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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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Interfacing biology, category theory and mathematical statistics [PDF]
Electronic Proceedings in Theoretical Computer Science, 2020 Motivated by the concept of degeneracy in biology (Edelman, Gally 2001), we establish a first connection between the Multiplicity Principle (Ehresmann, Vanbremeersch 2007) and mathematical statistics. Specifically, we exhibit two families of statistical tests that satisfy this principle to achieve the detection of a signal in noise.
Pastor, Dominique +3 more
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Towards a Hermeneutic Categorical Mathematics or why Category theory goes beyond Mathematical Structuralism [PDF]
, 2006 37 pages, no ...
Andrei Rodin
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Mathematics of General Intelligence With Homotopy Type Theory and Category Theory [PDF]
Prabhakar Balakrishnan
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Mathematical Morphology via Category Theory [PDF]
, 2020 Mathematical morphology contributes many profitable tools to image processing area. Some of these methods considered to be basic but the most important fundamental of data processing in many various applications. In this paper, we modify the fundamental of morphological operations such as dilation and erosion making use of limit and co-limit preserving
Sharifipour, Hossein Memarzadeh +1 more
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MATHEMATICS: FROM SET THEORY TO CATEGORY THEORY
Metaphysics, 2022 The basis of mathematics is set theory, to which almost all mathematical directions go back. However, the importance of category theory for mathematics as a whole is steadily increasing. If in set theory the determining role is played by the internal structure of the object under consideration, then in category theory an object is characterized by its ...
S. Ya. Serovaisky
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Tensor categories and the mathematics of rational and logarithmic conformal field theory [PDF]
Journal of Physics A: Mathematical and Theoretical, 2013 In response to the referees' helpful comments, further discussion of several issues is added, including in particular rigidity. Much of the paper is devoted to explaining what has been mathematically proved and where people can find these proofs. Several references added. 27 pages. Invited review article for publication in a special issue of J. Phys. A
Huang, Yi-Zhi, Lepowsky, James
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Mathematical modelling by help of category theory [PDF]
Die Lösung eines jeden ingenieurtechnischen Problems beginnt mit einem Modellierungsprozess, der ein Modell bereitstellt, das ein zu betrachtendes System darstellt. Die entscheidende Frage für die praktische Verwendung von Modellen besteht darin, zu beurteilen, ob das Modell und die Ergebnisse seiner Verwendung vertrauenswürdig sind.
Dmitrii Legatiuk
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A Mathematical Framework of Semantic Communication based on Category Theory [PDF]
While semantic communication (SemCom) has recently demonstrated great potential to enhance transmission efficiency and reliability by leveraging machine learning (ML) and knowledge base (KB), there is a lack of mathematical modeling to rigorously characterize SemCom system and quantify the performance gain obtained from ML and KB.
Hua, Shuheng +4 more
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Philosophical Sketches on Category Theory Applied to Music-Mathematical Polar Semiotics
MusMat: Brazilian Journal of Music and Mathematics, 2020 This is an attempt to combine Matthai philosophy (of Heraclitan inspiration) and Category Theory using the Yoneda Lemma as a means for harmonizing the traditionally opposite values and conceptions dissociated between the Euclidean tradition and Heraclitus thought.
Gabriel Pareyón
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