Lab. 2.2, building VII.




Abstract:
 
We begin with a very introductory overview of classical, intuitionistic, and linear logics. Several proof translations exist between classical and intuitionistic logic (negative translations) [1, 2, 3], as well as between intuitionistic and linear logic (Girard translations) [4, 5]. These translations serve various purposes, including transferring properties between systems, simplifying proofs, facilitating the extraction of constructive computational content from proofs, and controlling the use of logical resources.
 
We will show that all these systems can be expressed as extensions of a basic logical system (essentially, intuitionistic linear logic). By establishing a common logical basis, we are able to formalize a unified approach to devising and simplifying such proof translations [6]. This approach clarifies the relationships between different logical systems, and reveals the underlying structure that connects them. Through this simplification process, we obtain the most well-known translations in the literature.
 
This is joint work with Paulo Oliva and Clarence Protin.

References:

[1] A.S. Troelstra, D. van Dalen, Constructivism in mathematics: An introduction. In Studies in Logic and the Foundations of Mathematics, volume 1, 1988.

[2] M. Heine Sørensen, P. Urzyczyn, Lectures on the Curry-Howard Isomorphism, volume 149. Elsevier, 2006.
 
[3] G. Ferreira, P. Oliva, On various negative translations, Electronic Proceedings in Theoretical Computer Science, 47:21-33, 2011.

[4] J.-Y. Girard, Linear logic, Theoretical Computer Science, 50:1–101, 1987.
 
[5] J.-Y. Girard, A tutorial on linear logic. In Substructural Logics, Studies in Logic and Computation 2, pages 327–355. Oxford Science Publications, 1994.
 
[6] G. Ferreira, P. Oliva, C. Protin, On the various translations between classical, intuitionistic and linear logic. (subm.)
https://arxiv.org/abs/2409.02249

Statistics and Risk Management Seminar

Department of Mathematics, NOVA MATH/FCT NOVA

Title: On Generalized Mean Reverting Processes with Possible Structural Change

Speaker: Yunhong Lyu,Trent University, Peterborough, Canada

Date | Time: February 11, 2025 | 14h00

 Zoom: https://videoconf-colibri.zoom.us/j/88333359956

Abstract: In this presentation, we address the inference problem for the drift parameter in a generalized mean-reverting process, which is well-suited for modeling data exhibiting periodic characteristics. Additionally, we examine the case where linear constraints may be imposed on the drift parameters. We introduce three estimators: the unrestricted estimator, the restricted estimator, and the shrinkage estimator, and evaluate their relative efficiency. Furthermore, we explore change-point detection within this framework. Simulation studies validate the effectiveness of the proposed methods, which are subsequently applied to real-world environmental data. The results highlight the significance of accurate inference and timely change detection in environmental processes. Finally, the proposed methodology is expected to enhance the understanding and management of environmental systems.

Short Bio: Yunhong Lyu is an Assistant Professor in the Department of Mathematics & Statistics at Trent University, specializing in statistical modeling and structural change detection. Her research focuses on the inference problems in mean-reverting processes, such as parameter estimation, hypothesis testing and change-point detection, with applications in economics, health, and environmental studies. She holds a PhD from the University of Windsor and has published work on financial modeling, healthcare economics, and education policy. Beyond her research, she enjoys mentoring and teaching both undergraduate and graduate students.

Organizers: Mina Norouzirad & Isabel Natário

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This work is funded by national funds through the FCT – Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 (https://doi.org/10.54499/UIDB/00297/2020) and UIDP/00297/2020 (https://doi.org/10.54499/UIDP/00297/2020) (Center for Mathematics and Applications)

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  Seminar of Operations Research

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Title: A specialized second-order augmented Lagrangian method for mathematical programs with cardinality constraints

Speaker: Mariana da Rosa, UNICAMP, Brasil

Date | Time: February 12, 2025 | 15h00

Place: FCT NOVA, VII-Second Floor, Seminar room

Abstract:

In this talk, a practical and specialized second-order augmented Lagrangian method for solving mathematical programs with cardinality constraints (MPCaC) is presented. The seminar begins with a review of the stationarity conditions for MPCaC and a discussion of some augmented Lagrangian methods proposed in the literature. The presentation then considers a new approach that incorporates a second-order refinement step tailored to the structure of MPCaC. Under reasonable assumptions, the method ensures convergence to second-order stationary points, making it a potential tool for tackling this class of optimization problems.