Abstract: Importance sampling uses observations from one distribution to estimate for another distribution by weighting the observations. Including the target distribution as one component of a mixture distribution bounds the weights and makes importance sampling more reliable. The usual importance-sampling estimate is a weighted average with weights that do not sum to 1. We discuss simple normalization and other, more efficient normalization methods. These innovations make importance sampling useful in a wider variety of problems. We demonstrate with a case study of oil-inventory reliability at a large utility.

Abstract: Following a principal component analysis, it is fairly common practice to rotate some of the components, often using orthogonal rotation. It is a frequent misconception that orthogonal rotation will produce rotated components which are pairwise uncorrelated, and/or whose loadings are orthogonal In fact, it is not possible, using the standard definition of rotation, to preserve both these properties. Which of the two properties is preserved depends on the normalization chosen for the loadings, prior to rotation. The usual ‘default’ normalization leads to rotated components which possess neither property.

Abstract: Classification of galaxy spectral energy distributions in terms of orthogonal basis functions provides an objective means of estimating the number of significant spectral components that comprise a particular galaxy type. We apply the Karhunen-Lo\`{e}ve transform to derive a spectral eigensystem from a sample of ten galaxy spectral energy distributions. These spectra cover a wavelength range of 1200 \AA\ to 1 $\mu$m and galaxy morphologies from elliptical to starburst. We find that the distribution of spectral types can be fully described by the first two eigenvectors (or eigenspectra). The derived eigenbasis is affected by the normalization of the original spectral energy distributions. We investigate different normalization and weighting schemes, including weighting to the same bolometric magnitude and weighting by the observed distribution of morphological types. Projecting the spectral energy distributions on to their eigenspectra we find that the coefficients define a simple spectral classification scheme. The galaxy spectral types can then be described in terms of a one parameter family (the angle in the plane of the first two eigenvectors). We find a strong correlation in the mean between our spectral classifications and those determined from published morphological classifications.

Abstract: A method for searching a database of an information retrieval system in response to a query having a query length of at least one word, for applying the query word to the database and selecting information from the database according to the query word. The query is received and the length of the query is determined. Information is selected from the database according to the query. The relevance of the selected information is determined according to matches between the query and the information. The determined relevance of the selected information is adjusted according to the length of the query.

Abstract: Transform-domain adaptive filters refer to LMS filters whose inputs are preprocessed with a unitary data-independent transformation followed by a power normalization stage. The transformation is typically chosen to be the discrete Fourier transform (DFT), although other transformations, such as the cosine transform (DCT), the Hartley transform (DHT), or the Walsh-Hadamard transform, have also been proposed in the literature. The resulting algorithms are generally called DFT-LMS, DCT-LMS, etc. This preprocessing improves the eigenvalue distribution of the input autocorrelation matrix of the LMS filter and, as a consequence, ameliorates its convergence speed. In this paper, we start with a brief intuitive explanation of transform-domain algorithms. We then analyze the effects of the preprocessing performed in DFT-LMS and DCT-LMS for first-order Markov inputs. In particular, we show that for Markov-1 inputs of correlation parameter /spl rho//spl isin/[0,1], the eigenvalue spread after DFT and power normalization tends to (1+/spl rho/)l(1-/spl rho/) as the size of the filter gets large, whereas after DCT and power normalization, it reduces to (1+/spl rho/). For comparison, the eigenvalue spread before transformation is asymptotically equal to (1+/spl rho/)/sup 2//(1-/spl rho/)/sup 2/. The analytical method used in the paper provides additional insight into how the algorithms work and is expected to extend to other input signal classes and other transformations. >

Abstract: A method for storing input information in an information retrieval system database wherein a plurality of information subject categories are provided. A plurality of subject lexicons are provided, each subject lexicon of the plurality of subject lexicons corresponding to an information subject category of the plurality of information categories. Each subject lexicon contains information representative of its corresponding information subject category. The input information is compared with the subject lexicons and the input information is stored in a selected information subject category according to the comparing of the input information with the subject lexicons.

