Research

Research areas

The main research lines of the group are divided into:

Large deviations in stochastic processes.
Random geometry.
Stochastic calculus and applications.
Statistics.
Stochastic models in biology and epidemiology.

Some more specific lines of research are listed below.

Big data
Biostatistics
Estimation of sets and statistics on manifolds
Functional data statistics
Genomic modeling
Kac-Rice formulas
Hermite - Wiener expansions
Level sets of random fields
Machine learning
Mathematical modeling in music
Modeling in telecommunications

Nonparametric statistics
Optimal stopping problems
Probability on networks and their applications
Particle systems
Random polynomials and random polynomial systems
Random waves
Robust estimation
Statistics of stochastic processes
Statistics applied to sports
Stochastic financial math
Supervised, unsupervised, and semi-supervised learning

Publications and pre-prints

On the functional regression model and its finite-dimensional approximations. J.R. Berrendero, A. Cholaquidis, A. Cuevas. Statistical Papers, 65(8), pp. 5167–5201. Link.
Statistical analysis of measures of non-convexity. A. Cholaquidis, R. Fraiman, L. Moreno, B. Pateiro-López. Test - 33(1), pp. 180–203. Link.
On the notion of polynomial reach: A statistical application. A. Cholaquidis, A. Cuevas, L. Moreno. Electronic Journal of Statistics - 18(2), pp. 3437–3460. Link.
New advances in set estimation. A. Cholaquidis. Boletin de Estadística e Investigación Operativa - 40(1), pp. 5–21.
Diffusion spiders: Green kernel, excessive functions and optimal stopping. J. Lempa, E. Mordecki, P. Salminen. Stochastic Processes and their Applications 167 (2024) 104229. Link.
Two sided ergodic singular control and mean-field game for diffusions. S. Christensen, E. Mordecki, F. Oliú. Decisions in Economics and Finance (2024). Link.
A Note on Pricing Options on Interest Rates in Uruguay. G. Magnou, E. Mordecki and A. Sosa. Revista Brasileira de Economia (aceptado, por aparecer).
Dynkin games for Lévy processes. L. Aspirot, E. Mordecki, A. Sosa. ArXiv:2410.23509.
Two sided long-time optimization singular control problems for Lévy processes and Dynkin’s games. E. Mordecki, F. Oliú.. ArXiv:2403.05731.
Optimal stopping for Markov processes with positive jumps. F. Crocce, E. Mordecki. ArXiv:2411.08796.
Quasiconvex functions on regular trees. L.M. Del Pezzo, N. Frevenza, Julio D. Rossi. Revista Colombiana de Matemáticas, 58(1), 1–24, (2024). Link.
Average conditioning of underdetermined polynomial systems. F. Carrasco. ArXiv:2305.05965. Link.
On the logarithmic energy of solution to the polynomial eigenvalue problem. F. Carrasco. ArXiv:2305.05965. Link.
On the number of roots of Sturm-Liouville random sums. F. Dalmao, J.R. León. Electron. Commun. Probab. 29 (2024), Paper No. 73, 12 pp. Link.
A total variation version of Breuer-Major central limit theorem under D1,2 assumption. J. Angst, F. Dalmao, G. Poly. Electron. Commun. Probab. 29 (2024), Paper No. 13, 8 pp. Link.
Second Maximum of a Gaussian Random Field and Exact (t-)Spacing test. J-M. Azaïs, F. Dalmao, Y. De Castro. ArXiv:2406.18397.

