Mathematical Models of Discrete Optimization

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: 30 September 2024 | Viewed by 251

Special Issue Editor

1. Department of Information Technology, Uppsala University, 75236 Uppsala, Sweden
2. Department of Mathematics, Uppsala University, 75236 Uppsala, Sweden
Interests: digital geometry; mathematical morphology; discrete optimization; complex geometry; complex analys

Special Issue Information

Dear Colleagues,

Discretization is an important procedure in contemporary mathematics. This is true in the building of theories as well as in its many applications, which are of interest both in and of themselves as well as for the technology employed.

Discrete objects, such as carpets and mosaics, have been around for thousands of years, but the advent of computers and digital cameras has made them ubiquitous. 

Carpets, embroidery work, and mosaics are examples of artifacts that are discrete. All three can nevertheless represent pictures quite well—the human eye and the human brain work together to create images. As Eric Kandel writes:

   [...] we have learned that the brain is not a camera but a Homeric story teller [...]     (Kandel 2012:351)

Thus, this has transformed digital geometry into a type of geometry of growing interest. Discretization of sets and functions is studied from many perspectives: a discrete structure can appear as the result of the discretization of an object described by real or complex variables, but it can also be there from the beginning.

Mathematical morphology can be described as the study of shapes, carried out in a systematic way and using the theory of lattices and complete lattices pioneered by Garrett Birkhoff.

In today's rich world of discrete structures, discrete optimization is a natural counterpart to optimization using real variables.

To this, we can add the existence of many conferences of great importance, both socially and scientifically: the Discrete Geometry for Computer Imagery (DGCI), and the International Workshop for Computerized Image Analysis (IWCIA), as well as the International Symposium for Mathematical Morphology (ISMM), the two latter now joined into the Discrete Geometry and Mathematical Morphology (DGMM).

Reference

Kandel, Eric R. 2012. \textit{The Age of Insight: The Quest for Understanding the Unconscious in Art, Mind, and Brain, from Vienna 1900  to the Present}. New York, NY: Random House, Inc. 

Prof. Dr. Christer Oscar Kiselman
Guest Editor

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