2020:    

He was elected the first director of the newly founded “Institute of Artificial Intelligence” and member of the Council of the “University Research Center of Patras”.

  2020:    

One of his theorems was named “Miranda-Vrahatis theorem” in the following paper by Dr. Balázs Bánhelyi, Prof. Dr. Tibor Csendes and Prof. Dr. László Hatvani:
      ●   Bánhelyi B., Csendes T., Hatvan L., On the existence and stabilization of an upper unstable limit cycle of the damped forced pendulum [Journal of Computational and Applied Mathematics 371 (2020) 112702].
The named theorem is proved in the paper:
      ○   Vrahatis M.N., A short proof and a generalization of Miranda's existence theorem [Proceedings of the American Mathematical Society 107(3) (1989) 701–703].
The authors applied the above theorem to prove a crusial step of their main result on the existence of an unstable fixed point of the Poincaré map related to the damped and periodically forced pendulum around the upper equilibrium.

  2020:    

He was honored with the “Amity Researcher Award” for significant contribution in the field of “Natural Computing”, organized by the Amity School of Engineering & Technology, Amity University, Uttar Pradesh, Sec-125, Noida, India.

  2018:    

He was invited and elected member of the ESF College of Expert Reviewers. The European Science Foundation—ESF is an independent and non-profit organization that aims at facilitating research management processes across Europe. ESF is committed to promoting the highest quality science in Europe to drive progress in research and innovation. To be able to provide the best possible scientific assessments, ESF has set-up a College of Expert Reviewers.

  2018:    

One of his theorems was named “generalization of the intermediate value theorem for simplices” in the following paper by Prof. Dr. Paul R. Milgrom [Nobel Laureate in Economic Sciences in 2020] and Dr. Joshua Mollner:
      ●   Milgrom P., Mollner J., Equilibrium selection in auctions and high stakes games [Econometrica 86(1) (2018) 219–261].
The named theorem is proved in the paper:
      ○   Vrahatis M.N., Generalization of the Bolzano theorem for simplices [Topology and its Applications 202 (2016) 40–46].
The authors applied the above theorem to prove a crusial step of their main result on equilibrium selection in games with an emphasis on auctions.

  2017:    

He was honored with the “N.K. Artemiadis Award” of the Academy of Athens for the best scientific publication in the last three years in the area of “Mathematical Analysis” authored by Greek researchers working in Greece or abroad. The award, which is endowed with €3,000, was presented to him at the official ceremony “Panegyric Meeting” on December 21, 2017, in the presence of Academy members and Government and Parliament representatives. The scientific publication for which the award was received (for the time period of January 1, 2014 through December 31, 2016) is:
      ○   Vrahatis M.N., Generalization of the Bolzano theorem for simplices [Topology and its Applications 202 (2016) 40–46],
according to which the excerpt from the report read at the official ceremony of the Academy concludes as follows: “With this study, the award winner continues a consistent scientific progress”. In this publication, a generalization of the Bolzano theorem for simplices is given and its proof is based on the Knaster–Kuratowski–Mazurkiewicz covering principle.
      The first proofs of the very important and pioneering “Bolzano's theorem” also called “intermediate value theorem”, given independently by Bernard Bolzano in 1817 and Augustin–Louis Cauchy in 1821, were crucial in the procedure of “Arithmetization of Analysis” (which was a research program in the foundations of mathematics during the second half of the 19th century). A straightforward generalization of Bolzano's theorem to continuous mappings of an n–dimensional cube (parallelotope) into ℝⁿ was proposed without proof by Jules Henri Poincaré in 1883 and 1884 in his work on the “Three Body Problem”. For this reason, some authors call this theorem “Poincaré's intermediate value theorem”. The Poincaré theorem was soon forgotten and it has come to be known as “Miranda's theorem” which was independently proposed and proved by Carlo Miranda in 1940 that partly explains the nomenclature “Poincaré–Miranda theorem” or “Bolzano–Poincaré–Miranda theorem”. This theorem is closely related to important theorems in mathematical analysis and topology as well as it is an invaluable tool for verified solutions of numerical problems by means of interval arithmetic. Also, it has been shown by Carlo Miranda in 1940 that this theorem is equivalent to the “Brouwer fixed point theorem” (1912) due to Luitzen Egbertus Jan Brouwer and it is closely related to the existence theorems of Karol Borsuk (1933), Leonid Kantorovich (1948) [Nobel Laureate in Economic Sciences in 1975] and Stephen Smale (1986) [Fields Medalist in 1966].
     In the awarded paper, the obtained proof is based on the covering principle of Bronisław Knaster, Kazimierz Kuratowski and Stefan Mazurkiewicz (1929) known as “Knaster–Kuratowski–Mazurkiewicz lemma” or “KKM lemma” for short. This lemma constitutes the basis for the proof of many theorems including, among others, the famous “Brouwer's fixed point theorem” (1912) due to Luitzen Egbertus Jan Brouwer. It is worth noting that three pioneering classical results, namely, (a) the “Brouwer fixed point theorem” (1912), (b) the “Sperner lemma” (1928) due to Emanuel Sperner, and (c) the “KKM lemma” (1929) are mutually equivalent in the sense that each one can be deduced from another. The KKM lemma has numerous applications in various fields of pure and applied mathematics. In particular, among others, in the field of mathematical economics, the very important and pioneering extension of the KKM lemma due to Lloyd Stowell Shapley [Nobel Laureate in Economic Sciences in 2012] customarily called the “Knaster–Kuratowski–Mazurkiewicz–Shapley theorem” (1973) constitutes the basis for the proof of many theorems on the existence of solutions in “Game Theory” and in the “General Equilibrium Theory” of economic analysis.
     The generalizations of Bolzano's theorem are particular useful for tackling various problems including, among others, the existence of solutions of systems of nonlinear algebraic and/or transcendental equations, the existence of fixed points of functions of several variables, the localization of extrema of objective functions, the localization of periodic orbits of area preserving mappings and the localization of periodic orbits of conservative dynamical systems by using the Poincaré mapping on a surface of section. These generalized theorems require only the algebraic sign of the function values that is the smallest amount of information (one bit of information) necessary for the purpose needed, and not any additional information. Thus, these theorems are of major importance for tackling problems with imprecise (not exactly known) information. This kind of problems occurs in various fields in science and technology. This is so, because, in a large variety of applications, precise function values are either impossible or time consuming and computationally expensive to obtain.