2023

Home Range Estimation under a Restricted Sampling Scheme. A. Cholaquidis, R. Fraiman, M. Hernandez. (2023). Journal of Nonparametric Statistics. Link.
On the finiteness of the moments of the measure of level sets of random fields. D. Armentano, J-M. Azais, F. Dalmao, J. R. León, E. Mordecki. Brazilian Journal of Probability and Statistics, 2023, Vol. 37, No. 1, 219--245. Link.
Statistical Analysis of Measures of Non-convexity. A. Cholaquidis, R. Fraiman, L. Moreno, B. Pateiro-López. (2023). TEST. Link.
Level Sets of Depth Measures in Abstract Spaces. A. Cholaquidis, R. Fraiman, L. Moreno. (2023). TEST, Vol. 32, pp. 942–957. Link.
Minimum description length for selection of models of musical rhythm. V. Rumbo, E. Mordecki, M. Rocamora. Journal of Mathematics and Music, 2023, pp. 1--19, 2023. Link.
A Counter Example on a Borsuk Conjecture. A. Cholaquidis. (2023). Appl. Gen. Topol., Vol 24, Nro. 1, pp. 125–128. Link.
On a general Kac-Rice formula for the measure of a level set. D. Armentano, J-M. Azaïs, J.R. León. Link.
Universally Consistent Estimation of the Reach. A. Cholaquidis, R. Fraiman, L. Moreno (2023). Journal of Statistical Planning and Inference, Vol. 225, pp. 110-120. Link.
Weighted Lens Depth: Some Applications to Supervised Classification. A. Cholaquidis, R. Fraiman, Gamboa, F., L. Moreno. (2023). Can J Statistics, Vol. 51, pp. 652-673. Link.
Diffusion spiders: Green kernel, excessive functions and optimal stopping. J. Lempa, E. Mordecki, P. Salminen. Stochastic Processes and their Applications 167, 2024. Link.
Random and mean Lyapunov exponents for Gln(R). D. Armentano, G. Chinta, S. Sahi, M. Shub. Aceptado en Ergodic Theory and Dynamical Systems. Link.
High order numerical methods to approximate the singular value decomposition. D. Armentano, J-C. Yakoubsohn. Link.
A note on 3d-monochromatic random waves and cancellation. F. Dalmao. ALEA, Lat. Am. J. Probab. Math. Stat. 20, 1091–1109 (2023). Link
Winding number for stationary Gaussian processes using real variables. J-M Azaïs, F. Dalmao, J.R. León. Annales de l’Institut Henri Poincaré - Probabilités ́es et Statistiques, Vol. 59, No. 3, 1183–1202 (2023). Link.
A total variation version of Breuer--Major Central Limit Theorem under D1,2 assumption. J. Angst, F. Dalmao, G. Poly. Link
On the number of roots of Sturm-Liouville random sums. F. Dalmao, J.R. León. Link.

2022

Estimation of surface area. Catherine Aaron, Alejandro Cholaquidis, Ricardo Fraiman. Electronic Journal of Statistics. Link.
Central Limit Theorem for the volume of the zero set of Kostlan-Shub-Smale random polynomial systems. Diego Armentano, Jean-Marc Azaïs, Federico Dalmao, José R. León. Journal of Complexity, Vol. 72, 2022. Link.
Testing the existence of an unadmixed ancestor from a specific population t generations ago. Gabriel Illanes, María Inés Fariello, Lucía Spangenberg, Ernesto Mordecki, Hugo Naya. PLoS ONE 17(8): e0271097. Link.
A zero interest rate Black-Derman-Toy model. Grzegorz Krzyzanowski, Ernesto Mordecki, Andres Sosa. The Journal of Fixed Income, Winter 2022, 31 (3) 93-111. Link.
Universally consistent estimation of the reach. Alejandro Cholaquidis, Ricardo Fraiman, Leonardo Moreno. Journal of Statistical Planning and Inference. Link.
Random and mean Lyapunov exponents for GLn(R). Diego Armentano, Gautam Chinta, Siddhartha Sahi, Michael Shub. Link.
Facing spatial massive data in science and society: Variable selection for spatial models. Romina Gonella, Mathias Bourel, Liliane Bel. Spatial Statistics, Vol. 50, 100627, (2022). Link.
Large Deviation Principle for the Greedy Exploration Algorithm over Erdös-Rényi Graphs. Paola Bermolen, Valeria Goicoechea, Matthieu Jonckheere, Ernesto Mordecki. ALEA, Lat. Am. J. Probab. Math. Stat. 19, 439--456 (2022). Link.
Weighted lens depth: Some applications to supervised classification. Alejandro Cholaquidis, Ricardo Fraiman, Fabrice Gamboa, Leonardo Moreno. The Canadian Journal of Statistics. Link.
On the impact of the Covid-19 health crisis on GDP forecasting: an empirical approach. Gabriel Illanes, Andrés Sosa, Ernesto Mordecki. Journal of Dynamics and Games, 2022-4-2. Link.
An r-convex set which is not locally contractible. Alejandro Cholaquidis. Applied General Topology. Link.
An algorithm to solve optimal stopping problems for one-dimensional diffusions. Fabian Crocce, Ernesto Mordecki. ALEA, Lat. Am. J. Probab. Math. Stat. 19, 1353-1375 (2022). Link.
On the finiteness of the moments of the measure of level sets of random fields. Diego Armentano, Jean-Marc Azaïs, Federico Dalmao, José R. León, Ernesto Mordecki. Link.
Decoupling between SARS-CoV-2 transmissibility and population mobility associated with increasing immunity from vaccination and infection in South America. Marcelo Fiori, Gonzalo Bello, Nicolás Wschebor, Federico Lecumberry, Andrés Ferragut, Ernesto Mordecki. Sci Rep - Nature, 12, 6874 (2022). Link.
A note on 3d-monochromatic random waves and cancellation. Federico Dalmao. Link.

