Optimization of Analytic Window Functions

Analytic functions represent the state-of-the-art way of performing complex data analysis within a single SQL statement. In particular, an important class of analytic functions that has been frequently used in commercial systems to support OLAP and decision support applications is the class of window functions. A window function returns for each input tuple a value derived from applying a function over a window of neighboring tuples. However, existing window function evaluation approaches are based on a naive sorting scheme. In this paper, we study the problem of optimizing the evaluation of window functions. We propose several efficient techniques, and identify optimization opportunities that allow us to optimize the evaluation of a set of window functions. We have integrated our scheme into PostgreSQL. Our comprehensive experimental study on the TPC-DS datasets as well as synthetic datasets and queries demonstrate significant speedup over existing approaches.Comment: VLDB201

Cosmic Microwave Background Anisotropy Window Functions Revisited

The primary results of most observations of cosmic microwave background (CMB) anisotropy are estimates of the angular power spectrum averaged through some broad band, called band-powers. These estimates are in turn what are used to produce constraints on cosmological parameters due to all CMB observations. Essential to this estimation of cosmological parameters is the calculation of the expected band-power for a given experiment, given a theoretical power spectrum. Here we derive the "band power" window function which should be used for this calculation, and point out that it is not equivalent to the window function used to calculate the variance. This important distinction has been absent from much of the literature: the variance window function is often used as the band-power window function. We discuss the validity of this assumed equivalence, the role of window functions for experiments that constrain the power in {\it multiple} bands, and summarize a prescription for reporting experimental results. The analysis methods detailed here are applied in a companion paper to three years of data from the Medium Scale Anisotropy Measurement.Comment: 5 pages, 1 included .eps figure, PRD in press---final published versio

Observational Window Functions in Planet Transit Surveys

The probability that an existing planetary transit is detectable in one's data is sensitively dependent upon the window function of the observations. We quantitatively characterize and provide visualizations of the dependence of this probability as a function of orbital period upon several observing strategy and astrophysical parameters, such as length of observing run, observing cadence, length of night, transit duration and depth, and the minimum number of sampled transits. The ability to detect a transit is directly related to the intrinsic noise of the observations. In our simulations of observational window functions, we explicitly address non-correlated (gaussian or white) noise and correlated (red) noise and discuss how these two noise components affect transit detectability in fundamentally different manners, especially for long periods and/or small transit depths. We furthermore discuss the consequence of competing effects on transit detectability, elaborate on measures of observing strategies, and examine the projected efficiency of different transit survey scenarios with respect to certain regions of parameter space.Comment: 16 pages, 11 figures, 8 tables; accepted for publication in Ap

Window functions and sigmoidal behaviour of memristive systems

Summary: A common approach to model memristive systems is to include empirical window functions to describe edge effects and nonlinearities in the change of the memristance. We demonstrate that under quite general conditions, each window function can be associated with a sigmoidal curve relating the normalised time-dependent memristance to the time integral of the input. Conversely, this explicit relation allows us to derive window functions suitable for the mesoscopic modelling of memristive systems from a variety of well-known sigmoidals. Such sigmoidal curves are defined in terms of measured variables and can thus be extracted from input and output signals of a device and then transformed to its corresponding window. We also introduce a new generalised window function that allows the flexible modelling of asymmetric edge effects in a simple manner

Cross-Power Spectrum and Its Application on Window Functions in the WMAP data

Cross-power spectrum is a quadratic estimator between two maps that can provide unbiased estimate of the underlying power spectrum of the correlated signals, which is therefore used for extracting the power spectrum in the WMAP data. In this paper we discuss the limit of cross-power spectrum and derive the residual from uncorrelated signal, which is the source of error in power spectrum extraction. We employ the estimator to extract window functions by crossing pairs of extragalactic point sources. We desmonstrate its usefulness in WMAP Difference Assembly maps where the window functions are measured via Jupiter and then extract the window functions of the 5 WMAP frequency band maps.Comment: added the part of applying cross power spectrum on WMAP DA maps and frequency band maps and submitted to Ap

Electromagnetic Field Plot of an Inductive Window by the Moment Method

A moment method is used to plot the electromagnetic field of an inductive window in a TE10 -mode rectangular waveguide. Green\u27s dyadic functions are derived based on Tai\u27s approach, which is a modified form of Hansen\u27s vector wave functions. Based on the computed electric fields, the S matrix and the equivalent aperture reactance of the waveguide window are calculated. This calculation agrees with the previously published closed-form results of Marcuvitz