BeyondTheEdge – Graph vs Hypergraph Metrics.
Offer description.
A 3-year PhD position is available within the framework of the Marie Skłodowska-Curie Doctoral Network (MSCA-DN) “BeyondTheEdge”, funded by the European Union’s Horizon Europe Programme.
The candidate will be employed by the University of Zaragoza and enrolled as a PhD student in the Physics Program. The PhD project will be under the supervision of Prof. Yamir Moreno. During the doctoral program, two secondments are expected: 1) at CENTAI Institute, Italy, with Dr. Guilherme Ferraz de Arruda (6 months), and 2) CWTS, The Netherlands, with Dr. Vincent Traag (3 months).
Applications from all groups currently under-represented in academic posts are especially encouraged. We particularly welcome applications from women and people with an ethnic minority background.
PhD project description.
General Objective of the MSCA: Many systems that govern our everyday lives—from communication networks to the human brain—can be seen as networks of interconnected units. Traditionally, networks are equated with graphs where edges give pairwise relations between two units. However, in network dynamical systems, nonlinear higher-order interactions between more than two units often play a critical role in shaping the collective dynamical behavior of all units: For example, the spread of a disease depends not only on our behaviour as pairs of individuals but also how we behave in groups of more than two. Thus, elucidating the role of these higher-order interactions is critical to understanding and controlling the dynamics of complex systems that determine our lives and livelihoods, whether it is the spreading of a disease or the proper functioning of the human brain as a network of billions of neurons.
The doctoral network BeyondTheEdge will identify the role of non-pairwise higher-order interactions in the emergence of the complex dynamical behavior of networks of interacting units. BeyondTheEdge brings together key researchers in an international network that is interdisciplinary (from mathematics to neuroscience) and intersectoral (including academia, private research institutes, and industry) to develop new mathematical insights relevant to real-world problems. BeyondTheEdge will train a cohort of 10 PhD students through research, education, and complementary skills training. This will enable the PhD students to innovate, collaborate, and become leading professionals in academia, industry, or the public sector: Innovative training activities will ensure that all PhD students can apply their skills beyond the academic context and put them in perspective of the wider world. Supervisor training activities ensure that the more junior project partners can shape the PhD education of the future. Thus, BeyondTheEdge will make a lasting contribution that will far outlive the duration of the project.
Specific Objective: The last two decades have witnessed a revolution in the way in which interactions among a system’s constituents are measured and characterized, leading to more realistic and accurate models to describe real-world dynamical processes such as contagion or disease-like dynamics. Recently, evidence has shown that networks are more complex than graphs and that pairwise interactions do not capture many of the key features associated with group and other forms of higher-order interactions (HOIs). These discoveries have shifted the focus on the study of the structure and dynamics of/on hypergraphs. However, despite these advances, most of the metrics that are used to characterize higher-order networks are the same (or untested, direct generalizations) that were developed to characterize graphs, which hinders further advances in the mathematical characterization of real systems and the uncovering of new structures and phenomena associated with higher-order systems.
The main objective of this PhD project is to elucidate when graph metrics are suited to characterize HOIs, both in terms of the structure and the dynamics, and when and which new metrics need to be introduced. We will apply our results to different datasets and processes and unlock new methodological and mathematical tools to better capture the nature and consequences of HOIs. Critical questions are: How is the hypergraph structure relevant? How do HOIs impact dynamics? Are the answers to the previous questions conditioned to the metrics that are used to characterize the graph/hypergraph and the dynamics? We will start by determining how properties of graphs and hypergraphs relate mathematically, identifying in this way what metrics cannot be used to characterize HOIs and what new—not necessarily generalizations of existent—metrics are needed. We will then extend the study to find relevant order parameters to characterize dynamical processes and phase transitions. We will focus on processes that involve critical-mass dynamics to model social contagion, identifying new descriptors for the system’s critical properties that could not be uncovered using metrics for graphs. Our theoretical framework will be tested on several datasets including contact data and the optimization of task-assignment graphs subject to constraints [Secondment CENTAI] as well as authorship networks [Secondment CWTS]. This project will elucidate when hypergraphs are appropriate to analyze higher-order interactions and what metrics are suitable. Beyond the applications in the secondments, the resulting tools will find applications in robustness, optimization, and control of higher-order systems.
Expected Results: A new theoretical and computational framework with novel metrics to characterize the structure and the dynamics of HOIs described by hypergraphs as well as new mechanistic explanations of critical dynamics, isolating what mechanisms are deeply rooted in the higher-order nature of the interactions. Validation of the new metrics and theoretical methods in at least 3 different datasets or real problems.
Qualifications and eligibility.
- At the date of recruitment, candidates must hold a Master of Science degree (i.e. 2nd level title, as defined by the Bologna Process), issued by an officially recognized academic institution, which grants admission in PhD programs in the country of issuance. MSc in Physics, Mathematics, Engineering, Computer Science, or a related topic is strongly recommended.
- Candidates must not be already in possession of a doctoral degree at the date of the recruitment.
- To be eligible, candidates must undertake transnational mobility: must not have resided or carried out their main activity (work, studies, etc.) in Spain for more than 12 months in the 36 months immediately before their recruitment date. Short stays such as holidays are not considered.
- The candidate must be fluent in written and spoken English. This would be verified during the interview of shortlisted candidates.
Specific skills.
- Strong modeling, computational, and code development skills.
- Experience in network science, complex systems, statistical mechanics, statistics, or computational physics.
- Have good programming skills in at least one of the following languages: Python, C/C++.
- Highly collaborative spirit and personal initiative.
- Excellent personal skills
- An inquiring mind and the desire to challenge themselves
Application Deadline: May 12th, 2024 (AoE timezone).
How to Apply.
To apply please send the submission material to Prof. Yamir Moreno (yamir_dot_moreno_at_gmail_dot_com, or yamir_at_unizar_dot_es) by the deadline, mentioning in the subject “UNIZAR BeyondTheEdge PhD application”. Please include:
- a cover letter, which should describe past academic/research experience, motivation to do a PhD and to apply to this position, and expectations.
- a detailed CV.
- a list of courses and grades at the MSc level.
- Drafts of: the MSc thesis (if already available), and any research work (published or not) carried out.
- the names and e-mail addresses of two references.
- any other official documents which can be useful for the purpose of declaring the conformity of the title (i.e., diploma supplement, declaration of value, …).
Certificates and official documents shall be issued by the relevant university in one of the following languages: English, Spanish, or Italian.
Selection process.
The University of Zaragoza assures an open and transparent recruitment of researchers. The composition of the selection committee will be made public after the selection process and it will consist of at least three senior researchers -chaired by the PI Prof. Yamir Moreno. Rejected applications will receive constructive feedback, and the recruited candidate will be helped to complete the administrative procedures to enroll in the PhD program. After a first shortlisting based on applicants’ materials, selected candidates will be interviewed by the committee, either in person or remotely. For any further information, please contact Prof. Yamir Moreno.
Work Location.
Institute for Biocomputation and Physics of Complex Systems, University of Zaragoza, Zaragoza, Spain.