Why Do Cascade Sizes Follow a Power-Law?

We introduce random directed acyclic graph and use it to model the information diffusion network. Subsequently, we analyze the cascade generation model (CGM) introduced by Leskovec et al. [19]. Until now only empirical studies of this model were done. In this paper, we present the first theoretical proof that the sizes of cascades generated by the CGM follow the power-law distribution, which is consistent with multiple empirical analysis of the large social networks. We compared the assumptions of our model with the Twitter social network and tested the goodness of approximation.Comment: 8 pages, 7 figures, accepted to WWW 201

Gauge fixing and equivariant cohomology

The supersymmetric model developed by Witten to study the equivariant cohomology of a manifold with an isometric circle action is derived from the BRST quantization of a simple classical model. The gauge-fixing process is carefully analysed, and demonstrates that different choices of gauge-fixing fermion can lead to different quantum theories.Comment: 18 pages LaTe

Vacuum-UV negative photoion spectroscopy of CH3F, CH3Cl and CH3Br

Using tunable vacuum-UV radiation from a synchrotron, negative ions are detected by quadrupolar mass spectrometry following photoexcitation of three gaseous halogenated methanes CH$_3$X (X = F,Cl,Br). The anions X$^-$, H$^-$, CX$^-$, CHX$^-$ and CH$_2$X$^-$ are observed, and their ion yields recorded in the range 8-35 eV. The anions show a linear dependence of signal with pressure, showing that they arise from unimolecular ion-pair dissociation, generically described as AB + h$v$ $\rightarrow$ A$^-$ + B$^+$ (+ neutrals). Absolute cross sections for ion-pair formation are obtained by calibrating the signal intensities with those of F$^-$ from both SF$_6$ and CF$_4$. The cross sections for formation of X$^-$ + CH$_3$$^+$ are much greater than for formation of CH$_2$X$^-$ + H$^+$. In common with many quadrupoles, the spectra of $m$/$z$ 1 (H$^-$) anions show contributions from all anions, and only for CH$_3$Br is it possible to perform the necessary subtraction to obtain the true H$^-$ spectrum. The anion cross sections are normalised to vacuum-UV absorption cross sections to obtain quantum yields for their production. The appearance energies of X$^-$ and CH$_2$X$^-$ are used to calculate upper limits to 298 K bond dissociation energies for D$^o$ (H$_3$C-X) and D$^o$ (XH$_2$C-H) which are consistent with literature values. The spectra suggest that most of the anions are formed indirectly by crossing of Rydberg states of the parent molecule onto an ion-pair continuum. The one exception is the lowest-energy peak of F$^-$ from CH$_3$F at 13.4 eV, where its width and lack of structure suggest it may correspond to a direct ion-pair transition

Old and New Fields on Super Riemann Surfaces

The ``new fields" or ``superconformal functions" on $N=1$ super Riemann surfaces introduced recently by Rogers and Langer are shown to coincide with the Abelian differentials (plus constants), viewed as a subset of the functions on the associated $N=2$ super Riemann surface. We confirm that, as originally defined, they do not form a super vector space.Comment: 9 pages, LaTex. Published version: minor changes for clarity, two new reference

Filling the Void: A Low Cost, High-Yield Method to Addressing Incidental Findings in Trauma Patients

In this study we: Report the incidence of incidental findings in a suburban trauma center treating primarily blunt and elderly trauma Propose simple solutions to increase the rate of disclosure to patientshttps://jdc.jefferson.edu/patientsafetyposters/1070/thumbnail.jp

