相关论文: Describing urban evolution with the fractal parame…

We present a theoretical framework for understanding the wavefunctions and spectrum of an extensively studied paradigm for quasiperiodic systems, namely the Fibonacci chain. Our analytical results, which are obtained in the limit of strong…

Pedestrian attribute recognition has been an emerging research topic in the area of video surveillance. To predict the existence of a particular attribute, it is demanded to localize the regions related to the attribute. However, in this…

Fractals are defined as geometric shapes that exhibit symmetry of scale. This simply implies that fractal is a shape that it would still look the same even if somebody could zoom in on one of its parts an infinite number of times. This…

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…

We develop an effective model to describe the dynamics of a system of particle moving in circular configurations around a central mass, by considering the continuum limit of the angular distribution, to obtain the stable configurations for…

Fractals are geometric shapes that can display complex and self-similar patterns found in nature (e.g., clouds and plants). Recent works in visual recognition have leveraged this property to create random fractal images for model…

The image fractal analysis is actively used in all science branches. In particular in materials science the fractal analysis is applied to study microstructure of deformed metals because its structure can be interpreted as the fractal…

Given the importance of urban sustainability and resilience to the future of our planet, there is a need to better understand the interconnectedness between the social, economic, environmental, and governance outcomes that underline these…

If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze…

We define several new models for how to define anomalous regions among enormous sets of trajectories. These are based on spatial scan statistics, and identify a geometric region which captures a subset of trajectories which are…

This paper is an exposition, with some new applications, of our results on the growth of entropy of convolutions. We explain the main result on $\mathbb{R}$, and derive, via a linearization argument, an analogous result for the action of…

Selfsimilar space-time fractal fluctuations are generic to dynamical systems in nature such as atmospheric flows, heartbeat patterns, population dynamics, etc. The physics of the long-range correlations intrinsic to fractal fluctuations is…

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…

City size distributions are known to be well approximated by power laws across a wide range of countries. But such distributions are also meaningful at other spatial scales, such as within certain regions of a country. Using data from…

The science of fractography revolves around the correlation between topographic characteristics of the fracture surface and the mechanisms and external conditions leading to their creation. While being a topic of investigation for…

Hierarchies can be modeled by a set of exponential functions, from which we can derive a set of power laws indicative of scaling. The solution to a scaling relation equation is always a power law. The scaling laws are followed by many…

A city (or an urban cluster) is not an isolated spatial unit, but a combination of areas with closely linked socio-economic activities. However, so far, we lack a consistent and quantitative approach to define multi-level urban clusters…

We study the local dimension of the convolution of two measures. We give conditions for bounding the local dimension of the convolution on the basis of the local dimension of one of them. Moreover, we give a formula for the local dimension…

Allometry or the quantitative study of the relationship of body size to living organism physiology is an important area of biophysical scaling research. The West-Brown-Enquist (WBE) model of fractal branching in a vascular network explains…

Many fluctuating systems consist of macroscopic structures in addition to noisy signals. Thus, for this class of fluctuating systems, the scaling behaviors are very complicated. Such phenomena are quite commonly observed in Nature, ranging…