Related papers: Power Spectrum, Bispectrum, 2- and 3-Point Correla…
Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph. This non-linear transformation of the data is both the key of…
Cosmic inflation, which describes an accelerated expansion of the early Universe, yields the most successful predictions regarding temperature anisotropies in the cosmic microwave background (CMB). Nevertheless, the precise origin of the…
The bispectrum, the three-point function of density fluctuations in Fourier space, is the lowest order statistic that carries information about the spatial coherence of large-scale structures. For Gaussian initial conditions, when the…
We describe various expansion schemes that can be used to study gravitational clustering. Obtained from the equations of motion or their path-integral formulation, they provide several perturbative expansions that are organized in different…
The determination of cluster centers generally depends on the scale that we use to analyze the data to be clustered. Inappropriate scale usually leads to unreasonable cluster centers and thus unreasonable results. In this study, we first…
We compute the two-, three- and four-point correlation functions from the Wilkinson Microwave Anisotropy Probe (WMAP) first-year data, and compare these to a Monte Carlo ensemble of 5000 realizations, based on the best-fit WMAP…
Measurement of the cosmic microwave background (CMB) bispectrum, or three-point correlation function, has now become one of the principle efforts in early-Universe cosmology. Here we show that there is a odd-parity component of the CMB…
Apart from the role the clustering coefficient plays in the definition of the small-world phenomena, it also has great relevance for practical problems involving networked dynamical systems. To study the impact of the clustering coefficient…
A scenario with two subsequent periods of inflationary expansion in the very early universe is examined. The model is based on a potential motivated by symmetries being found in field theory at high energy. For various parameter sets of the…
The two point angular correlation function is an excellent measure of structure in the universe. To extract from it the three dimensional power spectrum, one must invert Limber's Equation. Here we perform this inversion using a Bayesian…
We present a method to analytically compute the quantum corrected two-point correlation function of a scalar field in leading order at each loop in a homogeneous, isotropic and spatially flat spacetime where the expansion rate is time…
Forthcoming galaxy surveys will provide measurements of galaxy clustering with an unprecedented level of precision, that will require comparably good accuracy. Current models for galaxy correlations rely on approximations and idealizations…
Likelihood fitting to two-point clustering statistics made from galaxy surveys usually assumes a multivariate normal distribution for the measurements, with justification based on the central limit theorem given the large number of…
We explore data analysis techniques for signatures from heavy particle production during inflation. Heavy particules can be produced by time dependent masses and couplings, which are ubiquitous in string theory. These localized excitations…
Bipartite Correlation clustering is the problem of generating a set of disjoint bi-cliques on a set of nodes while minimizing the symmetric difference to a bipartite input graph. The number or size of the output clusters is not constrained…
Inflationary cosmology provides a natural mechanism for the generation of primordial perturbations which seed the formation of observed cosmic structure and lead to specific signals of anisotropy in the cosmic microwave background…
Binary mixtures of hard-spheres with different diameters and square-well attraction between different particles are studied by theory and Monte Carlo simulations. In our mesoscopic theory, local fluctuations of the volume fraction of the…
We estimate large-scale curvature perturbations from isocurvature fluctuations in the waterfall field during hybrid inflation, in addition to the usual inflaton field perturbations. The tachyonic instability at the end of inflation leads to…
Cosmological perturbations, originating in the quantum fluctuations of the fields that drive inflation, are observed to be nearly scale invariant at the largest scales. At smaller scales, however, perturbations are not severely constrained…
In three-dimensional critical percolation we study numerically the number of clusters, $N_{\Gamma}$, which intersect a given subset of bonds, $\Gamma$. If $\Gamma$ represents the interface between a subsystem and the environment, then…