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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]

Abstract: Increase in refining demand and tighter environmental regulations have led to sharp increases in hydrogen consumption of oil refineries. Hydrogen conservation and effective use are of interest to refineries whose operations and profitability are constrained by hydrogen. Purification is widely used in hydrogen networks of refineries to reduce hydrogen production load. To minimize hydrogen utility consumption, it is necessary to optimize the hydrogen network with purification as a whole. In this paper, for hydrogen purification process, a triangle rule (which can be generalized to polygon rule) is proposed for graphical representation of its mass balance. The proposed procedure treats the product concentration and recovery rate of the purification process as adjustable parameters. An ensuing graphical method is developed for targeting the pinch point and minimum utility consumption of the hydrogen system with purification reuse. This graphical method can be used for any purification devices and in systems with any utility concentration. A refinery case is studied to demonstrate the optimization method. [ABSTRACT FROM AUTHOR]

Presents information on a study which determines a graphical method of exploring the mean structure in longitudinal data analysis. How longitudinal data arises; Error structure; Range of representation.

Suggested here is a simple graphical method for studying the goodness of fit in Cox's regression model for survival data. The method is easy to use, as it does not require the estimation of alternative models and only involves quantities similar to those already appearing in the partial likelihood expression that is needed in the parameter estimation. The rationale behind the graphs is very intuitive: They make a direct comparison between observed and expected failure frequencies, as estimated from the model. In a correctly specified model one anticipates an approximate balance between such frequencies; otherwise there will typically be groups of individuals for which the expected frequencies are systematically too high or too low to match with the data, and this shows in the graphs introduced here. In the concrete applications of the method the individuals are stratified in a way that depends on what aspect of the model is being checked against data. There is always one graph for each stratum. Simulated and real data are used to illustrate the method. In the simulations two types of defect that can come up in a Cox's model are considered: (a) an influential covariate has been deleted from the model, and (b) a common baseline hazard for all individuals has been assumed in a case in which the individuals should be stratified according to baseline hazard. Serious defects in the model are relatively easy to detect from the diagnostic graphs. As concrete applications of the method, studied briefly are the fitting of Cox's model to the well-known Stanford heart transplant data and to a data set describing the survival of malignant melanoma patients after operation. The article concludes with some general observations concerning the randomness in the graphs. [ABSTRACT FROM AUTHOR]

This article approaches the problem of selecting significant principal components from a Bayesian model selection perspective. The resulting Bayes rule provides a simple graphical technique that can be used instead of (or together with) the popular scree plot to determine the number of significant components to retain. We study the theoretical properties of the new method and show, by examples and simulation, that it provides more clear-cut answers than the scree plot in many interesting situations. [ABSTRACT FROM AUTHOR]

The goaf left behind after mining has the potential to induce serious geological disasters due to the damaged internal structure of the rock. Estimating the boundary of the underground goaf can effectively control the occurrence of such disasters. However, traditional geophysical methods are inefficient and expensive and are particularly difficult to apply for a wide detection range. This paper proposes a new method for estimating the boundary of underground goaf using the differential interference synthetic aperture radar technique (DInSAR). More specifically, DInSAR is used to obtain the isoline of the subsidence basin above the goaf, and the direction of the two main sections of the goaf is then determined according to the basic law of mining subsidence. Following this, the basic principles of the probability integral and the graphical methods are combined to determine the mining boundary of the strike section and the incline section of the goaf. Finally, six geometric parameters reflecting the boundary of the goaf are obtained. Experiments on simulated and measured data indicate that the proposed method is feasible, with the average relative errors of the simulated and measured data reaching and maintained at 2.2% and 3.7%, respectively. [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.

