M.A.Lerma's Index of Preprints
Mathematics.
 Putnam Training Problems (pdf)  Used for Putnam Training.

Notes on Discrete Mathematics (pdf)  Used for teaching in a CS program.

A Gradient Theorem for Lipschitz Continuous Functions (pdf)  A generalization of the Gradient Theorem for Line Integrals, used in another paper.
 Principal Components Analysis in 2D (pdf)  An overview.
I had to use it in a programming project and wanted to leave a record of it for future reference.
 How inefficient can a sort algorithm be? (pdf)
 https://arxiv.org/abs/1406.1077
 Tongue in cheek essay about how to build a pessimal "inefficient" sorting algorithm.

The Bernoulli Periodic functions (pdf)  Overview.

An Extremal Majorant for the Logarithm and its Aplications (pdf)  Dissertation.

Some Applications of Extremal Functions in Fourier Analysis (pdf)  Related to my doctoral dissertation, advised by Prof. Vaaler.

Construction of a Number Greater Than One Whose Powers
Are Uniformly Distributed Modulo One (pdf)  Proof of concept (and rather complicated, may need revision).

Distribution of Powers Modulo 1 and Related Topics (pdf)
 https://arxiv.org/abs/1312.5996  From my times as a graduate student.
 Some Results in Analysis (pdf)
 A list of mathematical results placed here to have them handy.
Physics.
 A Mirror Based Event Cloaking Device (pdf)
 https://arxiv.org/abs/1308.2606  Proof of concept, very simple.

A Simple Derivation of the Equation for the Brachistochrone Curve (pdf)  Just for fun.
Computer Science.
 Preprocessing of Pixel Data Information in the DICOM files of the LIDCIDRI Dataset
With M.Lucas et al. (on Artificial Intelligence and Deep Learning).
 A Vulnerability of Attribution Methods Using PreSoftmax Scores (2023) (pdf)  https://arxiv.org/abs/2307.03305  An example of how the paradoxical situation discussed in section 2.2 of "Pre or PostSoftmax Scores in Gradientbased Attribution Methods, What is Best?" can be exploited to implement an adversarial attack on a class of attribution methods.
 Code: https://github.com/mlerma54/adversarialattacksonsaliencymaps
 Pre or PostSoftmax Scores in Gradientbased Attribution Methods, What is Best? (2023) (pdf)  https://arxiv.org/abs/2306.13197  Advantages and disadvantages of using presoftmax versus postsoftmax network scores in gradientbased attribution methods.
 Visual Explanations from Deep Networks via RiemannStieltjes Integrated Gradientbased Localization (2022)  https://arxiv.org/abs/2205.10900  Gradient based attribution method for deep neural networks that is not affected by the vanishing gradients problems and can be applied to hidden layers.
 GradCAM++ is Equivalent to GradCAM with Positive Gradients (2022) (pdf)  https://arxiv.org/abs/2205.10838  We show that the GradCAM++ algorithm is equivalent to a very simple variation of GradCAM in which gradients are replaced with positive gradients.

SymmetryPreserving Paths in Integrated Gradients (2021) (pdf)
 https://arxiv.org/abs/2103.13533  Filling some "holes" in a mathematical argument found in a paper.
 On Evaluating Explanation Methods for Deep Networks (2021) (pdf)
 Slides. Challenges of getting empirical evaluations of explanation methods for deep networks.
Unfinished preprints.
 Physics: A Brief Summary (pdf) 
Mostly based on Math E11 Spring 1999 taught by Prof. Zaslow. Section on Quantum Field Theory added and still unfinished.
 Uncertainty Quantification in Machine Learning,
Miscellaneous Results (pdf) 
Miscellaneous definitions and results useful in uncertainty quantification for machine learning. Pending: Dropout Approach to Uncertainty Estimation.
Publications

