Influence Maximization with Bandits

We consider the problem of \emph{influence maximization}, the problem of maximizing the number of people that become aware of a product by finding the `best' set of `seed' users to expose the product to. Most prior work on this topic assumes that we know the probability of each user influencing each other user, or we have data that lets us estimate these influences. However, this information is typically not initially available or is difficult to obtain. To avoid this assumption, we adopt a combinatorial multi-armed bandit paradigm that estimates the influence probabilities as we sequentially try different seed sets. We establish bounds on the performance of this procedure under the existing edge-level feedback as well as a novel and more realistic node-level feedback. Beyond our theoretical results, we describe a practical implementation and experimentally demonstrate its efficiency and effectiveness on four real datasets.Comment: 12 page

Subsea salt flows in the Atlantis II Deep and Tethis Deep, Red Sea

In the area of today’s Red Sea, evaporites were widely deposited during the Miocene. Due to the ongoing rifting and seafloor spreading, the evaporites have lost their lateral constraint and started to move downslope. High sediment temperatures near the Red Sea graben and the weak rheology of halite may also favour evaporite movement. However, the deformation mechanism as well as the velocity of these flows is largely unknown. New high-resolution multibeam and seismic data were recorded in March 2011 (P408-2 cruise) within the framework of the project “The Jeddah Transect”, a cooperation between King Abdulaziz University, Saudi-Arabia and GEOMAR, Germany. The data give new insights into evaporite flows in the area of the Atlantis II Deep. This ~400 m deep seafloor depression is located at about 21°N in the central Red Sea graben and is partly filled with hot saline brine (T~68°C, S~270h. The brine-seawater interface at about 2050 mbsl coincides with the depth of a subseafloor salt layer in the seismic reflection data. The rough seafloor morphology of the Atlantis II Deep area is dominated by a sequence of normal faults showing vertical offsets of several hundred meters. However, SW-NE directed lineaments parallel to the seafloor gradient in the south east and possibly north-west of the deep, with typical heights between 20 and 40 m, widths between 300 and 1000 m and lengths exceeding 10 km in places, are interpreted as surface indications of subsurface evaporite flow. The fronts of some of these flows are well rounded, and their occurrence is limited to areas of low seafloor gradients. Generally, the appearance of evaporite flows in the Atlantis II Deep is comparable to salt flows in the Thetis Deep at ~23°N (Mitchell et al., 2010). Furthermore, deformed hemipelagic layers deposited on top of the Miocene evaporites indicate salt movement 60 km off the central rift axis. A second research cruise is planned in March 2012 (RV Pelagia) to obtain more high-resolution seismic data on the morphological structures related to the evaporite flows at 21°N. Additionally, repeated multibeam measurements in the Thetis Deep will constrain the maximum movement rate of the evaporites. Mitchell, N. C. ; Ligi, M. ; Ferrante, V. ; Bonatti, E. ; Rutter, E.: Submarine salt flows in the central Red Sea. In: Geological Society of America Bulletin vol. 122 (2010), Nr. 5-6, pp. 701–71

Hybrid Deterministic-Stochastic Methods for Data Fitting

Many structured data-fitting applications require the solution of an optimization problem involving a sum over a potentially large number of measurements. Incremental gradient algorithms offer inexpensive iterations by sampling a subset of the terms in the sum. These methods can make great progress initially, but often slow as they approach a solution. In contrast, full-gradient methods achieve steady convergence at the expense of evaluating the full objective and gradient on each iteration. We explore hybrid methods that exhibit the benefits of both approaches. Rate-of-convergence analysis shows that by controlling the sample size in an incremental gradient algorithm, it is possible to maintain the steady convergence rates of full-gradient methods. We detail a practical quasi-Newton implementation based on this approach. Numerical experiments illustrate its potential benefits.Comment: 26 pages. Revised proofs of Theorems 2.6 and 3.1, results unchange

The Decomposition of Hydrazine in the Gas Phase and over an Iridium Catalyst

Hydrazine is an important rocket fuel, used as both a monopropellant and a bipropellant. This paper presents theoretical results to complement the extensive experimental studies of the gas phase and Ir catalyzed decompositions involved in the monopropellant applications of hydrazine. Gas phase electronic structure theory calculations that include electron correlation predict that numerous molecular and free radical reactions occur within the same energy range as the basic free radical pathways: NN bond breaking around 65 kcal/mol and NH bond breaking around 81 kcal/mol. The data suggest that a revision to existing kinetics modeling is desirable, based on the energetics and the new elementary steps reported herein. A supported Ir6 octahedron model for the Shell 405 Iridium catalyst used in thrusters was developed. Self-Consistent Field and electron correlation calculations (with core potentials and associated basis sets) find a rich chemistry for hydrazine on this catalyst model. The model catalyst provides dramatically lower NN and NH bond cleavage energies and an even smaller barrier to breaking the NH bond by NH2 abstractions. Thus, the low temperature decomposition over the catalyst is interpreted in terms of consecutive NH2 abstractions to produce ammonia and nitrogen. The higher temperature channel, which has hydrogen and nitrogen products, may be due to a mixture of two mechanisms. These two mechanisms are successive NH cleavages with surface H + H recombinations, and the same type of assisted H2 eliminations found to occur in the gas phase part of this study

Does Methane Invert through Square Planar?

MCSCF calculations using a triple-t basis set augmented with diffuse and polarization functions are used to probe that part of the singlet methane potential energy surface that pertains to the inversion of CH4 from one t~trahedral structure t.o another. The true inversion transition state is found to have a distorted C, structure, quite different both ge?me.tncally ~nd energetically from the previously presumed square planar saddle point. At the secondorder configuration mte.ractl~n.level of theory, the barrier to inversion is predicted to be just 7-8 kcaljmol higher in energy than the bond diSSOCiation energy for the first C-H bond cleavage in methane