DSpace Collection:http://hdl.handle.net/10174/2032023-05-30T01:11:31Z2023-05-30T01:11:31ZThe Halpern-Mann iteration in CAT(0) spaces.Dinis, Brunohttp://hdl.handle.net/10174/336462023-02-03T10:13:05Z2022-01-01T00:00:00ZTitle: The Halpern-Mann iteration in CAT(0) spaces.
Authors: Dinis, Bruno
Abstract: Complete CAT(0) spaces, also known as Hadamard spaces, are a non-linear generalization of Hilbert spaces. Benefiting from ideas and tools from the proof mining program it was shown by Dinis and Pinto the strong convergence of an iterative schema which alternates between Halpern and Krasnoselskii-Mann style iterations in the general context of CAT(0) spaces. At the same time, the logical tools used allowed to obtain quantitative information in the form of rates of asymptotic regularity and rates of metastability (in the sense of T. Tao). If one restricts oneself to Hilbert spaces, the proof follows some standard arguments. However, to obtain the proof in the more general context of CAT(0) spaces the use of logical tools, and in particular the technique introduced by Ferreira et al., seem to be necessary.
In this talk I will explain the role of the logical tools in obtaining this result.2022-01-01T00:00:00ZConvergence: what’s logic got to do with it?Dinis, Brunohttp://hdl.handle.net/10174/336452023-02-03T10:15:22Z2022-11-01T00:00:00ZTitle: Convergence: what’s logic got to do with it?
Authors: Dinis, Bruno
Abstract: Proof mining is a program that makes use of tools from mathematical
logic in order to analyse mathematical proofs. This analysis is developed
with the purpose of extracting quantitative information from proofs, for example
in the form of effective bounds and/or algorithms. The success of the
proof mining program is due to the ability of extracting computational content
from non-constructive proofs which often allows to improve the results
analysed by weakening the hypotheses necessary to prove them. Moreover,
in the improved results the logical tools used to analyse the original proof
are not visible and can therefore be read by non-logicians. Nevertheless,
the understanding of certain logical principles, as well as their strength, is
crucial in order to perform the extraction of information from the proof.
In this talk I will give a soft introduction to the proof mining program
focusing on the somewhat simple example of the convergence of sequences.
As it turns out, this is a very fruitful example, related with Terence Tao’s
notion of metastability, which is has been paramount in different areas of
research.2022-11-01T00:00:00ZTeoremas básicos do sucesso escolarAlbuquerque, Ruihttp://hdl.handle.net/10174/244802019-02-06T15:28:55Z2018-06-27T23:00:00ZTitle: Teoremas básicos do sucesso escolar
Authors: Albuquerque, Rui
Abstract: Estudo quantitativo da dinâmico do sucesso escolar em disciplinas do Ensino Superior de muito baixa Taxa de Sucesso de Inscritos.2018-06-27T23:00:00ZReflexões estatísticasBraumann, Carlos A.http://hdl.handle.net/10174/196102017-01-10T11:56:49Z2016-01-01T00:00:00ZTitle: Reflexões estatísticas
Authors: Braumann, Carlos A.
Abstract: Reflexões sobre o uso dos testes de hipóteses, alguns desafios atuais da Estatística e o funcionamento dos Congressos da Sociedade Portuguesa de Estatística2016-01-01T00:00:00Z