  2016:    

One of his theorems was named in the title of the following paper by Prof. Dr. Emeritus Gerhard Heindl:
      ●   Heindl G., Generalizations of theorems of Rohn and Vrahatis [Reliable Computing 21 (2016) 109–116].
The cited theorem is the Theorem 2 in the paper:
      ○   Vrahatis M.N., A short proof and a generalization of Miranda's existence theorem [Proceedings of the American Mathematical Society 107(3) (1989) 701–703].

  2014:    

He has been invited and elected panel member of the ERC Starting Grant 2014 peer review process for the European Research Council—ERC, in the domain “Physical Sciences and Engineering (PE)—Computer Science and Informatics (PE6)”. The main goal of the ERC is to encourage high quality research in Europe through competitive funding.

  2006:    

The Empeirikion Foundation in Athens, at the award ceremony on February 25, 2006, awarded him financial support “in memory of Miltiadis Empeirikos” for the organization of a laboratory for research purposes. The competitive applications were submitted in response to a call issued by the Empeirikion Foundation on July 16, 2004 and his application, entitled: “Financial support of the Computational Intelligence Laboratory of the Department of Mathematics of the University of Patras” was approved on February 10, 2006 for financial support of €13,300.

  2002:    

One of his theorems was named “Vrahatis generalization theorem” in the following paper by Prof. Dr. Jan Mayer:
      ●   Mayer J., A generalized theorem of Miranda and the theorem of Newton–Kantorovich [Numerical Functional Analysis and Optimization, 23(3–4) (2002) 333–357].
The named theorem is the Theorem 2 in the paper:
      ○   Vrahatis M.N., A short proof and a generalization of Miranda's existence theorem [Proceedings of the American Mathematical Society 107(3) (1989) 701–703],
where a short proof of the “Miranda existence theorem”, (also known as “Poincaré's Intermediate Value Theorem”, “Poincaré–Miranda theorem” or “Bolzano–Poincaré–Miranda theorem”), is given. The proof is based on the homotopy invariance of the topological degree theory and the “Kronecker existence theorem” (1869) due to Leopold Kronecker. Following this proof, the considered domain of the classical Poincaré's intermediate value theorem can also be an n-dimensional rectangle and need not to be necessarily an n-dimensional cube. Furthermore, following this proof, a generalization (stated as Theorem 2) of the Miranda existence theorem is proved. This generalization is defined with respect to an arbitrary basis of ℝⁿ and eliminates the dependence of the classical Poincaré's intermediate value theorem on the standard basis of ℝⁿ.

  2001:    

His research activities were supported by the Deutsche Forschungsgemeinschaft—DFG/German National Research Foundation for research collaboration and lectures presentation at the Collaborative Research Center/Sonderforschungsbereich—SFB 531: Design and management of complex technical process and systems by means of computational intelligence methods, Technische Universität Dortmund, Germany.

  2000:    

He was supported by the American Mathematical Society—AMS, and the US National Science Foundation—NSF, in order to present an invited lecture at the “AMS-IMS-SIAM Joint Summer Research Conference in the Mathematical Sciences, Algorithms and their Complexity for Nonlinear Problems”, July 16-20, 2000, Mount Holyoke College, South Hadley, MA, USA.

  1997:    

The Hellenic Club of Writers in Athens, on March 28, 1997, awarded him an honorary diploma, stating that: “Honoring the virtue and the literary interest, we award this honorary diploma to reward his excellent efforts and achievements”.

  1992:    

His research activities were supported by the Ministero Italiano degli Affari Esteri e della Cooperazione Internazionale/Italian Ministry of Foreign Affairs and International Cooperation, for research collaboration and lectures presentation at the Istituto Nazionale di Fisica Nucleare—INFN/Dipartimento di Fisica, Università degli studi di Bologna, Bologna, Italy and at the European Organization for Nuclear Research—CERN/Organisation Européenne pour la Recherche Nucléaire—CERN, Geneva, Switzerland.

  ———    

Until the last update on December 15th 2018, his scientific research work has been cited in 250 international patents. More specifically, these citations have been appeared in (the alphabetically ordered list): (i) 7 Canadian patents, (ii) 47 Chinese patents, (iii) 23 European patents, (iv) 5 French patents, (v) 7 Japanese patents, (vi) 8 Korean patents, (vii) 121 United States patents and (viii) 32 World Intellectual Property Organization—WIPO patents.