Monte Carlo methods in PageRank computation: When one iteration is sufficient

PageRank is one of the principle criteria according to which Google ranks Web pages. PageRank can be interpreted as a frequency of visiting a Web page by a random surfer and thus it reflects the popularity of a Web page. Google computes the PageRank using the power iteration method which requires about one week of intensive computations. In the present work we propose and analyze Monte Carlo type methods for the PageRank computation. There are several advantages of the probabilistic Monte Carlo methods over the deterministic power iteration method: Monte Carlo methods provide good estimation of the PageRank for relatively important pages already after one iteration; Monte Carlo methods have natural parallel implementation; and finally, Monte Carlo methods allow to perform continuous update of the PageRank as the structure of the Web changes

The Effect of Neutral Atoms on Capillary Discharge Z-pinch

We study the effect of neutral atoms on the dynamics of a capillary discharge Z-pinch, in a regime for which a large soft-x-ray amplification has been demonstrated. We extended the commonly used one-fluid magneto-hydrodynamics (MHD) model by separating out the neutral atoms as a second fluid. Numerical calculations using this extended model yield new predictions for the dynamics of the pinch collapse, and better agreement with known measured data.Comment: 4 pages, 4 postscript figures, to be published in Phys. Rev. Let

Shockwave based nonlinear optical manipulation in densely scattering opaque suspensions

Optical manipulation of particulate-loaded, highly scattering (opaque) suspensions is considered impossible. Here we demonstrate theoretically and experimentally optical manipulation of the local properties of such opaque suspensions. We show that the optical forces exerted by multiply-scattered light give rise to dense shock fronts of particle concentration, propagating deep inside the opaque suspensions, where the optical field is completely diffuse. We exploit these waves to demonstrate a plethora of optofluidic manipulations, ranging from optical transport and concentration of large populations of nanoparticles, to light-induced \u27writing\u27 of concentrated spots in the suspensions and light-induced phase-transition from suspension to gel in localized volumes inside the fluids

Light-induced self-synchronizing flow patterns

In this paper, we present the observation of light-induced self-synchronizing flow patterns in a light-fluid system. A light beam induces local flow patterns in a fluid, which oscillate periodically or chaotically in time. The oscillations within different regions of the fluid interact with each other through heat-and surface-tension-induced fluid waves, and they become synchronized. We demonstrate optical control over the state of synchronization and over the temporal correlation between different parts of the flow field. Finally, we provide a model to elucidate these results and we suggest further ideas on light controlling flow and vice versa

Scaling of Self-Avoiding Walks in High Dimensions

We examine self-avoiding walks in dimensions 4 to 8 using high-precision Monte-Carlo simulations up to length N=16384, providing the first such results in dimensions $d > 4$ on which we concentrate our analysis. We analyse the scaling behaviour of the partition function and the statistics of nearest-neighbour contacts, as well as the average geometric size of the walks, and compare our results to $1/d$-expansions and to excellent rigorous bounds that exist. In particular, we obtain precise values for the connective constants, $\mu_5=8.838544(3)$, $\mu_6=10.878094(4)$, $\mu_7=12.902817(3)$, $\mu_8=14.919257(2)$ and give a revised estimate of $\mu_4=6.774043(5)$. All of these are by at least one order of magnitude more accurate than those previously given (from other approaches in $d>4$ and all approaches in $d=4$). Our results are consistent with most theoretical predictions, though in $d=5$ we find clear evidence of anomalous $N^{-1/2}$-corrections for the scaling of the geometric size of the walks, which we understand as a non-analytic correction to scaling of the general form $N^{(4-d)/2}$ (not present in pure Gaussian random walks).Comment: 14 pages, 2 figure

Prognostic role of serum cytokeratin 19 fragments in advanced non-small-cell lung cancer: association of marker changes after two chemotherapy cycles with different measures of clinical response and survival

Prognostic implication of serum cytokeratin 19 fragments (CYFRA 21-1) was explored in 60 advanced NSCLC patients, whereas in 45 patients assessable for serological response a ⩾35% CYFRA 21-1 decline after two chemotherapy cycles was strongly associated with non-progression (NP), defined as a sum of objective response (OR)+stable disease (P<0.0001) and survival (P=0.0002). Association of OR with survival was not significant. In multivariate survival analysis, ⩾35% marker decline and radiological NP status were found as major determinants of prolonged survival with RR: 0.37 (P=0.01) and 0.63 (P=0.01), respectively. In advanced NSCLC patients, NP reflects therapeutic efficacy better than traditional OR. CYFRA 21-1 ⩾35% decline seems to be a reliable surrogate marker of treatment efficacy in terms of survival

New Lower Bounds on the Self-Avoiding-Walk Connective Constant

We give an elementary new method for obtaining rigorous lower bounds on the connective constant for self-avoiding walks on the hypercubic lattice $Z^d$. The method is based on loop erasure and restoration, and does not require exact enumeration data. Our bounds are best for high $d$, and in fact agree with the first four terms of the $1/d$ expansion for the connective constant. The bounds are the best to date for dimensions $d \geq 3$, but do not produce good results in two dimensions. For $d=3,4,5,6$, respectively, our lower bound is within 2.4\%, 0.43\%, 0.12\%, 0.044\% of the value estimated by series extrapolation.Comment: 35 pages, 388480 bytes Postscript, NYU-TH-93/02/0

Hyperfine structure of Li and Be^+

A large-scale relativistic configuration-interaction (CI) calculation is performed for the magnetic-dipole and the electric-quadrupole hyperfine structure splitting in ^{7,6}Li and ^9Be^+. Numerical results for the 2^2S, 3^2S, 2^2P_{1/2}, and 2^2P_{3/2} states are reported. The CI calculation based on the Dirac-Coulomb-Breit Hamiltonian is supplemented with separate treatments of the QED, nuclear-magnetization distribution, recoil, and negative-continuum effects.Comment: 17 pages, 4 tables. The discussion of the induced quadrupole moment is changed in the modified version of the pape