Related papers: Moore's law, Wright's law and the Countdown to Exp…
The arrow of time is an irreversible phenomenon for a system of particles undergoing reversible dynamics. Since the time of Boltzmann to this day, the arrow of time has led to debate and research. However, the enormous growth of…
Over the last decades, impressive progresses have been made in many experimental domains, e.g. microscopic techniques such as single-particle tracking, leading to plethoric amounts of data. In a large variety of systems, from natural to…
Here we extract the geographical addresses of authors in the Citeseer database of computer science papers. We show that the productivity of research centres in the United States follows a power-law regime, apart from the most productive…
Power law distributions have been repeatedly observed in a wide variety of socioeconomic, biological and technological areas. In many of the observations, e.g., city populations and sizes of living organisms, the objects of interest evolve…
The development of inventions is theorized as a process of searching and recombining existing knowledge components. Previous studies under this theory have examined myriad characteristics of recombined knowledge and their performance…
The cause for first and second order electromagnetic equivalency of inertial systems is approached from a different point of view than that of special relativity. While special relativity applies dilatation to time and contraction to space…
Emergent technologies such as solar power, electric vehicles, and artificial intelligence (AI) often exhibit exponential or power function price declines and various ``S-curves'' of adoption. We show that under CES and VES utility, such…
The progress of some AI paradigms such as deep learning is said to be linked to an exponential growth in the number of parameters. There are many studies corroborating these trends, but does this translate into an exponential increase in…
The Universe that we know is populated by structures made up of aggregated matter that organizes into a variety of objects; these range from stars to larger objects, such as galaxies or star clusters, composed by stars, gas and dust in…
It is often claimed that the fundamental laws of physics are deterministic and time-symmetric and that therefore our experience of the passage of time is an illusion. This paper will critically discuss these claims and show that they are…
Based on the Langevin description of the Continuous Time Random Walk (CTRW), we consider a generalization of CTRW in which the waiting times between the subsequent jumps are correlated. We discuss the cases of exponential and slowly…
Constancy of the speed of light together with the Hubble law lead in a doctrine of expanding universe to a conclusion that universe evolution is not only an expansion of space but also a deceleration of the course of physical time (Taganov,…
Zipf's power-law distribution is a generic empirical statistical regularity found in many complex systems. However, rather than universality with a single power-law exponent (equal to 1 for Zipf's law), there are many reported deviations…
Linear systems with many degrees of freedom containing multiplicative and additive noise are considered. The steady state probability distribution for equations of this kind is examined. With multiplicative white noise it is shown that…
Staffing rules are an essential management tool in service industries for meeting target service levels. The square-root safety rule, based on the Poisson arrival assumption, has been commonly used. However, empirical findings suggest that…
We consider a random walk on the support of an ergodic simple point process on R^d, d>1, furnished with independent energy marks. The jump rates of the random walk decay exponentially in the jump length and depend on the energy marks via a…
Thanks to the increasing availability in computing power, high-dimensional engineering problems seem to be at reach. But the curse of dimensionality will always prevent us to try out extensively all the hypotheses. There is a vast…
We study the statistics of the amplitude of the synchronization error in chaotic electronic circuits coupled through linear feedback. Depending on the coupling strength, our system exhibits three qualitatively different regimes of…
Successful materials innovations can transform society. However, materials research often involves long timelines and low success probabilities, dissuading investors who have expectations of shorter times from bench to business. A…
A country's research success can be assessed from the power law function that links country and world rank numbers when publications are ordered by their number of citations; a similar function describes the distribution of country papers…