Modelling and Formal Verification of Neuronal Archetypes Coupling

International audienceIn 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

Computational Logic for Biomedicine and Neuroscience

We advocate here the use of computational logic for systems biology, as a \emph{unified and safe} framework well suited for both modeling the dynamic behaviour of biological systems, expressing properties of them, and verifying these properties. The potential candidate logics should have a traditional proof theoretic pedigree (including either induction, or a sequent calculus presentation enjoying cut-elimination and focusing), and should come with certified proof tools. Beyond providing a reliable framework, this allows the correct encodings of our biological systems. % For systems biology in general and biomedicine in particular, we have so far, for the modeling part, three candidate logics: all based on linear logic. The studied properties and their proofs are formalized in a very expressive (non linear) inductive logic: the Calculus of Inductive Constructions (CIC). The examples we have considered so far are relatively simple ones; however, all coming with formal semi-automatic proofs in the Coq system, which implements CIC. In neuroscience, we are directly using CIC and Coq, to model neurons and some simple neuronal circuits and prove some of their dynamic properties. % In biomedicine, the study of multi omic pathway interactions, together with clinical and electronic health record data should help in drug discovery and disease diagnosis. Future work includes using more automatic provers. This should enable us to specify and study more realistic examples, and in the long term to provide a system for disease diagnosis and therapy prognosis.Nous pr{\^o}nons ici l'utilisation d'une logique calculatoire pour la biologie des systèmes, en tant que cadre \emph{unifié et sûr}, bien adapté à la fois à la modélisation du comportement dynamique des systèmes biologiques,à l'expression de leurs propriétés, et à la vérification de ces propriétés.Les logiques candidates potentielles doivent avoir un pedigree traditionnel en théorie de la preuve (y compris, soit l'induction, soit une présentation en calcul des séquents, avec l'élimination des coupures et des règles ``focales''), et doivent être accompagnées d'outils de preuves certifiés.En plus de fournir un cadre fiable, cela nous permet d'encoder de manière correcte nos systèmes biologiques. Pour la biologie des systèmes en général et la biomédecine en particulier, nous avons jusqu'à présent, pour la partie modélisation, trois logiques candidates : toutes basées sur la logique linéaire.Les propriétés étudiées et leurs preuves sont formalisées dans une logique inductive (non linéaire) très expressive : le Calcul des Constructions Inductives (CIC).Les exemples que nous avons étudiés jusqu'à présent sont relativement simples. Cependant, ils sont tous accompagnés de preuves formelles semi-automatiques dans le système Coq, qui implémente CIC. En neurosciences, nous utilisons directement CIC et Coq pour modéliser les neurones et certains circuits neuronaux simples et prouver certaines de leurs propriétés dynamiques.En biomédecine, l'étude des interactions entre des voies multiomiques,ainsi que les études cliniques et les données des dossiers médicaux électroniques devraient aider à la découverte de médicaments et au diagnostic des maladies.Les travaux futurs portent notamment sur l'utilisation de systèmes de preuves plus automatiques.Cela devrait nous permettre de modéliser et d'étudier des exemples plus réalistes,et à terme de fournir un système pour le diagnostic des maladies et le pronostic thérapeutique

Discovering Causal Relations and Equations from Data

Physics is a field of science that has traditionally used the scientific method to answer questions about why natural phenomena occur and to make testable models that explain the phenomena. Discovering equations, laws and principles that are invariant, robust and causal explanations of the world has been fundamental in physical sciences throughout the centuries. Discoveries emerge from observing the world and, when possible, performing interventional studies in the system under study. With the advent of big data and the use of data-driven methods, causal and equation discovery fields have grown and made progress in computer science, physics, statistics, philosophy, and many applied fields. All these domains are intertwined and can be used to discover causal relations, physical laws, and equations from observational data. This paper reviews the concepts, methods, and relevant works on causal and equation discovery in the broad field of Physics and outlines the most important challenges and promising future lines of research. We also provide a taxonomy for observational causal and equation discovery, point out connections, and showcase a complete set of case studies in Earth and climate sciences, fluid dynamics and mechanics, and the neurosciences. This review demonstrates that discovering fundamental laws and causal relations by observing natural phenomena is being revolutionised with the efficient exploitation of observational data, modern machine learning algorithms and the interaction with domain knowledge. Exciting times are ahead with many challenges and opportunities to improve our understanding of complex systems.Comment: 137 page

An Approach for the Development of Complex Systems Archetypes

The purpose of this research is to explore the principles and concepts of systems theory in pursuit of a collection of complex systems archetypes that can be used for system exploration and diagnostics. The study begins with an examination of the archetypes and classification systems that already exist in the domain of systems theory. This review includes a critique of their purpose, structure, and general applicability. The research then develops and employs a new approach to grounded theory, using a visual coding model to explore the origins, relationships, and meanings of the principles of systems theory. The goal of the visual grounded theory approach is to identity underlying, recurrent imagery in the systems literature that will form the basis for the archetypes. Using coding models derived from the literature, the study then examines the interrelationships between system principles. These relationships are used to clearly define the environment where the archetypes are found in terms of energy, entropy and time. A collection of complex system archetypes is then derived which are firmly rooted in the literature, as well as being demonstrably manifested in the real world. The definitions of the emerging complex systems archetypes are consistent with the environmental definition and are governed by the system’s behavior related to energy collection, entropy displacement, and the pursuit of viability. Once the archetypes have been identified, this study examines the similarities and differences that distinguish them. The individual system principles that either define or differentiate each of the archetypes are described, and real-world manifestations of the archetypes are discussed. The collection of archetypes is then examined as a continuum, where they are related to one another in terms of energy use, entropy accumulation, self-modification and external-modification. To illustrate the applicability of these archetypes, a case study is undertaken which examines a medium-sized organization with multiple departments in an industrial setting. The individual departments are discussed in detail, and their archetypical forms are identified and described. Finally, the study examines future applications for the archetypes and other research that might enhance their utility for complex systems governance