On a level-set method for ill-posed problems with piecewise non-constant coefficients

We investigate a level-set type method for solving ill-posed problems, with the assumption that the solutions are piecewise, but not necessarily constant functions with unknown level sets and unknown level values. In order to get stable approximate solutions of the inverse problem we propose a Tikhonov-type regularization approach coupled with a level set framework. We prove the existence of generalized minimizers for the Tikhonov functional. Moreover, we prove convergence and stability of the regularized solutions with respect to the noise level, characterizing the level-set approach as a regularization method for inverse problems. We also show the applicability of the proposed level set method in some interesting inverse problems arising in elliptic PDE models. Keywords: Level Set Methods, Regularization, Ill-Posed Problems, Piecewise Non-Constant CoefficientsComment: Accepte

A Fractional SIRC Model For The Spread Of Diseases In Two Interacting Populations

In this contribution we address the following question: what is the behavior of a disease spreading between two distinct populations that interact, under the premise that both populations have only partial immunity to circulating stains of the disease? Our approach consists of proposing and analyzing a multi-fractional Susceptible (S), Infected  (I), Recovered (R) and Cross-immune (C)  compartmental model, assuming that the dynamics between the compartments of the same population is governed by a fractional derivative, while the interaction between distinct populations is characterized by the proportion of interaction between susceptible and infected individuals of both populations. We prove the well-posedness of the proposed dynamics, which is complemented with simulated scenarios showing the effects of fractional order derivatives (memory) on the dynamics

Identification of Nano-Beams Rigidity Coefficient: A Numerical Analysis Using the Landweber Method

Due to their supporting function, beams are one of the main elements in structural projects. With the intense technological development in the field of nanotechnology, beams at micro- and nanoscales have become objects of intense study and research interest, see for example [8]. In this approach, we analyze numerically the inverse problem of identifying the stiffness coefficient in micro-nano-beams as a function that implicitly depends on the fractal media map for the continuum from strain measurements. Such a problem is unstable with respect to noise in strain measurements, which is inherent in practical problems. We introduce the equations that compose Landweber's iterative regularization method as a strategy to obtain a stable and convergent approximate solution with respect to the noise level in the measurements. We show some scenarios with simulated data for identifying the stiffness coefficient for different noise levels in measurements and for different coefficient of transformation of fractal medium. The results found numerically show that Landweber's method is a regularization strategy for the problem of identifying the stiffness coefficient in micro/nano-beams

ARTE: una denúncia contra la violencia de género

Este artigo é uma apresentação da parte prática do Trabalho de Conclusão de Curso “Corpo-grito: a performance como denúncia da violência de gênero”, em História – Memória e Imagem, da UFPR (2023), no qual foi desenvolvido a montagem de uma videoperformance intitulada ARTE: uma denúncia contra a violência de gênero, disponível no YouTube. A pesquisa e a construção do roteiro ocorreram por meio do diálogo entre obras artísticas produzidas entre as décadas 1970-2010 que permitem uma discussão sobre a violência de gênero. Algumas dessas obras também discutem o próprio fazer artístico na produção de artistas mulheres. O objetivo da videoperformance foi construir um passeio em formato de vídeo através de uma “curadoria virtual” e, assim, convocar o(a) espectador(a) para a relação com diferentes linguagens artísticas. O processo criativo partiu de pesquisas que relacionam arte e movimento feminista a partir dos trabalhos teóricos de Roberta Barros e Luana Saturnino Tvardovskas. E, para a construção do roteiro e montagem, os estudos de Philippe Dubois, Arlindo Machado e Luciano Vinhosa foram fundamentais. Dessa forma, a videoperformance explanada neste artigo apresenta imagens e a mediação delas de forma narrada, abordando ao mesmo tempo a luta do movimento feminista nesse processo. No passeio, é possível encontrar: Adélia Prado, Anna Marina Maiolino, Lenora de Barros, Letícia Parente, Rosana Paulino, Berna Reale, Angélica Freitas, Leonarda Glück, Roseane Santos e Joana Queiroz.Este artículo es una presentación de la parte práctica del Trabajo de Finalización de Curso “Cuerpo-grito: una performance como denuncia de la violencia de género”, en História – Memória e Imagem, de la UFPR (2023), en el cual fue montado un video performance titulado ARTE: una denuncia contra la violencia de género, disponible en YouTube. La investigación y construcción del guión surgió a través del diálogo entre obras artísticas producidas entre las décadas de 1970 y 2010 que permiten una discusión sobre la violencia de género. Algunas de estas obras también abordan el propio proceso artístico en la producción de mujeres artistas. El objetivo de la videoperfomance fue construir un recorrido en formato de video a través de una “curaduría virtual” y, así, convocar al (a la) espectador(a) una relación con diferentes lenguajes artísticos. El proceso creativo partió de una investigación que relaciona el arte y el movimiento feminista a partir de los trabajos teóricos de Roberta Barros y Luana Saturnino Tvardovskas. Para la construcción del guión y el montaje, fueron fundamentales los estudios de Philippe Dubois, Arlindo Machado y Luciano Vinhosa. De esta forma, la videoperfomance explicada en este artículo presenta las imágenes y su mediación de forma narrada, abordando al mismo tiempo la lucha del movimiento feminista en este proceso. En el recorrido se encuentran: Adélia Prado, Anna Marina Maiolino, Lenora de Barros, Letícia Parente, Rosana Paulino, Berna Reale, Angélica Freitas, Leonarda Glück, Roseane Santos y Joana Queiroz

A Fractional SIRC Model For The Spread Of Diseases In Two Interacting Populations

In this contribution we address the following question: what is the behavior of a disease spreading between two distinct populations that interact, under the premise that both populations have only partial immunity to circulating stains of the disease? Our approach consists of proposing and analyzing a multi-fractional Susceptible (S), Infected  (I), Recovered (R) and Cross-immune (C)  compartmental model, assuming that the dynamics between the compartments of the same population is governed by a fractional derivative, while the interaction between distinct populations is characterized by the proportion of interaction between susceptible and infected individuals of both populations. We prove the well-posedness of the proposed dynamics, which is complemented with simulated scenarios showing the effects of fractional order derivatives (memory) on the dynamics

On the Choice of the Tikhonov Regularization Parameter and the Discretization Level: A Discrepancy-Based Strategy

We address the classical issue of appropriate choice of the regularization and discretization level for the Tikhonov regularization of an inverse problem with imperfectly measured data. We focus on the fact that the proper choice of the discretization level in the domain together with the regularization parameter is a key feature in adequate regularization. We propose a discrepancy-based choice for these quantities by applying a relaxed version of Morozov's discrepancy principle. Indeed, we prove the existence of the discretization level and the regularization parameter satisfying such discrepancy. We also prove associated regularizing properties concerning the Tikhonov minimizers.Comment: 28 pages, 4 figure