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Purpose: Dynamic 18F‐FDG PET allows quantitative estimation of cerebral glucose metabolism both at the regional and local (voxel) level. Although sensitive to noise and highly computationally expensive, nonlinear least‐squares (NLS) optimization stands as the reference approach for the estimation of the kinetic model parameters. Nevertheless, faster techniques, including linear least‐squares (LLS) and Patlak graphical method, have been proposed to deal with high resolution noisy data, representing a more adaptable solution for routine clinical implementation. Former research investigating the relative performance of the available algorithms lack precise evaluation of kinetic parameter estimates under realistic acquisition conditions. Methods: The present study aims at the systematic comparison of the feasibility and pertinence of kinetic modeling of dynamic cerebral 18F‐FDG PET using NLS, LLS, and Patlak method, based on numerical simulations and patient data. Numerical simulations were used to study the bias and variance of K1 and Ki parameters estimation under representative noise levels. Patient data allowed to assess the concordance between the three methods at the regional and voxel scale, and to evaluate the robustness of the estimations with respect to patient head motion. Results and Conclusions: Our findings indicate that at the regional level NLS and LLS provide kinetic parameter estimates (K1 and Ki) with similar bias and variance characteristics (K1 bias ± relative standard deviation [RSD] 0.0 ± 5.1% and 0.1% ± 4.9% for NLS and LLS respectively, Ki bias ± RSD 0.1% ± 4.5% and −0.7% ± 4.4% for NLS and LLS respectively). NLS estimates appear, however, to be slightly less sensitive to patient motion. At the voxel level, provided that patient motion is negligible or corrected, LLS offers an appealing alternative solution for local K1 mapping. It yields K1 estimates that are highly correlated, with high correlation with NLS values (Pearson's r = 0.95 on actual data) within computations times less than two orders of magnitude lower. Last, Patlak method appears as the most robust and accurate technique for the estimation of Ki values at the regional and voxel scale, with or without head motion. It provides low bias/low variance Ki quantification (bias ± RSD −1.5 ± 9.5% and −4.1 ± 19.7% for Patlak and NLS respectively) as well as smooth parametric images suitable for visual assessment. [ABSTRACT FROM AUTHOR]

The article analyses a Cockcroft-Walton circuit by graphical model. Many kinds of condenser diode voltage multipliere have been proposed so far, but the design procedures have been discussed little. An effective method is proposed to analyze the behavior of the Cockcroft-Walton circuit. This method makes it possible to calculate the output voltage much more accurately than the conventional design formulas. The proposed method would be useful for various circuits other than the Cockcroft-Walton circuit.

This paper presents a local search, based on a new neighborhood for the job-shop scheduling problem, and its application within a biased random-key genetic algorithm. Schedules are constructed by decoding the chromosome supplied by the genetic algorithm with a procedure that generates active schedules. After an initial schedule is obtained, a local search heuristic, based on an extension of the graphical method of Akers, is applied to improve the solution. The new heuristic is tested on a set of 205 standard instances taken from the job-shop scheduling literature and compared with results obtained by other approaches. The new algorithm improved the best-known solution values for 57 instances. [ABSTRACT FROM AUTHOR]

The potential of using differences in log crude mortality rates, matched age for age, as a simple means of comparing two mortality studies is investigated. Graphical displays of such differences, plotted against age, are advocated and a method of curve fitting described. A number of applications are presented, and the results of this approach compared with known results, where available. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The article presents the study on the method used for the flux underestimation from chamber deployment to measure soil-atmosphere exchange of gases. The method seeks to simplify the gas transport theory application in the determination of the magnitude of flux underestimation under specific soil and measurement solutions. It presents techniques such as the numerical technique and the graphical method in which the magnitude is determined. Results show that the actual predeployment flux is difficult to determine directly under field conditions due to instant feedback of chamber gas concentrations on soil-gas diffusion. It also concludes that the method is beneficial in the accuracy of fluxes obtained from chambers and makes a way to improve emissions assessments on studies and scales.

