Related papers: Tensor Entropy for Uniform Hypergraphs
We show that the (normalized) symmetric Laplacian of a simple graph can be obtained from the partial trace over a pure bipartite quantum state that resides in a bipartite Hilbert space (one part corresponding to the vertices, the other…
Shearer's inequality bounds the sum of joint entropies of random variables in terms of the total joint entropy. We give another lower bound for the same sum in terms of the individual entropies when the variables are functions of…
In this manuscript a unified framework for conducting inference on complex aggregated data in high dimensional settings is proposed. The data are assumed to be a collection of multiple non-Gaussian realizations with underlying undirected…
Since its origin in the thermodynamics of the 19th century, the concept of entropy has also permeated other fields of physics and mathematics, such as Classical and Quantum Statistical Mechanics, Information Theory, Probability Theory,…
Convolutional layers within graph neural networks operate by aggregating information about local neighbourhood structures; one common way to encode such substructures is through random walks. The distribution of these random walks evolves…
Shannon Entropy is the preeminent tool for measuring the level of uncertainty (and conversely, information content) in a random variable. In the field of communications, entropy can be used to express the information content of given…
The quality of image encryption is commonly measured by the Shannon entropy over the ciphertext image. However, this measurement does not consider to the randomness of local image blocks and is inappropriate for scrambling based image…
The ultimate purpose of the statistical analysis of ordinal patterns is to characterize the distribution of the features they induce. In particular, knowing the joint distribution of the pair Entropy-Statistical Complexity for a large class…
We prove a generalization of the strong subadditivity of the von Neumann entropy for bosonic quantum Gaussian systems. Such generalization determines the minimum values of linear combinations of the entropies of subsystems associated to…
Estimating the entropy of a discrete random variable is a fundamental problem in information theory and related fields. This problem has many applications in various domains, including machine learning, statistics and data compression. Over…
We present a problem relating measurements and information theory in spin foam models. In the three dimensional case of quantum gravity we can compute probabilities of spin network graphs and study the behaviour of the Shannon entropy…
The notion of entropy appears in many fields and this paper is a survey about entropies in several branches of Mathematics. We are mainly concerned with the topological and the algebraic entropy in the context of continuous endomorphisms of…
The concept of Entropy plays a key role in Information Theory, Statistics, and Machine Learning.This paper introduces a new entropy measure, called the t-entropy, which exploits the concavity of the inverse-tan function. We analytically…
In this paper we solve the problem of finding in a given weighted hypergraph a subhypergraph with a maximum possible density. We introduce the notion of a support matrix and prove that the density of an optimal subhypergraph is equal to…
We present a near-optimal quantum algorithm, up to logarithmic factors, for estimating the Shannon entropy in the quantum probability oracle model. Our approach combines the singular value separation algorithm with quantum amplitude…
The spectral density of random graphs with topological constraints is analysed using the replica method. We consider graph ensembles featuring generalised degree-degree correlations, as well as those with a community structure. In each case…
Information theory on a time-discrete setting in the framework of time series analysis is generalized to the time-continuous case. Considerations of the Roessler and Lorenz dynamics as well as the Ornstein-Uhlenbeck process yield for…
The logarithm of the number of Eulerian orientations, normalised by the number of vertices, is known as the residual entropy in studies of ice-type models on graphs. The spanning tree entropy depends similarly on the number of spanning…
Hypergraphs allow one to encode higher-order relationships in data and are thus a very flexible modeling tool. Current learning methods are either based on approximations of the hypergraphs via graphs or on tensor methods which are only…
Probability theory is fundamental for modeling uncertainty, with traditional probabilities being real and non-negative. Complex probability extends this concept by allowing complex-valued probabilities, opening new avenues for analysis in…