Related papers: Freezing Sets for Arbitrary Digital Dimension
We continue the study of freezing sets for digital images introduced in [4, 2, 3]. We prove methods for obtaining freezing sets for digital images (X, c_i) for X \subset Z^2 and i \in {1, 2}. We give examples to show how these methods can…
Cold sets and freezing sets belong to the theory of (approximate) fixed points for continuous self-maps on digital images. We study some properties of cold sets for digital images in the digital plane, and we examine some relationships…
We continue the study of freezing sets in digital topology, introduced in [2]. We show how to find a minimal freezing set for a "thick" convex disk X in the digital plane Z^2. We give examples showing the significance of the assumption that…
Cone and suspension constructions have been introduced in digital topology, modeled on those of classical topology. For digital cones and suspensions, and for some related digital images, we find (m, n)-limiting sets; especially (0,…
We study how the properties of irreducibility and rigidity in digital images interact with Cartesian products, wedges, and cold and freezing sets.
We continue the work of [10], studying properties of digital images determined by fixed point invariants. We introduce pointed versions of invariants that were introduced in [10]. We introduce freezing sets and cold sets to show how the…
We develop new tools for the construction of fixed point sets in digital topology. We define excludable points and show that these may be excluded from all freezing sets. We show that articulation points are excludable. We also present…
We use results of [6] to enlarge our knowledge of the approximate fixed point property (AFPP) for digital images in $\mathbb{Z}^2$. In particular, we study conditions under which the union of two convex digital disks has the AFPP.
We study properties of Cartesian products of digital images for which adjacencies based on the normal product adjacency are used. We show that the use of such adjacencies lets us obtain many "product properties" for which the analogous…
Quantum correlations in a composite system can be measured by resorting to a geometric approach, according to which the distance from the state of the system to a suitable set of classically correlated states is considered. Here we show…
Constructing a discretization of a given set is a major problem in various theoretical and applied disciplines. An offset discretization of a set $X$ is obtained by taking the integer points inside a closed neighborhood of $X$ of a certain…
A CNN-based interactive contrast enhancement algorithm, called IceNet, is proposed in this work, which enables a user to adjust image contrast easily according to his or her preference. Specifically, a user provides a parameter for…
We show the equivalence of several constructions of the category of condensed sets by using free resolutions of compact Hausdorff spaces. We also give an elementary construction of the condensed set associated to any presheaf on compact…
Many image segmentation techniques have been developed over the past two decades for segmenting the images, which help for object recognition, occlusion boundary estimation within motion or stereo systems, image compression, image editing.…
The realization of large-scale fully controllable quantum systems is an exciting frontier in modern physical science. We use atom-by-atom assembly to implement a novel platform for the deterministic preparation of regular arrays of…
In this article, we prove some subsets of the set of natural numbers $\mathbb{N}$ and any non-zero ideals of an order of imaginary quadratic fields are fractionally dense in $\mathbb{R}_{>0}$ and $\mathbb{C}$ respectively.
We apply freezing operators to relate different (quantum) upper cluster algebras. We prove that these operators send localized (quantum) cluster monomials to localized (quantum) cluster monomials. They also send bases to bases in many…
The measure of distance between two fuzzy sets is a fundamental tool within fuzzy set theory. However, current distance measures within the literature do not account for the direction of change between fuzzy sets; a useful concept in a…
In this report I attempt to outline the process of developing and building an absorption imaging system capable of imaging ultracold atoms. In the theory section I will discuss the elements required to estimate the atom number and derive…
We consider the problem of digitalizing Euclidean line segments from $\mathbb{R}^d$ to $\mathbb{Z}^d$. Christ {\em et al.} (DCG, 2012) showed how to construct a set of {\em consistent digital segment} (CDS) for $d=2$: a collection of…