Power-law distributions in empirical data

Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution -- the part of the distribution representing large but rare events -- and by the difficulty of identifying the range over which power-law behavior holds. Commonly used methods for analyzing power-law data, such as least-squares fitting, can produce substantially inaccurate estimates of parameters for power-law distributions, and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all. Here we present a principled statistical framework for discerning and quantifying power-law behavior in empirical data. Our approach combines maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov-Smirnov statistic and likelihood ratios. We evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches. We also apply the proposed methods to twenty-four real-world data sets from a range of different disciplines, each of which has been conjectured to follow a power-law distribution. In some cases we find these conjectures to be consistent with the data while in others the power law is ruled out.Comment: 43 pages, 11 figures, 7 tables, 4 appendices; code available at http://www.santafe.edu/~aaronc/powerlaws

A Novel Rare Sugar Inhibitor of Murine Herpes Simplex Keratitis.

Purpose To determine the therapeutic efficacy of a novel rare sugar, L-psicose, for the treatment of HSV-1 induced herpetic stromal keratitis (HSK) in a mouse eye model. Methods One rare sugar L-psicose was assayed for HSV-1 inhibition of in vitro virus adsorption. The IC50 and IC90 values of L-psicose were determined using plaque reduction assay (PRA) in CV-1 cell. Female Balb/c mice were corneally infected with HSV-1, strain KOS-GFP; A topical eye drop treatment of L-psicose was started 24 h after infection and continued four times daily for ten consecutive days. The severity of HSK was monitored by slit lamp examination in a masked fashion and Infectious HSV-1 shedding was determined by PRA. Results L-psicose was found to have anti-viral activity in vitro at an IC50 dose of 99.5 mM and an IC90 dose of 160 mM. Topical eye drop treatment with 200 mM L-psicose in PBS solution significantly reduced the severity of HSK compared to the mock treatment group. The in vivo mouse ocular model results of L-psicose therapy correlated with accelerated clearance of virus from eye swabs. Conclusion The results suggest that topical treatment with rare sugar L-psicose has efficacy against HSK through inhibition of HSV-1

Phi-Meson Production at RHIC, Strong Color Fields and Intrinsic Transverse Momenta

We investigate the effects of strong color fields and of the associated enhanced intrinsic transverse momenta on the phi-meson production in ultrarelativistic heavy ion collisions at RHIC. The observed consequences include a change of the spectral slopes, varying particle ratios, and also modified mean transverse momenta. In particular, the composition of the production processes of phi mesons, that is, direct production vs. coalescence-like production, depends strongly on the strength of the color fields and intrinsic transverse momenta and thus represents a sensitive probe for their measurement.Comment: 4 pages, 3 figure

Mid-Rapidity Direct-Photon Production in p+p Collisions at sqrt(s) = 200 GeV

A measurement of direct photons in p+p collisions at sqrt(s)=200 GeV is presented. A photon excess above background from pi^0 --> gamma+gamma, eta --> gamma+gamma, and other decays is observed in the transverse momentum range 5.5 < p_T < 7 GeV/c. The result is compared to a next-to-leading-order perturbative QCD calculation. Within errors, good agreement is found between the QCD calculation and the measured result.Comment: 330 authors, 7 pages text, RevTeX, 2 figures, 2 tables. Submitted to Physical Review D. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.htm

Centrality dependence of charged hadron production in deuteron+gold and nucleon+gold collisions at sqrt(s_NN)=200 GeV

We present transverse momentum (p_T) spectra of charged hadrons measured in deuteron-gold and nucleon-gold collisions at \sqrts = 200 GeV for four centrality classes. Nucleon-gold collisions were selected by tagging events in which a spectator nucleon was observed in one of two forward rapidity detectors. The spectra and yields were investigated as a function of the number of binary nucleon-nucleon collisions, \nu, suffered by deuteron nucleons. A comparison of charged particle yields to those in p+p collisions show that the yield per nucleon-nucleon collision saturates with \nu for high momentum particles. We also present the charged hadron to neutral pion ratios as a function of p_T.Comment: 330 authors, 15 pages text, 16 figures, 3 tables. Submitted to Phys. Rev. Lett. v2 has minor changes to reflect revisions during review process. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.htm

Charged hadron multiplicity fluctuations in Au+Au and Cu+Cu collisions from sqrt(s_NN) = 22.5 to 200 GeV

