Regino Criado - Biography#

Prof. Regino Criado is an active and recognized scientist in the fields of Complex Networks and Discrete Mathematics.

He began his research career by making a position of lecturer compatible with a scholarship in the Sub-directorate General of Studies and Documentation (Presidency of the Spanish Government) (1981-82). As a scholar of this Sub-directorate General he collaborated in the design and mathematical modeling of the documentary database S.A.R.I.; he has participated in several European research projects in the field of mathematics and information technologies (ESPRIT II and ESPRIT III) and in different research and development projects with companies and corporations in the fields of applied mathematics and computer science. In 1998 he taught the "Advanced Course on Artificial Intelligence and Expert Systems" for heads and officers of the Ministry of Defense (organized by the School of Computer Science of the Spanish Ministry of Defense).

After his first works in the field of topology, his main lines of research were related to Complex Networks, Discrete Mathematics and Statistics, maintaining a multidisciplinary vision in his different works linking mathematics with its applications in different contexts. Thus, in relation to these lines of research, his team of collaborators and himself were able to link graph and network theory with linear programming through several works that, starting from an algebraic approach, we advanced and solved a problem about the role played by certain tree structures (p-tangles) in the field of logic programming in the effort to find a mathematical model that would allow the analysis and representation of Prolog language programs through a formalism that would simplify their study. Within this line of research, the major achievement has been to identify a formalism, essentially algebraic, that is suitable for the description and management of the algebraic structures involved both in the expressions that are involved in the logical and functional programming languages and in the algebra of processes (ring of p-tangles), as well as the natural use of a special metric in this context for the description of the process convergence. Also in this context, about my contributions to cryptography, it is worth highlighting the related works in collaboration to the use of a linear congruential generator in order to maximize the period of the generated series of pseudo-random numbers in such a way that the period obtained is close to the theoretical upper bound of m!.

Since 2003, R. Criado has also been studying the structure of complex networks, their applications and, in this context, the relation between the structure and the functionality working on the definition, development and study of new structures: hyper-networks, hyper-structures, higher order networks, multiplex and multilayer networks, multiparty networks, multilevel networks, structures in the mesoscale, line graph, and their properties (vulnerability, centrality, efficiency, cost, controllability, location of nodes of interest, random walkers, evolutionary games,...). developing and studying, among other subjects, the different approaches to the concept of robustness and vulnerability in complex networks.

Innovative applications developed as a result of his studies it is worth mentioning the creation of a model introduced within the cyber-security domain for the management of intentional risks through the analysis of complex networks. In this model, following the paradigm provided by game theory, the concepts of accessibility, anonymity and value are introduced for the definition of static risk and dynamic risk, and several algorithms are provided for the specific numerical assignment of these parameters in the corresponding complex networks of intentionality. It is also worth mentioning in this context the formulation of a new tool for the construction of intrusion detection systems (IDS) based on the definition of a multiplex network associated to a time series, whose properties and characteristics are based on certain attributes of these time series.

Recently, several other influential research papers discussing PageRank centrality and its extensions to multiplex networks have been published. Also, in relation to the study of sets of rankings and their comparisons, it is also worth highlighting the papers about the definition of competitiveness graph, its relationship with the chordal, permutation and comparability graphs and its applications to the study and contrasts of different sets of rankings.

It is also worth noting here that in the last years R.Criado also co-authored two important and influential papers about synchronization in dynamical networks with unconstrained structure switching and synchronization in simplicial complexes.

The monograph “The structure and dynamics of multilayer networks”, published in Physics Reports on 2014, received more than 3100 citations (Google-Scholar), and converted into one of the most quoted papers appeared in the Annals of that Journal.

His activity has always been carried out with a multidisciplinary vision bridging applied mathematics, nonlinear and statstical physics and the theory of complex systems. Prof. Criado has participated in several European research projects in the field of applied mathematics and information technologies (ESPRIT II and ESPRIT III) and in different research and development projects with companies and corporations in the fields of computer science, applied mathematics and software development.

To date, Prof. Criado is Author of 164 papers which already received more than 5,500 citations (from Google Scholar). The monograph “The structure and dynamics of multilayer networks”, published in Physics Reports on 2014, received more than 3,100 citations (Google-Scholar), and converted into one of the most quoted papers appeared in the Annals of that Journal.

In terms of his research work in the field of network science, on which he has focused largely for the past twenty years, his work has been critical for understanding the delicate relationship between networks' structure and functionality, together with the development and study of new structures: hyper-networks, hyper-structures, higher order networks, multiplex and multilayer networks, multiparty networks, multilevel networks, structures in the mesoscale, line graph, and their properties (vulnerability, centrality, efficiency, cost, controllability, location of nodes of interest, random walkers, evolutionary games,...).

As one innovative application of Prof. Criado's work it is worth mentioning the creation of a model introduced within the cyber-security domain for the management of intentional risks.

R. Criado co-authored, furthermore, several influential papers discussing PageRank centrality and its extensions to multiplex networks, as well as synchronization in complex networks and hypergraphs.