Results 131 to 140 of about 1,477,961 (298)
Only up to isomorphism? Category Theory and the Foundations of Mathematics [PDF]
, 2010 Does category theory provide a foundation for mathematics that is autonomous with respect to the orthodox foundation in a set theory such as ZFC? We distinguish three types of autonomy: logical, conceptual, and justificatory.
Pettigrew, Richard, Linnebo, Øystein
core
Quantum current and holographic categorical symmetry
SciPost PhysicsWe establish the formulation for quantum current. Given a symmetry group G, let $\mathcal{C}$:=Rep G be its representation category. Physically, symmetry charges are objects of $\mathcal{C}$ and symmetric operators are morphisms in $\mathcal{C}$.
Tian Lan, Jing-Ren Zhou
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Molecular Oncology, EarlyView.Detecting circulating tumor cells (CTCs) in blood before surgery may help predict outcomes in patients with head and neck squamous cell carcinoma (HNSCC). Here, we show when combined with tumor size and lymph node involvement from routine imaging, CTC status identifies high‐risk patients with poorer survival—offering a simple, minimally invasive tool ...
Susanne Flach +9 more
wiley +1 more source
Engineering ProceedingsEffective candidate generation is a critical component of two-stage recommender systems; however, traditional methods such as Term Frequency–Inverse Document Frequency (TF-IDF) often fail to capture deep semantic context.
Balagangadhar Reddy Kandula, Lija Jacob
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Molecular Oncology, EarlyView.LUNAR is a liver‐specific long noncoding RNA (lncRNA) that is highly expressed in normal liver but becomes epigenetically silenced in hepatocellular carcinoma through promoter hypermethylation. Loss of LUNAR is associated with NOTCH activation, epithelial–mesenchymal transition, and metastasis, whereas restoring LUNAR restrains metastatic progression ...
Se Ha Jang +9 more
wiley +1 more source
Theory and Applications of Categories, 2013 We develop a theory of categories which are simultaneously (1) indexed over a base category S with finite products, and (2) enriched over an S-indexed monoidal category V. This includes classical enriched categories, indexed and fibered categories, and internal categories as special cases.
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Category-theoretic solution of recursive domain equations [PDF]
The solution of a recursive domain equation, of the form D ~= F(D) may be viewed as the finding of a fixpoint (up to isomorphism) of the functor F. This has led to the idea of formulating a category-theoretic analogue of Tarski's fixpoint theorem for ...
Smyth, M. B. (Michael B.)
core
Translating whole‐genome doubling into precision medicine in cancer
Molecular Oncology, EarlyView.Whole‐genome doubling creates a WGD‐positive tumor state characterized by persistent chromosomal instability, karyotypic diversification, and cellular stress. These same biological pressures drive aggressive tumor evolution while exposing therapeutic vulnerabilities, providing a rationale for WGD‐informed precision medicine. Whole‐genome doubling (WGD)
Sejung Lee, Junghyeok Lim, Jinhyuk Bhin
wiley +1 more source
Molecular Oncology, EarlyView.Single‐cell DNA methylation (scDNAme) profiling maps epimutational clonal evolution, revealing mechanisms of malignancy and therapeutic resistance across diverse cancer types. By providing a high‐resolution landscape of intratumoral heterogeneity, these technologies empower precise patient stratification, guide the development of enhanced ...
Ik Soo Kim
wiley +1 more source
Generalized enrichment of categories
Journal of Pure and Applied Algebra, 2002 We define the phrase `category enriched in an fc-multicategory' and explore some examples. An fc-multicategory is a very general kind of 2-dimensional structure, special cases of which are double categories, bicategories, monoidal categories and ordinary multicategories.
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