Related papers: On the Estimation of Pointwise Dimension
While sensitivity analysis improves the transparency and reliability of mathematical models, its uptake by modelers is still scarce. This is partially explained by its technical requirements, which may be hard to understand and implement by…
Principal Component Analysis (PCA) is known to be the most widely applied dimensionality reduction approach. A lot of improvements have been done on the traditional PCA, in order to obtain optimal results in the dimensionality reduction of…
We consider the problem of viscous fingering in the presence of quenched disorder that is both weak and short-range correlated. The two point correlation function of the harmonic measure is calculated perturbatively, and is used in order to…
Fractal dimensions of eigenfunctions for various critical random matrix ensembles are investigated in perturbation series in the regimes of strong and weak multifractality. In both regimes we obtain expressions similar to those of the…
Neural network models have recently demonstrated impressive prediction performance in complex systems where chaos and unpredictability appear. In spite of the research efforts carried out on predicting future trajectories or improving their…
The curves of scaling behavior is a significant concept in fractal dimension analysis of complex systems. However, the underlying rationale of this kind of curves for fractal cities is not yet clear. The aim of this paper is at researching…
Estimating accurate 3D locations of objects from monocular images is a challenging problem because of lacking depth. Previous work shows that utilizing the object's keypoint projection constraints to estimate multiple depth candidates…
We propose a novel method to measure the fractal dimension of a submonolayer metal adatom system grown under conditions of limited diffusivity on a surface. The method is based on measuring the specular peak attenuation of He atoms…
There are many research papers dealing with fractal dimension of real-valued fractal functions in the recent literature. The main focus of the present paper is to study fractal dimension of complex-valued functions. This paper also…
This paper serves as a complementary material to a poster presented at the XXXVI Dynamics Days Europe in Corfu, Greece, on June 6th-10th in 2016. In this study, fractal dimension ($D$) of two types of self-affine signals were estimated with…
What is the dimension of a network? Here, we view it as the smallest dimension of Euclidean space into which nodes can be embedded so that pairwise distances accurately reflect the connectivity structure. We show that a recently proposed…
Dimensionality is a major concern in analyzing large data sets. Some well known dimension reduction methods are for example principal component analysis (PCA), invariant coordinate selection (ICS), sliced inverse regression (SIR), sliced…
Following \cite{Visintin}, we exploit the fractional perimeter of a set to give a definition of fractal dimension for its measure theoretic boundary. We calculate the fractal dimension of sets which can be defined in a recursive way and we…
Dimensional correspondences have a long history in critical phenomena. Here, we review the effective dimension approach, which relates the scaling exponents of a critical system in $d$ spatial dimensions with power-law decaying interactions…
Part segmentation and motion estimation are two fundamental problems for articulated object motion analysis. In this paper, we present a method to solve these two problems jointly from a sequence of observed point clouds of a single…
Fractal geometry deals mainly with irregularity and captures the complexity of a structure or phenomenon. In this article, we focus on the approximation of set-valued functions using modern machinery on the subject of fractal geometry. We…
The present article is concerned scattered data approximation for higher dimensional data sets which exhibit an anisotropic behavior in the different dimensions. Tailoring sparse polynomial interpolation to this specific situation, we…
We develop new econometric methods for estimation and inference in high-dimensional panel data models with interactive fixed effects. Our approach can be regarded as a non-trivial extension of the very popular common correlated effects…
Urbanization is a phenomenon of concern for planning and public health: projections are difficult because of policy changes and natural events, and indicators are multiple. There are previous studies of development that used fractals, but…
We study policy evaluation of offline contextual bandits subject to unobserved confounders. Sensitivity analysis methods are commonly used to estimate the policy value under the worst-case confounding over a given uncertainty set. However,…