Daniel Gaffé

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

There exists many ways to connect two, three or more neurons together to form different graphs. We call archetypes only the graphs whose properties can be associated with specific classes of biologically relevant structures and behaviors. These archetypes are supposed to be the basis of typical instances of neuronal information processing. To model different representative archetypes and express their temporal properties, we use a synchronous programming language dedicated to reactive systems (Lustre). The properties are then automatically validated thanks to several model checkers supporting data types. The respective results are compared and depend on their underlying abstraction methods.

Computer-aided Formal Proofs about Dendritic Integration within a Neuron

This article is threefold: (i) we define the first formal framework able to model dendritic integration within biological neurons, (ii) we show how we can turn continuous time into discrete time consistently and (iii) we show how a Lustre model checker can automatically perform proofs about neuron input/output behaviours owing to our framework. Our innovative formal framework is a carefully defined trade-off between abstraction and biological relevance in order to facilitate proofs. This framework is hybrid: inputs entering the synapses as well as the soma output are discrete signals made of spikes but, inside the dendrites, we combine signals quantitatively using real numbers. The soma potential is inevitably specified as a differential equation to keep a biologically accurate modelling of signal accumulation. This prevents from performing simple formal proofs. This has been our motivation to discretize time. Owing to this discretization, we are able to encode our neuron models in Lustre. Lustre is a particularly well suited flow-based language for our purpose. We also encode in Lustre a property of input/output equivalence between neurons in such a way that the model checker Kind2 is able to automatically handle the proof.

Semantic Studies of a Synchronous Approach to Activity Recognition

Many important and critical applications such as surveillance or healthcare require some form of (human) activity recognition. Activities are usually represented by a series of actions driven and triggered by events. Recognition systems have to be real time, reactive, correct, complete, and dependable. These stringent requirements justify the use of formal methods to describe, analyze, verify, and generate effective recognition systems. Due to the large number of possible application domains, the researchers aim at building a generic recognition system. They choose the synchronous approach because it has a well-founded semantics and it ensures determinism and safe parallel composition. They propose a new language to represent activities as synchronous automata and they supply it with two complementary formal semantics. First a behavioral semantics gives a reference definition of program behavior using rewriting rules. Second, an equational semantics describes the behavior in a constructive way and can be directly implemented. This paper focuses on the description of these two semantics and their relation.

Modelling and Formal Verification of Neuronal Archetypes Coupling

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.

Wireless sensor network protocol property validation through the system's simulation in a dedicated framework

This article presents a new simulation framework for wireless sensor networks based on QEMU and SystemC that aims at validating the binary code of wireless protocols by checking that the protocols implementation complies with its property specifications during simulation. We describe the development of the model of a nodes precise hardware platform capable of executing the protocols binary code using TLMu, a QEMU wrapper that integrates into SystemC. Our simulation framework incorporates high abstraction level node models and highly detailed node models in a wireless network model based on SystemC. An observer module is added to the simulation framework to analyze exchanged frames and detect protocol property violations. Through our experimental study, we show the correct functionality of our hardware platform model through comparison with real frame exchange traces and the verification of one of the protocols properties during simulation.