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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.


S[B] adaptability checking
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Fig3: S[B] adaptability checking

Mentions: It is quite evident that the model described above can be applied when the system requirements are known a priori and the adaptation phase reduces to dynamic selection of possible states with respect to environmental changes. To overcome this limit and allow the definition of a model that can change the set of global constraints and consequently the set of computations at run-time, we adopt the IS metaphor to characterize the adaptation phase of an model. The global context is defined as a function of the topological invariants extracted from the analysis of the space of data: the Betti numbers. In the model proposed in previous section the Betti numbers and the interaction matrix faithfully represent the relations hidden in the current space of data. Thus, the adaptation phase of an system is indeed represented as the interplay capabilities of the immune system to identify, classify and learn the new relationship emerging among the actors of the system. Figure 3 graphically mimics the adaptability checking performed by an system; it starts on the upper left corner of the figure with the actual model that, when necessary, may be adapted to a new context provided by the topological analysis of the space of data (set of observations of real system). The changes in the context is determined by comparing the Betti numbers of the space of data with the Betti numbers of the actual model. If there is no new knowledge, the model remains otherwise it adapts to the new context by learning the knowledge provided by the Betti numbers, updating its computation with new set of relations and becoming . This learning process reminds us of what in literature is called recurrent neural network, a process based on active exploration of an unknown environment and the generation of a finite state automata model of the environment.Fig. 3


Topology driven modeling: the IS metaphor.

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

S[B] adaptability checking
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

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

Fig3: S[B] adaptability checking
Mentions: It is quite evident that the model described above can be applied when the system requirements are known a priori and the adaptation phase reduces to dynamic selection of possible states with respect to environmental changes. To overcome this limit and allow the definition of a model that can change the set of global constraints and consequently the set of computations at run-time, we adopt the IS metaphor to characterize the adaptation phase of an model. The global context is defined as a function of the topological invariants extracted from the analysis of the space of data: the Betti numbers. In the model proposed in previous section the Betti numbers and the interaction matrix faithfully represent the relations hidden in the current space of data. Thus, the adaptation phase of an system is indeed represented as the interplay capabilities of the immune system to identify, classify and learn the new relationship emerging among the actors of the system. Figure 3 graphically mimics the adaptability checking performed by an system; it starts on the upper left corner of the figure with the actual model that, when necessary, may be adapted to a new context provided by the topological analysis of the space of data (set of observations of real system). The changes in the context is determined by comparing the Betti numbers of the space of data with the Betti numbers of the actual model. If there is no new knowledge, the model remains otherwise it adapts to the new context by learning the knowledge provided by the Betti numbers, updating its computation with new set of relations and becoming . This learning process reminds us of what in literature is called recurrent neural network, a process based on active exploration of an unknown environment and the generation of a finite state automata model of the environment.Fig. 3

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.