Related papers: Quantities, Dimensions and Dimensional Analysis
To a finite group $G$, one can associate several notions of dimensions (or degrees). In this survey, we attempt to bring together some of the notions of dimensions or degrees defined using representations of the group in General Linear…
Summarization is one of the key features of human intelligence. It plays an important role in understanding and representation. With rapid and continual expansion of texts, pictures and videos in cyberspace, automatic summarization becomes…
This paper presents a geometric approach to the problem of modelling the relationship between words and concepts, focusing in particular on analogical phenomena in language and cognition. Grounded in recent theories regarding geometric…
A hierarchical scheme for clustering data is presented which applies to spaces with a high number of dimension ($N_{_{D}}>3$). The data set is first reduced to a smaller set of partitions (multi-dimensional bins). Multiple clustering…
We argue that dimensionality is not absolute, but that it depends on the scale of resolution, from the Planck to the macro scale.
This chapter provides an overview of the different techniques and methods that exist for the analysis and visualization of dynamic networks. Basic definitions and formal notations are discussed and important references are cited. A major…
Although the notion of a concept as a collection of objects sharing certain properties, and the notion of a conceptual hierarchy are fundamental to both Formal Concept Analysis and Description Logics, the ways concepts are described and…
We consider the dimensions of finite type of representations of a partially ordered set, i.e. such that there is only finitely many isomorphism classes of representations of this dimension. We give a criterion for a dimension to be of…
Data visualization is the process by which data of any size or dimensionality is processed to produce an understandable set of data in a lower dimensionality, allowing it to be manipulated and understood more easily by people. The goal of…
For more than half a century, moments have attracted lot ot interest in the pattern recognition community.The moments of a distribution (an object) provide several of its characteristics as center of gravity, orientation, disparity, volume.…
We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable, making the effective dimension state-dependent. Interestingly, systems of this form can exhibit enhanced symmetries…
Dimension reduction of data sets is a standard problem in the realm of machine learning and knowledge reasoning. They affect patterns in and dependencies on data dimensions and ultimately influence any decision-making processes. Therefore,…
In this article, we introduce the concept of lexicographic metric space and, after discussing some basic properties of these metric spaces, such as completeness, boundedness, compactness and separability, we obtain a formula for the metric…
The quantities of dimension one - known as the dimensionless quantities - are widely used in physics. However, the debate about some dimensionless units is still open. The paper brings new interrelated arguments that lead to the conclusion…
We introduce the notion of scale to generalize and compare different invariants of metric spaces and their measures. Several versions of scales are introduced such as Hausdorff, packing, box, local and quantization. They moreover are…
Measurement is an integral part of modern science, providing the fundamental means for evaluation, comparison, and prediction. In the context of visualization, several different types of measures have been proposed, ranging from approaches…
This article presents a general description of dynamical systems using the language of enriched functors and enriched natural transformations. This framework is essential to establish the equivalence of three descriptions of dynamics -- a…
We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.
Quantum software plays a critical role in exploiting the full potential of quantum computing systems. As a result, it is drawing increasing attention recently. As research in quantum programming reaches maturity with a number of active…
Quantiles are very important statistics information used to describe the distribution of datasets. Given the quantiles of a dataset, we can easily know the distribution of the dataset, which is a fundamental problem in data analysis.…