Related papers: Theory is Shapes
Probabilistic topic modeling is a popular and powerful family of tools for uncovering thematic structure in large sets of unstructured text documents. While much attention has been directed towards the modeling algorithms and their various…
We study approximations of theories both in general context and with respect to some natural classes of theories. Some kinds of approximations are considered, connections with finitely axiomatizable theories and minimal generating sets of…
Group theory involves the study of symmetry, and its inherent beauty gives it the potential to be one of the most accessible and enjoyable areas of mathematics, for students and non-mathematicians alike. Unfortunately, many students never…
Graph and network visualization supports exploration, analysis and communication of relational data arising in many domains: from biological and social networks, to transportation and powergrid systems. With the arrival of AI-based…
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…
We provide a treatment of isomorphism within a set-theoretic formulation of dependent type theory. Type expressions are assigned their natural set-theoretic compositional meaning. Types are divided into small and large types --- sets and…
Possibility theory offers either a qualitive, or a numerical framework for representing uncertainty, in terms of dual measures of possibility and necessity. This leads to the existence of two kinds of possibilistic causal graphs where the…
Graph theory provides a primary tool for analyzing and designing computer communication networks. In the past few decades, Graph theory has been used to study various types of networks, including the Internet, wide Area Networks, Local Area…
Working with data in table form is usually considered a preparatory and tedious step in the sensemaking pipeline; a way of getting the data ready for more sophisticated visualization and analytical tools. But for many people, spreadsheets…
We present modeling for conceptual combinations which uses the mathematical formalism of quantum theory. Our model faithfully describes a large amount of experimental data collected by different scholars on concept conjunctions and…
Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system…
Type theory plays an important role in foundations of mathematics as a framework for formalizing mathematics and a base for proof assistants providing semi-automatic proof checking and construction. Derivation of each theorem in type theory…
Time series is a collection of data instances that are ordered according to a time stamp. Stock prices, temperature, etc are examples of time series data in real life. Time series data are used for forecasting sales, predicting trends.…
Researchers got success in mining the Web usage data effectively and efficiently. But representation of the mined patterns is often not in a form suitable for direct human consumption. Hence mechanisms and tools that can represent mined…
Designers often create visualizations to achieve specific high-level analytical or communication goals. These goals require people to naturally extract complex, contextualized, and interconnected patterns in data. While limited prior work…
Topos theory has been suggested by D\"oring and Isham as an alternative mathematical structure with which to formulate physical theories. In particular, the topos approach suggests a radical new way of thinking about what a theory of…
At the heart of intuitionistic type theory lies an intuitive semantics called the "meaning explanations"; crucially, when meaning explanations are taken as definitive for type theory, the core notion is no longer "proof" but "verification".…
For real application and theoretical investigation of ordinary hypergraphs and non-ordinary hypergraphs, researchers need to establish standard rules and feasible operating methods. We propose a visualization tool for investigating…
Isomorphisms allow human cognition to transcribe a potentially unsolvable problem from one domain to a different domain where the problem might be more easily addressed. Current approaches only focus on transcribing structural information…
Datasets of visualization play a crucial role in automating data-driven visualization pipelines, serving as the foundation for supervised model training and algorithm benchmarking. In this paper, we survey the literature on visualization…