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Partial differential equations are central objects in the mathematical modeling of natural and social sciences (sound propagation, heat diffusion, thermodynamics, electromagnetism, elasticity, fluid dynamics, quantum mechanics, population…
At the eight-year anniversary of Watts & Strogatz's work on the collective dynamics of small-world networks and seven years after Barabasi & Albert's discovery of scale-free networks, the area of dynamical processes on complex networks is…
Introduced by the late Per Bak and his colleagues, self-organized criticality (SOC) has been one of the most stimulating concepts to come out of statistical mechanics and condensed matter theory in the last few decades, and has played a…
It is explained and stressed that the chaotic states in [1] are obtained by means of nonlinear switching.
Recent research on the decline in the paper disruption index (D-index) has sparked heated debates among scholars and garnered significant attention from policymakers and research institution leaders globally. To bridge the gap between…
We present a comprehensive study on the emergence of Computational Social Science (CSS) - an interdisciplinary field leveraging computational methods to address social science questions - and its impact on adjacent social sciences. We…
This Symposium is devoted to the Memory of Lev Kofman, June-17-1957-November-12-2009. The accelerated expansion of the Universe, which is today observed, shows that cosmological dynamics is dominated by the so-called Dark Energy field which…
Machine learning and deep learning techniques are contributing much to the advancement of science. Their powerful predictive capabilities appear in numerous disciplines, including chaotic dynamics, but they miss understanding. The main…
Two decades ago three pioneering papers turned the attention to complex networks and initiated a new era of research, establishing an interdisciplinary field called network science. Namely, these highly-cited seminal papers were written by…
In this expository and resources chapter we review selected aspects of the mathematics of dynamical systems, stability, and chaos, within a historical framework that draws together two threads of its early development: celestial mechanics…
The paper discusses the main ideas of the chaos theory and presents mainly the importance of the nonlinearities in the mathematical models. Chaos and order are apparently two opposite terms. The fact that in chaos can be found a certain…
The learning analytics (LA) community has recently reached two important milestones: celebrating the 15th LAK conference and updating the 2011 definition of LA to reflect the 15 years of changes in the discipline. However, despite LA's…
I review the history of scientific research on galaxy clusters, from 1784, the year of publication of Messier's catalogue, to 1983, the year of George O. Abell's premature death. My review covers four main topics: 1) the distribution of…
Nonlinear filtering is the problem of online estimation of a dynamic hidden variable from incoming data and has vast applications in different fields, ranging from engineering, machine learning, economic science and natural sciences. We…
Nowadays, chaos theory and nonlinear dynamics lack research focuses. Here we mention a few major open problems: 1. an effective description of chaos and turbulence, 2. rough dependence on initial data, 3. arrow of time, 4. the paradox of…
The origin of many elements of the periodic table remains an unsolved problem. While many nucleosynthetic channels are broadly understood, significant uncertainties remain regarding certain groups of elements such as the intermediate and…
The concept of observability of linear systems initiated with Kalman in the mid 1950s. Roughly a decade later, the observability of nonlinear systems appeared. By such definitions a system is either observable or not. Continuous measures of…
Exploration of the structure formation and dynamics of animate and inanimate matter on the nanometer scale is a highly interdisciplinary field of rapidly emerging research. It is relevant for various molecular and nanoscale systems of…
Ever since the link between nonlinear science and cryptography became apparent, the problem of applying chaotic dynamics to the construction of cryptographic systems has gained a broad audience and has been the subject of thousands of…
Through semiclassical methods the subject of quantum chaos motivates and depends on Hamiltonian chaos research. Presented here is a selection of Hamiltonian chaos topics that in this way get directly related to any of a variety of quantum…