Contract type : Internship
Level of qualifications required : Graduate degree or equivalent
Fonction : Internship Research
Network models are currently used in different contexts of application due to the possibility of representing data and their interconnections in an intuitive way. Topological Data Anal-ysis (TDA) provides a set of emerging tools to describe structured data, such as networks. For instance, Betti numbers and persistent homology are gaining attention in a wide variety offields with encouraging results both on the characterization of different graph models and on real-world data [2, 3]. For these reasons, we would like to apply these approaches in the context of brain functional connectivity to extend current state-of-the-art results. In neuroscience, network models can depict the system of connections among regions of the brain . These networks can be leveraged to analyze the brain under diverse conditions, such as in comatose or anesthetized subjects, or to determine discriminant network features. Brain functional connectivity networks usually exhibit small-world properties that will be refined during this internship. In addition, during the network extraction process, edges might be identified incorrectly. The impact of these spurious edges on the topology of the graphs will be evaluated in the second part of the internship.
- Get familiar with topological data analysis theory and algorithm tools.
- Explore the evolution of Betti numbers with regard to graph sparsity level for different datasets.
- Extend the work in  to small-world networks in order to determine subcategories of graphs in this regime.
- Explore the relation between the different Betti numbers and the usual graph metrics (clustering coefficients, efficiency, ...) on theoretical graphs (Watts-Strogatz, Erdös–Rényi, ...) and real-world functional connectivity graphs.
- Explore the impact of spurious edges on the Betti numbers of different theoretical and real-world graphs.
- Master 2 or 3rd-year engineering student in a relevant quantitative field
- Programming language: Python
- Applied mathematics: graph theory, topology would be a plus
- Subsidized meals
- Partial reimbursement of public transport costs
- Professional equipment available (videoconferencing, loan of computer equipment, etc.)
- Social, cultural and sports events and activities
- Access to vocational training
- Theme/Domain :
Modeling and Control for Life Sciences
Statistics (Big data) (BAP E)
- Town/city : Montbonnot
- Inria Center : CRI Grenoble - Rhône-Alpes
- Starting date : 2022-02-01
- Duration of contract : 5 months
- Deadline to apply : 2022-01-15
Inria is the French national research institute dedicated to digital science and technology. It employs 2,600 people. Its 200 agile project teams, generally run jointly with academic partners, include more than 3,500 scientists and engineers working to meet the challenges of digital technology, often at the interface with other disciplines. The Institute also employs numerous talents in over forty different professions. 900 research support staff contribute to the preparation and development of scientific and entrepreneurial projects that have a worldwide impact.
Instruction to apply
Defence Security :
This position is likely to be situated in a restricted area (ZRR), as defined in Decree No. 2011-1425 relating to the protection of national scientific and technical potential (PPST).Authorisation to enter an area is granted by the director of the unit, following a favourable Ministerial decision, as defined in the decree of 3 July 2012 relating to the PPST. An unfavourable Ministerial decision in respect of a position situated in a ZRR would result in the cancellation of the appointment.
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