My academic life is a sequence of (not necessarily different) topics and places ordered in time. It is a walk, but it is far from being random. It started at the beginning of the 1990’s in Cuba, where I was born in 1966 and grew up. My interest at that time was in the prediction of thermodynamical properties of organic molecules of biological interest using quantum chemistry. Doing scientific research in a developing country, which was additionally submerged into a deep economic crisis, was a gigantic challenge. I remember using a personal computer with an 80486 microprocessor for doing calculations. The university did not have such a PC at that time, so I obtained some computing time during the evenings at a centre outside the university. Thus, I was working the whole night at that centre, sleeping on the floor a couple of hours, and returning by bike to the University to do my teaching. As a result of this work, I am one of the coauthors of a patent of a novel antibacterial and antifungal drug, which is now used in clinics.

It was in 1992 when I made an important discovery. I had travelled to Havana, 300 km from my university, to do a literature search. Then I was shocked when I “discovered” the existence of “mathematical chemistry”. I immediately combined my knowledge of quantum chemistry with graph theory and produced my first paper, which was published in 1993. Now I had a topic for my PhD: the use of graphs in molecular design, which I presented in 1997. The same year I received a fellowship to visit the University of Valencia in Spain. I had already published more than 10 papers in mathematical chemistry, and my experience in drug design was very much enlarged during my stay in Valencia.

In June 1999 I decided to move to Santiago de Compostela, Spain to live. At the end of this year, I received a fellowship to work at the Hebrew University of Jerusalem. My topic of research was about the use of symmetry numbers to modify the rotational partition function of molecules without perfect symmetry. It was a very intense period of study and research, which culminated with a publication in the leading chemistry journal. The winter of 1999 to 2000 was very cold in Jerusalem. I had decided to save money from my fellowship to buy a laptop, so I did not expend it in heating. I remember sleeping with a jacket and gloves during one of the coldest nights in my life. But, in February of 2000 I was able to buy my first laptop.

In 2000 I received a fellowship from the Government of Spain, which allowed me to return to the University of Santiago de Compostela. I worked in Santiago for 2 years in topics mainly related to mathematical chemistry and molecular design. I had developed a method for molecular design based on the use of spectral properties of line graphs representing molecular graphs, known as TOPS-MODE (Topological Substructural-Molecular Design). It allows one to predict physical, chemical, pharmacological and toxicological properties of molecules. But more importantly, it allows one to express these properties as combination of molecular fragments, which was very useful to design new drug candidates. By this time, I had made important contributions to the design of novel anticonvulsant, anticancer, and anti-HIV drugs as well as to the prediction of many toxicological and environmental properties of chemicals, had published more than 50 papers and started to be invited as speaker at some of the main conference in these fields.

After my fellowship ended in 2002, I moved to England to work as research scientist at the Safety and Environmental Assurance Centre of Unilever in Colworth. My main responsibility was the development of mathematical models to predict toxicological and environmental properties of chemicals that reduce the use of animals in experiments. One year after, I moved back to Santiago de Compostela to take a position as a “Ramon y Cajal” researcher. This was a tenure track 5 years position in which I was responsible for the development of chemo- and bioinformatic tools for the emergent “omics” (genomics, proteomics, metabolomics) technologies. I started a transition from the analysis of “small” molecules to “large” biological macromolecules, such as proteins. By 2004 I made another important “discovery”: complex networks. My mother was visiting us in Santiago, and we have rented a house at the beach for holidays. I travelled with a pack of dozens of papers to read, all about this “new” field of “complex networks”. A complex network is a graph representing the skeleton of a complex system, from the social interactions in a society to ecological and infrastructural systems, including the many omics-interactions between biomolecules. In 2005 I published a paper introducing a new centrality index to characterize the relevance of the nodes in a complex network. This paper has received more than 1,200 citations and put the focus on what is nowadays known as the “Estrada index”. The index was first introduced in the context of protein folding in 2000, but it was not until the “subgraph centrality” was born that it was widely known in the literature. In 2008 I introduced the concept of “network communicability” in a paper which has been cited more than 600 times. This concept is nowadays widely used for the analysis of complex networks, particularly for the study of the brain.

My life changed again in 2008 when I received the Chair in Complex Systems at the University of Strathclyde in Glasgow. I was now full professor in one of the leading applied mathematics departments in the U.K. It was, however, a big challenge for me with respect to personal and academic life. At this time, I focused mainly on the analysis of matrix functions for the study of graphs and networks. As a result, I studied, apart from the matrix exponential, matrix hyperbolic functions, matrix ψ functions, matrix sign and modulus function, matrix Gaussian functions. They have given rise to new concepts in network theory and to important applications in different fields. In 2012 I developed the idea of the d-path Laplacian operators and their transforms to account for long-distance interactions in graphs. The same year I introduced the concepts of communicability geometry and the induced embedding of networks into n-dimensional Euclidean spheres. A wide range of applications ranging from the detection of genes involved in human diseases to the analysis of city traffic at rush hours emerged from this works.

In 2018 I moved back to Spain. This time to Zaragoza, with a position as ARAID researcher at the Institute of Mathematics and its Applications (IUMA). Without abandoning the areas of research that I started in the last 10 years I opened a new one here. It was related to the use of fractional calculus to analyze networks. A year after COVID-19 hit the world, I was involved in research for the analysis of impact of the virus on the human health. I made use of fractional diffusion, networks, and omics data to predict the multiorganic damages caused by the virus on humans. I also discovered and analyzed the potential impact of drugs targeting the main protease of the virus. Two years after this publication the first two drugs targeting such protein were marketed.

Since 2021, I have been a full research professor of the Spanish National Research Council (CSIC) at the Institute of Cross-Disciplinary Physics and Complex Systems (IFISC) in Palma de Mallorca, Spain. Here I am involved in research and collaborations about the own concept of complexity, network dynamics, anomalous diffusion, biased-dynamics, fractional calculus, signed graphs, and applications to many different systems. In a recent paper we have analyzed the global waste trade industry and its impact on the environment. We are now analyzing international relations and conflicts in the world since the 19th century, among other topics.

During this walk in which I have travelled back and forth among different applied mathematics areas, I have published more than 230 papers and two books, received more than 17,000 citations, given more than 60 invited lectures, visiting more than 30 countries, supervised 12 PhD Thesis, and received several distinctions (SIAM fellow, IMA fellow, Member of the Academia Europaea, Wolfson Research Merit Award). But, more importantly, I have enjoyed the company of many friends. It has been a long walk, but I recommend it.