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Abstract: In this discussion paper, we argue that category theory may play a key role in establishing and demonstrating results in ergodic theory, topogical dynamics, and open systems theory. We show how to identify Kolmogorov–Sinai, Shannon entropy, and topological entropy as the unique functors to the nonnegative reals satisfying some natural conditions.
Source link: https://doi.org/10.3390/e21030302
This paper focuses on the system engineering domain and its models. If we want the results to be useful, we need to have tools to demonstrate and maintain consistency between them as those models are independent of the architecture model. The original models' comparison results are expected to be used to determine consistency between the models' steps of abstraction to a common formalism, analysis, and concreteization of the comparison results. This paper introduces a mathematical framework that allows for the formalization of such a consistency relationship as well as a numerical description of the models. Because this is a mathematical theory that gives great tools for considering various abstraction levels and composition of relationships, we use category theory. We'll continue to explore how this mathematical framework can be used to a specific synchronization scheme with a real study case.
Source link: https://doi.org/10.3390/app12125880
However, the change from a conceptual schema to a logical multi-model representation schema of a specific DBMS is not straightforward. We expand our previous report of multi-model data representation for transformations between models in this paper by using category theory for transformations between models. We introduce a map involving multi-model results and their categorical representation and algorithms for mutual transformations between them.
Source link: https://doi.org/10.1186/s40537-022-00613-3
We propose an algebraic model for analogy that uses the terms of category theory to investigate analogy-related cognitive phenomena. First, we use commutative diagrams to examine the effect of playing particular educational board games on number learning. We finally have a formal learning system that shows that re-representation, language processing, and analogy making could be explained by the acquisition of rational numbers.
Source link: https://doi.org/10.1371/journal.pcbi.1005683
A functor generalizes the concept of a map between representational states and the inclusion of a map showing state shifts. In contrast to the first-order theories derived from Classicism or Connectionism, hierarchy in a formal sense is a necessary result of a higher-order theory of cognitive architecture. A re-conceptualization for cognitive science, akin to Copernicus' description of astronomy, in which representational states are no longer the center of the cognitive universe, but rather the relationships between the maps that transform them.
Source link: https://doi.org/10.1371/journal.pcbi.1000858
The model is built from modifying an existing model in the literature that can also produce dense scale-free networks, but with a different higher-order network layout. A duality structure that was not apparent in the previous model can be identified by category theory. This work is a new extension of category theory for creating a network model focusing on a universal algebraic framework.
Source link: https://doi.org/10.1038/s41598-020-79318-7
Different domain-specific viewpoints are used to describe the system from various domain-specific viewpoints due to the multitude of disciplines involved in mechatronic engineering, heterogeneous languages, and expert models. Detecting these inconsistencies at an early stage drastically reduces the number of engineering jobs re-execution. The mathematical theory, specifically category theory, is considered as a good way to establish a consistent and unifying framework for conflict detection and management. This paper introduces a comprehensive framework that supports conflict detection and resolution in the context of mechatronic collaborative innovation. Our proposed solution is applied to a collaborative scenario involving the electro-mechanical actuator of the aileron.
Source link: https://doi.org/10.3390/app11104486
The installation and expansion of subway systems in a rapidly growing world are both a major step toward improved livability conditions. Underground construction has not profited from well-established ontologies of semantic and geometric representation, including Building Information Modelling and City Geography Markup Language, but underground construction has not profited from well-established ontologies of semantic and geometric representation, such as Building Information Modelling and City Geography Markup Language. A model of knowledge representation based on Category Theory is used in this essay. Dependencies between objects are limited to functional relationships in an olog. The ologu2019s usability is shown by the ontological display of common items in two New York City metro stations' fare control areas.
Solution searching that complements a combinatorial explosion is one of the most significant topics in the age of artificial intelligence. In fact, we have demonstrated that a single-celled organism such as an amoeba can solve constraint satisfaction and related optimization issues, as well as demonstrate experimental methods based on non-organic technologies such as optical energy transfer involving near-field interactions. However, the fundamentals and limitations of solution searching based on natural processes have yet to be understood. paraphrasedoutput:u201d In addition, the octahedral and braid structures identified in triangulated categories provide a concrete indication of the system's time-dependent mechanisms, as well as a quantitative explanation of the difficulties of finding solutions based on homology dimension.
Source link: https://doi.org/10.3390/philosophies2030016
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