Related papers: Level spacing statistics and spectral correlations…
It is well-known that in a Bell experiment, the observed correlation between measurement outcomes -- as predicted by quantum theory -- can be stronger than that allowed by local causality, yet not fully constrained by the principle of…
Context. Galaxy clusters are the last and largest objects to form in the standard hierarchical structure formation scenario through merging of smaller systems. The substructure frequency in the past and present epoch provides excellent…
We analyse shapes of overdense regions (clusters and superclusters) in controlled N-body simulations of gravitational clustering with power law initial spectra P(k) \propto k^n, n = -3, -2, -1, 0. At values of the density just above the…
Networks or graphs can easily represent a diverse set of data sources that are characterized by interacting units or actors. Social networks, representing people who communicate with each other, are one example. Communities or clusters of…
We have used integral two-point spatial correlation function and its second derivative to analyze the distribution of quasars in three very deep surveys published in the literature. Statistically significant ($\sim 2-3\sigma $) correlations…
We revisit the theoretical performances of Spectral Clustering, a classical algorithm for graph partitioning that relies on the eigenvectors of a matrix representation of the graph. Informally, we show that Spectral Clustering works well as…
We measure the evolution of clustering for galaxies with different spectral types from 6495 galaxies with 17.5<=I_AB<=24 and measured spectroscopic redshift in the first epoch VIMOS-VLT Deep Survey. We classify our sample into 4 classes,…
By extending the Berry--Robnik approach for the nearly integrable quantum systems,\cite{[1]} we propose one possible scenario of the energy level spacing distribution that deviates from the Berry--Robnik distribution. The result described…
Consistency is a key property of all statistical procedures analyzing randomly sampled data. Surprisingly, despite decades of work, little is known about consistency of most clustering algorithms. In this paper we investigate consistency of…
Near-gate plasmons are a new type of plasma oscillations emerging in homogeneous two-dimensional electron systems where a gate provides partial screening of electron-electron interaction. Here we develop a theory of the near-gate plasmons…
We discuss some of the basic implications of recent results on galaxy correlations published by the SDSS collaboration. In particular we focus on the evidence which has been recently presented for the scale and nature of the transition to…
The characterization of the Galactic foregrounds has been shown to be the main obstacle in the challenging quest to detect primordial B-modes in the polarized microwave sky. We make use of the Planck-HFI 2015 data release at high…
We report on the construction of a granular network of particles to study the formation, evolution and statistical properties of clusters of particles developing at the vicinity of a liquid-solid-like phase transition within a vertically…
The counterintuitive fact that wave chaos appears in the bending spectrum of free rectangular thin plates is presented. After extensive numerical simulations, varying the ratio between the length of its sides, it is shown that (i) frequency…
This paper is to study a signal-plus-noise model in high dimensional settings when the dimension and the sample size are comparable. Specifically, we assume that the noise has a general covariance matrix that allows for heteroskedasticity,…
Introduced in the early days of random matrix theory, the autocovariances $\delta I^j_k={\rm cov}(s_j, s_{j+k})$ of level spacings $\{s_j\}$ accommodate a detailed information on correlations between individual eigenlevels. It was first…
We derive the exchange-correlation potential corresponding to the nonlocal van der Waals density functional [M. Dion, H. Rydberg, E. Schroder, D. C. Langreth, and B. I. Lundqvist, Phys. Rev. Lett. 92, 246401 (2004)]. We use this potential…
Recently, the scaling limit of cluster sizes for critical inhomogeneous random graphs of rank-1 type having finite variance but infinite third moment degrees was obtained (see previous work by Bhamidi, van der Hofstad and van Leeuwaarden).…
This paper reviews the measurements of galaxy correlations at high redshifts, and discusses how these may be understood in models of hierarchical gravitational collapse. The clustering of galaxies at redshift one is much weaker than at…
We carry out a numerical study of fluctuations in the spectrum of regular graphs. Our experiments indicate that the level spacing distribution of a generic k-regular graph approaches that of the Gaussian Orthogonal Ensemble of random matrix…