Related papers: Valeriepieris Circles for Spatial Data Analysis
Particle Image Velocimetry (PIV) estimates velocities through correlations of particle images within interrogation windows, leading to a spatial modulation of the velocity field. Although in principle Particle Tracking Velocimetry (PTV)…
Stereology allows shifting from the 3D distribution of the volumes of Poissonian Voronoi Diagrams to their 2D cross-sections. The basic assumption is that the 3D statistics of the volumes of the voids in the local Universe has a…
The widely applied density peak clustering (DPC) algorithm makes an intuitive cluster formation assumption that cluster centers are often surrounded by data points with lower local density and far away from other data points with higher…
Motivated by the problem of compressing point sets into as few bits as possible while maintaining information about approximate distances between points, we construct random nonlinear maps $\varphi_\ell$ that compress point sets in the…
This letter presents a new approach using the cosmic peculiar velocity field to characterize the morphology and size of large scale structures in the local Universe. The algorithm developed uses the three-dimensional peculiar velocity field…
We show that in a hierarchical clustering model the low-order statistics of the density and the peculiar velocity fields can all be modelled semianalytically for a given cosmology and an initial density perturbation power spectrum $P(k)$.…
Circles of a single size can pack together densely in a hexagonal lattice, but adding in size variety disrupts the order of those packings. We conduct simulations which generate dense random packings of circles with specified size…
Social media outlets such as Twitter constitute valuable data sources for understanding human activities in the virtual world from a geographic perspective. This paper examines spatial distribution of tweets and densities within cities. The…
Standard definitions of the density exhibit large fluctuations when the size of the measurement area is comparable with the size of a pedestrian. An alternative measurement method exists where a personal space, calculated through the…
The projected (PME) and virial mass estimator (VME) are revisited and tested using an N-body equilibrium system. It is found that the PME can overestimate the mass by approx 40% if a cluster is sampled only about its effective radius, Re.…
An uncertain graph $\mathcal{G} = (V, E, p : E \rightarrow (0,1])$ can be viewed as a probability space whose outcomes (referred to as \emph{possible worlds}) are subgraphs of $\mathcal{G}$ where any edge $e\in E$ occurs with probability…
In Computer Vision, edge detection is one of the favored approaches for feature and object detection in images since it provides information about their objects boundaries. Other region-based approaches use probabilistic analysis such as…
Many statistical and machine learning approaches rely on pairwise distances between data points. The choice of distance metric has a fundamental impact on performance of these procedures, raising questions about how to appropriately…
For X a finite subset of the circle and for 0 < r <= 1 fixed, consider the function f_r : X -> X which maps each point to the clockwise furthest element of X within angular distance less than 2 pi r. We study the discrete dynamical system…
Most real-world networks are too large to be measured or studied directly and there is substantial interest in estimating global network properties from smaller sub-samples. One of the most important global properties is the number of…
Clustering is a technique for the analysis of datasets obtained by empirical studies in several disciplines with a major application for biomedical research. Essentially, clustering algorithms are executed by machines aiming at finding…
For recursive circular filtering based on circular statistics, we introduce a general framework for estimation of a circular state based on different circular distributions, specifically the wrapped normal distribution and the von Mises…
Understanding the global organization of complicated and high dimensional data is of primary interest for many branches of applied sciences. It is typically achieved by applying dimensionality reduction techniques mapping the considered…
Spherical data is distributed on the sphere. The data appears in various fields such as meteorology, biology, and natural language processing. However, a method for analysis of spherical data does not develop enough yet. One of the…
Redistricting is the problem of dividing a state into a number $k$ of regions, called districts. Voters in each district elect a representative. The primary criteria are: each district is connected, district populations are equal (or nearly…