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In estimating the complexity of objects, in particular of graphs, it is common practice to rely on graph- and information-theoretic measures. Here, using integer sequences with properties such as Borel normality, we explain how these…
This is a review of group entropy and its application to permutation complexity. Specifically we revisit a new approach to the notion of complexity in time serie analysis, based on both permutation entropy and group entropy. As a result,…
Networks are widely used to model real-world systems and uncover their topological features. Network properties such as the degree distribution and shortest path length have been computed in numerous real-world networks, and most of them…
In computer vision, it is often observed that formulating regression problems as a classification task often yields better performance. We investigate this curious phenomenon and provide a derivation to show that classification, with the…
Ordinal regression is commonly formulated as a multi-class problem with ordinal constraints. The challenge of designing accurate classifiers for ordinal regression generally increases with the number of classes involved, due to the large…
Complex networks have been used intensively to investigate the flow and dynamics of many natural systems including the climate system. Here, we develop a percolation based measure, the order parameter, to study and quantify climate…
The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several…
There is a growing interest in methods for detecting and interpreting changes in experimental time evolution data. Based on measured time series, the quantitative characterization of dynamical phase transitions at bifurcation points of the…
We propose a method for computing the transfer entropy between time series using Ulam's approximation of the Perron-Frobenius (transfer) operator associated with the map generating the dynamics. Our method differs from standard transfer…
Neural networks have dramatically increased our capacity to learn from large, high-dimensional datasets across innumerable disciplines. However, their decisions are not easily interpretable, their computational costs are high, and building…
Transient phenomena play a key role in coordinating brain activity at multiple scales, however,their underlying mechanisms remain largely unknown. A key challenge for neural data science is thus to characterize the network interactions at…
An experiment to study the entropy method for an anomaly detection system has been performed. The study has been conducted using real data generated from the distributed sensor networks at the Intel Berkeley Research Laboratory. The…
The percolation phase transition in complex network systems attracts much attention and has numerous applications in various research fields. Finite size effects smooth the transition and make it difficult to predict the critical point of…
Subshifts of deterministic substitutions are ubiquitous objects in dynamical systems and aperiodic order (the mathematical theory of quasicrystals). Two of their most striking features are that they have low complexity (zero topological…
Networks are frequently used to model complex systems comprised of interacting elements. While edges capture the topology of direct interactions, the true complexity of many systems originates from higher-order patterns in paths by which…
The dynamics of systems of interacting agents is determined by the structure of their coupling network. The knowledge of the latter is, therefore, highly desirable, for instance, to develop efficient control schemes, to accurately predict…
Inferring the coupling structure of complex systems from time series data in general by means of statistical and information-theoretic techniques is a challenging problem in applied science. The reliability of statistical inferences…
Time series and signals are attracting more attention across statistics, machine learning and pattern recognition as it appears widely in the industry especially in sensor and IoT related research and applications, but few advances has been…
We find a criterion to compare POVM measurements and decide which ones can extract more information from physical systems, with coarser POVMs always extracting less information. This criteria generalizes the previous definition of coarser…
This paper addresses the large-scale acquisition of end-to-end network performance. We made two distinct contributions: ordinal rating of network performance and inference by matrix completion. The former reduces measurement costs and…