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Dynamic nonlinear systems exhibit distortions arising from coupled static and dynamic effects. Their intertwined nature poses major challenges for data-driven modeling. This paper presents a theoretical framework grounded in structured…
Collective organization in matter plays a significant role in its expressed physical properties. Typically, it is detected via an order parameter, appropriately defined for each given system's observed emergent patterns. Recent developments…
Data Science and Machine Learning have become fundamental assets for companies and research institutions alike. As one of its fields, supervised classification allows for class prediction of new samples, learning from given training data.…
This survey articles focuses on emerging connections between the fields of machine learning and data compression. While fundamental limits of classical (lossy) data compression are established using rate-distortion theory, the connections…
Coherent structures form spontaneously in nonlinear spatiotemporal systems and are found at all spatial scales in natural phenomena from laboratory hydrodynamic flows and chemical reactions to ocean, atmosphere, and planetary climate…
We recount recent history behind building compact models of nonlinear, complex processes and identifying their relevant macroscopic patterns or "macrostates". We give a synopsis of computational mechanics, predictive rate-distortion theory,…
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…
Quantum chaos is presented as a paradigm of information processing by dynamical systems at the bottom of the range of phase-space scales. Starting with a brief review of classical chaos as entropy flow from micro- to macro-scales, I argue…
We define a novel quantitative strategy inspired by the ecological notion of nestedness to single out the scale at which innovation complexity emerges from the aggregation of specialized building blocks. Our analysis not only suggests that…
Quantum machine learning (QML) holds promise for accelerating pattern recognition, optimization, and data analysis, but the conditions under which it can truly outperform classical approaches remain unclear. Existing research often…
Operation of autonomic communication networks with complicated user-oriented functions should be described as unreduced many-body interaction process. The latter gives rise to complex-dynamic behaviour including fractally structured…
The study of complex systems has attracted widespread attention from researchers in the fields of natural sciences, social sciences, and engineering. Prediction is one of the central issues in this field. Although most related studies have…
Sparsity is a ubiquitous feature of many real world signals such as natural images and neural spiking activities. Conventional compressed sensing utilizes sparsity to recover low dimensional signal structures in high ambient dimensions…
We propose to examine the predictability and the complexity characteristics of the Standard&Poor500 dynamics behaviors in a coarse-grained way using the symbolic dynamics method and under the prism of the Information theory through the…
The study of Complex Systems is considered by many to be a new scientific field, and is distinguished by being a discipline that has applications within many separate areas of scientific study. The study of Neural Networks, Traffic…
Decomposition and abstraction is an essential component of computational thinking, yet it is not always emphasized in introductory programming courses. In addition, as generative AI further reduces the focus on syntax and increases the…
One of the most fundamental problems in science is to define {\it quantitatively} the complexity of organized matters, i.e., {\it organized complexity}. Although many measures have been proposed toward this aim in previous decades, there is…
The advent of modern technology, permitting the measurement of thousands of characteristics simultaneously, has given rise to floods of data characterized by many large or even huge datasets. This new paradigm presents extraordinary…
The qualitatively new concept of dynamic complexity in quantum mechanics is based on a new paradigm appearing within a nonperturbational analysis of the Schroedinger equation for a generic Hamiltonian system. The unreduced analysis…
Big data refers to large and complex data sets that, under existing approaches, exceed the capacity and capability of current compute platforms, systems software, analytical tools and human understanding. Numerous lessons on the scalability…