Lattice Path in Discrete Mathematics - Explore the concept of lattice paths in discrete mathematics, including definitions, examples, and formulas to calculate the number of paths.
We study the computational complexity of various inverse problems in discrete tomography. These questions are motivated by demands from the material sciences for the reconstruction of crystalline structure from images produced by quantitative high resolution transmission electron microscopy.We completely settle...
Analogously, counting the number of lattice points contained in such a polytope is 4~P-complete, but polynomial-time solvable when the dimen- sion is fixed, an algorithm having been found only very recently [3]. In fact, the decision and counting questions are hard even for simplices, and...
One of the oldest and most extensively studied geometric questions concerning lattice points is the “no-three-in-line” problem raised by Dudeney [Du17] (pages 94 and 222) in the special casen= 8. What is the maximum number of points that can be selected from ann×nlattice square {1, ...
Despite its promise, lattice-based cryptography faces several challenges and open questions that must be addressed for widespread adoption. 6.1 Implementation Challenges Implementing lattice-based schemes securely and efficiently is non-trivial. Challenges include: ...
The objective of the experimental evaluation was to explore the following key questions: Discussion Taking the identification of accurate interesting labels for unobserved concepts into account, the results of Experiment I in Section 4 clearly show that IP converges to accurate labels that are very com...
We end with some open questions in Section 6. 2 Lattice Problems The main computational problem associated with lattices is the shortest vector problem (SVP). In SVP, given a lattice basis, we are supposed to output a shortest nonzero vector in the lattice. In fact, we will be mostly ...
One of the central questions in Geometric Tomography is to determine or to reconstruct a set K in the n-dimensional Euclidean space Rn by some of its lower dimensional “structures” (see [13]). Usually, these are projections on and sections with lower dimensional subspaces of Rn. A classica...
Retracts of monounary algebras were first studied in [4]; this paper was inspired by the investigation of retracts of posets ([2]). The investigation of monounary algebras has been shown to be useful tool for studying some questions concerning algebras of arbitrary type ([9]). Novotny´ ...
We investigate lattices of retracts of monounary algebras. Semimodularity and concepts related to semimodularity (M-symmetry and Mac Lane’s condition) are dealt with. Further, we give a description of all connected monounary algebras with modular retrac