Related papers: On Information Links
We calculate the leading contribution to the weak $\Lambda \Lambda K$ coupling in heavy baryon chiral perturbation theory, including the SU(3) breaking terms arising at one-loop. This coupling gives the leading one-boson exchange amplitude…
This paper is devoted to the mathematical study of some divergences based on the mutual information well-suited to categorical random vectors. These divergences are generalizations of the "entropy distance" and "information distance". Their…
The well-known Heisenberg--Robertson uncertainty relation for a pair of noncommuting observables, is expressed in terms of the product of variances and the commutator among the operators, computed for the quantum state of a system.…
Small-world networks, known for high local clustering and short path lengths, are a fundamental structure in many real-world systems, including social, biological, and technological networks. We apply the theory of (marked) local…
A selection of basic results on Borel reducibility of ideals and equivalence relations, especially those with comparably short proofs. This is an unfinished text as yet. Some proofs have missing parts and loose ends. [email protected] and…
We give a new, elementary proof of what we believe is the simplest known example of a ``natural'' problem in computational 3-dimensional topology that is $\mathsf{NP}$-hard -- namely, the \emph{Trivial Sublink Problem}: given a diagram $L$…
We characterize having Borel isomorphism relation among some weakly minimal trivial theories, namely the examples of families of finite equivalence relations from recent joint work with Laskowski, and tame expansions of…
The study of sums of possibly associated Bernoulli random variables has been hampered by an asymmetry between positive correlation and negative correlation. The Conway-Maxwell Binomial (COMB) distribution and its multivariate extension, the…
In theory, the probabilistic linkage method provides two distinct advantages over non-probabilistic methods, including minimal rates of linkage error and accurate measures of these rates for data users. However, implementations can fall…
There are strong evidences in the literature that quantum non-Markovianity would hinder the presence of Quantum Darwinism. In this Letter, we study the relation between quantum Darwinism and approximate quantum Markovianity for open quantum…
The mutual information between a set of stimuli and the elicited neural responses is compared to the corresponding decoded information. The decoding procedure is presented as an artificial distortion of the joint probabilities between…
Estimating entropy and mutual information consistently is important for many machine learning applications. The Kozachenko-Leonenko (KL) estimator (Kozachenko & Leonenko, 1987) is a widely used nonparametric estimator for the entropy of…
We characterize information as risk reduction between knowledge states represented by partitions of the underlying probability space. Entropy corresponds to risk reduction from no (or partial) knowledge to full knowledge about a random…
A remarkable achievement in algorithmic randomness and algorithmic information theory was the discovery of the notions of K-trivial, K-low and Martin-Lof-random-low sets: three different definitions turns out to be equivalent for very…
If the conditional information of a classical probability distribution of three random variables is zero, then it obeys a Markov chain condition. If the conditional information is close to zero, then it is known that the distance (minimum…
We study Bregman divergences in probability density space embedded with the $L^2$-Wasserstein metric. Several properties and dualities of transport Bregman divergences are provided. In particular, we derive the transport Kullback-Leibler…
A recent article proposed reduced mutual information for evaluation of clustering, classification and community detection. The motivation is that the standard normalized mutual information (NMI) may give counter-intuitive answers under…
We introduce and study strongly invertible Legendrian links in the standard contact three-dimensional space. We establish the equivariant analogs of basic results separately well-known for strongly invertible and Legendrian links, i.e. the…
We propose to use precise estimators of mutual information (MI) to find least dependent components in a linearly mixed signal. On the one hand this seems to lead to better blind source separation than with any other presently available…
While the linear Pearson correlation coefficient represents a well-established normalized measure to quantify the interrelation of two stochastic variables $X$ and $Y$, it fails for multidimensional variables such as Cartesian coordinates.…