Related papers: Generalised 3D Morton and Hilbert Orderings
The earlier approach is used for description of qubits and geometric phase parameters, the things critical in the area of topological quantum computing. The used tool, Geometric (Clifford) Algebra is the most convenient formalism for that…
We describe standard forms for elements of the higher-dimensional Thompson groups $nV$ arising from gridding subdivision processes. These processes lead to standard normal form descriptions for elements in these groups, and sizes of these…
Several convergence results in Hilbert scales under different source conditions are proved and orders of convergence and optimal orders of convergence are derived. Also, relations between those source conditions are proved. The concept of a…
An inventory of all possible homogenous Hilbert curves in two dimensions are reported. Six new Hilbert curves are described by introducing the reversion operation in the construction algorithm. For each curve, the set of affine…
This paper presents preliminary work on using deep neural networks to guide general-purpose heuristic algorithms for performing utilitarian combinatorial assignment. In more detail, we use deep learning in an attempt to produce heuristics…
A generic rectangulation is a partition of a rectangle into finitely many interior-disjoint rectangles, such that no four rectangles meet in a point. In this work we present a versatile algorithmic framework for exhaustively generating a…
In this article we study the possibilities of recovering the structure of port-Hamiltonian systems starting from ``unlabelled'' ordinary differential equations describing mechanical systems. The algorithm we suggest solves the problem in…
A class of high-order numerical algorithms for Riesz derivatives are established through constructing new generating functions. Such new high-order formulas can be regarded as the modification of the classical (or shifted) Lubich's…
As the unification of various models of ordered quantities, generalized order statistics act as a simplistic approach introduced in \cite{kamps1995concept}. In this present study, results pertaining to the expressions of marginal and joint…
We propose an error-disturbance relation for general observables on finite dimensional Hilbert spaces based on operational notions of error and disturbance. For two-dimensional systems we derive tight inequalities expressing the trade-off…
We introduce machine learning methodology to the study of lattice polytopes. With supervised learning techniques, we predict standard properties such as volume, dual volume, reflexivity, etc, with accuracies up to 100%. We focus on 2d…
Recent work has proven that training large language models with self-supervised tasks and fine-tuning these models to complete new tasks in a transfer learning setting is a powerful idea, enabling the creation of models with many…
We identify a new and important global (or non-binary) constraint. This constraint ensures that the values taken by two vectors of variables, when viewed as multisets, are ordered. This constraint is useful for a number of different…
This work shows several direct and recursive constructions of ordered covering arrays using projection, fusion, column augmentation, derivation, concatenation and cartesian product. Upper bounds on covering codes in NRT spaces are also…
The purpose of this article is to bring together the third-order Jacobsthal numbers and 3-parameter generalized quaternions, which are a general form of the quaternion algebra according to 3-parameters. With this purpose, we introduce and…
Based on geometric intuition, in this paper we are trying to give an idea and visualize the meaning of the determinants for the cubic-matrix. In this paper we have analyzed the possibilities of developing the concept of determinant of…
Applications of the three-dimensional transformation for rotating coordinate systems to quantum mechanics, general theory relativity and optics are considered.
This paper presents a general coding method where data in a Hilbert space are represented by finite dimensional coding vectors. The method is based on empirical risk minimization within a certain class of linear operators, which map the set…
This work discusses an approach to solving geometric construction problems in which the given figure is included in a set ordered by construction steps. The flow of information is carried through the chain, allowing the original problem to…
Recently we conjectured that a certain set of universal topological quantities characterize topological order in any dimension. Those quantities can be extracted from the universal overlap of the ground state wave functions. For systems…