In product development processes and in the engineering world in general, many situations arise in which a decision must be taken to choose the best alternative or concept from among several already existing ones. Among the most used methods in situations like these are those that use two-dimensional decision matrices, where the concepts or alternatives are compared by evaluating them according to the degree of compliance for preestablished quality criteria. The finally adopted decision is not only conditioned by the decision maker's assessment of each alternative but also by the weightings initially assigned to the criteria. This means that variation in the assessment of any alternative or in the weighting of a criterion can lead to a distinct alternative being selected. In this article, we propose a graphical method that makes it simpler to view the margin for variation, for both the assessments of the alternatives and the weightings for the quality criteria, that does not affect the finally adopted decision. In this way, the decision-making team can analyze in greater depth the more critical assessments and weightings that, although consisting of small changes, could affect the decision. Finally, the applicability of the proposed method is demonstrated in a case study involving an electrical switch design. [ABSTRACT FROM PUBLISHER]

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]

Focuses on the graphical method for assessing the logistic regression. Discrepancy measurement of the Bayes marginal model plot (BMMP); Methodology of BMMP; Use of standard continuous data smoothers in BMMP.

The major objective of the design of safe crowded transmitting antenna sites is not only to determine a safe zone around each individual antenna; rather, to establish safety areas at the antenna site itself, as well as, at the neighboring areas. The requirement is to ascertain the safety regions by considering the following parameters at each Test Point (TP) (or area segment): the contribution of N co-located radiating antennas to the total radiation incident at the TP, the radiation pattern of each antenna, the near/far field region of each antenna, and most importantly, the different Permissible Exposure Limits (PELs) associated with each operating frequency at the antenna site. Implementation of all the above-mentioned aspects in a suitable computer requires resources that only expert knowledgeable organizations possess. The graphically aided tool presented in this paper facilitates the calculation of a “safety zone” for RADHAZ around a crowded antenna site from the knowledge of the “safety ranges” which correspond to the individual transmitting antennas comprising it. [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]

We develop in detail a graphical tensor product reduction scheme, first described by Antoine and Speiser, for the simple rank 2 Lie algebras s o ( 5 ) = s p ( 2 ) , s u ( 3 ) , and g ( 2 ) . This leads to an efficient practical method to reduce tensor products of irreducible representations into sums of such representations. For this purpose, the 2-dimensional weight diagram of a given representation is placed in a “landscape” of irreducible representations. We provide both the landscapes and the weight diagrams for a large number of representations for the three simple rank 2 Lie algebras. We also apply the algebraic “girdle” method, which is much less efficient for calculations by hand for moderately large representations. Computer code for reducing tensor products, based on the graphical method, has been developed as well and is available from the authors upon request. [ABSTRACT FROM AUTHOR]

The rationale of Econographicology revolves around the efficacy of multidimensional graphs as the most effective visual tool to understand any economic phenomenon from a multidimensional view. The main motivation behind the creation of Econographicology is to evaluate multidimensional graphs evolved so far in economics and to develop new type of multidimensional graphs to facilitate the study of economics, as well as finance and business. Thereby, the mission of Econographicology is to offer academics, researchers and policy maker's an alternative multidimensional graphical modeling approach for the research and teaching-learning process of economics, finance and business from a multidimensional perspective. Hence, this alternative multidimensional graphical modeling approach is offer a set of multi-dimensional coordinate spaces to build different types of multidimensional graphs to study any economic phenomenon. The following new types of multi-dimensional coordinate spaces are presented: the 5-dimensional coordinate space (vertical position and horizontal position), the mega-dynamic disks coordinate space (vertical position and horizontal position), and the mega-disks networks mapping. [ABSTRACT FROM AUTHOR]

The methods proposed by Kezdi' and Sherard' are widely used to assess the internal stability of granular soils due to their simplicity, although their accuracy is questionable, especially for widely graded soils. A modification was thus developed to increase the accuracy of these methods while keeping them as straightforward as possible. A simple graphical method is proposed to determine the possible range of delimiting particle size and then the Kezdi and Sherard methods are applied only to this range. The proposed modification was verified with a large number of experimental test results. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new measure of fit which can be used in the case of quantile–quantile plots. This measure, when applied to Small's and Srivastava's graphical methods provides two new tests for assessing multivariate normality. For different sample sizes and numbers of variables, the critical values of these tests were evaluated via simulations. The power of the new tests and its comparison with some other tests for multivariate normality are presented herein. [ABSTRACT FROM AUTHOR]