Abstract: More than a dozen papers analyzing the COBE data have now appeared. We review the different techniques and compare them to a ``brute force" likelihood analysis where we invert the full 4038 x 4038 Galaxy-cut pixel covariance matrix. This method is optimal in the sense of producing minimal error bars, and is a useful reference point for comparing other analysis techniques. Our maximum-likelihood estimate of the spectral index and normalization are n=1.15 (0.95) and Q=18.2 (21.3) micro-Kelvin including (excluding) the quadrupole. Marginalizing over the normalization C_9, we obtain n=1.10 +/- 0.29 (n=0.90 +/- 0.32). When we compare these results with those of the various techniques that involve a linear ``compression'' of the data, we find that the latter are all consistent with the brute-force analysis and have error bars that are nearly as small as the minimal error bars. We therefore conclude that the data compressions involved in these techniques do indeed retain most of the useful cosmological information.

Abstract: The Renyi uncertainty measure has been proposed to be a measurement of complexity of signals. We further suggest that it can be used to evaluate the performance of different time-frequency distributions (TFDs). We provide two schemes of normalization in calculating the Renyi uncertainty measure. For the first one, TFDs are normalized by their energy, while for the second one, normalized with their volume. The behavior of the Renyi uncertainty measure under several situations is studied. A signal-dependent algorithm is developed to achieve TFDs with a minimal uncertainty measure. For the first normalization scheme, the Wigner distribution is found to be optimal or near-to-optimal under certain constraints. If the second scheme is used, our program can generate minimum uncertainty product kernels which are very effective at suppressing cross terms and maintaining high resolution.

Abstract: Power normalization parts calculate the average powers of input signals of a plurality of channels for each frame and divide the signals by the calculated average powers to generate normalized signals and, at the same time, generate weights corresponding to the normalization gains. The normalized signals of the plurality of channels are combined in a combining part into predetermined sequences and outputted therefrom as one or more interleaved signal vectors. The combining part combines the weights from the power normalization part into the same sequences of the normalized signal and outputs one or more interleaved weight vectors. In a vector quantization part the signal vectors are vector quantized by the interleaved weight vectors corresponding thereto, respectively, and quantization indexes and normalization indexes are outputted as results of coding.

Abstract: Optical character recognition (OCR) is the most commonly used technique to convert printed material into electronic form. Using OCR, large repositories of machine readable text can be created in a short time. An information retrieval system can then be used to search through large information bases thus created. Many information retrieval systems use sophisticated term weighting functions to improve the effectiveness of a search. Term weighting schemes can be highly sensitive to the errors in the input text, introduced by the OCR process. This study examines the effects of the well known cosine normalization method in the presence of OCR errors and proposes a new, more robust, normalization method. Experiments show that the new scheme is less sensitive to OCR errors and facilitates use of more diverse basic weighting schemes. It also yields significant improvements in retrieval effectiveness over cosine normalization.

Abstract: A method and apparatus for forming a three-dimensional article includes dispensing build material and thermally normalizing predetermined portions thereof at predetermined intervals during construction of the article The thermal energy may be provided by a heated body (87) advanced adjacent to or in contact with the surface portions (212) Thermal energy may also be supplied by a radiation source The thermal normalization may be performed after a predetermined number of successive layers are dispensed Related methods are also disclosed

Abstract: We introduce a new family of environmental compensation algorithms called multivariate gaussian based cepstral normalization (RATZ). RATZ assumes that the effects of unknown noise and filtering on speech features can be compensated by corrections to the mean and variance of components of Gaussian mixtures, and an efficient procedure for estimating the correction factors is provided. The RATZ algorithm can be implemented to work with or without the use of "stereo" development data that had been simultaneously recorded in the training and testing environments. "Blind" RATZ partially overcomes the loss of information that would have been provided by stereo training through the use of a more accurate description of how noisy environments affect clean speech. We evaluate the performance of the two RATZ algorithms using the CMU SPHINX-II system on the alphanumeric census database and compare their performance with that of previous environmental-robustness developed at CMU.

