Current research

Ranking-based reinforcement

In many contexts where people have to make decisions, their choices are informed by what many other people are doing. Some examples are whether to vaccinate one’s children or not, which book to read, which word form to use, and so on. This often creates a positive feedback loop, where popularity of a choice serves as a signal that reinforces itself, leading to dynamics that in different literatures are known as cumulative advantage, the rich get richer, preferential attachment, or the Matthew effect. Such dynamics, which reinforce initial (and often random) differences in popularity, are known to be able to sustain multiple equilibria, including states of inferior “lock-in”, where a majority of people adopts an intrinsically less appealing option, and this majority remains stable over time.

In a series of papers that range from mathematically-oriented to applied, my colleagues and I have been studying the dynamics of popularity and the possibility of lock-in when people’s choices are primarily driven by the way the various options rank in terms of popularity, rather than by quantitative differences in popularity. Specifically, in the first of these papers, we study the dynamics of rankings in the context of Markov processes and derive fundamental results regarding their long-term behavior. In a follow-up paper, we are specializing this study to popularity rankings and show how this leads to a unified framework for studying choice by a large number of people under a variety of behavioral assumptions that are relevant in economics. And in a third paper (currently under review), we are showing both mathematically and by analyzing past experimental data that the tendency of people to pay disproportionate attention to who is in the lead (independently of the exact differences in popularity) renders a system likely to lock in in cases that it wouldn’t do so otherwise.

Collaborators: Pantelis P. Analytis, Francesco Cerigioni, Gaël Le Mens, Hrvoje Stojic, Arnout van de Rijt

Inferring cumulative advantage from longitudinal records

What drives the success of extremely popular artists or highly cited researchers? Is it talent/inherent characteristics that make them successful, or have they just been lucky early in their careers and they are just riding on their already established fame?

It is widely accepted by social scientists that, in many endeavours in life, success breeds success. Yet observed differences in success can also be potentially attributed to differences in talent. How can we use observations about the time-evolution of success to prove that (at least part of) the differences in success are a result of cumulative advantage, i.e. the self-reinforcing character of success? In a paper under preparation, my colleagues and I are showing that distinguishing between cumulative advantage and differences in talent in observational records is theoretically impossible. Specifically, every model that incorporates cumulative advantage to explain differences in success has a twin talent-based model that is statistically indistinguishable from the first, and vice versa. This implies that observational (non-experimental) data, which have often been used to study patterns of success inequality over time, are inherently unsuitable for arguing for or against the presence of cumulative advantage.

Collaborators: Lucas Sage, Arnout van de Rijt

Earlier work

Brain oscillations and working memory

As a PhD student, I used dynamical systems models of biological neural networks to study the brain’s oscillatory activity. The work had both a neuroscientific focus and a mathematical one. On the neuroscience side, I studied the properties of a network that is believed to form part of the brain’s parietal cortex, and suggested that it may form a physiological substrate for a working memory buffer in humans. The work was published in PNAS (link) and has attracted attention from neuroscientists studying human memory.

On the mathematical side, I studied the mechanisms that underlie the behavior of the above network and that allow it to process new input without disrupting its ongoing activity. The results suggested a novel form of interaction of neural oscillations of different frequencies and were published in the Journal of Mathematical Neuroscience (link).

Collaborators: Nancy Kopell (PhD thesis supervisor), Miles A. Whittington.

Preprints and submitted articles

• Gelastopoulos, A., Analytis, P. P., Le Mens, G., & van de Rijt, A. (under review) Ranking-based social influence produces lock-in.
• Gelastopoulos, A., Sage, L., & van de Rijt, A. (2023). Inferring cumulative advantage from longitudinal records. arXiv preprint arXiv:2310.01096.
• Analytis, P. P., Cerigioni, F., Gelastopoulos, A., & Stojic, H. (2022). Sequential choice and self-reinforcing rankings. Pompeu Fabra University, Economics Working Paper Series, No. 1819.

Peer-reviewed journals

• Analytis, P. P., Gelastopoulos, A., & Stojic, H. (2023). Ranking-based rich-get-richer processes. The Annals of Applied Probability, 33(6A), 4366-4394.
• Gelastopoulos, A., & Kopell, N. J. (2020). Interactions of multiple rhythms in a biophysical network of neurons. The Journal of Mathematical Neuroscience, 10, 1-43.
• Gelastopoulos, A., Whittington, M. A., & Kopell, N. J. (2019). Parietal low beta rhythm provides a dynamical substrate for a working memory buffer. Proceedings of the National Academy of Sciences, 116(33), 16613-16620.
• Analytis, P. P., Wu, C. M., & Gelastopoulos, A. (2019). Make-or-Break: Chasing Risky Goals or Settling for Safe Rewards?. Cognitive science, 43(7), e12743. link

Conference Proceedings

• Analytis, P. P., Stojic, H., Gelastopoulos, A., & Moussaïd, M. (2017). Diversity of preferences can increase collective welfare in sequential exploration problems. arXiv preprint arXiv:1703.10970.

Expository articles

• What are the real numbers? (Part I) - This article introduces the rigorous definition of real numbers through Dedekind cuts in an approachable way, assuming only some familiarity with calculus.
• Entropy and Mutual Information - Information theory is widely applied across the sciences. Despite being very mathematical in nature and building upon the theory of probability, mathematicians are often unfamiliar with it, as it doesn't form part of a typical mathematics curriculum. This article, written as a project for a graduate course in Probability Theory, is a brief introduction to information theory intended for mathematicians, or anyone with a solid background in probability.

Courses taught

As main instructor

• Spring 2023: Introduction to Game Theory, Pompeu Fabra University
• Summer 2017: Probability, Boston University

As teaching assistant

• Fall 2018: Elementary Statistics, Boston University
• Fall 2016: Introduction to Analysis 1, Calculus 1 for Social Sciences, Boston University
• Spring 2013: Functional Analysis, Applied Differential Equations, Jacobs University Bremen
• Fall 2012: Linear Algebra 1, Perspectives of Mathematics 1, Jacobs University Bremen
• Spring 2012: Analysis 2, Jacobs University Bremen
• Fall 2011: Analysis 1, Jacobs University Bremen

Guest lectures

• Modeling and detecting cumulative advantage in the social sciences, BIGSSS Computational Social Science Summer School on Democratic Debate, Constructor University - July 2023
• Architecture and information processing in biological neural networks, M.Sc. in Data Science Program, University of Southern Denmark. - May 2022
• The mathematics of juggling, 1st Neo-meta-cabaret artists convention, Libertatia social center, Thessaloniki, Greece. - June 2021
• Principles of Biological Neural Networks, M.Sc. in Data Science Program, University of Southern Denmark. - April 2021
• Gambling, Circuits, and Facebook (with A. Kehagias and R. Grigoriou), 3rd Electrical and Computer Engineering Student Conference, Aristotle University of Thessaloniki - April 2009