Related papers: Conditional and unconditional information inequali…
In this short note we provide an analytical formula for the conditional covariance matrices of the elliptically distributed random vectors, when the conditioning is based on the values of any linear combination of the marginal random…
Symmetry properties of PDE's are considered within a systematic and unifying scheme: particular attention is devoted to the notion of conditional symmetry, leading to the distinction and a precise characterization of the notions of ``true''…
In this work we generalize standard Decision Theory by assuming that two outcomes can also be incomparable. Two motivating scenarios show how incomparability may be helpful to represent those situations where, due to lack of information,…
We prove some extensions of Andrews inequality.
We initiate an investigation how the fundamental concept of independence can be represented effectively in the presence of incomplete information in relational databases. The concepts of possible and certain independence are proposed, and…
In this paper, we point out that the definition of weak tracial approximation can be improved and strengthened. An example of weak tracial approximation is also provided.
In this paper, a lower bound of quantum conditional mutual information is obtained by employing the Peierls-Bogoliubov inequality and Golden Thompson inequality. Comparison with the bounds obtained by other researchers indicates that our…
Given a pair of predictor variables and a response variable, how much information do the predictors have about the response, and how is this information distributed between unique, redundant, and synergistic components? Recent work has…
Many numerical problems with input $x$ and output $y$ can be formulated as a system of equations $F(x, y) = 0$ where the goal is to solve for $y$. The condition number measures the change of $y$ for small perturbations to $x$. From this…
The information causality principle is a generalisation of the no-signalling principle which implies some of the known restrictions on quantum correlations. But despite its clear physical motivation, information causality is formulated in…
In this paper we provide a theoretical analysis of counterfactual invariance. We present a variety of existing definitions, study how they relate to each other and what their graphical implications are. We then turn to the current major…
This paper presents and discusses several methods for reasoning from inconsistent knowledge bases. A so-called argumentative-consequence relation taking into account the existence of consistent arguments in favor of a conclusion and the…
A `quantum inequality' (a conjectured relation between the energy density of a free quantum field and the time during which this density is observed) has recently been used to rule out some of the macroscopic wormholes and warp drives. I…
The paper describes several applications of information inequalities to problems in database theory. The problems discussed include: upper bounds of a query's output, worst-case optimal join algorithms, the query domination problem, and the…
The outcome of a weak quantum measurement conditioned to a subsequent postselection (a weak value protocol) can assume peculiar values. These results cannot be explained in terms of conditional probabilistic outcomes of projective…
We consider a hypothesis testing problem where a part of data cannot be observed. Our helper observes the missed data and can send us a limited amount of information about them. What kind of this limited information will allow us to make…
Hidden variable graphical models can sometimes imply constraints on the observable distribution that are more complex than simple conditional independence relations. These observable constraints can falsify assumptions of the model that…
We present a sufficient condition that a pseudointegrable system has weak mixing property. The result is derived from Veech's weak mixing theorem for interval exhange [Veech, W.A. Amer.J.Math. {\bf 106}, 1331 (1984)]. We also present an…
In this paper, we highlight a profound difference between conditional statements in mathematical logic and natural languages. This difference exists even when the conditional statements are used in mathematical theorems.
In this note, we find a new inequality involving primes and deduce several Bonse-type inequalities.