Roberto Reyes Carranza

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The instructor of mathematics Roberto Reyes learned to study this subject, mathematics, at the National University of Trujillo- Perú, where he was recruited by several professors, continuing his PhD studies and research at the University of Puerto Rico, Mathematical- Research Campus at San Juan and Mayagüez, Space and Sea Grant, and Land Grant University, Energy Department Partner and AMS Member, where he feels very comfortable to continue the pleasure of thinking on a wide range of mathematical theories, additionally, on his own initiative, design of algorithms and computational implementation of several complex processes in mathematics and its modeling.

Current Research

Right now he is doing the following research: "Fundamental Properties of Almost Perfect Nonlinear Functions, a Way to Measure its Nonlinearity and to construct its Highly Nonlinear Functions", paper in preparation, at an advanced stage, to be submitted 2014, and "APN Functions in Differential Cryptanalysis", attacking it from its roots, its definition, and even and again, strongly, with Prof. Dr. Heeralal Janwa http://www.cims.nyu.edu/~hjanwa/ http://math.nyu.edu/people/visitors.html and Prof. Dr. Moisés Delgado http://esta.uprrp.edu/facultad/mecu-delgadoM.php http://bsidespr.org/?page_id=147. His research interests in the Steinberg- Reissner Model (New Theory of Cosserat for micro-polar plates with moderate thickness) includes Elliptic PDE Systems with mixed boundary conditions corresponding to the bending problem, with Prof. Dr. Lev Steinberg http://math.uprm.edu/people/peoplefind.php?person=Steinberg,%20Lev

He have been invited because of his unusually strong application, to participate in the Complex Systems Summer School at Santa Fe Institute, New Mexico, USA. Selected participants (graduate students, postdoctoral fellows, and faculty) come from all over the world and represent a wide range of disciplines. Roberto was also awarded the Scholar of The Select Mathematics Group at GUE, An Own Initiative of GUE Faculty, GUE Highly Competitive Public School at Trujillo, Perú (visit Roberto's City! the largest earthen architecture city in pre-Columbian America http://whc.unesco.org/en/list/366). During his undergraduate studies, he attended twelve advanced Math courses and two of Physics as a "Visiting Student". Because of his powerful mathematical analysis, his meeting with Prof. Dr. Guihua Gong http://archive.sciencewatch.com/dr/erf/2011/11augerf/11augerfElli/ is not a coincidence. Roberto was nominated to be part of the Golden Key International Honour Society. And selected to participate in the project Research Integrity in Graduate International Collaborations and Contexts, a study sponsored by the NSF (grant # 1135345) and directed by the Council of Graduate Schools (CGS), as a PhD student at the UPR, Río Piedras, one of the 5 US universities nationwide selected.

Refereed Publications

Moisés Delgado and Roberto Reyes (Submitted Dec 2012) “APN Functions for Electronic Commerce Security” International Journal of Information and Computer Security IJICS, Paper ID: IJICS-2160.

Reyes, Roberto “Comparison of Elastic Plate Theories for Micro- polar Materials” 2011, ProQuest, ISBN: 9781124400891, Publication Number: AAT148756 http://search.proquest.com/docview/837356963#

Specialized Computational Libraries Produced

He owns an extensive programming experience with symbolic software (Computer Algebra Systems), and he has developed significant progresses, these contain an original analytical work plus the implementation of one rich set of functions, which also can be applied into several industrial purposes. He has managed to understand a significant amount of analytical foundations and techniques to make big projects.

“Library for Regularized Analytical Solutions for Steinberg- Reissner and Eringen II Families of Elliptic PDE Systems with Mixed Boundary Conditions corresponding to the Bending Problem”, written in Mathematica 4.0, presented at UPR, 2010.

With Professor Dr. Italo Dejter http://en.wikipedia.org/wiki/Italo_Jose_Dejter and the collaboration of Moisés Delgado and Eng. Araceli Feliciano, “Design of a Backtracking Algorithm for a type of Graph Coloring Problems and Symbolic Software”, implemented primarily on DOE Macsyma-GNU and also on MAGMA of the University of Sydney [carried out through a collaborative research between Dejter of UPR and the Dept. dEnginyeria de la Informació i de les Comunicacions, Universitat Autònoma de Barcelona] produced by Roberto Reyes, UPR, Nov 2013, to be presented at XXIX Inter-University Mathematical Sciences Research Seminar, to be held at Pontifical Catholic University, Ponce Campus, March 01 2014 http://i32441.wix.com/sidim-en

With Dr. Moisés Delgado, “APN Checker”, the APN Checker is a powerful computer tool to demonstrate if any function (defined over any finite field of characteristic 2) is APN, the implementation is given in Python and wxMaxima- GNU, from my KHIPU.PYTHON LIBRARY. A advanced version of this work was presented at the Information Theory and Bioinformatics Seminar "APN Functions for Secure Information Transmission, Implementation of APN CHECKER", organized by professor Heeralal Janwa, Math Dept, UPRRP, May 16 2012.

“An Existence Lemma for Classical Differential Geometry Generated by Polynomials”, As a Contribution to Classical Theory of Curves, implemented in Maxima and Mathematica, this work was produced by Roberto in the Math PhD Students Office at UPR, Apr 2012, and presented at Combinatorics and Its Applications Doctoral Seminar 2013, headed by professor Italo Dejter http://home.coqui.net/dejterij/ Math Dept, UPRRP, Apr 4 2013.

