相关论文: Universal Scale Laws for Colors and Patterns in Im…
We consider the asymptotic behaviour of a family of unidimensional lattice fermion models, which are in exact correspondence with certain probability laws on partitions and on unitary matrices. These models exhibit limit shapes, and in the…
We provide numerical evidence for the existence of a cascade of filament instabilities in the surface quasigeostrophic system for atmospheric and oceanic motions near a horizontal boundary. The cascade involves geometrically shrinking…
Power spectral density scaling with frequency $f$ as $1/f^\beta$ and $\beta \approx 1$ is widely found in natural and socio-economic systems. Consequently, it has been suggested that such self-similar spectra reflect the universal dynamics…
Universal conductance fluctuations are usually observed in the form of aperiodic oscillations in the magnetoresistance of thin wires as a function of the magnetic field B. If such oscillations are completely random at scales exceeding…
The fluctuation scaling law has universally been observed in a wide variety of phenomena. For counting processes describing the number of events occurred during time intervals, it is expressed as a power function relationship between the…
This essay fuses concepts and approaches used to describe fluctuating phenomena in climate systems and statistical mechanics, and explores new ideas essential for understanding such phenomena. Its starting points are the Langevin equation…
The quantum model of homogeneous and isotropic universe filled with the uniform scalar field is considered. This model predicts effective inverse square-law dependence of the mean total energy density <\rho> on the expectation value of…
This study addresses the challenge of, without training or fine-tuning, controlling the global color aspect of images generated with a diffusion model. We rewrite the guidance equations to ensure that the outputs are closer to a known color…
In this study we are testing whether the power law slopes ($\alpha_F$, $\alpha_E$) of fluxes $(F)$, fluences or energies $(E)$ are universal in their size distributions, $N(F) \propto F^{-\alpha_F}$ and $N(E) \propto E^{-\alpha_E}$, in…
We consider the asymptotic behaviour of the fluctuation process for large stochastic systems of interacting particles driven by both idiosyncratic and common noise with an interaction kernel \(k \in L^2(\R^d) \cap L^\infty(\R^d)\). Our…
Self-organization through noisy interactions is ubiquitous across physics, mathematics, and machine learning, yet how long-range structure emerges from local noisy dynamics remains poorly understood. Here, we investigate three paradigmatic…
Observing finite regions of a bigger system is a common experience, from microscopy to molecular simulations. In the latter especially, there is ongoing interest in predicting thermodynamic properties from tracking fluctuations in finite…
Given $\varepsilon>0$, there exists $f_0$ such that, if $f_0 \le f \le \Delta^2+1$, then for any graph $G$ on $n$ vertices of maximum degree $\Delta$ in which the neighbourhood of every vertex in $G$ spans at most $\Delta^2/f$ edges, (i) an…
Our numerical simulations with the Cahn-Hilliard equation show that coarsening of fractal clusters (FCs) is not a scale-invariant process. On the other hand, a typical coarsening length scale and interfacial area of the FC exhibit power…
The margins within the geographic range of species are often specific in terms of ecological and evolutionary processes, and can strongly influence the species' reaction to climate change. One of the frequently observed features at range…
We consider the fractal characteristic of the quantum mechanical paths and we obtain for any universal class of fractons labeled by the Hausdorff dimension defined within the interval 1$ $$ < $$ $$h$$ $$ <$$ $$ 2$, a fractal distribution…
We consider the hyperuniform model of d-dimensional integer lattice perturbed by independent random variables and we investigate the large scale asymptotic fluctuations of smoothed versions of the usual counting statistics, specifically of…
Images encode both the state of the world and its content. The former is useful for tasks such as planning and control, and the latter for classification. The automatic extraction of this information is challenging because of the…
Atmospheric flows exhibit long-range spatiotemporal correlations manifested as the fractal geometry to the global cloud cover pattern concomitant with inverse power law form for spectra of temporal fluctuations. Such non-local connections…
Regressing the illumination of a scene from the representations of object appearances is popularly adopted in computational color constancy. However, it's still challenging due to intrinsic appearance and label ambiguities caused by unknown…