Related papers: Key (critical) relations preserved by a weak near-…
The essential variables in a finite function $f$ are defined as variables which occur in $f$ and weigh with the values of that function. The number of essential variables is an important measure of complexity for discrete functions. When…
We formalize the general principle of significance with respect to binary relations which is a universal tool for description and analysis of various situations in and apart from mathematics. We derive the basic properties and focus on a…
We introduce trace definability, a weak notion of interpretability, and trace equivalence, a weak notion of equivalence for first order structures and theories. In particular we get an interesting weak equivalence notion for $\mathrm{NIP}$…
In this paper we first introduce the unified definition of the sharp constant that includes constants in three major problems of approximation theory, such as, inequalities for approximating elements, approximation of individual elements,…
Binary relations are an important abstraction arising in many data representation problems. The data structures proposed so far to represent them support just a few basic operations required to fit one particular application. We identify…
The problems that scientists face in creating well designed databases intersect with the concerns of data curation. Entity-relationship modeling and its variants have been the basis of most relational data modeling for decades. However,…
Relation extraction is the task of identifying predefined relationship between entities, and plays an essential role in information extraction, knowledge base construction, question answering and so on. Most existing relation extractors…
Uncertainty relation is one of the fundamental building blocks of quantum theory. Nevertheless, the traditional uncertainty relations do not fully capture the concept of incompatible observables. Here we present a stronger…
Uncertainty relations describe the lower bound of product of standard deviations of observables. By revealing a connection between standard deviations of quantum observables and numerical radius of operators, we establish a universal…
We present a relatively simple description of binary, definable subsets of models of weakly quasi-o-minimal theories. In particular, we closely describe definable linear orders and prove a weak version of the monotonicity theorem. We also…
In this paper we introduce a new concept of key polynomials for a given valuation $\nu$ on $K[x]$. We prove that such polynomials have many of the expected properties of key polynomials as those defined by MacLane and Vaqui\'e, for…
The class of threshold functions is known to be characterizable by functional equations or, equivalently, by pairs of relations, which are called relational constraints. It was shown by Hellerstein that this class cannot be characterized by…
We introduce a conceptually simple and effective method to quantify the similarity between relations in knowledge bases. Specifically, our approach is based on the divergence between the conditional probability distributions over entity…
The uncertainty relation, as one of the fundamental principles of quantum physics, captures the incompatibility of noncommuting observables in the preparation of quantum states. In this work, we derive two strong and universal uncertainty…
The rigid relation principle, introduced in this article, asserts that every set admits a rigid binary relation. This follows from the axiom of choice, because well-orders are rigid, but we prove that it is neither equivalent to the axiom…
The main problem of clone theory is to describe the clone lattice for a given basic set. For a two-element basic set this was resolved by E.L. Post, but for at least three-element basic set the full structure of the lattice is still…
Characterizations of "almost associative" binary operations generating a minimal clone are given for two interpretations of the term "almost associative". One of them uses the associative spectrum, the other one uses the index of…
This paper defines a new pseudometric for binary relations between finite sets that measures consensus among subsets. The main results are (1) a concise restatement of this pseudometric with an intuitively appealing interpretation via a…
Universal algebra and clone theory have proven to be a useful tool in the study of constraint satisfaction problems since the complexity, up to logspace reductions, is determined by the set of polymorphisms of the constraint language. For…
There are continuum many clones on a three-element set even if they are considered up to \emph{homomorphic equivalence}. The clones we use to prove this fact are clones consisting of \emph{self-dual operations}, i.e., operations that…