Related papers: Multivariate information measures: a unification u…
Due to the invariance properties of cross-ratio, M\"obius transformations are often used to map a set of points or other geometric object into a symmetric position to simplify a problem studied. However, when the points are mapped under a…
Mutual information (MI) is a fundamental measure of statistical dependence, with a myriad of applications to information theory, statistics, and machine learning. While it possesses many desirable structural properties, the estimation of…
In inverse problems, one attempts to infer spatially variable functions from indirect measurements of a system. To practitioners of inverse problems, the concept of "information" is familiar when discussing key questions such as which parts…
Mutual Information (MI) is a powerful statistical measure that quantifies shared information between random variables, particularly valuable in high-dimensional data analysis across fields like genomics, natural language processing, and…
We develop the information-theoretical concepts required to study the statistical dependencies among three variables. Some of such dependencies are pure triple interactions, in the sense that they cannot be explained in terms of a…
We investigate the scrambling of information in a hierarchical star-topology system using out-of-time-ordered correlation (OTOC) functions. The system consists of a central qubit directly interacting with a set of satellite qubits, which in…
This paper generalises inference functions (Godambe, 1960) to distributional statistical models, in which each probability measure is represented by a distribution--kernel pair $(T_\theta, \varphi) \in \mathcal S'(\mathbb R) \times \mathcal…
Three-level data structures arising from repeated measures on individuals clustered within larger units are common in health research studies. Missing data are prominent in such studies and are often handled via multiple imputation (MI).…
Markov processes on the lattices with arbitrary dimension are omnipresent in statistical mechanics; however their algebraic description is complete only in dimension 1, for which linear algebra provides many tools complementary to the…
In this work we study the relation between the set of symmetric operators and the set of mutually unbiased operators from finite plane geometry point of view. Here symmetric operators are generalization of symmetric informationally complete…
As an abstraction and generalization of the integral operator in analysis, integral operators (known as Rota-Baxter operators of weight zero) on associative algebras and Lie algebras have played an important role in mathematics and physics.…
This paper proposes an approach to information-based logics using many-logic modal structures (MLMS). These structures can express accessibility relations between worlds with different underlying logics by anchoring them to a base lattice,…
In distributed-parameter inverse problems in computational mechanics, spatially varying fields are inferred from noisy, indirect, and heterogeneous observations. The relevant identifiability question concerns which spatial perturbation…
We derive new Heisenberg-type uncertainty relations for both joint measurability and the error-disturbance tradeoff for arbitrary observables of finite-dimensional systems. The relations are formulated in terms of a directly operational…
Due to the fact that basic uncertain information provides a simple form for decision information with certainty degree, it has been developed to reflect the quality of observed or subjective assessments. In order to study the algebra…
We introduce three metrics on the set of quantum probability measures over a compact Hausdorff space and characterize them in terms of the completely bounded norm of the corresponding unital completely positive maps. We extend the existing…
Metabonomics time-course experiments provide the opportunity to understand the changes to an organism by observing the evolution of metabolic profiles in response to internal or external stimuli. Along with other omic longitudinal profiling…
Given the increasing popularity of algorithms for overlapping clustering, in particular in social network analysis, quantitative measures are needed to measure the accuracy of a method. Given a set of true clusters, and the set of clusters…
Mutual Information is the metric that is used to perform link adaptation, which allows to achieve rates near capacity. The computation of adaptive transmission modes is achieved by employing the mapping between the Signal to Noise Ratio and…
The maximal information coefficient (MIC), which measures the amount of dependence between two variables, is able to detect both linear and non-linear associations. However, computational cost grows rapidly as a function of the dataset…