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Neuronal Dynamics from a complex network perspective

Project Description

The human brain is possibly the most intriguing complex system we know. The combination of experimental work and theoretical approaches has gained many insides in the last century but we are still far away from a real understanding.

The goal of the project is to combine dynamical-system and statistical-mechanics tools to understand the functioning of neural networks. While most of computational neuroscience focuses on rate models, it is obvious that neurons communicate by emitting spikes and it is thereby worth, if not necessary, to explore more realistic setups involving pulse-coupled neurons. In such a context, we wish to make use of concepts such as synchronization, phase-transitions, response theory to improve our comprehension.

On a more specific level, the project unfolds by means of direct numerical simulations of the "microscopic" equations, combined with the analysis of "macroscopic" equations describing suitable probability densities.

Depending on the interest of the potential applicants, the focus can be adjusted and be more theoretically or numerically oriented.

The student will learn techniques to characterise dynamical systems by means of chaotic measures (e.g. Lyanunov exponents, entropy, dimension), network measures and universal approaches to analyse large data. The project will familiarise the student with model building with a neuronal context and beyond, transferable to other natural and manmade complex networks. This includes the understanding of different levels of abstraction, the necessary and meaningful choice of simplifications for the model building in the context of scientific question.

Candidates should have (or expect to achieve) a UK honours degree at 2.1 or above (or equivalent) in physics, mathematics, computational neuroscience and related degrees.

Essential background: mathematical background, programming skills are highly desirable


• Apply for Degree of Doctor of Philosophy in Physics
• State name of the lead supervisor as the Name of Proposed Supervisor
• State ‘Self-funded’ as Intended Source of Funding
• State the exact project title on the application form

When applying please ensure all required documents are attached:

• All degree certificates and transcripts (Undergraduate AND Postgraduate MSc-officially translated into English where necessary)
• Detailed CV
• Details of 2 academic referees

Informal inquiries can be made to Prof Antonio Politi () with a copy of your curriculum vitae and cover letter. All general enquiries should be directed to the Postgraduate Research School ()

Funding Notes

This project is advertised in relation to the research areas of the discipline of Physics and Applied Mathematics. The successful applicant will be expected to provide the funding for Tuition fees, living expenses and maintenance. Details of the cost of study can be found by visiting View Website. THERE IS NO FUNDING ATTACHED TO THESE PROJECTS.


E. Ullner and A. Politi,
Self-Sustained Irregular Activity in an Ensemble of Neural Oscillators,
Phys. Rev. X 6, 011015, (2016).

A. Politi, E. Ullner and A. Torcini,
Collective irregular dynamics in balanced networks of leaky integrate-and-re neurons,
Eur. Phys. J. Special Topics 227, 1185-1204, (2018).

E. Ullner, A. Politi and A. Torcini,
Ubiquity of collective irregular dynamics in balanced networks of spiking neurons,
Chaos 28, 081106, (2018).

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