Related papers: Characteristic Scales, Scaling, and Geospatial Ana…
The spatial distributions of cities fall into two groups: one is the simple distribution with characteristic scale (e.g. exponential distribution), and the other is the complex distribution without characteristic scale (e.g. power-law…
In stochastic geometry there are several instances of threshold phenomena in high dimensions: the behavior of a limit of some expectation changes abruptly when some parameter passes through a critical value. This note continues the…
Geographic space is better understood through the topological relationship of the underlying streets (note: entire streets rather than street segments), which enables us to see scaling or fractal or living structure of far more…
Cascading failures, wherein the failure of one component triggers subsequent failures in complex interconnected systems, pose a significant risk of disruptions and emerge across various domains. Understanding and mitigating the risk of such…
This article investigates the performance of grid computing systems whose interconnections are given by random and scale-free complex network models. Regular networks, which are common in parallel computing architectures, are also used as a…
Degree distributions of graph representations for compact urban patterns are scale-dependent. Therefore, the degree statistics alone does not give us the enough information to reach a qualified conclusion on the structure of urban spatial…
We discuss D-dimensional scalar field interacting with a scale invariant random metric which is either a Gaussian field or a square of a Gaussian field. The metric depends on d-dimensional coordinates (where d is less than D). By a…
We study the problem of similarity detection by sequence alignment with gaps, using a recently established theoretical framework based on the morphology of alignment paths. Alignments of sequences without mutual correlations are found to…
Most research concerning the influence of network structure on phenomena taking place on the network focus on relationships between global statistics of the network structure and characteristic properties of those phenomena, even though…
Time series classification is an important task in its own right, and it is often a precursor to further downstream analytics. To date, virtually all works in the literature have used either shape-based classification using a distance…
We investigate the static and dynamic properties of a celebrated model of social segregation, providing a complete explanation of the mechanisms leading to segregation both in one- and two-dimensional systems. Standard statistical physics…
Sampling technique has become one of the recent research focuses in the graph-related fields. Most of the existing graph sampling algorithms tend to sample the high degree or low degree nodes in the complex networks because of the…
There are three important types of structural properties that remain unchanged under the structural transformation of condensed matter physics and chemistry. They are the properties that remain unchanged under the structural periodic…
A new, coordinate-free (geometric) approach to multivariate statistical analysis. General multivariate linear models and linear hypotheses are defined in geometric form. A method of constructing statistical criteria is defined for linear…
Scale-free percolation is a stochastic model for complex networks. In this spatial random graph model, vertices $x,y\in\mathbb{Z}^d$ are linked by an edge with probability depending on i.i.d.\ vertex weights and the Euclidean distance…
The energy test is a powerful binning-free, multi-dimensional and distribution-free tool that can be applied to compare a measurement to a given prediction (goodness-of-fit) or to check whether two data samples originate from the same…
Real networks can be classified into two categories: fractal networks and non-fractal networks. Here we introduce a unifying model for the two types of networks. Our model network is governed by a parameter $q$. We obtain the topological…
Current astrophysical models of the interstellar medium assume that small scale variation and noise can be modelled as Gaussian random fields or simple transformations thereof, such as lognormal. We use topological methods to investigate…
Conventional statistics begins with a model, and assigns a likelihood of obtaining any particular set of data. The opposite approach, beginning with the data and assigning a likelihood to any particular model, is explored here for the case…
The magnitude of Pearson correlation between two scalar random variables can be visually judged from the two-dimensional scatter plot of an independent and identically distributed sample drawn from the joint distribution of the two…