CORSS: Cylinder Optimization of Rings, Skin, and Stringers

Launch vehicle designs typically make extensive use of cylindrical skin stringer construction. Structural analysis methods are well developed for preliminary design of this type of construction. This report describes an automated, iterative method to obtain a minimum weight preliminary design. Structural optimization has been researched extensively, and various programs have been written for this purpose. Their complexity and ease of use depends on their generality, the failure modes considered, the methodology used, and the rigor of the analysis performed. This computer program employs closed-form solutions from a variety of well-known structural analysis references and joins them with a commercially available numerical optimizer called the 'Design Optimization Tool' (DOT). Any ring and stringer stiffened shell structure of isotropic materials that has beam type loading can be analyzed. Plasticity effects are not included. It performs a more limited analysis than programs such as PANDA, but it provides an easy and useful preliminary design tool for a large class of structures. This report briefly describes the optimization theory, outlines the development and use of the program, and describes the analysis techniques that are used. Examples of program input and output, as well as the listing of the analysis routines, are included

Coherent Vector Meson Photo-Production from Deuterium at Intermediate Energies

We analyze the cross section for vector meson photo-production off a deuteron for the intermediate range of photon energies starting at a few GeVs above the threshold and higher. We reproduce the steps in the derivation of the conventional non-relativistic Glauber expression based on an effective diagrammatic method while making corrections for Fermi motion and intermediate energy kinematic effects. We show that, for intermediate energy vector meson production, the usual Glauber factorization breaks down and we derive corrections to the usual Glauber method to linear order in longitudinal nucleon momentum. The purpose of our analysis is to establish methods for probing interesting physics in the production mechanism for phi-mesons and heavier vector mesons. We demonstrate how neglecting the breakdown of Glauber factorization can lead to errors in measurements of basic cross sections extracted from nuclear data.Comment: 41 pages, 13 figures, figure 9 is compressed from previous version, typos fixe

Fast and Accurate Coarsening Simulation with an Unconditionally Stable Time Step

We present Cahn-Hilliard and Allen-Cahn numerical integration algorithms that are unconditionally stable and so provide significantly faster accuracy-controlled simulation. Our stability analysis is based on Eyre's theorem and unconditional von Neumann stability analysis, both of which we present. Numerical tests confirm the accuracy of the von Neumann approach, which is straightforward and should be widely applicable in phase-field modeling. We show that accuracy can be controlled with an unbounded time step Delta-t that grows with time t as Delta-t ~ t^alpha. We develop a classification scheme for the step exponent alpha and demonstrate that a class of simple linear algorithms gives alpha=1/3. For this class the speed up relative to a fixed time step grows with the linear size of the system as N/log N, and we estimate conservatively that an 8192^2 lattice can be integrated 300 times faster than with the Euler method.Comment: 14 pages, 6 figure

Global data for ecology and epidemiology: a novel algorithm for temporal Fourier processing MODIS data

Background. Remotely-sensed environmental data from earth-orbiting satellites are increasingly used to model the distribution and abundance of both plant and animal species, especially those of economic or conservation importance. Time series of data from the MODerate-resolution Imaging Spectroradiometer (MODIS) sensors on-board NASA's Terra and Aqua satellites offer the potential to capture environmental thermal and vegetation seasonality, through temporal Fourier analysis, more accurately than was previously possible using the NOAA Advanced Very High Resolution Radiometer (AVHRR) sensor data. MODIS data are composited over 8- or 16-day time intervals that pose unique problems for temporal Fourier analysis. Applying standard techniques to MODIS data can introduce errors of up to 30% in the estimation of the amplitudes and phases of the Fourier harmonics. Methodology/Principal Findings. We present a novel spline-based algorithm that overcomes the processing problems of composited MODIS data. The algorithm is tested on artificial data generated using randomly selected values of both amplitudes and phases, and provides an accurate estimate of the input variables under all conditions. The algorithm was then applied to produce layers that capture the seasonality in MODIS data for the period from 2001 to 2005. Conclusions/Significance. Global temporal Fourier processed images of 1 km MODIS data for Middle Infrared Reflectance, day- and night-time Land Surface Temperature (LST), Normalised Difference Vegetation Index (NDVI), and Enhanced Vegetation Index (EVI) are presented for ecological and epidemiological applications. The finer spatial and temporal resolution, combined with the greater geolocational and spectral accuracy of the MODIS instruments, compared with previous multi-temporal data sets, mean that these data may be used with greater confidence in species' distribution modelling