Abstract. New techniques are developed to show that the two-dimensional normal form for codimension one border collision bifurcations of fixed points of discrete time piecewise smooth dynamical systems has attractors which are themselves two dimensional. This makes it possible to prove the existence of these attractors for a countable set of parameter values which cannot be treated using the essentially onedimensional methods in the literature.PACS numbers: 05.45.-a
The two-dimensional border collision normal form is considered. It is known that multiple attractors can exist in this piecewise smooth system. We show that in appropriate parameter regions there can be a robust transition from a stable fixed point to multiple coexisting attractors with toological dimensions equal to two.
Gastrointestinal (GI) cancers are the major cause of cancer-related mortality globally. Medical imaging is an important auxiliary means for the diagnosis, assessment and prognostic prediction of GI cancers. Radiomics is an emerging and effective technology to decipher the encoded information within medical images, and traditional machine learning is the most commonly used tool. Recent advances in deep learning technology have further promoted the development of radiomics. In the field of GI cancer, although there are several surveys on radiomics, there is no specific review on the application of deep-learning-based radiomics (DLR). In this review, a search was conducted on Web of Science, PubMed, and Google Scholar with an emphasis on the application of DLR for GI cancers, including esophageal, gastric, liver, pancreatic, and colorectal cancers. Besides, the challenges and recommendations based on the findings of the review are comprehensively analyzed to advance DLR.
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