相关论文: The Scenery Flow for Self-Affine Measures

Learning permutations is fundamental to sorting, ranking, and matching, but existing differentiable methods based on entropy-regularized Sinkhorn produce a single softened solution and collapse under ambiguity. We present PermFlow, a…

A large-scale spanwise and wall-normal array of sonic anemometers in the atmospheric surface layer is used to acquire all three components of instantaneous fluctuating velocity as well as temperature in a range of stability conditions.…

We present three methods to construct majorizing measures in various settings. These methods are based on direct constructions of increasing sequences of partitions through a simple exhaustion procedure rather than on the construction of…

We study the pointwise dimension for a new class of projection measures on arbitrary fractal limit sets without separation conditions. We prove that the pointwise dimension exists a.e. for this class of measures associated to equilibrium…

What is the optimal way to approximate a high-dimensional diffusion process by one in which the coordinates are independent? This paper presents a construction, called the \emph{independent projection}, which is optimal for two natural…

The affinity dimension is a number associated to an iterated function system of affine maps, which is fundamental in the study of the fractal dimensions of self-affine sets. De-Jun Feng and the author recently solved a folklore open…

A new scaling is derived that yields a Reynolds number independent profile for all components of the Reynolds stress in the near-wall region of wall bounded flows, including channel, pipe and boundary layer flows. The scaling demonstrates…

Estimating the trajectories of multi-objects poses a significant challenge due to data association ambiguity, which leads to a substantial increase in computational requirements. To address such problems, a divide-and-conquer manner has…

We study the role of the electromagnetic field's frequency in time precision measurements using single photons as a paradigmatic system. For such, we independently identify the contributions of intensity and spectral resources and show that…

Scan line levelling, a ubiquitous and often necessary step in AFM data processing, can cause a severe bias on measured roughness parameters such as mean square roughness or correlation length. Although bias estimates have been formulated,…

This paper presents a nonparametric scene parsing approach that improves the overall accuracy, as well as the coverage of foreground classes in scene images. We first improve the label likelihood estimates at superpixels by merging…

It is a well-known result of T.\,Kato that given a continuous path of square matrices of a fixed dimension, the eigenvalues of the path can be chosen continuously. In this paper, we give an infinite-dimensional analogue of this result,…

It is shown that a random binary process with impulse-like autocorrelation can be generated by randomizing the length of symbols occurring in a random Bernoulli process. Such randomization is achieved by random (or judiciously designed…

For an autonomous vehicle it is essential to observe the ongoing dynamics of a scene and consequently predict imminent future scenarios to ensure safety to itself and others. This can be done using different sensors and modalities. In this…

The anisotropy parameter of two-dimensional equilibrium clusters of site percolation process in long-range self-affine correlated structures are studied numerically. We use a fractional Brownian Motion(FBM) statistic to produce both…

We show that, in a generic setting, self-affine and almost self-affine measures are exact dimensional, with local dimension equal almost everywhere to the information dimension and given by the zero of a superadditive pressure functional.

We consider an independent and identically distributed (i.i.d.) random dynamical system of simple linear transformations on the unit interval $T_{\beta}(x)=\beta x$ (mod $1$), $x\in[0,1]$, $\beta>0$, which are the so-called…

We estimate from above the rate at which a solution to the rescaled mean curvature flow on a closed hypersurface may converge to a limit self-similar solution, i.e. a shrinker. Our main result implies that any solution which converges to a…

We consider the problem of estimating the parameters of a multivariate Bernoulli process with auto-regressive feedback in the high-dimensional setting where the number of samples available is much less than the number of parameters. This…

In this paper, we propose to study spectral measures on local fields. Some basic results are presented, including the stability of Bessel sequences under perturbation, the Landau theorem on Beurling density, the law of pure type of spectral…