M.A.Lerma's Index of Preprints

  1. Distribution of Powers Modulo 1 and Related Topics (pdf) - (dvi) - (ps) - http://arxiv.org/abs/1312.5996
  2. Construction of a Number Greater Than One Whose Powers Are Uniformly Distributed Modulo One (pdf) - (dvi) - (ps).
  3. Some Applications of Extremal Functions in Fourier Analysis (pdf) - (dvi) - (ps).
  4. The Bernoulli Periodic functions (pdf) - (ps).
  5. Physics: A Brief Summary (pdf).
  6. A Mirror Based Event Cloaking Device (PDF) - http://arxiv.org/abs/1308.2606
  7. How inefficient can a sort algorithm be? (PDF) - http://arxiv.org/abs/1406.1077
  8. Principal Components Analysis in 2D (PDF)
  9. Putnam Training Problems (pdf).
  10. Notes on Discrete Mathematics (pdf)


Publications

  1. (with Castellanos, J.; Ríos, J.; Segovia, J.): Fast Training of Feedforward Multilayer Neural Networks By Means of a Weighted Least Mean Square Algorithm, Neural Network World 5/92, 423-436.
  2. (with Barrios, D.; Ríos, J.; Segovia, J.): Fast Training of Feedforward Multilayer Neural Networks by Means of Linear Methods: Experimental Tests, Proceedings of the Fifth International Symposium on Knowledge Engineering, Sevilla, Spain, October 5-9, 1992, pp.170-178.
  3. Ampliación al espacio de una aplicación de la integración en el campo complejo para la solución de una cuestión de informática gráfica, English summary: Extension to the Space of an Application of Complex Integration for Solving a Topic on Graphic Computation, Questiiò, Vol.16, N.1, 1992, pp.59-75, Barcelona, Spain. Find a copy here.
  4. (with Castellanos, J.; Ríos, J.; Segovia, J.): Approximation of Functions by Neural Networks: an Experimental Test, International Journal of Neural Networks, Vol.3, No.4, December 1992, pp.149-153.
  5. Introducción a las redes de Hopfield, in Olmeda, I., and Barba-Romero, S. (Ed.): Redes Neuronales Artificiales, Fundamentos y Aplicaciones, Servicio de Publicaciones de la Universidad de Alcalá de Henares, Alcalá de Henares, Spain, 1993.


Research

  1. 1989-1991: Neural Networks. New heuristic and constructive methods for fitting neural networks. School of Computer Science, Universidad Politécnica de Madrid. New training algorithms for feedforward multilayer neural networks were developed. They were based on considering the task of fitting the weights in all the layers of a neural network as a coupled set of linear optimization problems.
  2. 1991-1992: Computational Geometry. Extension to the n-dimensional space of the winding number algorithm for polygon inclusion, with applications to polyhedron and polytope inclusion. School of Computer Science, Universidad Politécnica de Madrid.
  3. 1992-1993: Development of computer tools. Proyecto Lope (Lope project), School of Computer Science, Universidad Politécnica de Madrid. Designing of a meta-environment for automatic generation of integrated environments for developing programming projects. The prototype environment, called LOPE, would allow editing the whole set of linked descriptions for a given piece of software, in a uniform manner through all phases of its development. LOPE would provide a useful set of consistent views of these descriptions, including documents, diagrams, source code, etc.
  4. 1995: Didactic computer projects. Development of documents in emacs bookmode implementing mathematical problems: Peano's space filling curves, Urysohn's lemma, topological operations, primality tests, RSA algorithm, and permutation matrices. Department of Mathematics, University of Texas at Austin.
  5. 1994-1996: Algebraic Number Theory. Applications of p-adic analysis to distribution of sequences modulo 1. Department of Mathematics, University of Texas at Austin.
  6. 1996-1998: Analytic Number Theory. Development of new analytic methods for the study of discrepancy of sequences. Extremal functions in Fourier Analysis. Department of Mathematics, University of Texas at Austin.
  7. 2000: LOCR - An Optical Character Recognition Program for Linux. Department of Mathematics, Northwestern University.