M. Lerma and M. Lucas, "Pre or PostSoftmax Scores in Gradientbased Attribution Methods, What is Best?," 2023 IEEE 13th International Conference on Pattern Recognition Systems (ICPRS), Guayaquil, Ecuador, 2023, pp. 14, doi: 10.1109/ICPRS58416.2023.10179032.  https://ieeexplore.ieee.org/document/10179032

Lucas M; Lerma M; Furst JD; Raicu DS (2022): Explainable Model for Localization of Spiculation in Lung Nodules, in Workshop on AIenabled Medical Image Analysis (AIMIA): Digital Pathology & Radiology/COVID19, held jointly with the European Conference on Computer Vision (ECCV) 2022, TelAviv, Israel, October 23 to 27, 2022 (link)

Lucas, M., Lerma M., Furst, J., Raicu, D. (2022). RSIGradCAM: Visual Explanations from Deep Networks via RiemannStieltjes Integrated GradientBased Localization. In: Bebis, G. et al (Ed.), Advances in Visual Computing. ISVC 2022. Lecture Notes in Computer Science, vol 13598. Springer, Cham. https://doi.org/10.1007/9783031207136_20 (link)
 Lerma M and Lucas M: GradCAM++ is Equivalent to GradCAM with
Positive Gradients (2022). In proceedings of the 24th
Irish Machine Vision and Image Processing Conference,
pages 113–120
(link to proceedings) (pics).
 Lucas M; Lerma M; Furst JD; Raicu DS (2021): Robust Heatmap Template
Generation for COVID19 Biomarker Detection, EAI Endorsed
Transactions on Bioengineering and Bioinformatics, issue 2, 2021,
bebi 21:e2, doi:10.4108/eai.2422021.168729
 Miguel A. Lerma (2021), Truck Versus Human 2.0: Mathematical
FollowUp Under Increasing Pressure, and How Kepler’s Laws Come to the
Rescue, The College Mathematics Journal, 52:1, 22–30,
DOI: 10.1080/07468342.2021.1847590
 Lucas M; Lerma M; Furst JD; Raicu DS (2020): Heatmap Template
Generation for COVID19 Biomarker Detection in Chest Xrays, The
20th IEEE International Conference on BioInformatics And
BioEngineering (BIBE 2020), USA, October 2628, 2020.
 Introducción a las redes de Hopfield, in Olmeda, I., and
BarbaRomero, S. (Ed.): Redes Neuronales Artificiales, Fundamentos
y Aplicaciones, Servicio de Publicaciones de la Universidad de
Alcalá de Henares, Alcalá de Henares, Spain, 1993.
 with Castellanos, J.; Ríos, J.; Segovia, J. (1992):
Approximation of Functions by Neural Networks: an Experimental
Test, International Journal of Neural Networks, Vol.3, No.4,
December 1992, pp.149–153.
 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.
 with Barrios, D.; Ríos, J.; Segovia, J. (1992): 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 59, 1992, pp.170–178.
 with Castellanos, J.; Ríos, J.; Segovia, J. (1992)): Fast
Training of Feedforward Multilayer Neural Networks By Means of a
Weighted Least Mean Square Algorithm, Neural Network World
5/92, 423436.
Research
 2017present: Artificial Intelligence, Neural Networks, Deep
Learning, Explainable AI.
 2000: LOCR  An Optical Character Recognition Program for
Linux. Department of Mathematics, Northwestern University.
 19961998: 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.
 19941996: Algebraic Number Theory. Applications of padic
analysis to distribution of sequences modulo 1. Department of
Mathematics, University of Texas at Austin.
 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.
 19921993: Development of computer tools. Proyecto Lope (Lope
project), School of Computer Science, Universidad Politécnica de
Madrid. Designing of a metaenvironment 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.
 19911992: Computational Geometry. Extension to the ndimensional
space of the winding number algorithm for polygon inclusion, with
applications to polyhedron and polytope inclusion. School of Computer
Science, Universidad Politécnica de Madrid.
 19891991: 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.