Growing complex network of citations of scientific papers -- measurements and modeling

To quantify the mechanism of a complex network growth we focus on the network of citations of scientific papers and use a combination of the theoretical and experimental tools to uncover microscopic details of this network growth. Namely, we develop a stochastic model of citation dynamics based on copying/redirection/triadic closure mechanism. In a complementary and coherent way, the model accounts both for statistics of references of scientific papers and for their citation dynamics. Originating in empirical measurements, the model is cast in such a way that it can be verified quantitatively in every aspect. Such verification is performed by measuring citation dynamics of Physics papers. The measurements revealed nonlinear citation dynamics, the nonlinearity being intricately related to network topology. The nonlinearity has far-reaching consequences including non-stationary citation distributions, diverging citation trajectory of similar papers, runaways or "immortal papers" with infinite citation lifetime etc. Thus, our most important finding is nonlinearity in complex network growth. In a more specific context, our results can be a basis for quantitative probabilistic prediction of citation dynamics of individual papers and of the journal impact factor.Comment: 26 pages, 24 figure

Spontaneous Scaling Emergence in Generic Stochastic Systems

We extend a generic class of systems which have previously been shown to spontaneously develop scaling (power law) distributions of their elementary degrees of freedom. While the previous systems were linear and exploded exponentially for certain parameter ranges, the new systems fulfill nonlinear time evolution equations similar to the ones encountered in Spontaneous Symmetry Breaking (SSB) dynamics and evolve spontaneously towards "fixed trajectories" indexed by the average value of their degrees of freedom (which corresponds to the SSB order parameter). The "fixed trajectories" dynamics evolves on the edge between explosion and collapse/extinction. The systems present power laws with exponents which in a wide range ($\alpha < -2.$) are universally determined by the ratio between the minimal and the average values of the degrees of freedom. The time fluctuations are governed by Levy distributions of corresponding power. For exponents $\alpha > -2$ there is no "thermodynamic limit" and the fluctuations are dominated by a few, largest degrees of freedom which leads to macroscopic fluctuations, chaos and bursts/intermitency.Comment: latex, 11 page

Unresolved issues in monetary policy

Solomon held the office of president during a period of notably successful anti-inflationary monetary policy as well as rapid financial innovation and deregulation. In this speech, he discusses monetary strategy — in particular the targeting of monetary aggregates, interest rates, and nominal GNP — in light of trends in inflation and the uncertainties introduced by changing financial markets.Monetary policy ; Money supply ; Federal Reserve System - History ; Gross national product

Efficient collinear third-harmonic generation in a single two-dimensional nonlinear photonic crystal

We propose novel multi-phase-matched process that starts with generation of a pair of symmetric second-harmonic waves. Each of them interacts again with the fundamental wave to produce two constructively interfering third harmonic waves collinear to the fundamental input wave.Comment: Summary of presentation at the IQEC/LAT-2002 conferenc

Models for discriminating image blur from loss of contrast

Observers can discriminate between blurry and low-contrast images (Morgan, 2017). Wang and Simoncelli (2004) demonstrated that a code for blur is inherent to the phase relationships between localized pattern detectors of different scale. To test whether human observers actually use local phase coherence when discriminating between image blur and loss of contrast, we compared phase-scrambled chessboards with unscrambled chessboards. Although both stimuli had identical amplitude spectra, local phase coherence was disrupted by phase-scrambling. Human observers were required to concurrently detect and identify (as contrast or blur) image manipulations in the 2x2 forced-choice paradigm (Nachmias & Weber, 1975; Watson & Robson, 1981) traditionally considered to be a litmus test for "labelled lines" (i.e. detection mechanisms that can be distinguished on the basis of their preferred stimuli). Phase scrambling reduced some observers’ ability to discriminate between blur and a reduction in contrast. However, none of our observers produced data consistent with Watson & Robson’s most stringent test for labelled lines, regardless whether phases were scrambled or not. Models of performance fit significantly better when either a) the blur detector also responded to contrast modulations, b) the contrast detector also responded to blur modulations, or c) noise in the two detectors was anticorrelate

Geodesics of positive Lagrangians in Milnor fibers

The space of positive Lagrangians in an almost Calabi-Yau manifold is an open set in the space of all Lagrangian submanifolds. A Hamiltonian isotopy class of positive Lagrangians admits a natural Riemannian metric $\Upsilon$, which gives rise to a notion of geodesics. We study geodesics of positive $O_n(\mathbb{R})$ invariant Lagrangian spheres in $n$-dimensional $A_m$ Milnor fibers. We show the existence and uniqueness of smooth solutions to the initial value problem and the boundary value problem. In particular, we obtain examples of smooth geodesics of positive Lagrangians in arbitrary dimension. As an application, we show that the Riemannian metric $\Upsilon$ induces a metric space structure on the space of positive $O_n(\mathbb{R})$ invariant Lagrangian spheres in the above mentioned Milnor fibers.Comment: 38 pages; added references and background, improved exposition, fixed minor error