Related papers: Key (critical) relations preserved by a weak near-…
We prove a version of symmetric criticality for ropelength-critical knots. Our theorem implies that a knot or link with a symmetric representative has a ropelength-critical configuration with the same symmetry. We use this to construct new…
Quantum uncertainty relations are formulated in terms of relative entropy between distributions of measurement outcomes and suitable reference distributions with maximum entropy. This type of entropic uncertainty relation can be applied…
We analyze uncertainty relations on finite dimensional Hilbert spaces expressed in terms of classical fidelity, which are stronger then metric uncertainty relations introduced by Fawzi, Hayden and Sen. We establish validity of fidelity…
The theory of two binary relations has the strong amalgamation property when the first relation is assumed to be coarser than the second relation, and each relation satisfies a chosen set of properties from the following list: transitivity,…
We introduce the notions of triviality and order-triviality for global invariant types in an arbitrary first-order theory and show that they are well behaved in the NIP context. We show that these two notions agree for invariant global…
Relation extraction aims to identify the target relations of entities in texts. Relation extraction is very important for knowledge base construction and text understanding. Traditional binary relation extraction, including supervised,…
This paper argues that an interlingual representation must explicitly represent some parts of the meaning of a situation as possibilities (or preferences), not as necessary or definite components of meaning (or constraints). Possibilities…
The arrow relation, a central concept in extremal set theory, captures quantitative relationships between families of sets and their traces. Formally, the arrow relation $(n, m) \rightarrow (a, b)$ signifies that for any family $\mathcal{F}…
Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas iff a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may…
Rough set theory is a new mathematical approach to imperfect knowledge. The notion of rough sets is generalized by using an arbitrary binary relation on attribute values in information systems, instead of the trivial equality relation. The…
We give a first-order definition of key polynomials, we show the links with previous definitions, that it is relevant to study key degrees, and to use a kind of valuations that we call partially multiplicative. We also prove or reprove…
In this paper we introduce a notion of tightness for a family of nonlinear expectations and show that the tightness can be applied to obtain weak compactness in a framework of nonlinear expectation space. This criterion is very useful for…
We establish a set of relations between several quite diverse types of weighted inequalities involving various integral operators and fairly general quasinorm-like functionals which we call sub-monotone. The main result enables one to solve…
We study a positive-definite function associated to a measure-preserving equivalence relation on a standard probability space and use it to measure quantitatively the proximity of subequivalence relations. This is combined with a recent…
The decoupling of zero-norm states leads to linear relations among 4-point functions in the high energy limit of string theory. Recently it was shown that the linear relations uniquely determine ratios among 4-point functions at the leading…
Uniqueness and independence are two fundamental properties of data. Their enforcement in database systems can lead to higher quality data, faster data service response time, better data-driven decision making and knowledge discovery from…
Cumulative logics are studied in an abstract setting, i.e., without connectives, very much in the spirit of Makinson's early work. A powerful representation theorem characterizes those logics by choice functions that satisfy a weakening of…
We investigate the problem whether a function of several arguments can be reconstructed from its identification minors. We focus on functions with a unique identification minor, and we establish some positive and negative results on the…
In this paper we establish the relation between key polynomials (as defined in \cite{SopivNova}) and minimal pairs of definition of a valuation. We also discuss truncations of valuations on a polynomial ring $K[x]$. We prove that a…
We introduce and study two new relations between function spaces over measure spaces of infinite measure, motivated by the question of establishing compactness. The first relation captures the uniform decay of function (quasi-)norms ``at…