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In this paper, we establish local and global elliptic type gradient estimates for a nonlinear parabolic equation on a smooth metric measure space whose underlying metric and potential satisfy a (k , m) -super Perelman–Ricci flow inequality. We discuss a number of applications and implications including curvature free global estimates and some constancy and Liouville type results. [ABSTRACT FROM AUTHOR]

Breast cancer is a prevalent disease worldwide and the accurate diagnosis and prognosis of breast cancer are essential for the development of effective treatment plans. Pathology remains the gold standard for diagnosis and prognosis but with limitations such as time-consuming manual scoring and some error-prone results. Recently, deep learning techniques, especially convolutional neural networks (CNN), have been proposed for the interpretation of immunohistochemistry (IHC) results in breast cancer. The objective of this systematic review is to critically assess the existing literature on computer-aided systems for the interpretation of IHC results in breast cancer based on deep learning algorithms. We included studies with models that use novel approaches such as deep learning for quantitative measurements of immunohistochemically stained Ki-67, ER, PR, and HER2 images. We systematically searched PubMed, Scopus, and web of science up to September 2022. 15 studies (seven HER2, seven Ki67, and one ER/PR scoring studies) met our inclusion criteria. Various AI-based assays have been developed for different applications in breast pathology, including diagnostic and prognostic applications, as well as predictive values and responses to treatment. These algorithms have shown promise in improving the accuracy of breast cancer diagnosis and prognosis. It is essential to consider the differences in training and inter-observer variability while designing tools, and there is an urgent need to integrate the detection and analysis of various biomarkers at the same place and time to facilitate the formation of patients' reports and treatment. [ABSTRACT FROM AUTHOR]

Badiou offers a concept of the subject that is completely intertwined with event and truth; in his view, the subject is not an isolated and secluded entity that is supposed to contemplate the world only, rather it is linked to the event, and as a faithful element, initiates the process of truth. Every human being is not necessarily a subject, but in the face of an event and the acceptance of its occurrence, the person in the situation can become the subject. For Badiou, the subject is only part of the process of truth, and this reduces the subject to a part of a material process that has no existential independence. He explicitly states that the subject subordinates to the truth and considers the subjectification of some members of the situation as the result of the occurrence of an event and the beginning of the process of truth. The authors are of the view that Badiou's theory of the subject eventually leads to the relativity of the subject and makes it impossible to provide any explanation about the existence of the subject. He considers truth to be not general but dependent on any particular situation in which the event takes place; again, in his view, truth has a general proclamation and address. But in the authors' view, his type of explanation of the subject also makes the generality of the proclamation of truth relative and so, the truth cannot be generic anymore. [ABSTRACT FROM AUTHOR]