Related papers: Descriptive Proximities I: Properties and interpla…
This introductory survey deals with mathematical and physical properties of discrete structures such as point sets and tilings. The emphasis is on proper generalizations of concepts and ideas from classical crystallography. In particular,…
This is a survey article on selected topics in approximation theory. The topics either use techniques from the theory of several complex variables or arise in the study of the subject. The survey is aimed at readers having an acquaintance…
Scene graph is a structured representation of a scene that can clearly express the objects, attributes, and relationships between objects in the scene. As computer vision technology continues to develop, people are no longer satisfied with…
Visual relationships capture a wide variety of interactions between pairs of objects in images (e.g. "man riding bicycle" and "man pushing bicycle"). Consequently, the set of possible relationships is extremely large and it is difficult to…
Can proximity make friendships more diverse? To address this question, we propose a learning-driven friendship formation model to study how proximity and similarity influence the likelihood of forming social connections. The model predicts…
A deep approximation is an approximating function defined by composing more than one layer of simple functions. We study deep approximations of functions of one variable using layers consisting of low-degree polynomials or simple conformal…
Common-sense physical reasoning in the real world requires learning about the interactions of objects and their dynamics. The notion of an abstract object, however, encompasses a wide variety of physical objects that differ greatly in terms…
The process of cognition is analysed to adjust the set theory to physical description. Postulates and basic definitions are revised. The specific sets of predicates, called presets, corresponding to the physical objects identified by an…
Structural approximations to positive, but not completely positive maps are approximate physical realizations of these non-physical maps. They find applications in the design of direct entanglement detection methods. We show that many of…
In this paper, we address the problem of landmark-based visual place recognition. In the state-of-the-art method, accurate object proposal algorithms are first leveraged for generating a set of local regions containing particular landmarks…
Compositionality in language refers to how much the meaning of some phrase can be decomposed into the meaning of its constituents and the way these constituents are combined. Based on the premise that substitution by synonyms is…
Let $\phi(z)$ be a non-isotrivial rational function in one-variable with coefficients in $\overline{\mathbb{F}}_p(t)$ and assume that $\gamma\in\mathbb{P}^1(\overline{\mathbb{F}}_p(t))$ is not a post-critical point for $\phi$. Then we prove…
Distant reading methodologies make use of computational processes to aid in the analysis of large text corpora which might not be pliable to traditional methods of scholarly analysis due to their volume. While these methods have been…
We establish common fixed point theorems for two pairs of weakly compatible self-mappings using an auxiliary function of two variables. Unlike classical results, our theorems do not assume continuity of the mappings and require completeness…
This paper introduces a model that identifies spatial relationships for a structural analysis based on the concept of simplicial complex. The spatial relationships are identified through overlapping two map layers, namely a primary layer…
We study links between first-order formulas and arbitrary properties for families of theories, classes of structures and their isomorphism types. Possibilities for ranks and degrees for formulas and theories with respect to given properties…
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a high-dimensional space and concepts are represented by regions in this space. Our recent…
The mathematical formalisms used to model biological systems induce both latent and ambiguous assumptions that can limit or distort their representational capabilities. Developing formalisms that can represent systems more precisely is…
Recently, a complete characterization of connected Lie groups with the Approximation Property was given. The proof used of the newly introduced property (T*). We present here a short proof of the same result avoiding the use of property…
We provide a mathematically rigorous definition of local approximation and demonstrate its applicability to some interesting classes of structures. In particular, we prove that any compact simple Lie group is locally approximated by finite…