Randomized Composable Core-sets for Distributed Submodular Maximization

An effective technique for solving optimization problems over massive data sets is to partition the data into smaller pieces, solve the problem on each piece and compute a representative solution from it, and finally obtain a solution inside the union of the representative solutions for all pieces. This technique can be captured via the concept of {\em composable core-sets}, and has been recently applied to solve diversity maximization problems as well as several clustering problems. However, for coverage and submodular maximization problems, impossibility bounds are known for this technique \cite{IMMM14}. In this paper, we focus on efficient construction of a randomized variant of composable core-sets where the above idea is applied on a {\em random clustering} of the data. We employ this technique for the coverage, monotone and non-monotone submodular maximization problems. Our results significantly improve upon the hardness results for non-randomized core-sets, and imply improved results for submodular maximization in a distributed and streaming settings. In summary, we show that a simple greedy algorithm results in a $1/3$-approximate randomized composable core-set for submodular maximization under a cardinality constraint. This is in contrast to a known $O({\log k\over \sqrt{k}})$ impossibility result for (non-randomized) composable core-set. Our result also extends to non-monotone submodular functions, and leads to the first 2-round MapReduce-based constant-factor approximation algorithm with $O(n)$ total communication complexity for either monotone or non-monotone functions. Finally, using an improved analysis technique and a new algorithm $\mathsf{PseudoGreedy}$, we present an improved $0.545$-approximation algorithm for monotone submodular maximization, which is in turn the first MapReduce-based algorithm beating factor $1/2$ in a constant number of rounds

Solution of large scale nuclear structure problems by wave function factorization

Low-lying shell model states may be approximated accurately by a sum over products of proton and neutron states. The optimal factors are determined by a variational principle and result from the solution of rather low-dimensional eigenvalue problems. Application of this method to sd-shell nuclei, pf-shell nuclei, and to no-core shell model problems shows that very accurate approximations to the exact solutions may be obtained. Their energies, quantum numbers and overlaps with exact eigenstates converge exponentially fast as the number of retained factors is increased.Comment: 12 pages, 12 figures (from 15 eps files) include

Performance and power regulation characteristics of two aileron-controlled rotors and a pitchable tip-controlled rotor on the Mod-O turbine

Tests were conducted on the DOE/NASA mod-0 horizontal axis wind turbine to compare and evaluate the performance and the power regulation characteristics of two aileron-controlled rotors and a pitchable tip-controlled rotor. The two aileron-controlled rotor configurations used 20 and 38 percent chord ailerons, while the tip-controlled rotor had a pitchable blade tip. The ability of the control surfaces to regulate power was determined by measuring the change in power caused by an incremental change in the deflection angle of the control surface. The data shows that the change in power per degree of deflection angle for the tip-controlled rotor was four times the corresponding value for the 2- percent chord ailerons. The root mean square power deviation about a power setpoint was highest for the 20 percent chord aileron, and lowest for the 38 percent chord aileron

Cepheid and Tip of the Red Giant Branch Distances To the Dwarf Irregular Galaxy IC10

We present color-magnitude diagrams and luminosity functions of stars in the nearby galaxy IC 10, based on VI CCD photometry acquired with the COSMIC prime-focus camera on the Palomar 5m telescope. The apparent I-band luminosity function of stars in the halo of IC 10 shows an identifiable rise at I~21.7 mag. This is interpreted as being the tip of the red giant branch (TRGB) at M_V~-4 mag. Since IC 10 is at a very low Galactic latitude, its foreground extinction is expected to be high and the uncertainty associated with that correction is the largest contributor to the error associated with its distance determination. Multi-wavelength observations of Cepheid variable stars in IC 10 give a Population I distance modulus of 24.1 +- 0.2 mag, which corresponds to a linear distance of 660 +- 66 kpc for a total line-of-sight reddening of E(B-V) = 1.16 +- 0.08 mag, derived self-consistently from the Cepheid data alone. Applying this Population I reddening to the Population II halo stars gives a TRGB distance modulus of 23.5 +- 0.2 mag, corresponding to 500 +- 50 kpc. We consider this to be a lower limit on the TRGB distance. Reconciling the Cepheid and TRGB distances would require that the reddening to the halo is $\Delta$E(B-V) = 0.31 mag lower than that into the main body of the galaxy. This then suggests that the Galactic extinction in the direction of IC10 is (B-V) ~ 0.85