A comprehensive survey of event-by-event fluctuations of charged hadron multiplicity in relativistic heavy ions is presented. The survey covers Au+Au collisions at sqrt(s_NN) = 62.4 and 200 GeV, and Cu+Cu collisions sqrt(s_NN) = 22.5, 62.4, and 200 GeV. Fluctuations are measured as a function of collision centrality, transverse momentum range, and charge sign. After correcting for non-dynamical fluctuations due to fluctuations in the collision geometry within a centrality bin, the remaining dynamical fluctuations expressed as the variance normalized by the mean tend to decrease with increasing centrality. The dynamical fluctuations are consistent with or below the expectation from a superposition of participant nucleon-nucleon collisions based upon p+p data, indicating that this dataset does not exhibit evidence of critical behavior in terms of the compressibility of the system. An analysis of Negative Binomial Distribution fits to the multiplicity distributions demonstrates that the heavy ion data exhibit weak clustering properties.Comment: 464 authors from 60 institutions, 17 pages, 12 figures, 1 table. Submitted to Physical Review C. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.htm

Azimuthal Angle Correlations for Rapidity Separated Hadron Pairs in d+Au Collisions at sqrt(s_NN) = 200 GeV

We report on two-particle azimuthal angle correlations between charged hadrons at forward/backward (deuteron/gold going direction) rapidity and charged hadrons at mid-rapidity in deuteron-gold (d+Au) and proton-proton (p+p) collisions at sqrt(s_NN) = 200 GeV. Jet structures are observed in the correlations which we quantify in terms of the conditional yield and angular width of away side partners. The kinematic region studied here samples partons in the gold nucleus carrying nucleon momentum fraction x~0.1 to x~0.01. Within this range, we find no x dependence of the jet structure in d+Au collisions.Comment: 330 authors, 6 pages text, 4 figures, no tables. Submitted to Phys. Rev. Lett. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.htm

Transverse-energy distributions at midrapidity in pp++pp, dd++Au, and Au++Au collisions at sNN=62.4\sqrt{s_{_{NN}}}=62.4--200~GeV and implications for particle-production models

Measurements of the midrapidity transverse energy distribution, d\Et/d\eta, are presented for $p$$+$$p$, $d$$+$Au, and Au$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV and additionally for Au$+$Au collisions at $\sqrt{s_{_{NN}}}=62.4$ and 130 GeV. The d\Et/d\eta distributions are first compared with the number of nucleon participants $N_{\rm part}$, number of binary collisions $N_{\rm coll}$, and number of constituent-quark participants $N_{qp}$ calculated from a Glauber model based on the nuclear geometry. For Au$+$Au, \mean{d\Et/d\eta}/N_{\rm part} increases with $N_{\rm part}$, while \mean{d\Et/d\eta}/N_{qp} is approximately constant for all three energies. This indicates that the two component ansatz, $dE_{T}/d\eta \propto (1-x) N_{\rm part}/2 + x N_{\rm coll}$, which has been used to represent $E_T$ distributions, is simply a proxy for $N_{qp}$, and that the $N_{\rm coll}$ term does not represent a hard-scattering component in $E_T$ distributions. The $dE_{T}/d\eta$ distributions of Au$+$Au and $d$$+$Au are then calculated from the measured $p$$+$$p$ $E_T$ distribution using two models that both reproduce the Au$+$Au data. However, while the number-of-constituent-quark-participant model agrees well with the $d$$+$Au data, the additive-quark model does not.Comment: 391 authors, 24 pages, 19 figures, and 15 Tables. Submitted to Phys. Rev. C. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are publicly available at http://www.phenix.bnl.gov/papers.htm

Deuteron and antideuteron production in Au+Au collisions at sqrt(s_NN)=200 GeV

The production of deuterons and antideuterons in the transverse momentum range 1.1 < p_T < 4.3 GeV/c at mid-rapidity in Au + Au collisions at sqrt(s_NN)=200 GeV has been studied by the PHENIX experiment at RHIC. A coalescence analysis comparing the deuteron and antideuteron spectra with those of protons and antiprotons, has been performed. The coalescence probability is equal for both deuterons and antideuterons and increases as a function of p_T, which is consistent with an expanding collision zone. Comparing (anti)proton yields p_bar/p = 0.73 +/- 0.01, with (anti)deuteron yields: d_bar/d = 0.47 +/- 0.03, we estimate that n_bar/n = 0.64 +/- 0.04.Comment: 326 authors, 6 pages text, 5 figures, 1 Table. Submitted to PRL. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.htm