2021

Two-sided optimal stopping for Lévy processes. E. Mordecki, F. Oliú Eguren. Electron. Commun. Probab. 26 (2021). Link.
Level set and density estimation on manifolds. A. Cholaquidis, R. Fraiman, L. Moreno. Journal of Multivariate Analysis. Link.
A combined strategy for multivariate density estimation. A. Cholaquidis, R. Fraiman, B. Ghattas, J. Kalemkerian. Journal of Nonparametric Statistics, Volume 33, 2021. Link.
Central limit theorem for the number of real roots of Kostlan Shub Smale random polynomial systems. D. Armentano, J.-M. Azaïs, F. Dalmao, J.R. León. Amer. J. Math. 143 (2021), no. 4, 1011–1042. Link.
On the finiteness of the moments of the measure of level sets of random fields. D. Armentano, J.-M. Azaïs, F. Dalmao, J.R. Léon, E. Mordecki. Link.
Large Deviation Principle for the Greedy Exploration Algorithm over Erdös-Rényi Graphs. P. Bermolen, V. Goicoechea, M. Jonckheere, E. Mordecki. ALEA, Lat. Am. J. Probab. Math. Stat. 19, 439–456 (2022). Link.
Level sets and drift estimation for reflected Brownian motion with drift. A. Cholaquidis, R. Fraiman, E. Mordecki, C. Papalardo. Statistica Sinica, v31 1 , p.:29 - 51, 2021. Link.
Convex and quasiconvex functions in metric graphs. L.M. Del Pezzo, N. Frevenza, J.D. Rossi. Networks & Heterogeneous Media 16 (4), 591-607 (2021). Link.
On 3-dimensional Berry's model. F. Dalmao, A. Estrade, J.R. León. ALEA Lat. Am. J. Probab. Math. Stat. 18 (2021), no. 1, 379-399. Link.
Large-Scale 802.11 Wireless Networks Data Analysis based on Graph Clustering. G. Capdehourat, P. Bermolen, M. Fiori, N. Frevenza, F. Larroca, G. Morales, C. Rattaro, G. Zunino), Wireless Personal Communications (120), 1791–1819 (2021), Link.
Large-Scale IoT Network Offloading to Cloud and Fog Computing: a Fluid Limit Model. G. Belcredi, L. Aspirot, P. Monzón, P. Belzarena. IEEE URUCON, 2021, pp. 377-381. Link.
Spatial clustering of extreme precipitation in Uruguay. F. Santiñaque, J. Kalemkerian, M. Renom. Aceptado en Revista Brasielira de Meteorología. Link.
Zero Black-Derman-Toy interest rate model. G. Krzyżanowski, E. Mordecki, A. Sosa. Journal of Fixed Income, v.: 31 4 , 2021. Link.
An independence test based on recurrence rates. An empirical study and applications to real data. J. Kalemkerian, D. Fernández. Aceptado en Communications in Statistics - Simulation and Computation. Link.
Short range vs long range dependence. an hypothesis test based on fractional iterated Ornstein--Uhlenbeck processes. J. Kalemkerian, A. Sosa. Link.
Assessing the impact of mobility reduction in the second wave of COVID-19. Á. Cabana, L. Etcheverry, M.I. Fariello, P. Bermolen, M. Fiori. XLVII Latin American Computing Conference (CLEI), 2021, pp. 1-10. Link.
Indigenous Ancestry and Admixture in the Uruguayan Population. L. Spangenberg, M.I. Fariello, D. Arce, G. Illanes, G. Greif, J.-Y. Shin, S.-K. Yoo, J.-S. Seo, C. Robello Carlos, C. Kim, J. Novembre, M. Sans, H. Naya. Frontiers in Genetics, Vol 12, 2021. Link.
Peaks over Manifold (POM): A Novel Technique to Analyze Extreme Events over Surfaces. G. Perera, A. Segura. Advances in Pure Mathematics, 12, 48-62, (2021). Link.
Monitoreo de calidad de agua y predicción de coliformes fecales en playas de Montevideo mediante algoritmos de aprendizaje automático. A.M. Segura, L. Sampognaro, G. López-Orrego, C. Crisci, M. Bourel, K. Eirin, C. Piccini, C. Kruk, G. Perera. Innotec, v.: 22 p.:1-27, (2021).
Machine learning methods for imbalanced data set for prediction of faecal contamination in beach waters. M. Bourel, A.M. Segura, C. Crisci, G. López-Orrego, L. Sampognaro, V. Vidal, C. Kruk, C. Piccini, G. Perera. Water Research, v.: 202 Sep. 1, 2021. Link.
A macroecological perspective on the fluctuations of exploited fish populations. A.M. Segura, R. Wiff, A. Jaureguizar, A.C. Milessi, G. Perera. Marine Ecology Progress Series, v.: 665 p.:177-183 (2021). Link.
Asymptotic extremal distribution for non-stationary, strongly-dependent data. C. Crisci, G. Perera. Link.
On the Impact of the Covid-19 Health Crisis on GDP Forecasting: an Empirical Approach. G. Illanes, E. Mordecki, A. Sosa.