Abstract: Normalization in three-dimensional (3-D) positron emission tomography (PET) comprises two aspects: correction for differential detector response and correction for geometric effects. Comparison of rotating rod source and uniform cylinder data suggests that the position of the source used to correct for sensitivity should be similar to that of the emission data. A plane source method has been devised that uses a moving line source that traverses the transaxial field-of-view, emulating a plane source, but without the problems associated with using a conventional plane source in 3-D (uniformity, scatter, cost, etc.). This device has been used to record high count density acquisitions for direct normalization of emission data and also to examine geometric effects with increasing azimuthal (/spl phi/) and polar (/spl theta/) angles in the 3 D data set. The data have confirmed observations of two distinct geometric patterns seen previously in two-dimensional PET: an overall transaxial sensitivity profile that decreases toward the center of the projection and a crystal interference profile that changes with position in the block. Correction for the first geometric component removes a low-sensitivity "hole" in 3-D PET reconstructions, and correction for the second component removes "ring" artifacts. The direct normalization approach produces an artifact along the central axis of the scanner. A quantitative index of nonuniformity for 1-pixel-thick annular regions of interest showed a reduction from 60% nonuniformity with no corrections to less than 15% when the plant source data were used to directly normalize the emission data. The moving line source provides high quality data and may be an appropriate normalization device for 3-D PET.

Abstract: A site–site Born–Green–Yvon (BGY) equation is derived for polymeric fluids. This relates the pair and triplet site distribution functions, and superposition approximations for the latter are analyzed. It is shown that the pair functions to be superposed are uniquely determined by the exact normalization equations and asymptotic conditions. The Kirkwood superposition of pair distribution functions is shown to be valid only for the case of sites on three different polymers; for the cases of two or three sites on the same polymer different pair functions must be superposed. The polymer BGY equation is derived for a soft bonding potential between adjacent sites; the result for infinitely stiff bonds is given as a limiting case. Numerical results are obtained for soft and stiff tangent hard‐sphere chains, and comparison is made with simulations for packing fractions up to 0.4 and chains with up to 12 sites.

Abstract: A new algorithm is developed for calculating normalization constants (partition functions) and moments of product-form steady-state distributions of closed queuing networks and related models. The essential idea is to numerically invert the generating function of the normalization constant and related generating functions appearing in expressions for the moments. It is known that the generating function of the normalization constant often has a remarkably simple form, but numerical inversion evidently has not been considered before. For p-dimensional transforms, as occur with queuing networks having p closed chains, the algorithm recursively performs p one-dimensional inversions. The required computation grows exponentially in the dimension, but the dimension can often be reduced by exploiting conditional decomposition based on special structure. For large populations, the inversion algorithm is made more efficient by computing large sums using Euler summation. The inversion algorithm also has a very low storage requirement. A key ingredient in the inversion algorithm is scaling. An effective static scaling is developed for multichain closed queuing networks with only single-server and (optionally) infinite-server queues. An important feature of the inversion algorithm is a self-contained accuracy check, which allows the results to be verified in the absence of alternative algorithms.

Abstract: Normalization of experimental fragment patterns for nucleic acid polymers having putatively known sequences starts with obtaining at least one raw fragment pattern for the experimental sample. The raw fragment pattern represents the positions of a selected nucleic acid base within the polymer as a function of migration time or distance. This raw fragment pattern is conditioned using conventional baseline correction and noise reduction technique to yield a clean fragment pattern. The clean fragment pattern is then evaluated to determine one or more "normalization coefficients." These normalization coefficients reflect the displacement, stretching or shrinking, and rate of stretching or shrinking of the clean fragment, or segments thereof, which are necessary to obtain a suitably high degree of correlation between the clean fragment pattern and a standard fragment pattern which represents the positions of the selected nucleic acid base within a standard polymer actually having the known sequence as a function of migration time or distance. The normalization coefficients are then applied to the clean fragment pattern to produce a normalized fragment pattern which is used for base-calling in a conventional manner. This method may be implemented in an apparatus comprising a computer processor programmed to determine normalization coefficients for an experimental fragment pattern. This computer may be separate from the electrophoresis apparatus, or part of an integrated unit.

