Related papers: A Thorough Formalization of Conceptual Spaces
Computer vision applications are omnipresent nowadays. The current paper explores the use of fuzzy logic in computer vision, stressing its role in handling uncertainty, noise, and imprecision in image data. Fuzzy logic is able to model…
Convex geometry has recently attracted great attention as a framework to formulate general probabilistic theories. In this framework, convex sets and affine maps represent the state spaces of physical systems and the possible dynamics,…
Various topological concepts are often involved in the research of mathematical logic, and almost all of these concepts can be regarded as developing from the Stone representation theorem. In the Stone representation theorem, a Boolean…
We treat the classical notion of convexity in the context of hard real analysis. Definitions of the concept are given in terms of defining functions and quadratic forms, and characterizations are provided of different concrete notions of…
In this paper we analyze the notion of morphisms of rings of superfunctions which is the basic concept underlying the definition of supermanifolds as ringed spaces (i.e. following Berezin, Leites, Manin, etc.). We establish a representation…
Geometric algebra is an optimal frame work for calculating with vectors. The geometric algebra of a space includes elements that represent all the its subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands this…
Two-dimensional patterns are used in many research areas in computer science, ranging from image processing to specification and verification of complex software systems (via scenarios). The contribution of this paper is twofold. First, we…
In this study, after given the definition of soft sets and their basic operations we define convex soft sets which is an important concept for operation research, optimization and related problems. Then, we define concave soft sets and give…
The paper provides a survey of semantic methods for solution of fundamental tasks in mathematical knowledge management. Ontological models and formalisms are discussed. We propose an ontology of mathematical knowledge, covering a wide range…
As the intermediate-level representations bridging the two levels, structured representations of visual scenes, such as visual relationships between pairwise objects, have been shown to not only benefit compositional models in learning to…
Establishing semantic correspondence across images when the objects in the images have undergone complex deformations remains a challenging task in the field of computer vision. In this paper, we propose a hierarchical method to tackle this…
Mathematical notation makes up a large portion of STEM literature, yet finding semantic representations for formulae remains a challenging problem. Because mathematical notation is precise, and its meaning changes significantly with small…
Perceptual geometry refers to the interdisciplinary research whose objectives focuses on study of geometry from the perspective of visual perception, and in turn, applies such geometric findings to the ecological study of vision. Perceptual…
Cognition is a core part of and a common topic among philosophy of mind, psychology, neuroscience, AI, and cognitive science. Through a mechanistic lens, I propose a framework of defining, modeling, and analyzing cognition mechanisms.…
Mathematical software systems are becoming more and more important in pure and applied mathematics in order to deal with the complexity and scalability issues inherent in mathematics. In the last decades we have seen a cambric explosion of…
Understanding 3D object shapes necessitates shape representation by object parts abstracted from results of instance and semantic segmentation. Promising shape representations enable computers to interpret a shape with meaningful parts and…
Point clouds have become increasingly vital across various applications thanks to their ability to realistically depict 3D objects and scenes. Nevertheless, effectively compressing unstructured, high-precision point cloud data remains a…
While many methods for learning vector space embeddings have been proposed in the field of Natural Language Processing, these methods typically do not distinguish between categories and individuals. Intuitively, if individuals are…
A general framework is described which associates geometrical structures to any set of $D$ finite-dimensional hermitian matrices $X^a, \ a=1,...,D$. This framework generalizes and systematizes the well-known examples of fuzzy spaces, and…
The definition of symbolic descriptions that consistently represent relevant geometrical aspects in manipulation tasks is a challenging problem that has received little attention in the robotic community. This definition is usually done…