2020

Surface and length estimation based on Crofton's formula. C. Aaron, A. Cholaquidis, R. Fraiman. arXiv.
On semi-supervised learning. A. Cholaquidis, R. Fraiman, M. Sued. Test, 2020, 29(4), pp. 914–937. Link.
Sample design to monitor COVID-19 disease. D. Morales, M.J. Lombardía, R. Fraiman, J.A.C. Albertos. Boletín de Estadística e Investigacion Operativa, 2020, 36(2), pp. 153–171. Link.
Nonparametric detection for univariate and functional data. A. Cuevas, R. Fraiman. Journal of Statistical Planning and Inference, 2020. Link.
Sensitivity indices for output on a Riemannian manifold. R. Fraiman, F. Gamboa, L. Moreno. International Journal for Uncertainty Quantification, 2020, 10(4), pp. 297–314. Link.
Nonparametric regression based on discretely sampled curves. L. Forzani, R. Fraiman, P. Llop. Revstat Statistical Journal, 2020, 18(1), pp. 1–26. Link.
On the finiteness of the moments of the measure of level sets of random fields. D. Armentano, J-M. Azaïs, F. Dalmao, J. R. Léon, E. Mordecki. arXiv.
Studying the winding number of a Gaussian process: the real method. J-M. Azaïs, F. Dalmao, J. R. León. arXiv.
Large Deviation Principle for the Greedy Exploration Algorithm over Erdos-Rényi Graphs. P. Bermolen, V. Goicoechea, M. Jonckheere, E. Mordecki. arXiv.
Sequential Algorithms and Independent Sets Discovering on Large Sparse Random Graphs. P. Bermolen, M. Jonckheere, F. Larroca, M. Saenz. arXiv.
Level set and density estimation on manifolds. A. Cholaquidis, R. Fraiman, L. Moreno. arXiv.
Set Estimation Under Biconvexity Restrictions. A. Cholaquidis, A. Cuevas. ESAIM: PS 24 770-788 (2020). Link.
On 3-dimensional Berry's model. F. Dalmao, A. Estrade, J. R. León. arXiv.
Convex envelopes on Trees. L. M. Del Pezzo, N. Frevenza, J. D. Rossi, Journal of Convex Analysis 27 (2020), No. 4, 1195--1218, Link.
Dirichlet-to-Neumann maps on Trees L. M. Del Pezzo, N. Frevenza, J. D. Rossi, Potential Analysis 53, (2020), Link.
Quasiconvex functions on regular trees. L. M. Del Pezzo, N. Frevenza, J. D. Rossi. arXiv
Sensitivity analysis in general metric spaces. F. Gamboa, T. Klein, A. Lagnoux, L. Moreno. arXiv
Retrieving the structure of probabilistic sequences of auditory stimuli from EEG data. N. Hernández, R. Machado de Azevedo Neto, A. Duarte, G. Ost, R. Fraiman, A. Galves, C. D. Vargas. arXiv
Parameter Estimation for Discretely Observed Fractional Iterated Ornstein--Uhlenbeck Processes. J. Kalemkerian. Arxiv
Zero Black-Derman-Toy interest rate model. G. Krzyżanowski, E. Mordecki, A. Sosa. arXiv
Performance analysis of Zero Black-Derman-Toy interest rate model in catastrophic events: COVID-19 case study. G. Krzyżanowski, A. Sosa. arXiv
QoS Provision in a Dynamic Channel Allocation Based on Admission Control Decisions. C. Rattaro, L. Aspirot, E. Mordecki, P. Belzarena, ACM Trans. Model. Perform. Eval. Comput. Syst. 5, (2020). Link.
Weighted lens depth: Some applications to supervised classification. A. Cholaquidis, R. Fraiman, F. Gamboa, L. Moreno. arXiv.
On a general definition of the functional linear model. J. R. Berrendero, A. Cholaquidis, A. Cuevas. arXiv.
Convex and quasiconvex functions in metric graphs. L. M. Del Pezzo, N. Frevenza, J. D. Rossi. arXiv.
Country risk index for emerging economies: a dynamical proposal with a case study. A. Sosa, E. Mordecki. Brazilian Review of Econometrics, v.: 40 2 , 2020.

The cover image belongs to the article Set estimation from reflected Brownian motion (Cholaquidis, Fraiman, Lugosi, Pateiro-López). These are data from the “Dunn Ranch Bison Tracking Project” that follow bison's trajectory in the Dunn Ranch Prairie, located in northwestern Missouri (USA).