Related papers: Compact Binary Relation Representations with Rich …
We present a simple yet general and efficient approach to representation of computational meshes. Meshes are represented as sets of mesh entities of different topological dimensions and their incidence relations. We discuss a…
We relate the notions of spectral gap for unitary representations and subfactors with definability of certain important sets in the corresponding structures. We give several applications of this relationship.
The distance of a binary operation from being associative can be "measured" by its associative spectrum, an appropriate sequence of positive integers. Particular instances and general properties of associative spectra are studied.
Isotopic pairs and their representations are considered in a general framework of the vector superalgebra. Numerous examples of finite-dimensional and infinite-dimensional isotopic pairs are discussed. Several types of their representations…
In the existing evidential networks with belief functions, the relations among the variables are always represented by joint belief functions on the product space of the involved variables. In this paper, we use conditional belief functions…
Knowledge graphs represent real-world entities and their relations in a semantically-rich structure supported by ontologies. Exploring this data with machine learning methods often relies on knowledge graph embeddings, which produce latent…
Logical relations constitute a key method for reasoning about contextual equivalence of programs in higher-order languages. They are usually developed on a per-case basis, with a new theory required for each variation of the language or of…
The multidimensional, heterogeneous, and temporal nature of speech databases raises interesting challenges for representation and query. Recently, annotation graphs have been proposed as a general-purpose representational framework for…
Representation learning of knowledge bases (KBs) aims to embed both entities and relations into a low-dimensional space. Most existing methods only consider direct relations in representation learning. We argue that multiple-step relation…
What is computable with limited resources? How can we verify the correctness of computations? How to measure computational power with precision? Despite the immense scientific and engineering progress in computing, we still have only…
Hypersphere classification is a classical and foundational method that can provide easy-to-process explanations for the classification of real-valued and binary data. However, obtaining an (ideally concise) explanation via hypersphere…
Motivated by the theory of unitary representations of finite dimensional Lie supergroups, we describe those Lie superalgebras which have a faithful finite dimensional unitary representation. We call these Lie superalgebras unitary. This is…
A central challenge for cognitive science is to explain how abstract concepts are acquired from limited experience. This has often been framed in terms of a dichotomy between connectionist and symbolic cognitive models. Here, we highlight a…
Hypergraphs provide a natural way of representing group relations, whose complexity motivates an extensive array of prior work to adopt some form of abstraction and simplification of higher-order interactions. However, the following…
This paper provides a general characterization of preferences that admit a Richter-Peleg representation without imposing completeness or transitivity. We establish that a binary relation on a nonempty set admits a Richter-Peleg…
The clone of term operations of an algebraic structure consists of all operations that can be expressed by a term in the language of the structure. We consider bounds for the length and the height of the terms expressing these functions,…
Visual representations are defined in terms of minimal sufficient statistics of visual data, for a class of tasks, that are also invariant to nuisance variability. Minimal sufficiency guarantees that we can store a representation in lieu of…
Rewriting systems are often defined as binary relations over a given set of objects. This simple definition is used to describe various properties of rewriting such as termination, confluence, normal forms etc. In this paper, we introduce a…
Representations are essential to mathematically model phenomena, but there are many options available. While each of those options provides useful properties with which to solve problems related to the phenomena in study, comparing results…
The use of high-dimensional features has become a normal practice in many computer vision applications. The large dimension of these features is a limiting factor upon the number of data points which may be effectively stored and processed,…