Results 11 to 20 of about 429,595 (233)
Mathematical Modelling by Help of Category Theory: Models and Relations between Them [PDF]
Mathematics, 2021 The growing complexity of modern practical problems puts high demand on mathematical modelling. Given that various models can be used for modelling one physical phenomenon, the role of model comparison and model choice is becoming particularly important. Methods for model comparison and model choice typically used in practical applications nowadays are
Dmitrii Legatiuk
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Introduction to Gestural Similarity in Music. An Application of Category Theory to the Orchestra
Journal of Mathematics and Music, 2018 Mathematics, and more generally computational sciences, intervene in several aspects of music. Mathematics describes the acoustics of the sounds giving formal tools to physics, and the matter of music itself in terms of compositional structures and ...
Mannone, Maria
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A non-standard analysis of a cultural icon: The case of Paul Halmos [PDF]
, 2016 We examine Paul Halmos' comments on category theory, Dedekind cuts, devil worship, logic, and Robinson's infinitesimals. Halmos' scepticism about category theory derives from his philosophical position of naive set-theoretic realism.
Blaszczyk, Piotr +6 more
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On Self-Predicative Universals in Category Theory
, 2015 1. This paper shows how the universals of category theory in mathematics provide a model (in the Platonic Heaven of mathematics) for the self-predicative strand of Plato's Theory of Forms as well as for the idea of a "concrete universal" in Hegel and ...
Ellerman, David
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Object-Free Definition of Categories [PDF]
, 2013 Category theory was formalized in Mizar with two different approaches [7], [18] that correspond to those most commonly used [16], [5]. Since there is a one-to-one correspondence between objects and identity morphisms, some authors have used an approach ...
Riccardi, Marco
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Valued Graphs and the Representation Theory of Lie Algebras [PDF]
, 2011 Quivers (directed graphs) and species (a generalization of quivers) and their representations play a key role in many areas of mathematics including combinatorics, geometry, and algebra.
Assem +14 more
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Categories without structures [PDF]
, 2009 The popular view according to which Category theory provides a support for Mathematical Structuralism is erroneous. Category-theoretic foundations of mathematics require a different philosophy of mathematics.
Rodin, Andrei
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Molecular Oncology, EarlyView.Tumors contain diverse cellular states whose behavior is shaped by context‐dependent gene coordination. By comparing gene–gene relationships across biological contexts, we identify adaptive transcriptional modules that reorganize into distinct vulnerability axes.
Brian Nelson +9 more
wiley +1 more source
FEBS Open Bio, EarlyView.Amino acids sequence of two different proteins with the same sequence (chameleon sequence—black boxes) represent in 3D structure of the proteins different secondary structures: HHHH—helical and BBB—Beta‐structural. The chains folded in water environment adopt different III‐order structures in which the chameleon fragments appear to adopt similar status
Irena Roterman +4 more
wiley +1 more source
, 2014 Quantity is the first category that Aristotle lists after substance. It has extraordinary epistemological clarity: "2+2=4" is the model of a self-evident and universally known truth. Continuous quantities such as the ratio of circumference to diameter of
Franklin, James
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