Contents

Articles

1. The effects of semantic simplifications on random BST-like expression-trees, with Florent Koechlin . To appear in the journal Discrete Mathematics, Volume 347, Issue 5, May 2024.
2. Lochs-type theorems beyond positive entropy, with Valérie Berthé, Eda Cesaratto, and Martín D. Safe. Published in the journal Monatshefte für Mathematik, Volume 200, pages 737-779, 6 January 2023. Preprint arXiv:2202.04008v1
3. A Probabilistic Model Revealing Shortcomings in Lua's Hybrid Tables, with Conrado Martínez and Cyril Nicaud. Published in the Proceedings of the 28th International Conference, Computing and Combinatorics COCOON 2022.
4. Simplifications of Uniform Expressions Specified by Systems, with Cyril Nicaud and Florent Koechlin . special issue DLT'20, International Journal of Foundations of Computer Science (IJFCS).
5. Random Regular Expression Over Huge Alphabets, with Cyril Nicaud. International Journal of Foundations of Computer Science, 2021.
6. Analysis of an efficient reduction algorithm for random regular expressions based on universality detection, with Florent Koechlin . Published in the Proceedings of the 16th International Computer Science Symposium, CSR 2021.
7. Absorbing patterns in BST-like expression-trees, with Florent Koechlin . Published in the Proceedings of the 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021).
8. On the Degeneracy of Random Expressions Specified by Systems of Combinatorial Equations, with Cyril Nicaud and Florent Koechlin . Published in the Proceedings of the 24th International Conference in Developments in Language Theory DLT 2020.
9. Two arithmetical sources and their associated tries, with Valérie Berthé, Eda Cesaratto, Frédéric Paccaut, Martín D. Safe and Brigitte Vallée. Published in the Proceedings of AofA 2020.
10. Uniform Random Expressions Lack Expressivity, with Cyril Nicaud and Florent Koechlin ; Published in the proceedings of the 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019).
11. Analysis of the Continued Logarithm Algorithm, with Brigitte Vallée and Alfredo Viola ; Published in the proceedings of LATIN 2018. Preprint arXiv:1801.10139
12. The recurrence function of a random Sturmian word, with Brigitte Vallée ; Published in the Proceedings of the Fourteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO 2017) . Preprint arXiv:1610.01479
13. Recurrence function on Sturmian words: a probabilistic study, with Valérie Berthé, Eda Cesaratto, Brigitte Vallée and Alfredo Viola ; Published in the proceedings the 40th International Symposium on Mathematical Foundations of Computer Science (MFCS 2015).

Submitted

• Mathematical Models to Analyze Lua Hybrid Tables and Why They Need a Fix , with Conrado Martínez and Cyril Nicaud. Long version. Preprint arXiv:2208.13602
• Heuristic detection of universal subtrees in random regular expressions, with Florent Koechlin . Long version.

In preparation

• Shannon weights for binary recurrent sources of zero entropy.
• The mirror expansion of complete systems.

Slides

• Change of basis in Numeration Systems, Meeting STIC-AmSud,EPAA, Buenos Aires, 23 October, 2024.
• A Probabilistic Model Revealing Shortcomings in Lua’s Hybrid Tables, Séminaire LIGM, 4 April, 2023.
• Lochs' index: weight function and change of basis, Meeting STIC-AmSud, RAPA2,Online, 7 December, 2021.
• Analysis of an efficient reduction algorithm for random regular expressions based on universality detection, CSR 2021, 30 June 2021.
• Absorbing patterns in BST-like expression-trees, STACS 2021, Online, March 2021. Video available here.
• Change of basis towards sources of zero entropy, Meeting of the project STIC-AmSud Rapa2, Online, 11 December 2020.
• Uniform random expressions lack expressivity, MFCS 2019, Aachen, Germany, August 28, 2019.
• Probabilistic studies in Number Theory and Word Combinatorics: instances of dynamical analysis, Seminaire Combinatoire, IRIF, Paris, May 24, 2018.
• The Continued Logarithm Algorithm. A probabilistic study, Seminaire ALGO, GREYC, Caen, February 20, 2018.
• Random Number Generation and Fitting Interval Partitions, Rencontre des projets AleaEnAmSud et Dyna3S, Univ. Caen, France, June 06, 2017. This is another subject I am interested in. See my related blogpost here.
• The recurrence function of a random Sturmian word, ANALCO 2017, Barcelona, January 16, 2017. This is a second probabilistic model

Miscellaneous

• Convergence and natural density, notes, 1 p., 2024.
• Generating a random variable by coin tossing, research notes, 7 pp., 2017.
• Compresión sin pérdida de imágenes utilizando códigos óptimos para distribuciones geométricas bidimensionales, report from my final project for Ingeniero en Computación, 128 pp., 2014.

PhD thesis

My thesis was entitled “Probabilistic studies in Number Theory and Word Combinatorics: instances of dynamical analysis”, and encompasses, for example, topics such as the probabilistic study of the recurrence function of Sturmian words and the “Continued Logarithm Algorithm”. I defended my thesis on the 27th september 2018.

The slides from the defence are available here, while the manuscript is available here.