Invalid PVT data provide high uncertainty in field development studies such as reservoir fluid compartmentalization, reserve estimation, reservoir simulation, production engineering, and surface facility design. Then, consistency check should be conducted to ensure the validity of PVT data and to identify the most representative PVT sample(s). In this paper, preliminary and complementary consistency check of PVT laboratory methods was applied to design a new comprehensive validity check procedure for verification of the reservoir fluid properties. This procedure would be ascertained whether or not the data could be used as the most representative fluid sample in further studies. The data used in this study were collected from seven undersaturated oil reservoirs, and challenges were observed through the 28 full set of available PVT laboratory data. In our study quality checking procedure of PVT samples consists of different methods such as graphical method, recombination and material balance check for well stream composition test, Buckley, modified Wilson and Hoffman plot, Watson characterization factor, Y-function of CCE test, Y-function of DL test, compositional material balance of DL test, overall mass balance for density, Bo and GOR of DL test and density check for separator test. After implementing the applicable proposed checking procedure to detect the validity of laboratory PVT sample, only 9 out of 28 PVT samples were satisfied all the preliminary and complementary check methods. Furthermore, a practical strategy, to select representative reservoir fluid sample, was also provided and discussed based on the consistency check, well condition check and comparison of fluid properties. [ABSTRACT FROM AUTHOR]

Azeotropic distillation as an early and important special distillation process is commonly used in laboratory and industry. It can be used for separating the mixture with close boiling point or forming azeotrope. This paper tries to provide a review on azeotropic distillation for general readers, focusing on entrainer selection and mathematical models. Since the 1950s, along with extractive distillation, azeotropic distillation has gained a wide attention. Like extractive distillation, the entrainer, i.e., the third component added to the system, is also the core of azeotropic distillation. In the process design and synthesis, the graphical method (in most cases refer to as triangular diagram) is often employed. But it is better to take on the results from graphical method as the initial values of rigorous equilibrium (EQ) stage/non-equilibrium (NEQ) stage models. One outstanding characteristic of the EQ/NEQ stage models different from extractive distillation and catalytic distillation is to describe phase split for heterogeneous azeotropic distillation. In general, the operation process is very sensitive to some parameters in the case of more than one azeotrope formed, and thus the phenomenon of multiple steady states (MSS) tends to appear. [ABSTRACT FROM AUTHOR]

Generalized functions, in particular the Heaviside unit step H(t) and the Dirac delta impulse δ(t), are valuable teaching tools in many contexts of electric circuits. However, engineering undergraduate courses and textbooks normally cover only an introduction to these functions along with their basic properties, without tackling the rigorous mathematical framework of the theory of distributions. In this work, the Heaviside function is used to represent a square wave signal f(t), and the Dirac function appears when the derivative is calculated. The steps for obtaining f'(t) compare a graphical method with analytical procedures that employ the chain rule. The topic is further extended with the presentation of a theorem and a proposed corollary related to the study of the chain rule applied to general functions involving H(t) and δ(t). Thus, the work provides an appropriate mathematical support for the intuitive graphical method of analysis, which is very familiar in engineering practice. [ABSTRACT FROM AUTHOR]

The article deals with a study on a graphical method which sequences the individual activities that make up a project. This simple graphical method sequences the individual activities that make up a project, at the same time obtaining a preliminary early start schedule. More elementary than the Critical Path Method (CPM), it uses ordinary counting of time units rather than topological networks. The real-time procedure is especially helpful when considering expediting. The performance time tells how many time units it takes to perform the activity. Several activities may be carried out at once if all precedence requirements have been met. The object is to finish the project as soon as possible, and to determine what restrictions the minimum project time imposes on scheduling the various activities. As an arrow is shortened to show shorter performance time, the following arrow structures are pulled back, eventually encountering other arrow points, as new critical paths emerge. The loading capability of the method was grasped immediately as a technique for scheduling limited facilities such as oven and counter space.

