Moore's law, Wright's law and the Countdown to Exponential Space

Explorers have made breakthroughs in many fields of astrophysics. The science from both these missions contributed to three Nobel Prizes - Giacconi (2002), Mather, and Smoot (2006). Explorers have: marked the definitive beginning of precision cosmology, discovered that short gamma-ray bursts are caused by compact star mergers and have measured metalicity to redshifts z>6. NASA Explorers do cutting-edge science that cannot be done by facility-class instruments. The Explorer pr...

Many studies in Economics and other disciplines have been reporting distributions following power-law behavior (i.e distributions of incomes (Pareto's law), city sizes (Zipf's law), frequencies of words in long sequences of text etc.)[1, 6, 7]. This widespread observed regularity has been explained in many ways: generalized Lotka-Volterra (GLV) equations, self-organized criticality and highly optimized tolerance [2,3,4]. The evolution of the phenomena exhibiting power-law beh...

In the present work, via computational simulation we study the statistical distribution of people versus number of steps acquired by them in a learning process, considering Darwin classical theory of evolution, i.e. competition, learning and survival for the fittest. We consider that learning ability is normally distributed. We found that the number of people versus step acquired by them in a learning process is given through a power law (N(n)=cn^-alpha). As competition, lear...

Mathematical methods of analysis of data and of predicting growth are discussed. The starting point is the analysis of the growth rates, which can be expressed as a function of time or as a function of the size of the growing entity. Application of these methods is illustrated using the world economic growth but they can be applied to any other type of growth.

Recent years have seen unprecedentedly fast-growing prosperity in the commercial space industry. Several privately funded aerospace manufacturers, such as Space Exploration Technologies Corporation (SpaceX) and Blue Origin have innovated what we used to know about this capital-intense industry and gradually reshaped the future of human civilization. As private spaceflight and multi-planetary immigration gradually become realities from science fiction (sci-fi) and theory, both...

The modern ability to collect vast quantities of data poses a challenge for parameter estimation problems. When posed as a nonlinear least squares problem fitting a model to data, the cost of each iteration grows linearly with the amount of data and it can easily become prohibitively expensive to perform many iterations. Here we develop an approach that projects the data onto a low-dimensional subspace of the high-dimensional data that preserves the information in the origina...

We face unprecedented resource stresses in the 21st Century such as global climate disruptions, freshwater scarcity, expanding energy demands, and the threat of global pandemics. Historically, societies have relieved resource stress by increasing trade, innovating technologically, expanding territorially, regulating, redistributing, making alliances, creating new economic models, training new skills, as well as conducting war. Do we continue depleting our already strained res...

This article describes a methodology for fitting experimental data to the discrete power-law distribution and provides the results of a detailed simulation exercise used to calculate accurate cutoff values used to assess the fit to a power-law distribution when using the maximum likelihood estimation for the exponent of the distribution. Using massively parallel programming computing, we were able to accelerate by a factor of 60 the computational time required for these calcu...

Learning curves provide insight into the dependence of a learner's generalization performance on the training set size. This important tool can be used for model selection, to predict the effect of more training data, and to reduce the computational complexity of model training and hyperparameter tuning. This review recounts the origins of the term, provides a formal definition of the learning curve, and briefly covers basics such as its estimation. Our main contribution is a...

Technology leads discovery in astronomy, as in all other areas of science, so growth in technology leads to the continual stream of new discoveries which makes our field so fascinating. Derek de Solla Price had analysed the discovery process in science in the 1960s and he introduced the terms 'Little Science' and 'Big Science' as part of his discussion of the role of exponential growth in science. I will show how the development of astronomical facilities has followed this sa...