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

Construction of Simulation Wavefunctions for Aqueous Species: D3O+

This paper investigates Monte Carlo techniques for construction of compact wavefunctions for the internal atomic motion of the D3O+ ion. The polarization force field models of Stillinger, et al and of Ojamae, et al. were used. Initial pair product wavefunctions were obtained from the asymptotic high temperature many-body density matrix after contraction to atom pairs using Metropolis Monte Carlo. Subsequent characterization shows these pair product wavefunctions to be well optimized for atom pair correlations despite that fact that the predicted zero point energies are too high. The pair product wavefunctions are suitable to use within variational Monte Carlo, including excited states, and density matrix Monte Carlo calculations. Together with the pair product wavefunctions, the traditional variational theorem permits identification of wavefunction features with significant potential for further optimization. The most important explicit correlation variable found for the D3O+ ion was the vector triple product {\bf r}$_{OD1}\cdot$({\bf r}$_{OD2}\times${\bf r}$_{OD3}$). Variational Monte Carlo with 9 of such explicitly correlated functions yielded a ground state wavefunction with an error of 5-6% in the zero point energy.Comment: 17 pages including 6 figures, typos correcte

Ill-posedness in the Einstein equations

It is shown that the formulation of the Einstein equations widely in use in numerical relativity, namely, the standard ADM form, as well as some of its variations (including the most recent conformally-decomposed version), suffers from a certain but standard type of ill-posedness. Specifically, the norm of the solution is not bounded by the norm of the initial data irrespective of the data. A long-running numerical experiment is performed as well, showing that the type of ill-posedness observed may not be serious in specific practical applications, as is known from many numerical simulations.Comment: 13 pages, 3 figures, accepted for publication in Journal of Mathematical Physics (to appear August 2000

Minimal Stability in Maximal Supergravity

Recently, it has been shown that maximal supergravity allows for non-supersymmetric AdS critical points that are perturbatively stable. We investigate this phenomenon of stability without supersymmetry from the sGoldstino point of view. In particular, we calculate the projection of the mass matrix onto the sGoldstino directions, and derive the necessary conditions for stability. Indeed we find a narrow window allowing for stable SUSY breaking points. As a by-product of our analysis, we find that it seems impossible to perturb supersymmetric critical points into non-supersymmetric ones: there is a minimal amount of SUSY breaking in maximal supergravity.Comment: 27 pages, 1 figure. v2: two typos corrected, published versio

Hysteresis Switching Loops in Ag-manganite memristive interfaces

Multilevel resistance states in silver-manganite interfaces are studied both experimentally and through a realistic model that includes as a main ingredient the oxygen vacancies diffusion under applied electric fields. The switching threshold and amplitude studied through Hysteresis Switching Loops are found to depend critically on the initial state. The associated vacancy profiles further unveil the prominent role of the effective electric field acting at the interfaces. While experimental results validate main assumptions of the model, the simulations allow to disentangle the microscopic mechanisms behind the resistive switching in metal-transition metal oxide interfaces.Comment: 14 pages, 3 figures, to be published in Jour. of Appl. Phy

Carbon fibre tips for scanning probe microscopy based on quartz tuning fork force sensors

We report the fabrication and the characterization of carbon fibre tips for their use in combined scanning tunnelling and force microscopy based on piezoelectric quartz tuning fork force sensors. We find that the use of carbon fibre tips results in a minimum impact on the dynamics of quartz tuning fork force sensors yielding a high quality factor and consequently a high force gradient sensitivity. This high force sensitivity in combination with high electrical conductivity and oxidation resistance of carbon fibre tips make them very convenient for combined and simultaneous scanning tunnelling microscopy and atomic force microscopy measurements. Interestingly, these tips are quite robust against occasionally occurring tip crashes. An electrochemical fabrication procedure to etch the tips is presented that produces a sub-100 nm apex radius in a reproducible way which can yield high resolution images.Comment: 14 pages, 10 figure

The underlying structure of the English Cancer Patient Experience Survey: Factor analysis to support survey reporting and design

BACKGROUND: The English Cancer Patient Experience Survey (CPES) is a regularly conducted survey measuring the experience of cancer patients. We studied the survey's underlying structure using factor analysis to identify potential for improvements in reporting or questionnaire design. METHODS: Cancer Patient Experience Survey 2015 respondents (n = 71,186, response rate 66%) were split into two random subgroups. Using exploratory factor analysis (EFA) on the first subgroup, we identified the survey's latent structure. EFA was then applied to 12 sets of items. A first ("core") set was formed by questions that applied to all participants. The subsequent sets contained the "core set" plus questions corresponding to specific care pathways/patient groups. We used confirmatory factor analysis (CFA) on the second data subgroup for cross-validation. RESULTS: The EFA suggested that five latent factors underlie the survey's core questions. Analysis on the remaining 11 care pathway/patient group items also indicated the same five latent factors, although additional factors were present for questions applicable to patients with an overnight stay or those accessing specialist nursing. The five factors models had an excellent fit (comparative fit index = 0.95, root mean square error of approximation = 0.045 for core set of questions). Items loading on each factor generally corresponded to a specific section or subsection of the questionnaire. CFA findings were concordant with the EFA patterns. CONCLUSION: The findings suggest five coherent underlying sub-constructs relating to different aspects of cancer health care. The findings support the construction of evidence-based composite indicators for different domains of experience and provide options for survey re-design

The Bethe Ansatz for AdS5 x S5 Bound States

We reformulate the nested coordinate Bethe ansatz in terms of coproducts of Yangian symmetry generators. This allows us to derive the nested Bethe equations for the bound state string S-matrices. We find that they coincide with the Bethe equations obtained from a fusion procedure. The bound state number dependence in the Bethe equations appears through the parameters x^{\pm} and the dressing phase only.Comment: typos correcte