Multifractality is ubiquitously observed in complex natural and socioeconomic systems.
Multifractal analysis provides powerful tools to understand the complex nonlinear nature of …

This short review presents a selected history of the mutual fertilization between physics and
economics—from Isaac Newton and Adam Smith to the present. The fundamentally different …

The use of extended reality (XR) technologies is growing rapidly in a range of industries
from gaming to aviation. However, how this technology should be implemented in …

We develop the concept of``dragon-kings''corresponding to meaningful outliers, which are
found to coexist with power laws in the distributions of event sizes under a broad range of …

Model validation metrics have been developed to provide a quantitative measure that
characterizes the agreement between predictions and observations. In engineering design …

The topics of verification and validation have increasingly been discussed in the field of
computational biomechanics, and many recent articles have applied these concepts in an …

We present a novel variant of decision making based on the mathematical theory of
separable Hilbert spaces. This mathematical structure captures the effect of superposition of …

Abstract Model invalidation is a good thing. It means that we are forced to reconsider either
model structures or the available data more closely, that is to challenge our fundamental …

A dynamical analogy supported by five scale-free statistics (the Gutenberg-Richter
distribution of event sizes, the distribution of interevent intervals, the Omori and inverse …

Validating models with correlated multivariate outputs involves the comparison of multiple
stochastic quantities. Considering both uncertainty and correlations among multiple …