Ly-alpha forest: efficient unbiased estimation of second-order properties with missing data

Context. One important step in the statistical analysis of the Ly-alpha forest data is the study of their second order properties. Usually, this is accomplished by means of the two-point correlation function or, alternatively, the K-function. In the computation of these functions it is necessary to take into account the presence of strong metal line complexes and strong Ly-alpha lines that can hidden part of the Ly-alpha forest and represent a non negligible source of bias. Aims. In this work, we show quantitatively what are the effects of the gaps introduced in the spectrum by the strong lines if they are not properly accounted for in the computation of the correlation properties. We propose a geometric method which is able to solve this problem and is computationally more efficient than the Monte Carlo (MC) technique that is typically adopted in Cosmology studies. The method is implemented in two different algorithms. The first one permits to obtain exact results, whereas the second one provides approximated results but is computationally very efficient. The proposed approach can be easily extended to deal with the case of two or more lists of lines that have to be analyzed at the same time. Methods. Numerical experiments are presented that illustrate the consequences to neglect the effects due to the strong lines and the excellent performances of the proposed approach. Results. The proposed method is able to remarkably improve the estimates of both the two-point correlation function and the K-function.Comment: A&A accepted, 12 pages, 15 figure

Directionally Convex Ordering of Random Measures, Shot Noise Fields and Some Applications to Wireless Communications

Directionally convex ($dcx$) ordering is a tool for comparison of dependence structure of random vectors that also takes into account the variability of the marginal distributions. When extended to random fields it concerns comparison of all finite dimensional distributions. Viewing locally finite measures as non-negative fields of measure-values indexed by the bounded Borel subsets of the space, in this paper we formulate and study the $dcx$ ordering of random measures on locally compact spaces. We show that the $dcx$ order is preserved under some of the natural operations considered on random measures and point processes, such as deterministic displacement of points, independent superposition and thinning as well as independent, identically distributed marking. Further operations such as position dependent marking and displacement of points though do not preserve the $dcx$ order on all point processes, are shown to preserve the order on Cox point processes. We also examine the impact of $dcx$ order on the second moment properties, in particular on clustering and on Palm distributions. Comparisons of Ripley's functions, pair correlation functions as well as examples seem to indicate that point processes higher in $dcx$ order cluster more. As the main result, we show that non-negative integral shot-noise fields with respect to $dcx$ ordered random measures inherit this ordering from the measures. Numerous applications of this result are shown, in particular to comparison of various Cox processes and some performance measures of wireless networks, in both of which shot-noise fields appear as key ingredients. We also mention a few pertinent open questions.Comment: Accepted in Advances in Applied Probability. Propn. 3.2 strengthened and as a consequence Cor 6.1,6.2,6.

Branching mechanism of intergranular crack propagation in three dimensions

We investigate the process of slow intergranular crack propagation by the finite element method model, and show that branching is induced by partial arresting of crack front owing to the geometrical randomness of grain boundaries. A possible scenario for branching instability of crack propagation in disordered continuum medium is also discussed.Comment: 4 pages, submitted to Phys.Rev.E; v2:corrected typos v3: final version to be publishe

Discreteness and the transmission of light from distant sources

We model the classical transmission of a massless scalar field from a source to a detector on a background causal set. The predictions do not differ significantly from those of the continuum. Thus, introducing an intrinsic inexactitude to lengths and durations - or more specifically, replacing the Lorentzian manifold with an underlying discrete structure - need not disrupt the usual dynamics of propagation.Comment: 16 pages, 1 figure. Version 2: reference adde

Stochastic inequalities for single-server loss queueing systems

The present paper provides some new stochastic inequalities for the characteristics of the $M/GI/1/n$ and $GI/M/1/n$ loss queueing systems. These stochastic inequalities are based on substantially deepen up- and down-crossings analysis, and they are stronger than the known stochastic inequalities obtained earlier. Specifically, for a class of $GI/M/1/n$ queueing system, two-side stochastic inequalities are obtained.Comment: 17 pages, 11pt To appear in Stochastic Analysis and Application

Discreteness without symmetry breaking: a theorem

This paper concerns sprinklings into Minkowski space (Poisson processes). It proves that there exists no equivariant measurable map from sprinklings to spacetime directions (even locally). Therefore, if a discrete structure is associated to a sprinkling in an intrinsic manner, then the structure will not pick out a preferred frame, locally or globally. This implies that the discreteness of a sprinkled causal set will not give rise to ``Lorentz breaking'' effects like modified dispersion relations. Another consequence is that there is no way to associate a finite-valency graph to a sprinkling consistently with Lorentz invariance.Comment: 7 pages, laTe

Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. II. Anisotropy in particle shape

We extend the results from the first part of this series of two papers by examining hyperuniformity in heterogeneous media composed of impenetrable anisotropic inclusions. Specifically, we consider maximally random jammed packings of hard ellipses and superdisks and show that these systems both possess vanishing infinite-wavelength local-volume-fraction fluctuations and quasi-long-range pair correlations. Our results suggest a strong generalization of a conjecture by Torquato and Stillinger [Phys. Rev. E. 68, 041113 (2003)], namely that all strictly jammed saturated packings of hard particles, including those with size- and shape-distributions, are hyperuniform with signature quasi-long-range correlations. We show that our arguments concerning the constrained distribution of the void space in MRJ packings directly extend to hard ellipse and superdisk packings, thereby providing a direct structural explanation for the appearance of hyperuniformity and quasi-long-range correlations in these systems. Additionally, we examine general heterogeneous media with anisotropic inclusions and show for the first time that one can decorate a periodic point pattern to obtain a hard-particle system that is not hyperuniform with respect to local-volume-fraction fluctuations. This apparent discrepancy can also be rationalized by appealing to the irregular distribution of the void space arising from the anisotropic shapes of the particles. Our work suggests the intriguing possibility that the MRJ states of hard particles share certain universal features independent of the local properties of the packings, including the packing fraction and average contact number per particle.Comment: 29 pages, 9 figure