Abstract: A program for the normalization of relations that is written in Prolog has several advantages relative to programs written in conventional programming languages: notably, conciseness and clarity. The program presented here implements several normalization algorithms and is suitable for the interactive design of small database applications and as a teaching aid.

Abstract: The subject invention relates to a new and improved method of dynamic signature verification. In accordance with the subject invention output signals, generated by a stylus, are normalized such that they are insensitive to the rotational position of the stylus with respect to the writer's grip. In operation, pressure measurements are sampled at discrete intervals and a normalization angle is calculated, representative of the average direction of the signature. Each sample is then assigned a vector length which is rotated by the normalization angle. The normalized samples are utilized to perform signature analysis.

Abstract: Publisher Summary This chapter presents an analysis of handwriting in the general context of a trajectory formation, considering specific modeling and computational aspects, and discusses the normalization and coding of a cursive script. Normalization included time scaling, baseline compensation, slant compensation, and size scaling. Without a rigid hierarchy among the normalization factors, motor activities are classified as a multiplicity of action paradigms, including muscle contractions, joint rotations, trajectories, and tasks. The chapter also discusses complex trajectory formation patterns and handwritings. Different elements of a trajectory formation—including coordination, timing, and geometric transformations—are discussed in the chapter with regard to motor activities of increasing complexity. A trajectory formation model is presented in the chapter based on the hypothesis of a kinematic planning of fundamental motor patterns.

Abstract: Structural equation models with latent variables have been popular in the social sciences for some time. Recently such models have been used to make comparisons between groups, within dyads, and ac...

Abstract: SummaryConsider a Hamiltonian system (H, ℝ2n,ω). LetM be a symplectic submanifold of (ℝ2n,ω). The system (H, ℝ2n,ω) constrained toM is (H∣M, M, ω∣M). In this paper we give an algorithm which normalizes the system on ℝ2n in such a way that restricted toM we have normalized the constrained system. This procedure is then applied to perturbed Kepler systems such as the lunar problem and the main problem of artificial satellite theory.ZusammenfassungWir betrachten ein Hamiltonisches System (H, ℝ2n,ω). SeiMein symplectisches Submanifold von (ℝ2n,ω). Das System (H, ℝ2n,ω), aufM beschränkt, ist (H∣M,M,ω∣M). In der vorliegenden Arbeit wird ein Algorithmus vorgeschlagen, der dieses System so auf ℝ2n normalisiert, daß das aufM beschränkte System auch normalisiert ist. Dieser Algorithmus wird dann auf gestörte Keplersysteme, wie z. B. das Hill-sche Mondproblem und das Hauptproblem der Theorie der künstlichen Satelliten, angewendet.

Abstract: On decrit une methode simple de reduction de la normalisation forte pour les fonctionnelles recursives primitives avec couplage surjectif

Abstract: Normalizing the initial estimates of the seasonal factors in Winters' seasonal forecasting systems is a universally recommended practice. Once forecasting begins, however, the seasonal factors lose their normalization. It is often recommended that these factors be renormalized either seasonally or continuously, i.e., with every observation. We show that this latter procedure is never necessary in the case of the additive model, since a simple change in the smoothing constants can achieve the same ends. We also give a simpler and more efficient method of obtaining seasonally renormalized forecasts for this model.

Abstract: Orthogonal output signals generated by a stylus (40), are normalized such that they are insensitive to the rotational position of the stylus (40) with respect to the writer's grip. Pressure measurements made by strain gauges (52) on a flexible diaphragm (50) in the stylus (40) are sampled at discrete intervals and a normalization angle of writing movement is calculated, representative of the average direction of the signature, by a processor (60). Each sample of orthogonal output signals is then assigned a vector length which is rotated by the normalization angle. The normalized samples are utilized to perform signature analysis by a comparison with a stored reference signature set of normalized orthoganal samples carried out by the processor (60).

