Abstract: 

We consider nonconvex stochastic optimization problems in the
asynchronous centralized distributed setup where the communication times
from workers to a server can not be ignored, and the computation and
communication times are potentially different for all workers. Using an
unbiased compression technique, we develop a new method—Shadowheart
SGD—that provably improves the time complexities of all previous
centralized methods. Moreover, we show that the time complexity of
Shadowheart SGD is optimal in the family of centralized methods with
compressed communication. We also consider the bidirectional setup,
where broadcasting from the server to the workers is non-negligible, and
develop a corresponding method.

Title: Stability of heteroclinic cycles: a new approach.

Speaker: Telmo Peixe (REM/CEMAPRE/ISEG - Universidade de Lisboa, Portugal).

Time: Wednesday, 17 April 2024, from 14:15 to 15:15.

Place: Room1.6, building VII.

Abstract: In this work we analyse the stability of cycles within a heteroclinic network lying in a three-dimensional manifold formed by six cycles, for a one-parameter model developed in the context of polymatrix replicator equations. We show the asymptotic stability of the network for a range of parameter values compatible with the existence of an interior equilibrium and we describe an asymptotic technique to decide which cycle (within the network) is visible in numerics. The technique consists of reducing the relevant dynamics to a suitable one-dimensional map, the so called projective map. Stability of the fixed points of the projective map determines the stability of the associated cycles. The description of this new asymptotic approach is applicable to more general types of networks and is potentially useful in computational dynamics. This is a joint work with Alexandre Rodrigues (ISEG, CEMAPRE).

Abstract: Gliomas are among the most aggressive tumors, showing a large intertumoral heterogeneity, making it crucial the search for novel biomarkers and targeted therapies. The knowledge about this disease is rapidly evolving, leading to recent updates in the glioma classification guidelines by the World Health Organization (WHO). The objective of this study was to identify transcriptomic and methylomic biomarkers of glioma heterogeneity, aiming at contributing to disease understanding and ultimately to improved diagnosis and disease management. The analysis considered transcriptomics and methylomics datasets obtained from The Cancer Genome Atlas (TCGA), with patients’ diagnoses according to the 2016 and 2021 WHO guidelines. Our results, obtained through robust sparse multinomial logistic regression models, uncovered relevant biological information regarding glioma heterogeneity with high accuracy.

Short Bio: João F. Carrilho is a Ph.D. student in the Department of Mathematics at NOVA School of Science and Technology in Caparica, Portugal. He has a bachelor’s degree in Mathematics from the same University and a master’s degree in Mathematics and Applications. In the scope of his Master’s Dissertation under the supervision of Dr. Marta B. Lopes, he was awarded the 2022 Best Paper Award by the Brazilian Journal of Biometrics, an Honorable Mention on Poster Communication at the 5th Statistics on Health Decision Making: Personalized Medicine and the 2nd place in the ‘Best Poster’ award at the XXVI Congress of the Portuguese Statistical Society – SPE 2023. His areas of interest include dimensionality reduction and robust statistics.