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

Shaping Social Activity by Incentivizing Users

Events in an online social network can be categorized roughly into endogenous events, where users just respond to the actions of their neighbors within the network, or exogenous events, where users take actions due to drives external to the network. How much external drive should be provided to each user, such that the network activity can be steered towards a target state? In this paper, we model social events using multivariate Hawkes processes, which can capture both endogenous and exogenous event intensities, and derive a time dependent linear relation between the intensity of exogenous events and the overall network activity. Exploiting this connection, we develop a convex optimization framework for determining the required level of external drive in order for the network to reach a desired activity level. We experimented with event data gathered from Twitter, and show that our method can steer the activity of the network more accurately than alternatives

Geometric picture of quantum discord for two-qubit quantum states

Among various definitions of quantum correlations, quantum discord has attracted considerable attention. To find analytical expression of quantum discord is an intractable task. Exact results are known only for very special states, namely, two-qubit X-shaped states. We present in this paper a geometric viewpoint, from which two-qubit quantum discord can be described clearly. The known results about X state discord are restated in the directly perceivable geometric language. As a consequence, the dynamics of classical correlations and quantum discord for an X state in the presence of decoherence is endowed with geometric interpretation. More importantly, we extend the geometric method to the case of more general states, for which numerical as well as analytica results about quantum discord have not been found yet. Based on the support of numerical computations, some conjectures are proposed to help us establish geometric picture. We find that the geometric picture for these states has intimate relationship with that for X states. Thereby in some cases analytical expressions of classical correlations and quantum discord can be obtained.Comment: 9 figure

Disentangling effects of nuclear structure in heavy element formation

Forming the same heavy compound nucleus with different isotopes of the projectile and target elements allows nuclear structure effects in the entrance channel (resulting in static deformation) and in the dinuclear system to be disentangled. Using three isotopes of Ti and W, forming 232Cm, with measurement spanning the capture barrier energies, alignment of the heavy prolate deformed nucleus is shown to be the main reason for the broadening of the mass distribution of the quasifission fragments as the beam energy is reduced. The complex, consistently evolving mass-angle correlations that are observed carry more information than the integrated mass or angular distributions, and should severely test models of quasifission

An extended model to support detailed GPGPU reliability analysis

General Purpose Graphics Processing Units (GPGPUs) have been used in the last decades as accelerators in high demanding data processing applications, such as multimedia processing and high-performance computing. Nowadays, these devices are becoming popular even in safety-critical applications, such as autonomous and semi-autonomous vehicles. However, these devices can suffer from the effects of transient faults, such as those produced by radiation effects. These effects can be represented in the system as Single Event Upsets (SEUs) and are able to generate intolerable application misbehaviors in safety critical environments. In this work, we extended the capabilities of an open-source VHDL GPGPU model (FlexGrip) in order to study and analyze in a much more detailed manner the effects of SEUs in some critical modules within a GPGPU. Simulation results showed that scheduler controller has different levels of SEU sensibility depending on the affected location. Moreover, a reduced number of execution units, in the GPGPU can decrease the system reliability

Methane storms as a driver of Titan's dune orientation

Titan's equatorial regions are covered by eastward propagating linear dunes. This direction is opposite to mean surface winds simulated by Global Climate Models (GCMs), which are oriented westward at these latitudes, similar to trade winds on Earth. Different hypotheses have been proposed to address this apparent contradiction, involving Saturn's gravitational tides, large scale topography or wind statistics, but none of them can explain a global eastward dune propagation in the equatorial band. Here we analyse the impact of equinoctial tropical methane storms developing in the superrotating atmosphere (i.e. the eastward winds at high altitude) on Titan's dune orientation. Using mesoscale simulations of convective methane clouds with a GCM wind profile featuring superrotation, we show that Titan's storms should produce fast eastward gust fronts above the surface. Such gusts dominate the aeolian transport, allowing dunes to extend eastward. This analysis therefore suggests a coupling between superrotation, tropical methane storms and dune formation on Titan. Furthermore, together with GCM predictions and analogies to some terrestrial dune fields, this work provides a general framework explaining several major features of Titan's dunes: linear shape, eastward propagation and poleward divergence, and implies an equatorial origin of Titan's dune sand.Comment: Published online on Nature Geoscience on 13 April 201

