New Algorithms for Distributed Sliding Windows

Computing functions over a distributed stream of data is a significant problem with practical applications. The distributed streaming model is a natural computational model to deal with such scenarios. The goal in this model is to maintain an approximate value of a function of interest over a data stream distributed across several computational nodes. These computational nodes have a two-way communication channel with a coordinator node that maintains an approximation of the function over the entire data stream seen so far. The resources of interest, which need to be minimized, are communication (primary), space, and update time. A practical variant of this model is that of distributed sliding window (dsw), where the computation is limited to the last W items, where W is the window size. Important problems such as sampling and counting have been investigated in this model. However, certain problems including computing frequency moments and metric clustering, that are well studied in other streaming models, have not been considered in the distributed sliding window model. We give the first algorithms for computing the frequency moments and metric clustering problems in the distributed sliding window model. Our algorithms for these problems are a result of a general transfer theorem we establish that transforms any algorithm in the distributed infinite window model to an algorithm in the distributed sliding window model, for a large class of functions. In particular, we show an efficient adaptation of the smooth histogram technique of Braverman and Ostrovsky, to the distributed streaming model. Our construction allows trade-offs between communication and space. If we optimize for communication, we get algorithms that are as communication efficient as their infinite window counter parts (upto polylogarithmic factors)

Complexes of Cut (II), Ni(II) & Co(II) with 3,5-Dimethyl-I-nitroguanylpyrazole

978-98

INFLUENCE OF ORGANIC MANURES AND GIBBERELLIC ACID ON GROWTH AND YIELD OF STRAWBERRY (Fragaria X ananassa DUCH.)

A field experiment was conducted to study the effect of organic manures and growth regulators on the growth and yield of two varieties of strawberry namely ‘Sweet Charlie’ and ‘Winter Dawn’. Six treatments were taken combining three organic manures viz. Vermicompost @ 3.0 t/ha, Mustard oil cake @ 1.0 t/ha and Neem cake @ 1.0 t/ha and two concentrations of gibberellic acid (GA3) viz. 75 ppm and 100 ppm along with a control. Foliar application of GA3 was carried out at 40 and 60 days after planting whereas organic manures were applied as basal dose. Results of the study suggested that higher doses i.e. 100 ppm of GA3 along with vermicompost exhibited more vegetative growth whereas 75 ppm GA3 resulted in higher fruit set and yield in both the varieties. It was found that vermicompost @ 3.0 t/ha combined with 100 ppm GA3 recorded the highest plant height (24.7 cm and 21.4 cm) and numbers of leaves per plant (46.0 and 68.7) in both Sweet Charlie and Winter Dawn varieties, respectively. Whereas, highest fruit diameter (3.3cm and 3.4cm), fruit length (4.6cm and 4.8cm), fruit weight (18.2 g and 17.9 g), number of fruits per plant (24.6 and 32.0), yield per plant (447.8 g and 572.1 g) and yield per hectare (18.80 t and 24.03 t) were recorded under vermicompost @ 3.0 t/ha in combination with 75 ppm GA3 in both Sweet Charlie and Winter Dawn varieties, respectively. It was observed that Winter Dawn variety produced a 28.0% higher yield as compared to Sweet Charlie under the best treatment i.e. vermicompost @ 3.0 t/ha in combination with 75 ppm GA3

Wave Motion due to a Ring Source in Two Superposed Fluids Covered by a Thin Elastic Plate

The problem of wave generation by a horizontal ring of wave sources of the same time-dependent strength present in any one layer of a two-layer fluid is investigated here. The upper fluid is of finite height above the interface and is covered by a floating thin infinite elastic plate (modeling a thin sheet of ice) while the lower fluid extends infinitely downwards. Assuming linear theory, the problem is formulated as an initial value problem and the Laplace transform in time is employed to solve it. For time-harmonic source strength, the asymptotic representations of the potential functions describing the motion in the two layers for large time and distance are derived. In these representations, the two different coefficients for each of the surface and interface wave modes have the same numerical values although it has not been possible to prove their equivalence analytically. This shows that the steady-state analysis of the potential functions produces outgoing progressive waves at the surface and at the interface. The forms of the surface and interface waves are depicted graphically for different values of the flexural rigidity of the elastic plate and the ring source being submerged in the lower or upper layer

On Approximating Total Variation Distance

Total variation distance (TV distance) is a fundamental notion of distance between probability distributions. In this work, we introduce and study the computational problem of determining the TV distance between two product distributions over the domain {0, 1}n. We establish the following results. 1. Exact computation of TV distance between two product distributions is #P-complete. This is in stark contrast with other distance measures such as KL, Chi-square, and Hellinger which tensorize over the marginals. 2. Given two product distributions P and Q with marginals of P being at least 1/2 and marginals of Q being at most the respective marginals of P, there exists a fully polynomial-time randomized approximation scheme (FPRAS) for computing the TV distance between P and Q. In particular, this leads to an efficient approximation scheme for the interesting case when P is an arbitrary product distribution and Q is the uniform distribution. We pose the question of characterizing the complexity of approximating the TV distance between two arbitrary product distributions as a basic open problem in computational statistics

Total Variation Distance Estimation Is as Easy as Probabilistic Inference

In this paper, we establish a novel connection between total variation (TV) distance estimation and probabilistic inference. In particular, we present an efficient, structure-preserving reduction from relative approximation of TV distance to probabilistic inference over directed graphical models. This reduction leads to a fully polynomial randomized approximation scheme (FPRAS) for estimating TV distances between distributions over any class of Bayes nets for which there is an efficient probabilistic inference algorithm. In particular, it leads to an FPRAS for estimating TV distances between distributions that are defined by Bayes nets of bounded treewidth. Prior to this work, such approximation schemes only existed for estimating TV distances between product distributions. Our approach employs a new notion of $partial$ couplings of high-dimensional distributions, which might be of independent interest.Comment: 24 page

Raman spectra of unfilled and filled carbon nanotubes: Theory

The Raman spectra of two G-bands and a radial breathing mode (RBM) of unfilled and filled single-wall semiconducting and metallic carbon nanotubes have been investigated theoretically, in the presence of electron-phonon and phonon-phonon interactions. Excitation of low frequency optical plasmons in the metallic nanotube is responsible for the peak known as the Breit-Wigner-Fano (BWF) line shape in the G-band Raman spectra. In a filled nanotube there is an additional peak due to excitation of the phonon of the filling atom or molecule. Positions, shapes and relative strengths of these Raman peaks depend on the phonon frequencies of the nanotube and that of the filling atoms, and strengths and forms of the plasmon-phonon and phonon-phonon interactions. For example, filling atoms with phonon frequency close to the RBM frequency of the nanotube may broaden and lower the RBM Raman peak to such an extent that it may become barely visible. Hybridization between the G-bands and the filling atom phonon is also strong when these two frequencies are close to each other and it has important effects on the G-band and the BWF line shapes. When the phonon frequency of the filling atom is far from the RBM and G-band frequencies, it gives rise to a separate peak with modest effects on the RBM and G-band spectra. Raman spectra of semiconducting unfilled and filled nanotubes have similar behavior as those of metallic nanotubes except that normally they have Lorentzian line shapes and do not show a BWF line shape. However, if a semiconducting nanotube is filled with donor atoms, it is predicted that the BWF type line shape may be observed near the RBM, or the G-band or the filling atom Raman peak.Comment: To be published in Physical Review