Related papers: Computing 3 point correlation function randoms cou…
To reduce cost in storing, processing and visualizing a large-scale point cloud, we consider a randomized resampling strategy to select a representative subset of points while preserving application-dependent features. The proposed strategy…
Clustering is a fundamental tool for analyzing large data sets. A rich body of work has been devoted to designing data-stream algorithms for the relevant optimization problems such as $k$-center, $k$-median, and $k$-means. Such algorithms…
Cosmological perturbation theory is a powerful tool to predict the statistics of large-scale structure in the weakly non-linear regime, but even at 1-loop order it results in computationally expensive mode-coupling integrals. Here we…
We introduce space-efficient plane-sweep algorithms for basic planar geometric problems. It is assumed that the input is in a read-only array of $n$ items and that the available workspace is $\Theta(s)$ bits, where $\lg n \leq s \leq n…
We study the set of image tuples arising from fixed cameras observing varying planar 3-dimensional point configurations. We derive a formula for the number of complex critical points of the triangulation problem, which seeks to reconstruct…
The estimation of the number of point-sources in the sky is one the oldest problems in astronomy, yet an easy and efficient method for estimating the uncertainty on these counts is still an open problem. Probabilistic cataloging solves the…
Order statistics play a fundamental role in statistical procedures such as risk estimation, outlier detection, and multiple hypothesis testing as well as in the analyses of mechanism design, queues, load balancing, and various other…
We present a comparative study of the accuracy and precision of correlation function methods and full-field inference in cosmological data analysis. To do so, we examine a Bayesian hierarchical model that predicts log-normal fields and…
The joint cumulative distribution function for order statistics arising from several different populations is given in terms of the distribution function of the populations. The computational cost of the formula in the case of two…
We present a new geometrical method which uses weak gravitational lensing effects in clusters to constrain the cosmological parameters Omega and Lambda. On each background galaxy, a cluster induces a convergence and a shear terms, which…
We present measurements of the spatial clustering statistics in redshift space of various scalar field modified gravity simulations. We utilise the two-point and the three-point correlation functions to quantify the spatial distribution of…
Astronomical instruments make intensity measurements; any precise astronomical experiment ought to involve modeling those measurements. People make catalogues, but because a catalogue requires hard decisions about calibration and detection,…
A recent result of Eden, Levi, and Ron (ECCC 2015) provides a sublinear time algorithm to estimate the number of triangles in a graph. Given an undirected graph $G$, one can query the degree of a vertex, the existence of an edge between…
In this talk, I will show how to determine the biasing factor $b$ from the high-order moments of galaxies. The determination is based on the analytical modeling of primordial peaks and virialized halos and is independent of the currently…
This paper considers the problem of cardinality estimation in data stream applications. We present a statistical analysis of probabilistic counting algorithms, focusing on two techniques that use pseudo-random variates to form…
The fluctuations in the cosmic microwave background radiation may contain deviations from gaussian statistics which would be reflected in a nonzero value of three-point correlation function of $\Delta T$. However, any potential observation…
Third-order lensing statistics contain a wealth of cosmological information that is not captured by second-order statistics. However, the computational effort for estimating such statistics on forthcoming stage IV surveys is prohibitively…
We study the problem of estimating the number of triangles in a graph stream. No streaming algorithm can get sublinear space on all graphs, so methods in this area bound the space in terms of parameters of the input graph such as the…
In this paper we consider the unconstrained minimization problem of a smooth function in ${\mathbb{R}}^n$ in a setting where only function evaluations are possible. We design a novel randomized derivative-free algorithm --- the stochastic…
We present a new method for the mitigation of observational systematic effects in angular galaxy clustering via corrective random galaxy catalogues. Real and synthetic galaxy data, from the Kilo Degree Survey's (KiDS) 4$^{\rm{th}}$ Data…