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The history of computing in Mexico cannot be thought without the name of Prof. Harold V. McIntosh (1929–2015). For almost 50 years, in Mexico, he contributed to the development of computer science with wide international recognition. Approximately in 1964, McIntosh began working in the Physics Department of the Advanced Studies Center (CIEA) of the National Polytechnic Institute (IPN), now called CINVESTAV. In 1965, at the National Center of Calculus (CeNaC), he was a founding member of the Master in Computing, first in Latin America. With the support of Mario Baez Camargo and Enrique Melrose, McIntosh continues his research of Martin-Baltimore Computer Center and University of Florida at IBM 709.

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Harold V. McIntosh mars 11, 1929 — november 30, 2015 Harold V. McIntosh died November 30, 2015 in Puebla, Mexico. He was an American mathematical physicist who became interested in what is now known as computer algebra to solve problems in physics, leading to his early adoption of the programming language LISP and to programming language design. In addition, his deep understanding of Weyl’s theory for second order differential equations, Schrödinger quantization as an eigenvalue problem and his proposed computational scheme for Weyl’s mfunction provided a novel way to investigate metastable states in atomic and molecular physics and reformulate standard scattering theory from a new angle. McIntosh was born in Colorado in 1929. In 1949 he received a B.Sc. in physics from the Colorado Agricultural and Mechanical College, and in 1952 he received a M.Sc. in mathematics from Cornell University. Mac (as he preferred to be called) was widely regarded for his research, writing and teaching. Even as a graduate student his gift for inducing people to learn was evident. In a profile of Sheldon Glashow published in The Atlantic Monthly in 1984, (1) Glashow asserted that what he learned as an undergraduate at Cornell from Mac about group theory “was as relevant as any course [he] took there.” Mac did further graduate studies at Brandeis, but stopped before receiving a Ph.D. to take a job at the Aberdeen Proving Ground. Two years later, he moved to RIAS (Research Institute for Advanced Studies), a division of the Glenn L. Martin Company. Around 1962 he accepted a position in the Physics and Astronomy department and the Quantum Theory Project at the University of Florida. After two years at the University of Florida, Mac was invited to work in Mexico, where he was offered “access to all the computer time he could use,” an offer that, he said, was fully honored. Mac worked from 1964 to 1965 at the Department of Physics of the CIEA del IPN, now Cinvestav (Center for Research and Advanced Studies of the National Polytechnic Institute); the design and implementation of the programming language CONVERT took place during this period. From 1965 to 1966, Mac was director of the programming department at the Electronic Computing Center of the National Autonomous University of Mexico, where he designed and developed the programming language REC. Over the following nine years, Mac was a professor at the School of Physics and Mathematics (ESFM) of the IPN, where he became coordinator of the Applied Mathematics group. Under his guidance, compilers for REC were built for newer computers arriving at the IPN’s CeNaC (National Computing Center), and he personally developed software packages for use in the various courses he taught. Of fourteen bachelor’s theses he directed at the ESFM, one stands out for having been published as three separate articles in the Journal of Mathematical Physics, one of which (2) discusses a problem in a class that is now called “MICZ Kepler systems”, the initials standing for McIntosh, Cisneros and Zwanziger. Also from this period, Mac’s paper Symmetry and Degeneracy (3) was cited enthusiastically three times in the second edition of Herbert Goldstein’s renowned classical mechanics book.4 He took a one-year leave from ESFM in 1972 to obtain his Ph.D. in Quantum Chemistry, which was awarded with the highest distinction, at Uppsala University. Mac’s contributions to the Uppsala Resonance Group led to several doctoral dissertations in Sweden. Between 1970 and 1975 Mac was also a consultant at the National Nuclear Energy Institute (INEN, now ININ), and in 1975 he and his group moved to the Autonomous University of Puebla (UAP), where he founded the Department of Microcomputer Applications in the UAP’s Institute of Sciences, and where he remained until his passing. He taught courses to computer science students from UAP’s School of Physical and Mathematical Sciences and over the last two and a half decades his interests turned to the study of cellular automata, in which he also became a recognized expert. Mac will be missed by his friends, colleagues and former students, especially for his lifelong dedication to teaching, high standards and uncompromising principles. 1. R.P. Crease and C.C. Mann, “How the Universe works,” The Atlantic Monthly, Aug. 1984, pp. 66–93. 2. H.V. McIntosh and A. Cisneros, “Degeneracy in the Presence of a Magnetic Monopole,” J. Math. Phys. 11, 896–916 (1970). 3. H.V. McIntosh, “Symmetry and Degeneracy,” in Group Theory and its Applications, Vol. 2, Ernest M. Loebl, ed. (New York: Academic Press, 1971, pp. 75–144) 4. Herbert Goldstein, Classical Mechanics, 2nd. ed. (Reading, MA: AddisonWesley, 1980). Submitted by: Gerardo Cisneros1 and Erkki Brändas2 Affiliations: 1 Mexico City 2 Uppsala University Uppsala, Sweden
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Theory of Self-Reproducing Automata
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neurons The human brain consists of about 10 11 neurons of various types; each neuron typically connects, via an axon that eventually branches out into strands and substrands, to many thousand neurons. The firing of a neuron is mostly an all-or-nothing business; this discrete character is retained as the pulse travels down an axon. However, upon arrival to a destination neuron the pulse is handled by a synaptic interface characterized by an analog parameter (typically, an excitation or inhibition weight) whose value may be to some extent history-dependent. The complete physiological picture is rather complex. A drastically simplified model of a neuron, proposed by McCulloch and Pitts[38], is shown in Fig. 5. The neuron can be in one of two states, +1 and Gamma1, which may be thought of as `on' and `off', or `true' and `false'; this state appears at the neuron's output. The inputs may come from other neurons or from external stimuli. State updating may be synchronous (all neurons ...
