#ABOUT 
Year 2 in Nice;

Stochastic Modelling in Neuroscience

The specialisation track “Stochastic modelling in neuroscience” will be offered at the Université de la Côte d’Azur in Nice. The teaching staff are affiliated to the CRNS Laboratoire J. A. Dieudonne, in particular to the Probability and Statistics Team, featuring experts in the field at outstanding level, such as Francois Delarue (AMS Doob Prize 2020), Patricia Reynaud-Bouret (Director of the “NeuroMod” Institute), and Cédric Bernardin (a leading international figure in the field of stochastic calculus and applications). The former two are acknowledged researchers in the applications of probability and stochastic analysis to neuroscience. Part of the courses will be taught by staff at the “NeuroMod” Institute for Modelling in Neuroscience and Cognition.

The course “Stochastic calculus with applications to neuroscience”, taught by Cédric Bernardin, will provide stochastic calculus tools to be applied to the dynamics of biological neural networks. The course “Probabilistic numerical methods” will address Monte Carlo and quasi Monte Carlo numerical methods. It will be taught by Etienne Tanré, who runs several projects in this field. The course “Stochastic control and interacting systems” addresses a very innovative field at the interface of optimal control, stochastic calculus, and mathematical analysis, which has relevant contributions to mathematical modelling in neuroscience. It will be taught by one of the most important experts in the field such as Francois Delarue. Two courses will be taken from the existing Modelling for Neural and Cognitive Systems MSc program: “Stochastic models in neurocognition and their statistical inference”, taught by the Director of the NeuroMod Institute Patricia Reynaud-Bouret, and “ Behavioural and cognitive neuroscience”, taught by Alice Guyon, research director at CNRS at the Institute of Molecular and Cellular Pharmacology. The latter is the application-driven course of this track, it will be exclusively focused on neuroscience modelling and it will analyse the neurobiological basis for higher mental functions through several examples.

This specialisation track will give the opportunity to spend the thesis semester in one of the institutes involved with the teaching or in one of the industrial partners, such as Fotonower, a company devoted to artificial intelligence and image processing.

September 2022

September 2022

September 2023

🎓 Graduation

#Year 2 in Nice EMJMD InterMaths Study Track

Stochastic Modelling in Neuroscience;

Campus

University of Côte d'Azur

Year

2

Semester

1

ECTS Credits

30

Language

English
Behavioural and cognitive neuroscience

ECTS Credits: 6   |   Semester: 1   |   Year: 2   |   Campus: University of Côte d'Azur   |   Language: English

Unit Coordinator: Alice Guyon, Ingrid Bethus

Aims:

Neuronal and cognitive systems cannot be modeled without knowledge of the basics of Neurosciences, from the molecular to the integrated level, involved in cognition and behaviors.

The first part of the program focuses on elementary neurophysiology and neuroanatomy. What are the different subparts constituting the nervous system and what are their main roles? How are neurons constituted? How do they generate activity and communicate with other neurons?

The second part of the program explores, with an integrative perspective, the neurobiological basis for higher mental functions through several examples. Sensorimotor functions are at the root of all the other processes. So the study of feeding behaviors is a good way to learn about the bio-logic of elementary behaviors, starting from the physiology of the autonomic nervous system and ending with neuroethological issues. Learning and memory are the basic processes of higher mental functions and also hot topics with applications in many domains.

In addition to all these fundamentals, the course also explains the materials and methods used in cognitive neurosciences to obtain data at the different levels of organization of nervous, cognitive and behavioral systems. This course is taught by a teaching staff member of the Master Programme Mod4NeuCog at UCA.

Content:

  • Neuronal and cognitive systems
  • Neurophysiology and neuroanatomy
  • Neurobiological basis for higher mental functions

Stochastic control and interacting systems

ECTS Credits: 6   |   Semester: 1   |   Year: 2   |   Campus: University of Côte d'Azur   |   Language: English

Unit Coordinator: François Delarue

Aims:

The course has two purposes. The first one is to provide the basic knowledge in stochastic control, control for discrete and continuous processes, dynamic programming principle, dynamic programming equation, Hamilton-Jacobi-Bellman equation.

The second part of the course will address interacting particle systems, as some of them are now currently used in the modelling of large neural networks. Applications to self-organisation and phase transition in neuroscience will be considered and, in connection with the first part of course, some learning methods will be discussed as well. 

Content:

  • Stochastic control
  • Dynamic programming principle
  • HJB equation, interacting particle system
  • Mean field models 
  • Learning methods

Pre-requisites:

Probability with measure theory, optimization, stochastic calculus

#Final Semester Dissertation;

The thesis topic can be proposed by the track coordinator or by the student. In any case, the local coordinator has the responsibility to provide an advisor. The student’s taste and expectations are met whenever possible. The student must write a short thesis project, with the help of her/his advisor, to be submitted to the Executive Committee, which has to approve the thesis project before its formal start. The thesis topic will preferably deal with a problem proposed by a private company, if possible chosen among the Consortium Industrial Partners.

The final master’s degree examination, while respecting the local regulations, will consist as a general rule in two parts: an oral examination on the topic of the thesis, and the defense of the thesis.

In this examination the candidate will be required to demonstrate good knowledge of his/her specialization track and a capability for working independently and solving problems on experimental, numerical, technological, design or modelling applications. The semester may include an internship within a collaborating company or institution. In this case, a tutor from the involved partner and an academic supervisor will be appointed.

Students who have satisfied all the requirements of the degree programme will be awarded a Joint Master Degree in Interdisciplinary Mathematics by the Universities where the student has spent at least one semester

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