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The discovery of universe's late-time acceleration and dark energy has overseen a great deal of research into cosmological singularities and in this brief review, we discuss all the prominent developments in this field for the best part of…
After preamble about Darwin, my talk described the conformality approach to extending the standard model of particle phenomenology using an assumption of no conformal anomaly at high energy. Topics included quiver gauge theory, the…
Atmospheric flows, an example of turbulent fluid flows, exhibit fractal fluctuations of all space-time scales ranging from turbulence scale of mm -sec to climate scales of thousands of kilometers - years and may be visualized as a nested…
Based at a talk given at the Kato Centennial Symposium in Sept. 2017, this article discusses the scientific life and some of the scientific work of T. Kato.
The mood at this conference is summarized in David Hughes' comment, ``this decade will be amazing.'' We've just had a pretty good ten years of advances in cosmology and extragalactic astronomy; why should we expect a repeat, another decade…
One of the major breakthroughs in science of the last (20th) century was building a bridge between the worlds of stochastic (random) systems and deterministic (dynamical) systems. It was started by the celebrated 1958 paper by…
In the last decade, there has been a growing body of literature addressing the utilization of complex network methods for the characterization of dynamical systems based on time series. While both nonlinear time series analysis and complex…
These are lecture notes, which summarize the current status of the Semiclassical theory, as well as Monopoles, Instantons, Instanton-dyons and Flux tubes. The emphasis is on QCD and QCD-like theories (deformed QCD), although relevant points…
Continual learning, also known as incremental learning or life-long learning, stands at the forefront of deep learning and AI systems. It breaks through the obstacle of one-way training on close sets and enables continuous adaptive learning…
In this set of lectures, we review briefly some of the recent developments in the study of the chaotic dynamics of nonlinear oscillators, particularly of damped and driven type. By taking a representative set of examples such as the…
The study of random graphs and networks had an explosive development in the last couple of decades. Meanwhile, techniques for the statistical analysis of sequences of networks were less developed. In this paper we focus on networks…
Chaos presents complex dynamics arising from nonlinearity and a sensitivity to initial states. These characteristics suggest a depth of expressivity that underscores their potential for advanced computational applications. However,…
Characterizing the emergence of chaotic dynamics of complex networks is an essential task in nonlinear science with potential important applications in many fields such as neural control engineering, microgrid technologies, and ecological…
Cosmology as an exact physical science is of new date, but it has long roots in the past. This essay is concerned with four important themes in the history of cosmological thought which, if taken together, offer a fairly comprehensive…
Dynamical chaos is a term that encompasses a wide range of nonlinear phenomena such as turbulence, neuronal avalanches, weather patterns, and many others. However, despite much work in the field of chaos, its fundamental physical origin…
There has been a long history of research into the structure and evolution of mankind's scientific endeavor. However, recent progress in applying the tools of science to understand science itself has been unprecedented because only recently…
Recent decades have witnessed a dramatic shift in the cross-border collaboration mode of researchers, with countries increasingly cooperating and competing with one another. It is crucial for leaders in academia and policy to understand the…
Changes in the number of publications in a certain field might reflect the dynamic of scientific progress in this field, since an increase in the number of publications can be interpreted as an increase in the field-specific knowledge. In…
The number of scientific publications continues to rise exponentially, especially in Computer Science (CS). However, current solutions to analyze those publications restrict access behind a paywall, offer no features for visual analysis,…
This paper formulates a new approach to the study of chaos in discrete dynamical systems based on the notions of inverse ill-posed problems, set-valued mappings, generalized and multivalued inverses, graphical convergence of a net of…