J. Nordfalk and N. K. Petersen