The Effect of Lime and Phosphate on Nitrification in an Acid Soil

The nitrate content in all soils is maintained through the action of microorganisms upon ammonia. This process of nitrate production is called nitrification. It is interesting to note the effect that lime and rock phosphate has upon the nitrate producing power in an acid soil

The Effects of Potash and Crop Residues on Available Potassium in Some Alkali Soils of Iowa

Many investigators have found that high-lime soils may often be deficient in available potassium. According to the present theory, the low availability of the potassium in such soils is probably due to the high concentrations of calcium salts. The so-called alkali soils of Iowa have been found to contain high concentrations of both calcium carbonate and calcium bicarbonate. Apparently the concentrations of these salts are so high that they tend to depress the availability of the potassium in the soil

Some Effects of Fertilization on Nitrification in High-Lime Soils

Applications of potassium chloride at the rate of 100, 200 and 500 pounds per acre were made on two soils containing a high calcium content. Oat straw at the rate of 2 tons of dry matter per acre was applied alone and in combination with potassium chloride. Sweet clover at the rate of 2 tons of dry matter per acre was applied alone and in combination with potassium chloride. Samples of the soils were taken 4 weeks after treatment in the greenhouse and again after 5 months for nitrification determinations

Trace checking of Metric Temporal Logic with Aggregating Modalities using MapReduce

Modern complex software systems produce a large amount of execution data, often stored in logs. These logs can be analyzed using trace checking techniques to check whether the system complies with its requirements specifications. Often these specifications express quantitative properties of the system, which include timing constraints as well as higher-level constraints on the occurrences of significant events, expressed using aggregate operators. In this paper we present an algorithm that exploits the MapReduce programming model to check specifications expressed in a metric temporal logic with aggregating modalities, over large execution traces. The algorithm exploits the structure of the formula to parallelize the evaluation, with a significant gain in time. We report on the assessment of the implementation - based on the Hadoop framework - of the proposed algorithm and comment on its scalability.Comment: 16 pages, 6 figures, Extended version of the SEFM 2014 pape

The Variable Stars and Blue Horizontal Branch of the Metal-Rich Globular Cluster NGC 6441

We present time-series VI photometry of the metal-rich ([Fe/H] = -0.53) globular cluster NGC 6441. Our color-magnitude diagram shows that the extended blue horizontal branch seen in Hubble Space Telescope data exists in the outermost reaches of the cluster. The red clump slopes nearly parallel to the reddening vector. A component of this slope is due to differential reddening, but part is intrinsic. The blue horizontal branch stars are more centrally concentrated than the red clump stars. We have discovered about 50 new variable stars near NGC 6441, among them eight or more RR Lyrae stars which are very probably cluster members. Comprehensive period searches over the range 0.2-1.0 days yielded unusually long periods (0.5-0.9 days) for the fundamental pulsators compared with field RR Lyrae of the same metallicity. Three similar long-period RR Lyrae are known in other metal-rich globulars. With over ten examples in hand, it seems that a distinct sub-class of RR Lyrae is emerging. The observed properties of the horizontal branch stars are in reasonable agreement with recent models which invoke deep mixing to enhance the atmospheric helium abundance, while they conflict with models which assume high initial helium abundance. The light curves of the c-type RR Lyrae seem to have unusually long rise times and sharp minima. Reproducing these light curves in stellar pulsation models may provide another means of constraining the physical variables responsible for the anomalous blue horizontal branch extension and sloped red clump observed in NGC 6441.Comment: 30 pages plus 6 EPS and 6 JPEG figures; uses AAS TeX. Accepted by the Astronomical Journal. Minor changes include computing He abundance, modifications to Figs 1 and 8, and expansion on idea that blue HB stars may be produced in binarie

The Composition of Inorganic Colloids Extracted from Three Iowa Soils

The purpose of this work was to determine the colloidal content of certain soils and to make analyses of the inorganic colloids extracted from these soils. These soils ranging from a pH of 5.53 to a pH of 7.60 were obtained and the total colloidal content determined. The inorganic colloids were then extracted according to Truog and Drosdorff\u27s procedure (2) and analyzed for total SiO2 , Al2O3 , Fe2O3 , TiO2 , P2O5 and available K2O. The total SiO2, Fe2O3, Al2O3 and TiO2 were determined by Hillebrand\u27s method (1). The phosphorus content was determined by the magnesium nitrate method. The available K2O was determined by the Aspergillus niger method