Stronger arithmetic equivalence

This paper considers two alternative strengthenings of the notion of arithmetic equivalence, which the author calls local integral equivalence and solvable equivalence. (The latter turns out to be strictly stronger than the former.) They have the advantage of being easier to check than Prasad’s notion, which the author calls integral equivalence. Furthermore, solvable equivalence, which the author shows does not imply integral equivalence, is nevertheless a sufficient condition to imply that the invariants considered by Prasad are equal. This opens the door to easier proofs of Prasad’s result, and lessens the reliance on Scott’s construction: the author finds a generalization of this construction that yields infinitely many examples of solvable equivalence. The paper also contains several examples to clarify the relationships between the various different notions of equivalence. Some of these examples (which are mainly found with the help of a computer) answer open questions from the group theory literature.

Local Integral Regression Network for Cell Nuclei Detection

Nuclei detection is a fundamental task in the field of histopathology image analysis and remains challenging due to cellular heterogeneity. Recent studies explore convolutional neural networks to either isolate them with sophisticated boundaries (segmentation-based methods) or locate the centroids of the nuclei (counting-based approaches). Although these two methods have demonstrated superior success, their fully supervised training demands considerable and laborious pixel-wise annotations manually labeled by pathology experts. To alleviate such tedious effort and reduce the annotation cost, we propose a novel local integral regression network (LIRNet) that allows both fully and weakly supervised learning (FSL/WSL) frameworks for nuclei detection. Furthermore, the LIRNet can output an exquisite density map of nuclei, in which the localization of each nucleus is barely affected by the post-processing algorithms. The quantitative experimental results demonstrate that the FSL version of the LIRNet achieves a state-of-the-art performance compared to other counterparts. In addition, the WSL version has exhibited a competitive detection performance and an effortless data annotation that requires only 17.5% of the annotation effort.

Empoderamiento de la ciudadanía a través de la participación ciudadana para un gobierno local integral

La presente investigación tuvo como objetivo, determinar la importancia del empoderamiento de la ciudadanía a través de participación ciudadana para una gestión integral, la investigación es básica de diseño descriptivo con revisión sistemática, para profundizar el conocimiento sobre participación ciudadana se realizó un análisis de 21 artículos de las variables estudiadas tanto a nivel nacional como internacional; de los hallazgos estudiados se encontró que ciertas similitudes de algunos autores como Carrasco(2021) y Nieto (2020) afirman que la participación ciudadana es casi nula por la insatisfacción de la población y la falta de interés del gobierno, Chaparro (2021) Montalba y Grau (2019) proponen la implementación de un modelo que fomente la participación ciudadana en los gobiernos locales, estas propuestas se ven complementadas con una propuesta educativa para el aprendizaje de una ciudadanía activa de Aguado, Melero y Gil(2020); por otro lado en cuanto a la gestión municipal encontramos que en gran parte los autores la consideran como deficiente en cuanto a planificación, organización, del mismo modo Pompilio(2020) manifiesta que durante el proceso de modernización municipal las autoridades solo se han preocupado solo por cumplir con la norma mas no por ver los resultados. Finamente concluimos que las herramientas utilizadas durante la implementación de la participación ciudadana tienen muchas falencias por diferentes factores, por lo que se recomienda que los gobiernos locales deban emprender una campaña de concientización en cuanto a la relevancia de la colaboración ciudadana en decisiones del gobernante para lograr el desarrollo de la población.

Non-local approximation of the Griffith functional

An approximation, in the sense of $$\Gamma $$ Γ -convergence and in any dimension $$d\ge 1$$ d ≥ 1 , of Griffith-type functionals, with p-growth ($$p>1$$ p > 1 ) in the symmetrized gradient, is provided by means of a sequence of non-local integral functionals depending on the average of the symmetrized gradients on small balls.

AVERAGING IN MULTIFREQUENCY SYSTEMS WITH DELAY AND LOCAL INTEGRAL CONDITIONS

Multifrequency systems of dierential equations were studied with the help of averaging method in the works by R.I. Arnold, Ye.O. Grebenikov, Yu.O. Mitropolsky, A.M. Samoilenko and many other scientists. The complexity of the study of such systems is their inherent resonant phenomena, which consist in the rational complete or almost complete commensurability of frequencies. As a result, the solution of the system of equations averaged over fast variables in the general case may deviate from the solution of the exact problem by the quantity O (1). The approach to the study of such systems, which was based on the estimation of the corresponding oscillating integrals, was proposed by A.M. Samoilenko, which allowed to obtain in the works by A.M. Samoilenko and R.I. Petryshyn a number of important results for multifrequency systems with initial , boundary and integral conditions. For multifrequency systems with an argument delay, the averaging method is substantiated in the works by Ya.Y. Bihun, R.I. Petryshyn, I.V. Krasnokutska and other authors. In this paper, the averaging method is used to study the solvability of a multifrequency system with an arbitrary nite number of linearly transformed arguments in slow and fast variables and integral conditions for slow and fast variables on parts of the interval [0, L] of the system of equations. An unimproved estimate of the error of the averaging method under the superimposed conditions is obtained, which clearly depends on the small parameter and the number of linearly transformed arguments in fast variables.