10,705 research outputs found
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 in -dimensional Euclidean space
, 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 . 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
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