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The foundational assumption of machine learning is that the data under consideration is separable into classes; while intuitively reasonable, separability constraints have proven remarkably difficult to formulate mathematically. We believe this problem is rooted in the mismatch between existing statistical techniques and commonly encountered data; object representations are typically high dimensional but statistical techniques tend to treat high dimensions a degenerate case. To address this problem, we develop a dedicated statistical framework for machine learning in high dimensions. The framework derives from the observation that object relations form a natural hierarchy; this leads us to model objects as instances of a high dimensional, hierarchal generative processes. Using a distance based statistical technique, also developed in this paper, we show that in such generative processes, instances of each process in the hierarchy, are almost-always encapsulated by a distinctive-shell that excludes almost-all other instances. The result is shell theory, a statistical machine learning framework in which separability constraints (distinctive-shells) are formally derived from the assumed generative process. [ABSTRACT FROM AUTHOR]

Esophageal cancer is one of the most common malignant tumors, and the 5-year overall survival rate is only 20%. Esophageal squamous cell carcinoma (ESCC) is the primary histological type of esophageal carcinoma in China. Protein phosphatase 1 regulatory subunit 18 (PPP1r18) is one of the actin-regulatory proteins and is able to bind to protein phosphatase 1 catalytic subunit alpha (PPP1CA). Yet, little is known about the role of PPP1r18 in esophageal squamous cell carcinoma (ESCC). This study aimed to elucidate the biological functions of PPP1r18 in the ESCC progression. Clinical samples first confirmed that PPP1r18 expression was upregulated in ESCC, and PPP1r18 was correlated with tumor invasion depth, lymph node metastasis, distant metastasis, and reduced overall survival. We then observed that PPP1r18 overexpression enhanced cell proliferation in vitro and in vivo. Mechanistically, PPP1r18 regulated tumor progression of ESCC through activating the calcineurin-mediated ERK pathway, rather than binding to PPP1CA. Collectively, our results suggest that PPP1r18 promotes ESCC progression by regulating the calcineurin-mediated ERK pathway. PPP1r18 might be a potential target for the diagnosis and treatment of ESCC., (© The Author(s) 2024. Published by Oxford University Press. All rights reserved. For commercial re-use, please contact reprints@oup.com for reprints and translation rights for reprints. All other permissions can be obtained through our RightsLink service via the Permissions link on the article page on our site—for further information please contact journals.permissions@oup.com.)