Related papers: Formal Ways for Measuring Relations between Concep…

Computing conceptual structures, like formal concept lattices, is in the age of massive data sets a challenging task. There are various approaches to deal with this, e.g., random sampling, parallelization, or attribute extraction. A so far…

Social polarization is a growing concern worldwide, as it strains social relations, erodes trust in institutions, and thus threatens democratic societies. Academic efforts to understand this phenomenon have traditionally approached it from…

What is a visualization? There is limited utility in trifling with definitions, except insofar as one serves as a tool for communicating and conceptualizing our subject matter; a statement of identity for a community. To establish…

The basic elements of the geometric approach to a consistent quantization formalism are summarized, with reference to the methods of the old quantum mechanics and the induced representations theory of Lie groups. A possible relationship…

The general concept of symmetry is realized in manifold ways in different realms of reality, such as plants, animals, minerals, mathematical objects or human artefacts in literature, fine arts and society. In order to arrive at a common…

The degree to which subjects differ from each other with respect to certain properties measured by a set of variables, plays an important role in many statistical methods. For example, classification, clustering, and data visualization…

There is a contemporary trend toward geometrizing all mathematical theories, as proposed by the Langlands program, and, by extension, physical theories as well. Within this paradigm, it becomes possible to represent physical objects as…

The growing complexity of modern practical problems puts high demands on the mathematical modelling. Given that various models can be used for modelling one physical phenomenon, the role of model comparison and model choice becomes…

Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical…

Relevance is an underlying concept in the field of Information Science and Retrieval. It is a cognitive notion consisting of several different criteria or dimensions. Theoretical models of relevance allude to interdependence between these…

The richness that characterizes relationships is often absent when they are modeled using computational methods in network science. Typically, relationships are represented simply as links, perhaps with weights. The lack of finer…

We propose several hierarchical graphs that represent the semantic relations between physical theories, their fundamental constants and units of measurement. We begin with an alternative representation of Zelmanov's cube of fundamental…

We elaborate on a new interpretation of quantum mechanics which we introduced recently. The main hypothesis of this new interpretation is that quantum particles are entities interacting with matter conceptually, which means that pieces of…

In this article, the author proposes another way to define the completion of a metric space, which is different from the classical one via the dense property, and prove the equivalence between two definitions. This definition is based on…

Finite metric spaces arise in many different contexts. Enormous bodies of data, scientific, commercial and others can often be viewed as large metric spaces. It turns out that the metric of graphs reveals a lot of interesting information.…

Social concepts referring to non-physical objects--such as revolution, violence, or friendship--are powerful tools to describe, index, and query the content of visual data, including ever-growing collections of art images from the Cultural…

One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…

Visualization researchers and visualization professionals seek appropriate abstractions of visualization requirements that permit considering visualization solutions independently from specific problems. Abstractions can help us design,…

The concept of complexity appears in virtually all areas of knowledge. Its intuitive meaning shares similarities across fields, but disagreements between its details hinders a general definition, leading to a plethora of proposed…

Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the…