Abstract: Optimal control techniques are used to drive the numerical error (truncation, roundoff, commutation) in computing the quaternion vector to zero. The normalization of the quaternion is carried out by appropriate choice of a performance index, which can be optimized. The error equations are derived from Friedland's (1978) theoretical development, and a matrix Riccati equation results for the computation of the gain matrix. Simulation results show that a high precision of the order of 10 to the -12th can be obtained using this technique in meeting the q(T)q=1 constraint. The performance of the estimator in the presence of the feedback control that maintains the normalization, is studied.

Abstract: Publisher Summary This chapter examines the problems associated with averaging handwriting signals beyond those of electrophysiological recordings. These problems include the choice of the entities to be averaged by the absence of external time-reference points and by a duration variability. The problem of the stroke-duration variability can be dealt with by time-axis normalization prior to averaging. Examples of averaging at the stroke, letter, and word levels are also presented in the chapter. Results indicated that up to four letters can be averaged without a noticeable distortion in the spatial domain. The time-normalization technique can be a valuable tool in movement analysis, pattern matching, and simulation. Before it can be applied, careful inspection of the stroke-onset time variability is required. When the homothetic assumptions are violated in a handwriting segment, subsegments have to be defined, thereby warping the time axis. In movement analysis, time normalization and averaging can be used to detect special strategies in the velocity profiles that are used by the subject to obtain specific curvature shape in the spatial domain. In pattern matching of handwriting signals, the technique can be of use by providing reliable averages that are used as templates. In the simulation of handwriting, time-axis normalization is used to obtain reliable averages of letters and connecting strokes from a writer.

Abstract: A Comment on the Letter by S. V. Akulinichev e-italict-italic a-italicl-italic., Phys. Rev. Lett. 55, 2239 (1985).

Abstract: Several recent reports have addressed the problem of estimating the response slope from repeated measurements of paired data when both stimulus and response variables are subject to biological variability. These earlier approaches suffer from several drawbacks: useful information about the relationships between the error components in a closed-loop system is not fully utilized; the response intercept cannot be directly estimated; and the normalization procedure required in some methods may fail under certain circumstances. This paper proposes a new, general method of simultaneously estimating the response slope and intercept from corrupted stimulus-response data when the errors in both variables are specifically related by the system structure. A direct extension of the least-squares approach, this method [directed least squares (DLS)] reduces to ordinary least-squares methods when either of the measured variables is error free and to the reduced-major-axis (RMA) method of Kermack and Haldane (Biometrics 37: 30-41, 1950) when the magnitudes of the normalized errors are equal. The DLS estimators are scale invariant, statistically unbiased and always assume the minimum variance. With simple modifications, the method is also applicable to paired data. If, however, the relation between error components is uncertain, then the RMA method is optimal, i.e., having the least possible asymptotic bias and variance. These results are illustrated by using various types of closed-loop respiratory response data.

Abstract: By computing probabilities from the normalization of the F distribution (instead of by numerical integration methods), statistical capabilities in spreadsheet operations can be greatly expanded and enhanced.

Abstract: Subjective probability considered as a logic of partial belief succumbs to three fundamental fallacies. These concern the representation of preference via expectation, the measurability of partial belief, and the normalization of belief.

Abstract: The calculation of orientation distribution functions from incomplete pole figures can be carried out by a least squares approximation of the texture coefficients Clμν and the normalization factors Nhkl to the available experimental data. This procedure is less susceptable to instabilities due to experimental errors if the normalization factors can be calculated independently of the coefficients Clμν. In the case of cubic materials, the relationship F20 = 0 to be fulfilled by pole figure values provides an independent condition for the calculation of the normalization factor. This condition can still be improved by taking the slopes of the pole density curves at α = αmax⁡ and α = 90° into account. An economic way to consider the slope in the pole figures is to use a cubic spline interpolation.