Actual pumping tests may involve continuously decreasing rates over a certain period of time, and the hydraulic conductivity (K) and specific storage (Ss) of the tested confined aquifer cannot be interpreted from the classical constant‐rate test model. In this study, we revisit the aquifer drawdown characteristics of a pumping test with an exponentially decreasing rate using the dimensionless analytical solution for such a variable‐rate model. The drawdown may decrease with time for a short period of time at intermediate pumping times for such pumping tests. A larger ratio of initial to final pumping rate and a smaller radial distance of the observation well will enhance the decreasing feature. A larger decay constant results in an earlier decrease, but it weakens the extent of such a decrease. Based on the proposed dimensionless transformation, we have proposed two graphical methods for estimating K and Ss of the tested aquifer. The first is a new type curve method that does not employ the well function as commonly done in standard type curve analysis. Another is a new analytic method that takes advantage of the decreasing features of aquifer drawdown during the intermediate pumping stage. We have demonstrated the applicability and robustness of the two new graphical methods for aquifer characterization through a synthetic pumping test. [ABSTRACT FROM AUTHOR]

This research proposes a novel, autonomous, regression‐based methodology for Allan variance analysis of inertial measurement unit (IMU) sensors. Current methods for Allan variance analysis have been rooted in the human‐based interpretation of linear trends, referred to as the slope method. The slope method is so prolific; it is referenced among electrical and electronics engineering standards for IMU error analysis. However, the graphical nature and visual‐inspection–based use of the method limit its ability to be programmed as a generalized algorithm, which hinders the autonomy desired in modern‐day navigation computations. Using nonlinear regression with a ridge‐regression initial guess, the proposed method is shown to produce comparable results to the gold standard slope method when using standard‐length data collections and outperforms the slope method when the amount of available data is limited. This development directly enables accurate navigation solutions for all vehicles in land, air, sea, and space operations. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the generalized output synchronization problem for discrete dynamic networks with non-identical nodes. We consider two cases: output synchronization for fixed topology and arbitrary switching topology. For the first case, we establish several criteria for generalized output synchronization using the geometrical dissipativity property. For the other case, we present a LaSalle invariance principle for discrete switched systems, based on which criteria for generalized output synchronization under arbitrary switching topology are given. Finally, an example is provided to illustrate the effectiveness of the main results. [ABSTRACT FROM AUTHOR]

The investigation of heterogeneity remains an essential but difficult issue in the conduct of meta-analysis. We reviewed standard and graphical methods used to explore heterogeneity in meta-analysis and publications from January 2005 to April 2007 regarding meta-analyses that focused on perinatal health topics. We assessed their approaches to the investigation of heterogeneity, including: (1) whether statistical testing for heterogeneity was performed and, if so, which test was used, (2) how a finding of statistically significant heterogeneity was handled, and (3) how the analyses were conducted in the presence of heterogeneity. [ABSTRACT FROM AUTHOR]

We introduce the concept of process capability plots, which are powerful tools to monitor and improve the capability of industrial processes. An advantage of using a process capability plot, compared with using a traditional process capability index alone, when deciding whether a process can be considered capable or not, is that we will instantly get information about the location and spread of the studied characteristic. When the process is non-capable, the plots are helpful when trying to understand if it is the variability, the deviation from target or both that need to be reduced to improve the capability. In this way the proposed graphical methods give a clear direction of quality improvement. We evaluate two different process capability plots, the (δ*, γ*)-plot and the confidence rectangle plot, from a theoretical as well as a practical point of view. When studying them from a theoretical point of view, among other things, a simulation study is conducted to investigate the ability of each of the two methods to identify that a process is capable when it actually is. The comparison from a practical point of view is made by discussing the advantages and disadvantages of the two methods in different practical situations. Based on the above-mentioned comparisons, the recommendation is that the practitioner should use the (δ*, γ*)-plot. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Illustrates the use of graphical analysis as a complementary diagnostic tool in financial classification problem. Classification problem and financial distress; Use of the scatterplot matrix.