This paper proposes a method for determining an development of the rotation surface is the rotation of hypocycloids around a vertical axis represents the axis of symmetry of the curve. It has been chosen a four-cusped hypocycloid called astroid, because, due to its aesthetic shape, this could be used in engineering and architecture. This paper proposes getting the development for a semi- astroidoid. It is applied the graphical method of descriptive geometry by analogy with the blank sphere drawing method of spherical gores. This approximate graphical method is applied relatively simple and can be used when a high precision is not required. [ABSTRACT FROM AUTHOR]

A simple graphical method is presented to classify aerosol types based on a combination of aerosol optical thickness (AOT) and aerosol relative optical thickness (AROT). Six aerosol types, including maritime (MA), desert dust (DD), continental (CO), sub-continental (SC), urban industry (UI) and biomass burning (BB), are discriminated in a two dimensional space of AOT 440 and AROT 1020/440 . Numerical calculations are performed using MIE theory based on a multi log-normal particle size distribution, and the AROT ranges for each aerosol type are determined. More than 5 years of daily observations from 8 representative aerosol sites are applied to the method to confirm spatial applicability. Finally, 3 individual cases are analyzed according to their specific aerosol status. The outcomes indicate that the new graphical method coordinates well with regional characteristics and is also able to distinguish aerosol variations in individual situations. This technique demonstrates a novel way to estimate different aerosol types and provide information on radiative forcing calculations and satellite data corrections. [ABSTRACT FROM AUTHOR]

This paper studies the consensus problem of multi-agent systems (MASs) with false data injection (FDI) attacks and noises. Based on the graphical method and Kalman filter framework, distributed state estimators are designed for the agents to estimate the states of neighbors. A threshold comparison approach is proposed to obtain the secure states. Combining the state estimation approach with the threshold scheme, security mechanism is put forward to ensure the mean square consensus of MASs subject to FDI attacks. Finally, numerical simulations are provided to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

The complex alias pattern between main effects and two-factor interactions for two-level nonregular designs has been considered a problem when analyzing these designs. If only a few two-factor interactions are active, however, the pattern induced into the estimated main effects contrasts from the active interactions may be very structured. This is, in particular, true for the 12-run and the 20-run Plackett–Burman (PB) designs, probably the two most important designs for physical experimentation. This article presents a graphical method for the analysis of nonregular two-level designs. The method consists of two steps. The first step is called contrast plots interpretation and is directed toward revealing the cause for the pattern observed in contrast plots. The second step is called alias reduction and aims at simplifying the interpretation of the contrast plots by reducing the aliasing caused by effects that, with a high degree of certainty, may be considered active. The method is tested on the 12-run PB design both with simulated and real data and on the 20-run PB design for one particular case with real data. Supplementary materials (MINITAB codes for performing calculations and plots) are available online. [ABSTRACT FROM AUTHOR]

The aim of this work was to quantify the brain distribution of the enzyme aromatase in the female baboon with positron emission tomography and the tracer [11C]vorozole using three different quantification methods for estimating the total distribution volume (VT): a graphical method, compartment modeling, and a tissue to plasma ratio. The graphical model and the compartment modeling gave similar estimates to the data and similar values (correlation R = .988; p = .0001). [11C]Vorozole shows a rapid uptake by the brain followed by a relatively constant accumulation, suggesting the possibility of using the tissue to plasma ratio as an estimate of VT. The highest uptake of [11C]vorozole in the baboon brain was measured in the amygdala, followed by the preoptic area and hypothalamus, basal ganglia, and cortical areas, Pretreatment studies with vorozole or letrozole showed a generalized decrease in brain accumulation and VT. The results suggested that the physiologic changes in gonadal hormone levels accompanying the menstrual cycle had a significant effect on brain aromatase VT. [ABSTRACT FROM AUTHOR]