MBLISP was never properly documented, although some of its features were the subject of a series of Program Notes from the Quantum Chemistry Group of the University of Florida. One
  • H V Mcintosh
McIntosh HV. The fundamental logic translator I. A scheme for the automatic programming of large electronic computers. Baltimore: RIAS. (Technical report 62-2); The fundamental logic translator II. List processor. Baltimore: RIAS. (Technical report 62-9). MBLISP was never properly documented, although some of its features were the subject of a series of Program Notes from the Quantum Chemistry Group of the University of Florida. One, "Operators for MBLISP", Program Note no. 9, has some importance as a precursor of the REC, 1962.
The mathematical theory of machines, Boolean algebra, combinatorial and sequential circuits, semigroups. Escuela Superior de Física y Matemáticas
  • H V Mcintosh
McIntosh HV. The mathematical theory of machines, Boolean algebra, combinatorial and sequential circuits, semigroups. Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, México, 1967.
Ecuaciones diferenciales y teoría de weyl sistemas lineales de ecuaciones diferenciales con un enfoque geométrico-matricial. México: Porra Print
  • S V Chapa-Vergara
  • A Menéses
  • H V Mcintosh
Chapa-Vergara SV, Menéses A, McIntosh HV. Ecuaciones diferenciales y teoría de weyl sistemas lineales de ecuaciones diferenciales con un enfoque geométrico-matricial. México: Porra Print; 2015.
  • M M Soriano
  • C Lemaitre
  • Primera Década De La Computación En Mxico
Soriano MM, Lemaitre C. Primera década de la computación en Mxico: 1958-1968. Ciencia y Desarrollo. Vol. 60-61. CONACyT; 1985.
Calculating ancestors in one-dimensional cellular automata
  • J C Seck-Tuoh-Mora
  • G J Martínez
  • H V Mcintosh
Seck-Tuoh-Mora JC, Martínez GJ, McIntosh HV. Calculating ancestors in one-dimensional cellular automata. Inter J Mod Phys C. 2004;15(8):1151-1169.
Procedures for calculating reversible one-dimensional cellular automata
  • J C Seck-Tuoh-Mora
  • S V Chapa-Vergara
  • G J Martínez
Seck-Tuoh-Mora JC, Chapa-Vergara SV, Martínez GJ, et al. Procedures for calculating reversible one-dimensional cellular automata. Phys D Nonlinear Phen. 2005;202(1-2):134-141.
Rule 110 as it relates to the presence of gliders
  • H V Mcintosh
McIntosh HV. Rule 110 as it relates to the presence of gliders. 1999. Available from: http://delta.cs.cinvestav.mx/ mcintosh/comun/RULE110W/rule110.pdf
Computing with virtual cellular automata collider
  • G J Martínez
  • A Adamatzky
  • H V Mcintosh
Martínez GJ, Adamatzky A, McIntosh HV. Computing with virtual cellular automata collider. Proceedings of the 2015 Science and Information Conference (SAI);
  • U K London
London, UK, 2017. p. 62-68. DOI:10.1109/SAI.2015.7237127
Difusión y divulgación de la computación cuántica en méxico y allende sus fronteras
  • S E Venegas Andraca
Venegas Andraca SE. Difusión y divulgación de la computación cuántica en méxico y allende sus fronteras. XXII Congreso Nacional de Divulgación de la Ciencia y la Técnica. Guanajuato, Mxico: Universidad de Guanajuato; 2018.
  • G J Martínez
  • Obituary
  • V Harold
  • Mcintosh
Martínez GJ. Obituary: prof. Harold V. McIntosh. J Cell Auto. 2016;11(23):265-269.
13 volumes of the collection of SIG/M programs (Special Interest Group for Computer of New Jersey), dedicated to the distribution of CP/M programs. Each volume was distributed on an 8-inch disc
  • H V Mcintosh
McIntosh HV. 13 volumes of the collection of SIG/M programs (Special Interest Group for Computer of New Jersey), dedicated to the distribution of CP/M programs. Each volume was distributed on an 8-inch disc. Especially a program from this collection, 80T86, originally written in Convert, was widely used in the US. UU To translate programs in 8080 processor code to programs for the 8086 processor. 1986.