“A Interactive Computer-Assisted Proof of Convergence and Homogeneity property of Solutions of Elastic Plate Theories for Micro-polar Materials on a Zero Neighborhood”, written in Mathematica 4.0, presented at IX Annual Research Forum, TU, March 2011.

“Theorem of the Weighted Directed Graph as a Class of Polynomials, a Generalization, Properties and Implementation”, programmed in wxMaxima- GNU, December 2011.

Professional Memberships and Affiliations

Society for Industrial and Applied Mathematics (SIAM), Massachusetts Institute of Technology- Computer Science and Artificial Intelligence Laboratory (CSAIL), International Association of Engineers (IAENG), Society for the Foundations of Computational Mathematics (FoCM) and American Mathematical Society (AMS)

Teaching Experience

Instructor on campuses of public and private, peruvian and US universities such as UPR, an AMS member and Energy Department Partner, SUAGM System (Univ. of Turabo at Gurabo, main campus, Research Projects at SUAGM: http://amisr.suagm.edu/Information/index.html Partnerships: http://srdc.suagm.edu/Partnerships/index.asp) and Inter American University, an AMS member, with progressive faculty responsibilities [Course Coordinator of Quantitative Methods I and Calculus III: Multi-Variable Calculus and Introduction to Differential Equations]. “I feel honored for the support and recommendations I have received from the Mathematics Departments to give extra tuition. Also, I have had the pleasure of welcoming several visiting students interested in my classes”.

Other Contributions to Research

[Author's Acknowledgments to Roberto Reyes for the computations related with the Bending Problem, pg. 23] Steinberg, Lev “Deformation of Micro- polar Plates of Moderate Thickness” 2010 International Journal of Applied Mathematics and Mechanics IJAMM e- Journal System http://ijamm.bc.cityu.edu.hk/ijamm/outbox/Y2010V6N17P1C57668704.pdf

[Author's Gratitude to Roberto Reyes by his work on symbolic computations about the conference topic, pg. 15] Moises Delgado “APN functions against differential attacks” XXVIII Inter University Seminar on Mathematical Sciences Research, Metropolitan University (SUAGM), March 2013 PR, Sponsored by the National Science Foundation and Ana G. Mendez University System http://www.suagm.edu/umet/im/sidim/pdf/libro.pdf

Selected Presentations http://mathkhipu.blogspot.com

“On Necessary and Sufficient Conditions for Second-order Elliptic Field Equations of Elastic Plate Theories” XII Congress of Research and Academic Development of UPR at Ponce, Committee of Research and Academic Development, Dean of Academic Affairs, UPR at Ponce, May 13, 2011 PR, https://sites.google.com/a/upr.edu/congresouprp/topics

“Homogeneity property of Maximum Micro- rotation Vector of Steinberg-Reissner and Eringen Models on a Neighborhood of Zero” IX Annual Research Forum, Doctoral Studies Center, University of Turabo at Gurabo, March 11, 2011 PR, US http://www.suagm.edu/utdoctoral/pdfs/Programa-IX-Encuentro-Investigadores-UT.pdf

“Comparison of Elastic Plate Theories for Micropolar Materials” SIDIMXXV Feb 2010 http://sidim.uprh.edu/Memorias/2010/libroSIDIM2010.pdf

“Decomposition and Reconstruction of a Signal through Semi-orthogonal Wavelet Transform” A formalization for mathematicians of several concepts and methods that are used in departments of electrical engineering as well as in recent progresses in electromagnetic research (PIERS) and IEEE Microwave Theory and Technique (IEEE-MTT), Department of Mathematics, National University of Trujillo, 2006 Perú.

“Method of Berlekamp for Factorization of Polynomials over the Field Zp” V Italian- Latin American Conference on Applied and Industrial Mathematics ITLA, Dec 15-18, 2004 http://www.mail-archive.com/notiamca@venus.ceride.gov.ar/msg00484.html which is one of Member Society Meetings and Major International Congresses of the International Council for Industrial and Applied Mathematics (ICIAM) http://www.iciam.org/council/node9.html

Math Khipu Program

I'm involved with Math Khipu Program, which possesses a powerful research and administrative team. I have the honor to introduce my Math Khipu Group, we have set out to continue this great project: Prof. Dr. Moisés Delgado Olortegui, UPR, moises.delgado@upr.edu Project Advisor Eng. Araceli Feliciano Noriega (and also our Computer Technician) University of Puerto Rico at Mayagüez, celi_feli@yahoo.com aracelis.feliciano@upr.edu and Roberto C. Reyes Carranza PhD (expected- Dec 2014) UPR at San Juan roberto.reyes@upr.edu

(*) Prof. Dr. Obidio Rubio http://dl.acm.org/citation.cfm?id=606350.606376&coll=DL&dl=GUIDE&CFID=195485711&CFTOKEN=55864884 http://obidio.matematicos.pe/wp-content/uploads/2012/10/viscoelastic.pdf http://scholar.qsensei.com/content/471tk http://onlinelibrary.wiley.com/doi/10.1002/fld.1015/abstract