A Hölder estimate for nonlinear parabolic systems of p-Laplacian type

AbstractWe extend the Hölder regularity results for weak solutions of the p-Laplacian systems originally obtained by DiBenedetto to a larger class of right-hand side terms. By appropriately arranging two scale parameters on the sizes of a local parabolic cylinder and of the gradient of the solutions, we get the same Hölder exponent as in the scalar case. Our method can also recover the classical parabolic case p=2

ON SINGULARITY FOR THE m-HARMONIC FLOW (Theory of function spaces and related topics)

We study local regularity and singularity for the evolution of m-harmonic maps on ℝ[m] into a smooth compact Riemannian manifold, called m-harmonic flow. For any initial data of finite m-energy, the global existence of them-harmonic flow, which is regular except at most finitely many timespace points, is reported. The key ingredient is the uniform local regularity estimate for regular m-harmonic flows

Regularity Estimates for the p-Sobolev Flow

We study doubly nonlinear parabolic equation arising from the gradient flow for p-Sobolev type inequality, referred as p-Sobolev flow from now on, which includes the classical Yamabe flow on a bounded domain in Euclidean space in the special case . In this article we establish a priori estimates and regularity results for the p-Sobolev type flow, which are necessary for further analysis and classification of limits as time tends to infinity.Peer reviewe

Global existence for the p-Sobolev flow

In this paper, we study a doubly nonlinear parabolic equation arising from the gradient flow for p-Sobolev type inequality, referred as p-Sobolev flow. In the special case p = 2 our theory includes the classical Yamabe flow on a bounded domain in Euclidean space. Our main aim is to prove the global existence of the p-Sobolev flow together with its qualitative properties. (C) 2021 Published by Elsevier Inc.Peer reviewe

Quality Assurance of Computer-Aided Detection and Diagnosis in Colonoscopy

Recent breakthroughs in artificial intelligence (AI), specifically via its emerging sub-field “Deep Learning,” have direct implications for computer-aided detection and diagnosis (CADe/CADx) for colonoscopy. AI is expected to have at least 2 major roles in colonoscopy practice; polyp detection (CADe) and polyp characterization (CADx). CADe has the potential to decrease polyp miss rate, contributing to improving adenoma detection, whereas CADx can improve the accuracy of colorectal polyp optical diagnosis, leading to reduction of unnecessary polypectomy of non-neoplastic lesions, potential implementation of a resect and discard paradigm, and proper application of advanced resection techniques. A growing number of medical-engineering researchers are developing both, CADe and CADx systems, some of which allow real-time recognition of polyps or in vivo identification of adenomas with over 90% accuracy. However, the quality of the developed AI systems as well as that of the study designs vary significantly, hence raising some concerns regarding the generalization of the proposed AI systems. Initial studies were conducted in an exploratory or retrospective fashion using stored images and likely overestimating the results. These drawbacks potentially hinder smooth implementation of this novel technology into colonoscopy practice. The aim of this article is to review both contributions and limitations in recent machine learning based CADe/CADx colonoscopy studies and propose some principles that should underlie system development and clinical testing

Novel anti‐tumor mechanism of galanin receptor type 2 in head and neck squamous cell carcinoma cells

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/102710/1/cas12315.pd