Phylogenetic studies based on molecular sequence alignments are expected to become more accurate as the number of sites in the alignments increases. With the advent of genomic-scale data, where alignments have very large numbers of sites, bootstrap values close to 100% and posterior probabilities close to 1 are the norm, suggesting that the number of sites is now seldom a limiting factor on phylogenetic accuracy. This provokes the question, should we be fussy about the sites we choose to include in a genomic-scale phylogenetic analysis? If some sites contain missing data, ambiguous character states, or gaps, then why not just throw them away before conducting the phylogenetic analysis? Indeed, this is exactly the approach taken in many phylogenetic studies. Here, we present an example where the decision on how to treat sites with missing data is of equal importance to decisions on taxon sampling and model choice, and we introduce a graphical method for illustrating this. [ABSTRACT FROM AUTHOR]

In order to gather the information about the lifetime distribution of a product, a standard life testing method at normal operating conditions is not practical when the product has an extremely long lifespan. Accelerated life testing solves this diffcult issue by subjecting the test units at higher stress levels than normal for quicker and more failure data. The lifetime at the design stress is then estimated through extrapolation using an appropriate regression model. Estimation of the regression parameters based on exponen- tially distributed lifetimes from accelerated life tests has been considered by a number of authors using numerical methods but without systematic or an- alytical validation. In this article, we propose an alternative approach based on a simple and easy-to-apply graphical method, which also establishes the existence and uniqueness of the maximum likelihood estimates for constant- stress and step-stress accelerated life tests under progressive censorings. [ABSTRACT FROM AUTHOR]

Abstract Consistency is related with reasonableness. This paper proposes a graphical method to visualize and rectify different inconsistencies for fuzzy reciprocal preference relations (FPRs), and the consistency includes the ordinal and cardinal consistencies. Ordinal inconsistency implies cardinal inconsistency, but not vice versa, and cardinal consistency of FPRs includes additive consistency and multiplicative consistency. Therefore, there are four types of inconsistencies, includes: (1) the additive inconsistency; (2) the multiplicative inconsistency; (3) the ordinal and additive inconsistencies, and (4) the ordinal and multiplicative inconsistencies. First, Gower plots are proposed to visualize the ordinal and cardinal inconsistencies on a two-dimensional plane. Then, some optimization models are formulated to rectify the four different types of inconsistences, respectively. Some examples are illustrated to show how the models work, and comparisons with the existing methods are also offered to show the advantages of the proposed methods. [ABSTRACT FROM AUTHOR]

The worksheets that presumably contained Newton's early development of the fundamental concepts in his Principia have been lost. A plausible reconstruction of this development is presented based on Newton's exchange of letters with Robert Hooke in 1679, with Edmund Halley in 1686, and on some clues in the diagram associated with Proposition 1 in Book 1 of the Principia that have been ignored in the past. A graphical construction associated with this proposition leads to a rapidly convergent method to obtain orbits for central forces, which elucidates how Newton may have have been led to formulate some of his most fundamental propositions in the Principia. [ABSTRACT FROM AUTHOR]

Purpose: This study was designed to apply artificial neural network (ANN) classification methods for the prediction of late fecal incontinence (LFI) after high-dose prostate cancer radiation therapy and to develop a ready-to-use graphical tool.Materials and Methods: In this study, 598 men recruited in 2 national multicenter trials were analyzed. Information was recorded on comorbidity, previous abdominal surgery, use of drugs, and dose distribution. Fecal incontinence was prospectively evaluated through self-reported questionnaires. To develop the ANN, the study population was randomly split into training (n = 300), validation (n = 149), and test (n = 149) sets. Mean grade of longitudinal LFI (ie, expressed as the average incontinence grade over the first 3 years after radiation therapy) ≥1 was considered the endpoint. A suitable subset of variables able to better predict LFI was selected by simulating 100,000 ANN configurations. The search for the definitive ANN was then performed by varying the number of inputs and hidden neurons from 4 to 5 and from 1 to 9, respectively. A final classification model was established as the average of the best 5 among 500 ANNs with the same architecture. An ANN-based graphical method to compute LFI prediction was developed to include one continuous and n dichotomous variables.Results: An ANN architecture was selected, with 5 input variables (mean dose, previous abdominal surgery, use of anticoagulants, use of antihypertensive drugs, and use of neoadjuvant and adjuvant hormone therapy) and 4 hidden neurons. The developed classification model correctly identified patients with LFI with 80.8% sensitivity and 63.7% ± 1.0% specificity and an area under the curve of 0.78. The developed graphical tool may efficiently classify patients in low, intermediate, and high LFI risk classes.Conclusions: An ANN-based model was developed to predict LFI. The model was translated in a ready-to-use graphical tool for LFI risk classification, with direct interpretation of the role of the predictors. [ABSTRACT FROM AUTHOR]