Abstract: In the current versions of the Dempster-Shafer theory, the only essential restriction on the validity of the rule of combination is that the sources of evidence must be statistically independent. Under this assumption, it is permissible to apply the Dempster-Shafer rule to two or more distinct probability distributions. An essential step in the Dempster-Shafer rule of combination of evidence is that of normalization. The validity of normalization is open to question, particularly in application to probability distributions (Zadeh, 1976). At this juncture, the validity of normalization is a controversial issue. In this paper, we construct a relational model for the Dempster-Shafer theory which greatly simplifies the derivation of its main results and cast considerable light on the validity of the rule of combination. The relational model is augmented with what is called the ball-box analogy, yielding an intuitively simple way of visualizing the concepts of belief and plausibility.

Abstract: PURPOSE: To perform a data conversion at high speed, by providing a first instruction which performs the data conversion from a binary floating point data to a hexadecimal floating point data, and a second conversion instruction which performs the reverse data conversion. CONSTITUTION: In a form conversion at a binary to hexadecimal conversion processing part, a data 1 of form IE 3 is fetched, and when it is the data other than a de-normalized number, or, a non-or-infinity number, a data 2 of the HEX form can be obtained through processes of an index correction 2, a normalization quantity calculation 3, a hidden bit addition 4, a HEX normalization 5, and a result storing 6. Meanwhile, in the form conversion at a hexadecimal to binary conversion processing part, a data 2 of the HEX form is fetched, and when it is other than '0', the processes of an index correction 9, a mantissa normalization 10, an index normalization correction 11, an underflow check 12, and an overflow check 13, are performed, and a data 1 of form IE 3 can be obtained. COPYRIGHT: (C)1987,JPO&Japio

Abstract: As is well known, in general some kind of normalization conditions is needed in order to guarantee the uniquness of solutions to the boundary value problems for elliptic equations with natural boundary conditions. A prototype is the Neumann problem for the Laplace equation in a bounded domain. Here a simple normalization condition may be the vanishing integral of the solution over the domain. In the numerical implementation, these normalization conditions will cause inconvenience in choosing the appropriate approximate function spaces. In this paper, we propose a modified Galerkin scheme for treating such problems. By augmenting the system under consideration with suitable eigensolutions, we will show that standard finite elements are readily employed.

Abstract: : Knowledge of the noise probability density function is central in signal detection problems, not only for optimum receiver structures but also for processing procedures such as power normalization. The statistical knowledge must be acquired since the classical assumption of a Gaussian noise PDF is often not valid in underwater acoustics. This report studies statistical modeling by a Gaussian-Gaussian mixture for three different underwater noise samples. One of them can adequately be described by a Gaussian-Gaussian mixture, one is very close to a Gaussian model and is described by a mixture with a very small perturbating term, whereas the third one seems closer to the Middleton class A model but is non-stationary. The first noise is studied with emphasis on the normalization needed in the receiver in order to achieve a constant false alarm probability and also on the optimal receiver structure for the detection of a deterministic signal. It is shown that the classical noise power estimate, calculating the norm L-squared of the observation vector, is a good approximation to the square of the maximum likelihood estimator of the noise amplitude for the Gaussian-Gaussian mixture.

Abstract: Weather normalization of electricity sales adjusts actual electricity sales to the levels that would have occured if weather had been normal. Normalization facilities performance evaluation by shareholders and regulators as well as providing valuable input for internal electric utility planning functions. The major concern utility analysts have expressed over their existing weather normalization procedures involves the extent to which non-weather variables are accounted for. This investigation demonstrates the significance for the weather normalization of electricity sales to schools of one particular non-weather variable, viz a changing distribution of types of heating, ventilating, and air conditioning equipment.

Abstract: Vowel classification is considered from the viewpoint of cluster separation in a vector space, with Mahalanobis distance as the criterion. The number of significant axes of variation needed to characterize each speaker, weighted with respect to cluster separation, is found from actual formant data to be on the order of four, and the potential improvement in separation accountable to structure in the data is estimated at about 3 db by comparison with results for the same procedure applied to random data.

Abstract: Table 1 in the original paper is practical and useful. But a normalization factor needs to be pointed out to make the table ready to use.