Scalable Influence Maximization for Multiple Products in Continuous-Time Diffusion Networks

A typical viral marketing model identifies influential users in a social network to maximize a single product adoption assuming unlimited user attention, campaign budgets, and time. In reality, multiple products need campaigns, users have limited attention, convincing users incurs costs, and advertisers have limited budgets and expect the adoptions to be maximized soon. Facing these user, monetary, and timing constraints, we formulate the problem as a submodular maximization task in a continuous-time diffusion model under the intersection of a matroid and multiple knapsack constraints. We propose a randomized algorithm estimating the user influence in a network ($|\mathcal{V}|$ nodes, $|\mathcal{E}|$ edges) to an accuracy of $\epsilon$ with $n=\mathcal{O}(1/\epsilon^2)$ randomizations and $\tilde{\mathcal{O}}(n|\mathcal{E}|+n|\mathcal{V}|)$ computations. By exploiting the influence estimation algorithm as a subroutine, we develop an adaptive threshold greedy algorithm achieving an approximation factor $k_a/(2+2 k)$ of the optimal when $k_a$ out of the $k$ knapsack constraints are active. Extensive experiments on networks of millions of nodes demonstrate that the proposed algorithms achieve the state-of-the-art in terms of effectiveness and scalability

Distilling Information Reliability and Source Trustworthiness from Digital Traces

Online knowledge repositories typically rely on their users or dedicated editors to evaluate the reliability of their content. These evaluations can be viewed as noisy measurements of both information reliability and information source trustworthiness. Can we leverage these noisy evaluations, often biased, to distill a robust, unbiased and interpretable measure of both notions? In this paper, we argue that the temporal traces left by these noisy evaluations give cues on the reliability of the information and the trustworthiness of the sources. Then, we propose a temporal point process modeling framework that links these temporal traces to robust, unbiased and interpretable notions of information reliability and source trustworthiness. Furthermore, we develop an efficient convex optimization procedure to learn the parameters of the model from historical traces. Experiments on real-world data gathered from Wikipedia and Stack Overflow show that our modeling framework accurately predicts evaluation events, provides an interpretable measure of information reliability and source trustworthiness, and yields interesting insights about real-world events.Comment: Accepted at 26th World Wide Web conference (WWW-17

Expansion of magnetic clouds in the outer heliosphere

A large amount of magnetized plasma is frequently ejected from the Sun as coronal mass ejections (CMEs). Some of these ejections are detected in the solar wind as magnetic clouds (MCs) that have flux rope signatures. Magnetic clouds are structures that typically expand in the inner heliosphere. We derive the expansion properties of MCs in the outer heliosphere from one to five astronomical units to compare them with those in the inner heliosphere. We analyze MCs observed by the Ulysses spacecraft using insitu magnetic field and plasma measurements. The MC boundaries are defined in the MC frame after defining the MC axis with a minimum variance method applied only to the flux rope structure. As in the inner heliosphere, a large fraction of the velocity profile within MCs is close to a linear function of time. This is indicative of} a self-similar expansion and a MC size that locally follows a power-law of the solar distance with an exponent called zeta. We derive the value of zeta from the insitu velocity data. We analyze separately the non-perturbed MCs (cases showing a linear velocity profile almost for the full event), and perturbed MCs (cases showing a strongly distorted velocity profile). We find that non-perturbed MCs expand with a similar non-dimensional expansion rate (zeta=1.05+-0.34), i.e. slightly faster than at the solar distance and in the inner heliosphere (zeta=0.91+-0.23). The subset of perturbed MCs expands, as in the inner heliosphere, at a significantly lower rate and with a larger dispersion (zeta=0.28+-0.52) as expected from the temporal evolution found in numerical simulations. This local measure of the expansion also agrees with the distribution with distance of MC size,mean magnetic field, and plasma parameters. The MCs interacting with a strong field region, e.g. another MC, have the most variable expansion rate (ranging from compression to over-expansion)