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We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We firstly define a purely structural…
We investigate multiscale Gibbs measures from a variational and probabilistic viewpoint, focusing on the structural asymmetry among conditional entropies that characterizes their construction. We show how this asymmetry emerges both from…
Recent studies have shown great promise in applying graph neural networks for multivariate time series forecasting, where the interactions of time series are described as a graph structure and the variables are represented as the graph…
A graph $G$ is a \emph{max point-tolerance (MPT)} graph if each vertex $v$ of $G$ can be mapped to a \emph{pointed-interval} $(I_v, p_v)$ where $I_v$ is an interval of $\mathbb{R}$ and $p_v \in I_v$ such that $uv$ is an edge of $G$ iff $I_u…
The von Neumann entropy of a graph is a spectral complexity measure that has recently found applications in complex networks analysis and pattern recognition. Two variants of the von Neumann entropy exist based on the graph Laplacian and…
Objective: Due to the non-linearity of numerous biomedical signals, non-linear analysis of multi-channel time series, notably multivariate multiscale entropy (mvMSE), has been extensively used in biomedical signal processing. However, mvMSE…
Deriving Bayesian inference for exponential random graph models (ERGMs) is a challenging "doubly intractable" problem as the normalizing constants of the likelihood and posterior density are both intractable. Markov chain Monte Carlo (MCMC)…
Multivariate meta-analysis is gaining prominence in evidence synthesis research because it enables simultaneous synthesis of multiple correlated outcome data, and random-effects models have generally been used for addressing between-studies…
Like natural complex systems such as the Earth's climate or a living cell, semiconductor lithography systems are characterized by nonlinear dynamics across more than a dozen orders of magnitude in space and time. Thousands of sensors…
In this work we prove sufficient conditions for the Glauber dynamics corresponding to a sequence of (non-product) measures on finite product spaces to be rapidly mixing, i.e. that the mixing time with respect to the total variation distance…
This paper proposes two distinct contributions to econometric analysis of large information sets and structural instabilities. First, it treats a regression model with time-varying coefficients, stochastic volatility and exogenous…
Several studies demonstrate that there are critical differences between real wireless networks and simulation models. This finding has permitted to extract spatial and temporal properties for links and to provide efficient methods as biased…
We address the problem of merging graph and feature-space information while learning a metric from structured data. Existing algorithms tackle the problem in an asymmetric way, by either extracting vectorized summaries of the graph…
Behavior of the entropy numbers of classes of multivariate functions with mixed smoothness is studied here. This problem has a long history and some fundamental problems in the area are still open. The main goal of this paper is to develop…
A Bayesian multivariate model with a structured covariance matrix for multi-way nested data is proposed. This flexible modeling framework allows for positive and for negative associations among clustered observations, and generalizes the…
Multiscale entropy (MSE) has been a prevalent algorithm to quantify the complexity of fluctuations in the local mean value of biomedical time series. Recent developments in the field have tried to improve the MSE by reducing its variability…
Background: Transitioning from an old medical coding system to a new one can be challenging, especially when the two coding systems are significantly different. The US experienced such a transition in 2015. Objective: This research aims to…
Byte-Pair Encoding (BPE) has become a widely adopted subword tokenization method in modern language models due to its simplicity and strong empirical performance across downstream tasks. However, applying BPE to unsegmented languages such…
This paper presents an entropy based adaptive measurement sequence strategy for quantum sensing of magnetic fields. To physically ground our ideas we consider a sensor employing a nitrogen vacancy center in diamond, however our approach is…
We introduce the entropic measure transform (EMT) problem for a general process and prove the existence of a unique optimal measure characterizing the solution. The density process of the optimal measure is characterized using a…