Research and projects

Study of the evolution of the collaboration networks of physics in Spain

Final degree project

In 2014 I started to work with Dr. Albert Diaz Guilera in the development of a tool to visualize the collaboration networks in the Univerity of Barcelona. Inspired by this work, in 2015 we decided to take profit on that tools and study the evolution of the collaboration networks of phisicists in Spain.



Co-authosrhip network of Spanish physicists with all the papers published in the APS from 1947 to 2012. Colors represents the communities inferred via modularity maximization.

For that purpose, we used the papers published in the American Physical Society (APS) with Spanish collaborators. Using techniques of communities detection based on modularity, the titles of the papers, the PACS and the journals that the papers were published we could identify and also characterized the communities that the Spanish physicists form. I also have developed an interactive web application that allows to visualize these networks.



Evolution of the percentage of papers published with a certain PACS. Each color represents a PACS, and are counted in time windows of three years.

Thanks to this analysis, we have discovered that the most relevant PACS are that ones that belongs to General, Condensed Matter: Structural, Mechanical and Thermal Properties and Condensed Matter: Electronic Structure, Electrical, Magnetic, and Optical Properties.

Also, an analysis to the researcher level have been done. In that case, we compute for each researcher the entropy of the PACS distribution of their papers. These entropies measures how interdisciplinar is each physicist. Doing that for each physicist and each time interval, we can see the individual evolution of their interdisciplinarity. To study the general trend, we compute the mean of the entropy in each time interval. As a conclussion, we can see that despite the mean entropy is low, a general trend to increase their interdisciplanrity as time pass.

Transitions in Bayesian model selection problems

PhD thesis

In this thesis I have being studying the balance between the likelihood and the prior when Bayesian inference methods are used to solve model selection problems. Bayesian inference in the context of the model selection problem tries to look for the most plausible model \(\mathcal{M}\) given the dataset \(\mathcal{D}\), that is, the model that maximizes the posterior probability \(P(\mathcal{M}|\mathcal{D})\): $$P(\mathcal{M}|\mathcal{D}) = \frac{1}{P(\mathcal{M})}e^{-\mathcal{D}(\mathcal{M})}$$ Where \( \mathcal{D}(\mathcal{M}) \) is the description length of the model \(\mathcal{M}\) and the data \(\mathcal{D}\). The description length can be divided into two additive parts: $$\mathcal{D}(\mathcal{M}) = \mathcal{D}_L(D|\mathcal{M}) + \mathcal{D}_P(\mathcal{M})$$ Where:

• \(\mathcal{D}_L(D|\mathcal{M})\) is the contribution of the description length of the likelihood. This value gets lower as the model fits more with the dataset.
• \( \mathcal{D}_P(\mathcal{M})\) is the contribution of the prior. The prior is a bias that you add to your model selection problem, benefiting the models that you believe, a priori, are the correct models and harming that models that you don't believe that are the correct ones.

The fact that both terms sums, it implies that depending on how much are the contributions of the likelihood and the prior, the inference process can be driven by one, the other or both. To show you more in detail this phenomena, let's suppose that can change



This is Oscar Fajardo Fontiveros

Interactive figure where it shows you which would the behaviour in a inference problem depending on the data size and its noise. If you tap or hover on each expression, it will show you what is going to happen in each case.

Prediction and modelization of the incidence of COVID-19 in several countries using symbolic regression

First postdoc

In my first postdoc I worked in a collaboration project with the SeesLab and the Alephsys Lab both groups in Tarragona. The main goal of the project was to predict the incidence of COVID-19 in several countries using symbolic regression. The way to do that is by using a algorithm called the Bayesian Machine Scientist.

Here we tried to get the mathematical expressions that describe the amount of people with COVID-19 but who have not been tested positive. The data that we used as the real incidence is a deconvolution from the deaths by COVID-19 from 9 different countries.

A paper with the results is being peer reviewing now at PloS One Computational Biology

Study of contagious tree models

Second postdoc

My current postdoc working along Dr Eduardo G. Altmann in the University of Sydney.The goal of this project is to focus more in a more complex network point of view to model contagious trees networks and use them to answer questions. From one side I developed a MCMC algorithm that allow us to inspect the whole landscape of posteriors. From the other side, we want to use genetic data and or contact tracing to see how the landscape changes and see how effective are this extra information to understand what is happening. As before in my first project, here we are going to maximize the posterior using as a likelihood the infection tree model and as a prior, a model related with the metadata (a phylogeny model for example).

Also, with collaboration from epidemiologists from the Westmead Hospital, we want to see if we can use our approach to be applied in policy making.

Example of a contagious tree network. Each node represents a person with the disease and each link tells who infects who. Orange nodes () represents people who didn't get positives, while blue represents () the people who tested positive.

Publications

• Node Metadata Can Produce Predictability Crossovers in Network Inference Problems

  Oscar Fajardo-Fontiveros, Roger Guimerà, and Marta Sales-Pardo Phys. Rev. X 12, 011010 – Published 14 January 2022

• Fundamental limits to learning closed-form mathematical models from data

  Fajardo-Fontiveros, O., Reichardt, I., De Los Ríos, H.R. et al. Fundamental limits to learning closed-form mathematical models from data. Nat Commun 14, 1043 (2023)

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