Abstract: The film-diffusion and the intraparticle-diffusion models are widely used to analyze the mechanism of adsorption. The plots of these models often have a multi-linear nature, and in general, the graphical method is employed to analyze the data in which the linear segments are determined visually. This method suffers from subjectivity and therefore its estimated diffusion parameters are not very reliable. An alternative statistical method, piecewise linear regression (PLR) is presented and applied to experimental data. The results demonstrate that the use of PLR is practical and leads to diffusion estimates that may be quite different from the graphical method. PLR also determined the exact time periods for each diffusion regime, which opens new possibilities for analyzing and understanding the mechanism of diffusion. In order to encourage the testing and application of PLR, an easy to use Microsoft® Excel™ spreadsheet is made available. [Copyright &y& Elsevier]

The problem of enforcing two-variable nonlinear interaction code provisions within a spectral superposition approach to design, is addressed. An analytical procedure based on the linearization of the interaction curve through a set of tangents or secants is developed. Safety with respect to the interaction curve is approximated by requiring safety with respect to that set of straight lines. For calculating the required estimators, the cross-estimator based formula for estimators of the linear combination of variables, derived in a companion paper, is used.The analytical method developed was shown to be equivalent to a graphical method proposed by Gupta, based on inscribing an estimator ellipse within the interaction curve. The analytical method is more straightforward and handles the directional maximum in single-component excitation, which the graphical method does not. The analytical method is much easier to apply. However, if a study calls for actually drawing the estimator ellipse, straightforward construction methods are presented, making unnecessary a cumbersome equivalent modal response approximation that had been suggested. The inherent antisymmetry of the spectral superposition formula, and its implications, are discussed. The effect of static loading and of symmetry of the interaction curve is also analyzed.Within the analysis of an example, the work required for the application of the procedure for nonlinear interaction for design purposes is discussed. It is found that its implementation can be achieved through a very simple function written for any standard numerical computation software package. The example also makes quite apparent the advantages of the analytical over the graphical method.The application example, which considers the design of a concrete column in a simple 10-storey building structure, shows the overconservativeness of a design based only in the standard estimators. The design criterion used in the example is that of the most unfavorable direction of a single-component earthquake. [Copyright &y& Elsevier]

Proposes a graphical method for assessing parametric transformation of the response in a linear regression model. Examples of response formations using data from an experiment on the behavior of worsted yarns; Details of the proposed method; Application of the linearity condition to the marginal distribution of the predictors.

We provide unconstrained parameterisation for and model a covariance using covariates. The Cholesky decomposition of the inverse of a covariance matrix is used to associate a unique unit lower triangular and a unique diagonal matrix with each covariance matrix. The entries of the lower triangular and the log of the diagonal matrix are unconstrained and have meaning as regression coefficients and prediction variances when regressing a measurement on its predecessors. An extended generalised linear model is introduced for joint modelling of the vectors of predictors for the mean and covariance subsuming the joint modelling strategy for mean and variance heterogeneity, Gabriel's antedependence models, Dempster's covariance selection models and the class of graphical models. The likelihood function and maximum likelihood estimators of the covariance and the mean parameters are studied when the observations are normally distributed. Applications to modelling nonstationary dependence structures and multivariate data are discussed and illustrated using real data. A graphical method, similar to that based on the correlogram in time series, is developed and used to identify parametric models for nonstationary covariances. [ABSTRACT FROM PUBLISHER]