Abstract: Image size normalization is a crucial preprocessing stage in the development of robust object recognizers. A new method of image size normalization based on multirate filter theory is proposed. Comparisons with ratio-based normalization and simple scaling are made. The effect of each normalization method on handwritten digit recognition is evaluated. Recognition incorporates global and local features extracted from normalized digit images and used with a neural network and K-nearest neighbor classifier performance evaluation is based on recognition accuracy, reject versus error graph, figure of merit and processing time required by each method. Multirate-based normalization yields better recognition performance at the cost of increased computation, whereas ratio-based normalization and simple scaling method require less processing time with reduced recognition performance.

Abstract: Normalization, which makes up the core of the design theory for relational databases, is also considered an important technique to improve the quality of ER schemata. We first present a framework for describing ER schema transformations. Then a normal form, ER-BCNFnull, is defined which corresponds to BCNF but takes null values into account. Finally, a set of transformations is suggested which might be used to achieve this normal form.

Abstract: We proposed an augmented cepstral mean normalization algorithm that differentiates noise and speech during normalization, and computes a different mean for each. The new procedure reduced the error rate slightly for the case of sameenvironment testing, and significantly reduced the error rate by 25% when an environmental mismatch exists over the case of standard cepstral mean normalization.

Abstract: To offer a floating-point addition/subtraction processing apparatus and a method thereof, capable of shortening the computation time, the floating-point calculation processing apparatus includes an approximate shift mount predicting unit for predicting a shift amount for normalization by using the input floating-point data to be addition/subtraction processed within an error of 1 bit, a shift error detecting unit for detecting a difference between the predicted shift amount and a correct shift amount, and an bit shifter for correcting a result, obtained by normalization using the predicted shift amount, by the detected difference of the two shift amounts, wherein a round-off determination and a shift amount calculation are processed in parallel before a normalization shift processing is executed.

Abstract: Deprit and Miller have conjectured that normalization of integrable Hamiltonians may produce normal forms exhibiting degenerate equilibria to very high order. Several examples in the class of coupled elliptic oscillators are known. In order to test the utility of normalization as a detector of integrability we normalize, to high order, a perturbed Keplerian system known to have several integrable limits; the generalized van der Waals Hamiltonian for a hydrogen atom. While the separable limits give rise to high order degeneracy we find a non-separable, integrable limit for which the normal form does not exhibit degeneracy. We conclude that normalization may, in certain cases, indicate integrability but is not guaranteed to uncover all integrable limits.

Abstract: During the information systems development process within an organization, data resource is typically analyzed in the form of a data model. During this data analysis phase, the data model is further refined so that it obeys certain rules of good behavior. Normalization is the process of grouping data into such well refined structures. Determining an appropriate normal form has not been clear to database systems analysts. This paper proposes an effective methodology for determining normal forms by employing a cost/benefit model coupled with a decision tree. Three primary variables that impact the benefits and costs of normalization are addressed. The resulting cost/ benefit analysis enables database analysts to produce more cost-effective normalized databases.

Abstract: The signal‐to‐noise ratio in a time‐resolved Fourier transform (FT) infrared emission experiment is improved by pulse‐to‐pulse normalization. The signal from the FT spectrometer is normalized by the total infrared fluorescence produced on each laser pulse. A factor of 20 enhancement in signal‐to‐noise ratio is demonstrated with normalization when the fluctuation of the laser pulse energy is the dominant noise source. Applications are discussed pertaining to cases where other noise sources such as detector and amplifier noise cannot be neglected and when information from the time evolution of the spectrum is required.

Abstract: With the advent of the COBE detection of fluctuations in the Cosmic Microwave Background radiation, the study of inhomogeneous cosmology has entered a new phase. It is now possible to accurately normalize fluctuations on the largest observable scales, in the linear regime. In this paper we present a model-independent method of normalizing theories to the full COBE data. This technique allows an extremely wide range of theories to be accurately normalized to COBE in a very simple and fast way. We give the best fitting normalization and relative peak likelihoods for a range of spectral shapes, and discuss the normalization for several popular theories. Additionally we present both Bayesian and frequentist measures of the goodness of fit of a representative range of theories to the COBE data.