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Long memory plays an important role in many fields by determining the behaviour and predictability of systems; for instance, climate, hydrology, finance, networks and DNA sequencing. In particular, it is important to test if a process is exhibiting long memory since that impacts the accuracy and confidence with which one may predict future events on the basis of a small amount of historical data. A major force in the development and study of long memory was the late Benoit B. Mandelbrot. Here we discuss the original motivation of the development of long memory and Mandelbrots influence on this fascinating field. We will also elucidate the sometimes contrasting approaches to long memory in different scientific communities
We reconstruct the chain of events, intuitions and ideas that led to the formulation of the Gorini, Kossakowski, Lindblad and Sudarshan equation.
Gurzadyan-Xue Dark Energy was derived in 1986 (twenty years before the paper of Gurzadyan-Xue). The paper by the present author, titled The Planck Length as a Cosmological Constant, published in Astrophysics Space Science, Vol. 127, p.133-137, 1986 c
The idea of breaking time-translation symmetry has fascinated humanity at least since ancient proposals of the perpetuum mobile. Unlike the breaking of other symmetries, such as spatial translation in a crystal or spin rotation in a magnet, time tran
In 2015, the New Horizons spacecraft flew past Pluto and its moon Charon, providing the first clear look at the surface of Charon. New Horizons images revealed an ancient surface, a large, intricate canyon system, and many fractures, among other geol
The Edgeworth-Kuiper belt encodes the dynamical history of the outer solar system. Kuiper belt objects (KBOs) bear witness to coagulation physics, the evolution of planetary orbits, and external perturbations from the solar neighborhood. We criticall