14 research outputs found
Landauer's principle as a special case of Galois connection
It is demonstrated how to construct a Galois connection between two related
systems with entropy. The construction, called the Landauer's connection,
describes coupling between two systems with entropy. It is straightforward and
transfers changes in one system to the other one preserving ordering structure
induced by entropy. The Landauer's connection simplifies the description of the
classical Landauer's principle for computational systems. Categorification and
generalization of the Landauer's principle opens area of modelling of various
systems in presence of entropy in abstract terms.Comment: 24 pages, 3 figure
Entropy in Thermodynamics: from Foliation to Categorization
summary:We overview the notion of entropy in thermodynamics. We start from the smooth case using differential forms on the manifold, which is the natural language for thermodynamics. Then the axiomatic definition of entropy as ordering on a set that is induced by adiabatic processes will be outlined. Finally, the viewpoint of category theory is provided, which reinterprets the ordering structure as a category of pre-ordered sets
Chemometric approach to characterization of the selected grape seed oils based on their fatty acids composition and FTIR spectroscopy
Addressing the issues arising from the production and trade of low-quality foods necessitates developing new quality control methods. Cooking oils, especially those produced from the grape seeds, are an example of food products that often suffer from questionable quality due to various adulterations and low-quality fruits used for their production. Among many methods allowing for fast and efficient food quality control, the combination of experimental and advanced mathematical approaches seems most reliable. In this work a method for grape seed oils compositional characterization based on the infrared (FTIR) spectroscopy and fatty acids profile is reported. Also, the relevant parameters of oils are characterized using a combination of standard techniques such as the Principal Component Analysis, k-Means, and Gaussian Mixture Model (GMM) fitting parameters. Two different approaches to perform unsupervised clustering using GMM were investigated. The first approach relies on the profile of fatty acids, while the second is FT-IR spectroscopy-based. The GMM fitting parameters in both approaches were compared. The results obtained from both approaches are consistent and complementary and provide the tools to address the characterization and clustering issues in grape seed oils.O
Selected aspects of complex, hypercomplex and fuzzy neural networks
This short report reviews the current state of the research and methodology
on theoretical and practical aspects of Artificial Neural Networks (ANN). It
was prepared to gather state-of-the-art knowledge needed to construct complex,
hypercomplex and fuzzy neural networks.
The report reflects the individual interests of the authors and, by now
means, cannot be treated as a comprehensive review of the ANN discipline.
Considering the fast development of this field, it is currently impossible to
do a detailed review of a considerable number of pages.
The report is an outcome of the Project 'The Strategic Research Partnership
for the mathematical aspects of complex, hypercomplex and fuzzy neural
networks' meeting at the University of Warmia and Mazury in Olsztyn, Poland,
organized in September 2022.Comment: 46 page
An Explanation of the Landauer bound and its ineffectiveness with regard to multivalued logic
We discuss, using recent results on the thermodynamics of multivalued logic, the difficulties and pitfalls of how to apply the Landauer’s principle to thermodynamic computer memory models. The presentation is based on Szilard’s version of Maxwell’s demon experiment and use of equilibrium Thermodynamics. Different versions of thermodynamic/mechanical memory are presented – a one-hot encoding version and an implementation based on a reversed Szilard’s experiment. The relationship of the Landauer’s principle to the Galois connection is explained in detail