相关论文: Inside singularity sets of random Gibbs measures
In this paper, we discuss the self-shrinking systems in higher codimensional spaces. We mainly obtain several Bernstein type results and a sharp growth estimate.
We report measurements of conditional Eulerian and Lagrangian structure functions in order to assess the effects of non-universal properties of the large scales on the small scales in turbulence. We study a 1m $\times$ 1m $\times$ 1.5m flow…
Building on recent results regarding symmetric probabilistic constructions of countable structures, we provide a method for constructing probability measures, concentrated on certain classes of countably infinite structures, that are…
Scale invariance (fractality) is a prominent feature of the large-scale behavior of many stochastic systems. In this work, we construct an algorithm for the statistical identification of the Hurst distribution (in particular, the scaling…
Reproducibility is essential to reliable scientific discovery in high-throughput experiments. In this work we propose a unified approach to measure the reproducibility of findings identified from replicate experiments and identify putative…
Our study addresses the inference of jumps (i.e. sets of discontinuities) within multivariate signals from noisy observations in the non-parametric regression setting. Departing from standard analytical approaches, we propose a new…
Fine structure of giant resonances (GR) has been established in recent years as a global phenomenon across the nuclear chart and for different types of resonances. A quantitative description of the fine structure in terms of characteristic…
We study correlation measures for complex systems. First, we investigate some recently proposed measures based on information geometry. We show that these measures can increase under local transformations as well as under discarding…
Inhomogeneities in deposition may lead to formation of rough surfaces, whose height fluctuations can be probed directly by scanning microscopy, or indirectly by scattering. Analytical or numerical treatments of simple growth models suggest…
The study of Fourier transforms of probability measures on fractal sets plays an important role in recent research. Faster decay rates are known to yield enhanced results in areas such as metric number theory. This paper focuses on…
We consider a mass-conservative fragmentation of the unit interval. The main purpose of this work is to specify the Hausdorff dimension of the set of locations having exactly an exponential decay. The study relies on an additive martingale…
Multimodal distributions of some physics based model parameters are often encountered in engineering due to different situations such as a change in some environmental conditions, and the presence of some types of damage and nonlinearity.…
Small number statistics may heavily affect the structure of the broadening function in integrated spectra of galactic globular cluster centers. As a consequence, it is a priori unknown how closely line broadening measure- ments gauge the…
The scaling behaviour of the diffraction intensity near the origin is investigated for (partially) ordered systems, with an emphasis on illustrative, rigorous results. This is an established method to detect and quantify the fluctuation…
We consider statistical methods based on finite samples of locally randomized measurements in order to certify different degrees of multiparticle entanglement in intermediate-scale quantum systems. We first introduce hierarchies of…
This topic review communicates working experiences regarding interaction of a multiplicity of processes. Our experiences come from climate change modelling, materials science, cell physiology and public health, and macroeconomic modelling.…
Language models famously improve under a smooth scaling law, but some specific capabilities exhibit sudden breakthroughs in performance. Advocates of "emergence" view these capabilities as unlocked at a specific scale, but others attribute…
The observation of scaling in processes in which a weakly interacting probe delivers large momentum ${\bf q}$ to a many-body system reflects the dominance of incoherent scattering off target constituents. While a suitably defined scaling…
Multifractals are inhomogeneous measures (or functions) which are typically described by a full spectrum of real dimensions, as opposed to a single real dimension. Results from the study of fractal strings in the analysis of their geometry,…
We analyze invariant measures of two coupled piecewise linear and everywhere expanding maps on the synchronization manifold. We observe that though the individual maps have simple and smooth functions as their stationary densities, they…