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Topology driven modeling: the IS metaphor.

Merelli E, Pettini M, Rasetti M - Nat Comput (2015)

Bottom Line: The data topological analysis will select global features, reducible neither to a mere subgraph nor to a metric or vector space.How the immune system reacts, how it evolves, how it responds to stimuli is the result of an interaction that took place among many entities constrained in specific configurations which are relational.Within this metaphor, the proposed method turns out to be a global topological application of the S[B] paradigm for modeling complex systems.

View Article: PubMed Central - PubMed

Affiliation: School of Science and Technology, University of Camerino, Camerino, Italy.

ABSTRACT

In order to define a new method for analyzing the immune system within the realm of Big Data, we bear on the metaphor provided by an extension of Parisi's model, based on a mean field approach. The novelty is the multilinearity of the couplings in the configurational variables. This peculiarity allows us to compare the partition function [Formula: see text] with a particular functor of topological field theory-the generating function of the Betti numbers of the state manifold of the system-which contains the same global information of the system configurations and of the data set representing them. The comparison between the Betti numbers of the model and the real Betti numbers obtained from the topological analysis of phenomenological data, is expected to discover hidden n-ary relations among idiotypes and anti-idiotypes. The data topological analysis will select global features, reducible neither to a mere subgraph nor to a metric or vector space. How the immune system reacts, how it evolves, how it responds to stimuli is the result of an interaction that took place among many entities constrained in specific configurations which are relational. Within this metaphor, the proposed method turns out to be a global topological application of the S[B] paradigm for modeling complex systems.

No MeSH data available.


model
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Fig2: model

Mentions: Figure 2 shows a simple adaptive system represented by finite state machines, which is the most general among other models, such as complex automata, higher dimensional automata, hypernetworks, recurrent neural network, multiagent, etc. On the left hand side, the two components are entangled in such a way that the emergent behaviour is subject to the global constraints while the global structure is affected by the emergent behavior. On the right, an system is depicted as a light oval that embeds a dark round , showing the adaptation phase that takes place whenever the computation can no longer evolve in the current context (the on the lower right corner). The adaptation phase allows to relax the set of constraints so as to permit further computations—in the figure the black arrow drawn between the two components, represents the change of the global context, and the dashed arrow between the dark rounds represents the unfolding of the computation. The evolution of such a model relies on the ability of the system to adapt its computation to global requirements.Fig. 2


Topology driven modeling: the IS metaphor.

Merelli E, Pettini M, Rasetti M - Nat Comput (2015)

model
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4541713&req=5

Fig2: model
Mentions: Figure 2 shows a simple adaptive system represented by finite state machines, which is the most general among other models, such as complex automata, higher dimensional automata, hypernetworks, recurrent neural network, multiagent, etc. On the left hand side, the two components are entangled in such a way that the emergent behaviour is subject to the global constraints while the global structure is affected by the emergent behavior. On the right, an system is depicted as a light oval that embeds a dark round , showing the adaptation phase that takes place whenever the computation can no longer evolve in the current context (the on the lower right corner). The adaptation phase allows to relax the set of constraints so as to permit further computations—in the figure the black arrow drawn between the two components, represents the change of the global context, and the dashed arrow between the dark rounds represents the unfolding of the computation. The evolution of such a model relies on the ability of the system to adapt its computation to global requirements.Fig. 2

Bottom Line: The data topological analysis will select global features, reducible neither to a mere subgraph nor to a metric or vector space.How the immune system reacts, how it evolves, how it responds to stimuli is the result of an interaction that took place among many entities constrained in specific configurations which are relational.Within this metaphor, the proposed method turns out to be a global topological application of the S[B] paradigm for modeling complex systems.

View Article: PubMed Central - PubMed

Affiliation: School of Science and Technology, University of Camerino, Camerino, Italy.

ABSTRACT

In order to define a new method for analyzing the immune system within the realm of Big Data, we bear on the metaphor provided by an extension of Parisi's model, based on a mean field approach. The novelty is the multilinearity of the couplings in the configurational variables. This peculiarity allows us to compare the partition function [Formula: see text] with a particular functor of topological field theory-the generating function of the Betti numbers of the state manifold of the system-which contains the same global information of the system configurations and of the data set representing them. The comparison between the Betti numbers of the model and the real Betti numbers obtained from the topological analysis of phenomenological data, is expected to discover hidden n-ary relations among idiotypes and anti-idiotypes. The data topological analysis will select global features, reducible neither to a mere subgraph nor to a metric or vector space. How the immune system reacts, how it evolves, how it responds to stimuli is the result of an interaction that took place among many entities constrained in specific configurations which are relational. Within this metaphor, the proposed method turns out to be a global topological application of the S[B] paradigm for modeling complex systems.

No MeSH data available.