Related papers: Using the Memories of Multiscale Machines to Chara…

We present a novel approach to learn the formulae characterising the emergent behaviour of a dynamical system from system observations. At a high level, the approach starts by devising a statistical dynamical model of the system which…

We present a measure of local information transfer, derived from an existing averaged information-theoretical measure, namely transfer entropy. Local transfer entropy is used to produce profiles of the information transfer into each…

Physical systems with many degrees of freedom can often be understood in terms of transitions between a small number of metastable states. For time-homogeneous systems with short-term memory these transitions are fully characterized by a…

We present a new data structure called the \emph{Compressed Random Access Memory} (CRAM) that can store a dynamic string $T$ of characters, e.g., representing the memory of a computer, in compressed form while achieving asymptotically…

Recent research has shown that performance in signal processing tasks can often be significantly improved by using signal models based on sparse representations, where a signal is approximated using a small number of elements from a fixed…

A method for correcting for detector smearing effects using machine learning techniques is presented. Compared to the standard approaches the method can use more than one reconstructed variable to infere the value of the unsmeared quantity…

Machine learning has had a major impact on data compression over the last decade and inspired many new, exciting theoretical and applied questions. This paper describes one such direction -- relative entropy coding -- which focuses on…

Ordinal measures provide a valuable collection of tools for analyzing correlated data series. However, using these methods to understand the information interchange in networks of dynamical systems, and uncover the interplay between…

Our increasingly digital and connected world has led to the generation of unprecedented amounts of data. This data must be efficiently managed, transmitted, and stored to preserve resources and allow scalability. Data compression has…

The metriplectic formalism is useful for describing complete dynamical systems which conserve energy and produce entropy. This creates challenges for model reduction, as the elimination of high-frequency information will generally not…

Recent studies have demonstrated that correntropy is an efficient tool for analyzing higher-order statistical moments in nonGaussian noise environments. Although correntropy has been used with complex data, no theoretical study was pursued…

Metriplectic systems are learned from data in a way that scales quadratically in both the size of the state and the rank of the metriplectic data. Besides being provably energy conserving and entropy stable, the proposed approach comes with…

We propose a new way to measure the balance between freedom and coherence in a dynamical system and a new measure of its internal variability. Based on the concept of entropy and ideas from neuroscience and information theory, we define…

We present a quantum information-inspired framework for analyzing complex systems through multivariate time series. In this approach the system's state is encoded into a density matrix, providing a compact representation of higher-order…

Estimating the entropy rate of discrete time series is a challenging problem with important applications in numerous areas including neuroscience, genomics, image processing and natural language processing. A number of approaches have been…

Entropy has been a common index to quantify the complexity of time series in a variety of fields. Here, we introduce increment entropy to measure the complexity of time series in which each increment is mapped into a word of two letters,…

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 define an entropy based on a chosen governing probability distribution. If a certain kind of measurements follow such a distribution it also gives us a suitable scale to study it with. This scale will appear as a link function that is…

Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less…

The search for patterns in time series is a very common task when dealing with complex systems. This is usually accomplished by employing a complexity measure such as entropies and fractal dimensions. However, such measures usually only…