Search results for "mutual information"
showing 10 items of 66 documents
Mutual information and spontaneous symmetry breaking
2015
We show that the metastable, symmetry-breaking ground states of quantum many-body Hamiltonians have vanishing quantum mutual information between macroscopically separated regions, and are thus the most classical ones among all possible quantum ground states. This statement is obvious only when the symmetry-breaking ground states are simple product states, e.g. at the factorization point. On the other hand, symmetry-breaking states are in general entangled along the entire ordered phase, and to show that they actually feature the least macroscopic correlations compared to their symmetric superpositions is highly non trivial. We prove this result in general, by considering the quantum mutual …
Genuine quantum and classical correlations in multipartite systems
2011
PACS numbers: 03.67.Mn, 03.65.Ud
Inferring networks from high-dimensional data with mixed variables
2014
We present two methodologies to deal with high-dimensional data with mixed variables, the strongly decomposable graphical model and the regression-type graphical model. The first model is used to infer conditional independence graphs. The latter model is applied to compute the relative importance or contribution of each predictor to the response variables. Recently, penalized likelihood approaches have also been proposed to estimate graph structures. In a simulation study, we compare the performance of the strongly decomposable graphical model and the graphical lasso in terms of graph recovering. Five different graph structures are used to simulate the data: the banded graph, the cluster gr…
Information Functionals and the Notion of (Un)Certainty: Random Matrix Theory - Inspired Case
2007
Information functionals allow one to quantify the degree of randomness of a given probability distribution, either absolutely (through min/max entropy principles) or relative to a prescribed reference one. Our primary aim is to analyze the “minimum information” assumption, which is a classic concept (R. Balian, 1968) in the random matrix theory. We put special emphasis on generic level (eigenvalue) spacing distributions and the degree of their randomness, or alternatively — information/organization deficit.
Snowball ICA: A Model Order Free Independent Component Analysis Strategy for Functional Magnetic Resonance Imaging Data
2020
In independent component analysis (ICA), the selection of model order (i.e., number of components to be extracted) has crucial effects on functional magnetic resonance imaging (fMRI) brain network analysis. Model order selection (MOS) algorithms have been used to determine the number of estimated components. However, simulations show that even when the model order equals the number of simulated signal sources, traditional ICA algorithms may misestimate the spatial maps of the signal sources. In principle, increasing model order will consider more potential information in the estimation, and should therefore produce more accurate results. However, this strategy may not work for fMRI because …
Multi-modal Medical Image Registration by Local Affine Transformations
2018
Image registration is the process of finding the geometric transformation that, applied to the floating image, gives the registered image with the highest similarity to the reference image. Registering a pair of images involves the definition of a similarity function in terms of the parameters of the geometric transformation that allows the registration. This paper proposes to register a pair of images by iteratively maximizing the empirical mutual information through coordinate gradient descent. Hence, the registered image is obtained by applying a sequence of local affine transformations. Rather than adopting a uniformly spaced grid to select image blocks to locally register, as done by s…
Effective and Efficient Interpolation for Mutual Information based Multimodality Elastic Image Registration
2009
Mutual information (MI) is a popular similarity metric for multimodality image registration purpose. However, it is negatively influenced by artifacts due to interpolation effects. As a result, registration algorithms performance could be affected. In this paper a novel interpolation scheme is presented. It is both effective and efficient. Effective because it limits the presence of local maxima in the mutual information curve, efficient because it is simple to compute being based on simple and optimized distance measures. The method is validated and compared against other techniques both from performance and time complexity persepectives. Differently from other reference works, which perfo…
Information – theoretic characterization of concurrent activity of neural spike trains
2021
The analysis of massively parallel spike train recordings facilitates investigation of communications and synchronization in neural networks. In this work we develop and evaluate a measure of concurrent neural activity, which is based on intrinsic firing properties of the recorded neural units. An overall single neuron activity is unfolded in time and decomposed into working and non-firing state, providing a coarse, binary representation of the neurons functional state. We propose a modified measure of mutual information to reflect the degree of simultaneous activation and concurrency in neural firing patterns. The measure is shown to be sensitive to both correlations and anti-correlations,…
Mutual Information Analysis of Brain-Heart Interactions in Epileptic Children
2021
In this work we apply the network physiology paradigm to retrieve information from central and autonomic nervous systems before focal epileptic seizure, represented respectively by electroencephalogram (EEG) signals and R-R intervals (RRI), and investigate on the presence and strength of brain-heart interactions by computing mutual information (MI) measures. Statistical significance of MI values was tested through surrogate time series generated with the random shuffle approach. Our results suggest that the proposed method for aligning signals representing brain and heart activity measured with different sampling rates, is capable of revealing coupling between RRI representing heart system,…
Estimating the decomposition of predictive information in multivariate systems
2015
In the study of complex systems from observed multivariate time series, insight into the evolution of one system may be under investigation, which can be explained by the information storage of the system and the information transfer from other interacting systems. We present a framework for the model-free estimation of information storage and information transfer computed as the terms composing the predictive information about the target of a multivariate dynamical process. The approach tackles the curse of dimensionality employing a nonuniform embedding scheme that selects progressively, among the past components of the multivariate process, only those that contribute most, in terms of co…