Related papers: Moore's Law is dead, long live Moore's Law!
Quantal systems are predicted to show a change-over from exponential decay to power law decay at very long times. Although most theoretical studies predict integer power-law exponents, recent measurements by Rothe et al. of decay…
This paper provides theorems aimed at shedding light on issues in the foundations of quantum mechanics. These theorems can be used to propose new interpretations to the theory, or to better understand, evaluate and improve current…
In the framework of the solvable model of cosmology constructed in the Earth-related coordinate system, we derive the modified Hubble law. This law carries the slowly time-varying Hubble parameter. The modified Hubble law eliminates the…
The Born rule is part of the collapse axiom in the standard version of quantum theory, as presented by standard textbooks on the subject. We show here that its signature quadratic dependence follows from a single additional physical…
We are entering the post-Moore era where we no longer enjoy the free ride of the performance growth from simply shrinking the transistor features. However, this does not necessarily mean that we are entering a dark era of computing. On the…
Monte carlo simulation of paths of a large number of impinging electrons in a multi-layered solid allows to define area of spreading electrons (A) to capture overall behavior of the solid. This parameter 'A' follows power law with electron…
When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf's law or the Pareto distribution. Power laws appear…
Quantum theory has evolved from a set of provisional rules to an indispensable framework that underlies much of modern technology and infrastructure. Yet, after a century, Born's probability postulate remains at odds with the theory's…
The predictability of discrete-time processes is studied in a deterministic setting. A family of one-step-ahead predictors is suggested for processes of which the energy decays at higher frequencies. For such processes, the prediction error…
The muon optimizer has picked up much attention as of late as a possible replacement to the seemingly omnipresent Adam optimizer. Recently, care has been taken to document the scaling laws of hyper-parameters under muon such as weight decay…
A generalization of the economic model of natural growth, which takes into account the power-law memory effect, is suggested. The memory effect means the dependence of the process not only on the current state of the process, but also on…
Well protected human and laboratory animal populations with abundant resources are evolutionary unprecedented, and their survival far beyond reproductive age may be a byproduct rather than tool of evolution. Physical approach, which takes…
In dynamical systems theory, there is a lack of a straightforward rule to distinguish exact center solutions from decaying center-like solutions, as both require the damping force function to be zero [1, 2]. By adopting a multi-scale…
This note introduces a new Bayesian control chart to compare two processes by monitoring the ratio of their percentiles under Weibull assumption. Both in-control and out-of-control parameters are supposed unknown. The chart analyses the…
More than one billion data sampled with different frequencies from several financial instruments were investigated with the aim of testing whether they involve power law. As a result, a known power law with the power exponent around -4 was…
Applied machine learning (ML) has rapidly spread throughout the physical sciences; in fact, ML-based data analysis and experimental decision-making has become commonplace. We suggest a shift in the conversation from proving that ML can be…
Model Predictive Control (MPC) can efficiently control constrained systems in real-time applications. MPC feedback law for a linear system with linear inequality constraints can be explicitly computed off-line, which results in an off-line…
Single quantum dots and other materials exhibit irregular switching between on and off states; these on-off states follow power-law statistics giving rise to 1/f noise. We transfer this phenomenon (also referred to as on-off intermittency)…
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…
Many systems exhibit a digit bias. For example, the first digit base 10 of the Fibonacci numbers, or of $2^n$, equals 1 not 10% or 11% of the time, as one would expect if all digits were equally likely, but about 30% of the time. This…