Related papers: Tomography of scaling
In the present paper, we analyze the consequences of scaling hypotheses on dynamic functions, as two times correlations $C(t,t')$. We show, under general conditions, that $C(t,t')$ must obey the following scaling behavior $C(t,t') =…
We give a method for proactively identifying small, plausible shifts in distribution which lead to large differences in model performance. These shifts are defined via parametric changes in the causal mechanisms of observed variables, where…
Scaling laws illuminate Nature's fundamental biological principles and guide bioinspired materials and structural designs. In simple cases they are based on the fundamental principle that all laws of nature remain unchanged (i.e.,…
In modelling of chemical, physical or biological systems it may occur that the coefficients, multiplying various terms in the equation of interest, differ greatly in magnitude, if a particular system of units is used. Such is, for instance,…
Scale selection methods based on local extrema over scale of scale-normalized derivatives have been primarily developed to be applied sparsely --- at image points where the magnitude of a scale-normalized differential expression…
The dependence of the scaling properties of the structure factor on space dimensionality, range of interaction, initial and final conditions, presence or absence of a conservation law is analysed in the framework of the large-N model for…
Previous work has established the usefulness of the resolvent operator that maps the terms nonlinear in the turbulent fluctuations to the fluctuations themselves. Further work has described the self-similarity of the resolvent arising from…
A complex network is said to show topological isotropy if the topological structure around a particular node looks the same in all directions of the whole network. Topologically anisotropic networks are those where the local neighborhood…
This article introduces the Stochastic Texture Difference method for analyzing data at prescribed spatial and value scales. This method relies on constrained random walks around each pixel, describing how nearby image values typically…
Pinning models are built from discrete renewal sequences by rewarding (or penalizing) the trajectories according to their number of renewal epochs up to time $N$, and $N$ is then sent to infinity. They are statistical mechanics models to…
Scale independence is a ubiquitous feature of complex systems which implies a highly skewed distribution of resources with no characteristic scale. Research has long focused on why systems as varied as protein networks, evolution and stock…
Spatial relationships in multi-species data can indicate and affect system outcomes and behaviors, ranging from disease progression in cancer to coral reef resilience in ecology; therefore, quantifying these relationships is an important…
Temperature scaling is a simple method that allows to control the uncertainty of probabilistic models. It is mostly used in two contexts: improving the calibration of classifiers and tuning the stochasticity of large language models (LLMs).…
In this paper, we apply recent findings from urban scaling theory to evaluate how it could be applied to a one-dimensional archetypal city. Our focus is on how the simplicity of a one-dimensional model can provide intuitive insights that…
Predictions are often probabilities; e.g., a prediction could be for precipitation tomorrow, but with only a 30% chance. Given such probabilistic predictions together with the actual outcomes, "reliability diagrams" help detect and diagnose…
The scaling of the fundamental limits of the second hyperpolarizability is used to define the intrinsic second hyperpolarizability, which aids in identifying material classes with ultralarge nonlinear-optical response per unit of molecular…
We numerically study the distribution function of the conductivity (transmission) in the one-dimensional tight-binding Anderson model in the region of fluctuation states. We show that while single parameter scaling in this region is not…
A new scaling formalism is used to analyze nonlinear I-V data in the vicinity of metal-insulator transitions (MIT) in five manganite systems. An exponent, called the nonlinearity exponent, and an onset field for nonlinearity, both…
The scaling of the thermoremanent magnetization and of the dissipative part of the non-equilibrium magnetic susceptibility is analysed as a function of the waiting-time $s$ for a simple ferromagnet undergoing phase-ordering kinetics after a…
Characteristic scale is a notion that pervades the geophysical sciences, but it has no widely accepted precise definition. The wavelet transform decomposes a time series into coefficients that are associated with different scales. The…