Author: Gorodkin Srensen Winther
Abstract: The genotype-phenotype relation for the 256 elementary cellular automata is studied using neural networks. Neural network are trained to learn the mapping from each genotype rule to its corresponding Li-Packard phenotype class. By investigating learning curves and networks pruned with Optimal Brain Damage on all 256 rules, we find that there is a correspondence between the complexity of the phenotype class and the complexity (net size needed and test error) of the net trained on the class. For Li-Packard Class A (null rules) it is possible to extract a simple logical relation from the pruned network. The observation that some rules are harder for the networks to classify leads ...
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9.3) Autômatos Celulares e Sistemas Imunológicos
Immunology is a rather new field of research; although the first description of immunization dates back to Thucydides' Historu of the Pelloponesian Wars and the first experiments on vaccinations were performed by Jenner in the 18th century; the birth of immunology as a modern science was in the late 19th century when Kock proved the infectious diseases were caused by pathogenic microorganisms, Pasteur devised vaccines against anthrax and rabies and finally von Behring discovered antibodies.
Nowadays immunology is composed of a hard core of well accepted and proven facts covered by an unstable crust of many unproven theories and real facts of unknown relevance. In the context the use of mathematical models and computer simulations (in machine experiments) turns out to be a useful tool for testing hypothesis and planning real in vivo and in vitro experiments.
Many different models have been proposed to study some of more controversial features of immune responses like diversity, memory and regulation.
The defense mechanisms used by the body against an attack from foreign substances (antigens) are several, they include: physical barriers, phagocyte cells, different clones of particular white blood cells (lymphocytes) and various blood-borne molecules (e.g., antibodies). Some of these mechanisms are present prior to exposure to antigens and their response doesn't change upon further exposure to the same antigen. This kind of response is called natural immunity. There are other mechanisms with more specific behavior, antigens induce them and their response increases in magnitude and defense capabilities with successive exposure to the same antigens. These mechanisms are called acquired (or specific) immunity and are those considered in most of models.
The main features of specific immunity are: Specificity, Diversity, Maturation, Memory, and Discrimination of self from non-self.
Cellular Automata Models
Many models of immune response based on cellular automata have been introduced. The first CA approach to immunology was the model proposed by Kaufman, Urbain and Thomas.
They considered five populations: Antibodies A, helper cells H, suppressor cells S, cells B, and the virus V. All of them are considered binary variables: 1 corresponds to high concentrations, 0 to low ones. The evolution rules are (where primes indicates the updated state):
A' = V and Band H
H' = H or V and not S
S' = H or S
B' = H and (V or B)
V' = V and not A
Where OR, AND and Not are the usual logical operators. We have five states CA with long-range couplings. The system has the following fixed points
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Final State
|
A
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H
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S
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B
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V
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Virgin
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0
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0
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0
|
0
|
0
|
Vaccinated
|
0
|
1
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1
|
0
|
0
|
Immune
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0
|
1
|
1
|
1
|
0
|
Paralyzed
|
0
|
0
|
1
|
0
|
0
|
Paralyzed and Sick
|
0
|
0
|
1
|
0
|
1
|
Starting from one of the first three states (virgin, vaccinated and immune) and adding a virus, we let the system reach the immune state. The transient time is shorter starting from vaccinated and immune state. this very simple model is then able to reproduce some basic features of immune response. This model has been extended and analyzed further by Kaufman and Thomas and Kaufman where they add different stages of activation for the cells and considerer also an analysis in term of differential equations. All possible five Boolean variables automata have been studied by Chowdhury and Stauffer.
Autoimmune disease like multiple sclerosis, cancer and AIDS are simulated with similar automata. a probabilistic CA for AIDS was proposed and more AIDS models are discussed.
Bibliografia:
Fonte: http://citeseer.nj.nec.com
Referências Principais:
Title: Modeling Evolution and Immune System by Cellular Automata Author: Bezzi Sissa Via
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