Comparative analysis of two discretizations of Ricci curvature for complex networks

We have performed an empirical comparison of two distinct notions of discrete Ricci curvature for graphs or networks, namely, the Forman-Ricci curvature and Ollivier-Ricci curvature. Importantly, these two discretizations of the Ricci curvature were developed based on different properties of the classical smooth notion, and thus, the two notions shed light on different aspects of network structure and behavior. Nevertheless, our extensive computational analysis in a wide range of both model and real-world networks shows that the two discretizations of Ricci curvature are highly correlated in many networks. Moreover, we show that if one considers the augmented Forman-Ricci curvature which also accounts for the two-dimensional simplicial complexes arising in graphs, the observed correlation between the two discretizations is even higher, especially, in real networks. Besides the potential theoretical implications of these observations, the close relationship between the two discretizations has practical implications whereby Forman-Ricci curvature can be employed in place of Ollivier-Ricci curvature for faster computation in larger real-world networks whenever coarse analysis suffices.Comment: Published version. New results added in this version. Supplementary tables can be freely downloaded from the publisher websit

Social media, news media and the stock market

We study the effect on stock volatility and turnover of coverage by traditional news media and social media. We find that coverage by traditional news media predicts decreases in subsequent volatility and turnover, but coverage by social media predicts increases in volatility and turnover. These patterns are inconsistent with rational models where social and news media both convey information. We show that they are consistent with a model of “echo chambers”, where social networks repeat news, but some investors interpret repeated signals as genuinely new information

Hyperuniform long-range correlations are a signature of disordered jammed hard-particle packings

We show that quasi-long-range (QLR) pair correlations that decay asymptotically with scaling $r^{-(d+1)}$ in $d$-dimensional Euclidean space $\mathbb{R}^d$, trademarks of certain quantum systems and cosmological structures, are a universal signature of maximally random jammed (MRJ) hard-particle packings. We introduce a novel hyperuniformity descriptor in MRJ packings by studying local-volume-fraction fluctuations and show that infinite-wavelength fluctuations vanish even for packings with size- and shape-distributions. Special void statistics induce hyperuniformity and QLR pair correlations.Comment: 10 pages, 3 figures; changes to figures and text based on review process; accepted for publication at Phys. Rev. Let

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

Exact Constructions of a Family of Dense Periodic Packings of Tetrahedra

The determination of the densest packings of regular tetrahedra (one of the five Platonic solids) is attracting great attention as evidenced by the rapid pace at which packing records are being broken and the fascinating packing structures that have emerged. Here we provide the most general analytical formulation to date to construct dense periodic packings of tetrahedra with four particles per fundamental cell. This analysis results in six-parameter family of dense tetrahedron packings that includes as special cases recently discovered "dimer" packings of tetrahedra, including the densest known packings with density $\phi= 4000/4671 = 0.856347...$. This study strongly suggests that the latter set of packings are the densest among all packings with a four-particle basis. Whether they are the densest packings of tetrahedra among all packings is an open question, but we offer remarks about this issue. Moreover, we describe a procedure that provides estimates of upper bounds on the maximal density of tetrahedron packings, which could aid in assessing the packing efficiency of candidate dense packings.Comment: It contains 25 pages, 5 figures