Related papers: A concept for resemblance in large scale geometry
Biomolecular structure comparison not only reveals evolutionary relationships, but also sheds light on biological functional properties. However, traditional definitions of structure or sequence similarity always involve superposition or…
The notions of distance and similarity play a key role in many machine learning approaches, and artificial intelligence (AI) in general, since they can serve as an organizing principle by which individuals classify objects, form concepts…
We propose a general framework for converting global and local similarities between biological sequences to quasi-metrics. In contrast to previous works, our formulation allows asymmetric distances, originating from uneven weighting of…
The goal of this paper is to retrieve an image based on instance, attribute and category similarity notions. Different from existing works, which usually address only one of these entities in isolation, we introduce a cooperative embedding…
Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical spaces, which can be constrained by boundaries and…
Learning from unordered sets is a fundamental learning setup, recently attracting increasing attention. Research in this area has focused on the case where elements of the set are represented by feature vectors, and far less emphasis has…
This paper aims to examine the version of the topological group structure in proximity and especially descriptive proximity spaces, that is, the concepts of proximal group and descriptive proximal group are introduced. In addition, the…
We develop a unified framework for the study of properties involving diagonalizations of dense families in topological spaces. We provide complete classification of these properties. Our classification draws upon a large number of methods…
We propose a general deep architecture for learning functions on multiple permutation-invariant sets. We also show how to generalize this architecture to sets of elements of any dimension by dimension equivariance. We demonstrate that our…
We analyze the statistical properties of bubble models for the large-scale distribution of galaxies. To this aim, we realize static simulations, in which galaxies are mostly randomly arranged in the regions surrounding bubbles. As a first…
Survey talk on certain aspects of the subject, stressing the neighbor relation as a basic notion in differential geometry.
In [1] we introduced the concept of structured space, which is a topological space that locally resembles some algebraic structures. In [2] we proceeded the study of these spaces, developing two cohomology theories. The aim of this paper is…
In the paper the main attention is paid to conditions on algebras from a given variety which provide coincidence of their algebraic geometries. The main part here play the notions mentioned in the title of the paper.
Multidimensional scaling (MDS) is the act of embedding proximity information about a set of $n$ objects in $d$-dimensional Euclidean space. As originally conceived by the psychometric community, MDS was concerned with embedding a fixed set…
We introduce several highness notions on degrees related to the problem of computing isomorphisms between structures, provided that isomorphisms exist. We consider variants along axes of uniformity, inclusion of negative information, and…
The thesis presents the subject of synthetic topology, especially with relation to metric spaces. A model of synthetic topology is a categorical model in which objects possess an intrinsic topology in a suitable sense, and all morphisms are…
In this paper, we present a new metric distance for comparing two large graphs to find similarities and differences between them based on one of the most important graph structural properties, which is Node Adjacency Information, for all…
In this work we present a principle which says that quasimorphisms can be obtained via "local data" of the group action on certain appropriate spaces. In a rough manner the principle says that instead of starting with a given group and try…
John Roe \cite{Roe lectures} introduced coarse structures for arbitrary sets $X$ by considering subsets of $X\times X$. That definition, while natural for analysts, is a bit more difficult to digest for topologists and geometers. In this…
These Lecture Notes are devoted to an introductory description of some of the most widely applied statistical methods for the analysis of the Large-Scale Structure (LSS) of the Universe. Rather than providing technical details about the…