Sketch-based Influence Maximization and Computation: Scaling up with Guarantees

Propagation of contagion through networks is a fundamental process. It is used to model the spread of information, influence, or a viral infection. Diffusion patterns can be specified by a probabilistic model, such as Independent Cascade (IC), or captured by a set of representative traces. Basic computational problems in the study of diffusion are influence queries (determining the potency of a specified seed set of nodes) and Influence Maximization (identifying the most influential seed set of a given size). Answering each influence query involves many edge traversals, and does not scale when there are many queries on very large graphs. The gold standard for Influence Maximization is the greedy algorithm, which iteratively adds to the seed set a node maximizing the marginal gain in influence. Greedy has a guaranteed approximation ratio of at least (1-1/e) and actually produces a sequence of nodes, with each prefix having approximation guarantee with respect to the same-size optimum. Since Greedy does not scale well beyond a few million edges, for larger inputs one must currently use either heuristics or alternative algorithms designed for a pre-specified small seed set size. We develop a novel sketch-based design for influence computation. Our greedy Sketch-based Influence Maximization (SKIM) algorithm scales to graphs with billions of edges, with one to two orders of magnitude speedup over the best greedy methods. It still has a guaranteed approximation ratio, and in practice its quality nearly matches that of exact greedy. We also present influence oracles, which use linear-time preprocessing to generate a small sketch for each node, allowing the influence of any seed set to be quickly answered from the sketches of its nodes.Comment: 10 pages, 5 figures. Appeared at the 23rd Conference on Information and Knowledge Management (CIKM 2014) in Shanghai, Chin

Exact Computation of Influence Spread by Binary Decision Diagrams

Evaluating influence spread in social networks is a fundamental procedure to estimate the word-of-mouth effect in viral marketing. There are enormous studies about this topic; however, under the standard stochastic cascade models, the exact computation of influence spread is known to be #P-hard. Thus, the existing studies have used Monte-Carlo simulation-based approximations to avoid exact computation. We propose the first algorithm to compute influence spread exactly under the independent cascade model. The algorithm first constructs binary decision diagrams (BDDs) for all possible realizations of influence spread, then computes influence spread by dynamic programming on the constructed BDDs. To construct the BDDs efficiently, we designed a new frontier-based search-type procedure. The constructed BDDs can also be used to solve other influence-spread related problems, such as random sampling without rejection, conditional influence spread evaluation, dynamic probability update, and gradient computation for probability optimization problems. We conducted computational experiments to evaluate the proposed algorithm. The algorithm successfully computed influence spread on real-world networks with a hundred edges in a reasonable time, which is quite impossible by the naive algorithm. We also conducted an experiment to evaluate the accuracy of the Monte-Carlo simulation-based approximation by comparing exact influence spread obtained by the proposed algorithm.Comment: WWW'1

Undercooling of acoustically levitated molten drops

It was observed that the acoustically levitated molten SCN (succinonitrile) drops can generally be undercooled to a degree where the impurities in the drop are responsible for the nucleation of the solid phase. However, it was also observed that ultrasound occasionally terminates undercooling of the levitated drops by initiating the nucleation of the solid at an undercooling level which is lower than that found for the nucleation catalyzed by the impurities in the drop. This premature nucleation can be explained by thermodynamic considerations which predict an increase in effective undercooling of the liquid upon the collapse of cavities. Pre-existing gas microbubbles which grow under the influence of ultrasound are suggested as the source of cavitation. The highly undercooled SCN drops can be utilized to measure the growth velocity of the solid in the deeply undercooled region including the hypercooled region

Optimum Arrangement of Resonator in Micro-bunch Free Electron Laser(III. Accelerator, Synchrotron Radiation, and Instrumentation)

Using a short-bunched beam of electrons from a linear accelator, the output of the micro-bunch FEL has been studied experimentally to clarify the optimum arrangement of an open resonator on the electron orbit. The output depends sharply on the arrangement, and the maximum output is observed when the resonator axis intersects the electron orbit with the angle of 3°

Ferromagnetism at 300 K in spin-coated anatasea and rutile Ti0.95Fe0.05O2 films

Thin films of Ti1-xFexO2 (x=0 and 0.05) have been prepared on sapphire substrates by spin-on technique starting from metal organic precursors. When heat treated in air at 550 and 700 degrees C respectively, these films present pure anatase and rutile structures as shown both by X-ray diffraction and Raman spectroscopy. Optical absorption indicate a high degree of transparency in the visible region. Such films show a very small magnetic moment at 300 K. However, when the anatase and the rutile films are annealed in a vacuum of 1x10-5 Torr at 500 degrees C and 600 degrees C respectively, the magnetic moment, at 300 K, is strongly enhanced reaching 0.46 $\mu$B/Fe for the anatase sample and 0.48 $\mu$B/Fe for the rutile one. The ferromagnetic Curie temperature of these samples is above 350 K.Comment: 13 october 200

Atomic Transport in Dense, Multi-Component Metallic Liquids

Pd43Ni10Cu27P0 has been investigated in its equilibrium liquid state with incoherent, inelastic neutron scattering. As compared to simple liquids, liquid PdNiCuP is characterized by a dense packing with a packing fraction above 0.5. The intermediate scattering function exhibits a fast relaxation process that precedes structural relaxation. Structural relaxation obeys a time-temperature superposition that extends over a temperature range of 540K. The mode-coupling theory of the liquid to glass transition (MCT) gives a consistent description of the dynamics which governs the mass transport in liquid PdNiCuP alloys. MCT scaling laws extrapolate to a critical temperature Tc at about 20% below the liquidus temperature. Diffusivities derived from the mean relaxation times compare well with Co diffusivities from recent tracer diffusion measurements and diffsuivities calculated from viscosity via the Stokes-Einstein relation. In contrast to simple metallic liquids, the atomic transport in dense, liquid PdNiCuP is characterized by a drastical slowing down of dynamics on cooling, a q^{-2} dependence of the mean relaxation times at intermediate q and a vanishing isotope effect as a result of a highly collective transport mechanism. At temperatures as high as 2Tc diffusion in liquid PdNiCuP is as fast as in simple liquids at the melting point. However, the difference in the underlying atomic transport mechanism indicates that the diffusion mechanism in liquids is not controlled by the value of the diffusivity but rather by that of the packing fraction

Structural characterization and electrical properties of sintered magnesium-titanate ceramics

In this article the influence of ball miling process on structure of MgO-TiO2 system, as well as the electrical properties of samples after sintering, was investigated. The mixtures of MgO-TiO2 powders were mechanically activated in a planetary ball mill for the time period from 0 to 120 min. The influence of mechanical activation and sintering on the lattice vibrational spectra was studied by Raman spectroscopy at room temperature. Structural investigations have been performed on produced powders. Nitrogen adsorption method was used to determine the BET specific surface area and pore size distribution. Unusual results have been obtained: specific surface area continuosly decreased up to 40 min of activation and increased after that, reaching its minimun value of 5.5 m(2)/g. The Raman spectra of activated powders have shown that anatase modes have been decreasing in intensity and broadening as the time of activation extended. Also, the additional modes attributed to TiO2 II, srilankite and rutile phases started to appear as a consequence of activation. The small differences noticed in the Raman spectra of sintered samples have been explained by structural modification of MgTiO3 phase due to the presence of defects. The effects of activation and sintering process on microstructure were investigated by scanning electron microscopy (SEM). The electrical measurements showed difference in dielectric constant (epsilon(r)), loss tangent (tg delta) and specific resistance (rho) as a function of time of mechanical treatment