Related papers: Analysis of shape grammars: continuity of rules
While the strength of Topological Data Analysis has been explored in many studies on high dimensional numeric data, it is still a challenging task to apply it to text. As the primary goal in topological data analysis is to define and…
Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information,…
Shape analysis methods have in the past few years become very popular, both for theoretical exploration as well as from an application point of view. Originally developed for planar curves, these methods have been expanded to higher…
Stable fold maps are fundamental tools in a generalization of the theory of Morse functions on smooth manifolds and its application to studies of geometric properties of smooth manifolds. Round fold maps were introduced as stable fold maps…
We study the topology associated with physical vector and scalar fields. A mathematical object, e.g., a ball, can be continuously deformed, without tearing or gluing, to make other topologically equivalent objects, e.g., a cube or a solid…
Biabduction-based shape analysis is a compositional verification and analysis technique that can prove memory safety in the presence of complex, linked data structures. Despite its usefulness, several open problems persist for this kind of…
State-of-the-art results in typical classification tasks are mostly achieved by unexplainable machine learning methods, like deep neural networks, for instance. Contrarily, in this paper, we investigate the application of rule learning…
Discovering business rules from business process models are of advantage to ensure the compliance of business processes with business rules. Furthermore it provides the agility of business processes in case of business rules evolution.…
Due to its high spatial and spectral information content, hyperspectral imaging opens up new possibilities for a better understanding of data and scenes in a wide variety of applications. An essential part of this process of understanding…
A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…
An unsupervised shape analysis is proposed to learn concepts reflecting shape commonalities. Our approach is two-fold: i) a spatial topology analysis of point cloud segment constellations within objects is used in which constellations are…
Finite elements of higher continuity, say conforming in $H^2$ instead of $H^1$, require a mapping from reference cells to mesh cells which is continuously differentiable across cell interfaces. In this article, we propose an algorithm to…
Topological data analysis is an approach to study shape of a data set by means of topology. Its main object of study is the persistence diagram, which represents the topological features of the data set at different spatial resolutions.…
Words can be represented by composing the representations of subword units such as word segments, characters, and/or character n-grams. While such representations are effective and may capture the morphological regularities of words, they…
The verification community has studied dynamic data structures primarily in a bottom-up way by analyzing pointers and the shapes induced by them. Recent work in fields such as separation logic has made significant progress in extracting…
Networks are important representations in computer science to communicate structural aspects of a given system of interacting components. The evolution of a network has several topological properties that can provide us information on the…
Knowledge is a network of interconnected concepts. Yet, precisely how the topological structure of knowledge constrains its acquisition remains unknown, hampering the development of learning enhancement strategies. Here we study the…
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…
We investigate straight-line drawings of topological graphs that consist of a planar graph plus one edge, also called almost-planar graphs. We present a characterization of such graphs that admit a straight-line drawing. The…
Learning curves provide insight into the dependence of a learner's generalization performance on the training set size. This important tool can be used for model selection, to predict the effect of more training data, and to reduce the…