Verification of Temporal Properties of Neuronal Archetypes Modeled as Synchronous Reactive Systems

Maria, Elisabetta De; Muzy, Alexandre; Gaffé, Daniel; Ressouche, Annie; Grammont, Franck

doi:10.1007/978-3-319-47151-8_7

Cited by 12 publications

(17 citation statements)

References 18 publications

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“…The properties were automatically verified thanks to the model checker kind2. Such a tool, which relies on Satisfiability Modulo Theories (SMT) based k-induction, turned out to be more efficient than other model checkers based on convex polyhedra representation of integers and reals [2].…”

Section: Discussionmentioning

confidence: 99%

“…Given a contralateral inhibition archetype with two or more neurons, if a sequence of 1 is given as input, starting from a given time one neuron is activated and the other ones are inhibited. Some further properties concerning the different archetypes can be found in [3].…”

Section: (F ))mentioning

confidence: 99%

“…In our central nervous system, neurons seem to form some small specific graphs presenting biologically relevant structures and behaviors [2]. These graphs, to which we refer as archetypes, can be coupled to constitute the elementary bricks of bigger neuronal networks.…”

Section: Introductionmentioning

confidence: 99%

“…The paper, which is the follow-up of [2], is organized as follows. In Section 2 we present a discrete version of the LI&F model.…”

Section: Introductionmentioning

confidence: 99%

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Modelling and Formal Verification of Neuronal Archetypes Coupling

Maria

L’Yvonnet

Gaffé

et al. 2017

Proceedings of the 8th International Conference on Computational Systems-Biology and Bioinformatics

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In the literature, neuronal networks are often represented as graphs where each node symbolizes a neuron and each arc stands for a synaptic connection. Some specific neuronal graphs have biologically relevant structures and behaviors and we call them archetypes. Six of them have already been characterized and validated using formal methods. In this work, we tackle the next logical step and proceed to the study of the properties of their couplings. For this purpose, we rely on Leaky Integrate and Fire neuron modeling and we use the synchronous programming language Lustre to implement the neuronal archetypes and to formalize their expected properties. Then, we exploit an associated model checker called kind2 to automatically validate these behaviors. We show that, when the archetypes are coupled, either these behaviors are slightly modulated or they give way to a brand new behavior. We can also observe that different archetype couplings can give rise to strictly identical behaviors. Our results show that time coding modeling is more suited than rate coding modeling for this kind of studies.

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Section: Discussionmentioning

confidence: 99%

Section: (F ))mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The paper, which is the follow-up of [2], is organized as follows. In Section 2 we present a discrete version of the LI&F model.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modelling and Formal Verification of Neuronal Archetypes Coupling

Maria

L’Yvonnet

Gaffé

et al. 2017

Proceedings of the 8th International Conference on Computational Systems-Biology and Bioinformatics

Self Cite

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“…As far as human neural networks are concerned, there is recent work that has focused on their formal verification. In [21,22], the authors consider the synchronous paradigm to model and verify some specific graphs composed of a few biological neurons. These graphs or mini-circuits, characterized by biologically relevant structures and behaviors, are referred to as archetypes and constitute the fundamental elements of neuronal information processing.…”

Section: Introductionmentioning

confidence: 99%

Modelling and Verifying Dynamic Properties of Biological Neural Networks in Coq

Bahrami

Maria

Felty

2018

Proceedings of the 9th International Conference on Computational Systems-Biology and Bioinformatics

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Formal verification has become increasingly important because of the kinds of guarantees that it can provide for software systems. Verification of models of biological and medical systems is a promising application of formal verification. Human neural networks have recently been emulated and studied as a biological system. Some recent research has been done on modelling some crucial neuronal circuits and using model checking techniques to verify their temporal properties. In large case studies, model checkers often cannot prove the given property at the desired level of generality. In this paper, we provide a model using the Coq Proof Assistant and prove properties concerning the dynamic behavior of some basic neuronal structures. Understanding the behavior of these modules is crucial because they constitute the elementary building blocks of bigger neuronal circuits. By using a proof assistant, we guarantee that the properties are true for any input values, any length of input, and any amount of time. With such a model, there is the potential to detect inactive regions of the human brain and to treat mental disorders. Furthermore, our approach can be generalized to the verification of other kinds of networks, such as regulatory, metabolic, or environmental networks.

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