Overdispersion is a common feature in categorical data analysis and several methods have been developed for detecting and handling it in generalized linear models. The first aim of this study is to clarify the relationships among various score statistics for testing overdispersion and to compare their performances. In addition, we investigate a principled way to correct finite sample bias in the score statistic caused by estimating regression parameters with restricted likelihood. The second aim is to reconsider the current practice for handling overdispersed categorical data. Although the conventional models are based on substantially different mechanisms for generating overdispersion, model selection in practice has not been well studied. We perform an intensive numerical study for determining which method is more robust to various overdispersion mechanisms. In addition, we provide some graphical tools for identifying the better model. The last aim is to reconsider the key assumption for deriving the score statistics. We study the meaning of testing overdispersion when this assumption is violated, and we analytically show the conditions for which it is not appropriate to employ the current statistical practices for analyzing overdispersed data. [ABSTRACT FROM AUTHOR]

The paper proposes an approximate graphical method for determining the development of the revolution surface obtained by means of the deltoid. The approximate development of the revolution surfaces are based on general methods of development, provided by Descriptive Geometry. [ABSTRACT FROM AUTHOR]

When users input their passwords in a public place, they may be at risk of attackers stealing their password. An attacker can capture a password by direct observation or by recording the individual's authentication session. This is referred to as shoulder-surfing and is a known risk, of special concern when authenticating in public places. Attacker can also use various keylogger tools which are freely available over internet. This paper reports on the design and evaluation of a game-like graphical method of authentication that is resistant to shoulder-surfing. Since conventional password schemes are vulnerable to shoulder surfing, many shoulder surfing resistant graphical password schemes have been proposed. However, as most users are more familiar with textual passwords than pure graphical passwords, text-based graphical password schemes have been proposed. Unfortunately, none of existing text-based shoulder surfing resistant graphical password schemes is both secure and efficient enough. In this paper, we propose an improved text-based shoulder surfing resistant graphical password scheme by using colors. In the proposed scheme, the user can easily and efficiently login system. Next, we analyze the security and usability of the proposed scheme, and show the resistance of the proposed scheme to shoulder surfing and accidental login. [ABSTRACT FROM AUTHOR]

Abstract: The aim of this work is to show how the modeling of an electromechanical system can be addressed using the energy-based graphical modeling technique named “Power-Oriented Graphs” (POG). Differences and analogies of POG against Bond Graphs modeling technique are discussed. The paper presents the POG dynamic model of an automatic corking machine for threaded plastic caps: the system is composed by two electric motors moving a ball screw/spline that realizes the linear/rotary motion necessary to screw a plastic cap on a bottle. First an extended POG model is presented, together with the equivalent Bond Graph model, then some proper congruent state space transformations and a POG-based graphical method are introduced to transform and reduce the system dynamic model. Simulation and experimental results are finally presented and compared. [Copyright &y& Elsevier]

Abstract: Thanks to the electron multiplying function that can effectively convert the weak incident photon signal to amplified electron output, electron multiplying charged-coupled devices (EMCCDs) are becoming useful and popular detectors in photon counting regimes necessitating also spatial resolution. A multi-imaging strategy has been already proposed and experimentally tested to improve the accuracy of photon counting with an EMCCD, by taking into account the random nature of its on-chip gain and the possibility of multiple photodetection events on 1pixel. In this paper, referring to the thresholding procedure developed for photon counting, we present a clear graphical method for the threshold and the optimal light level estimations. Thanks to the graphical visualization of the probabilities involved in the detection errors on 1pixel, we are able to derive in a straightforward way and for any EMCCD, the threshold level and thus the best mean level of illumination to be used in order to minimize the false detection probabilities that might ruin the image statistics, especially in cases where quantum spatial effects might be observed. [Copyright &y& Elsevier]

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.

Abstract: One of the problems of analysis of forensic evidence such as glass fragments, is the determination of their use-type category, e.g. does a glass fragment originate from an unknown window or container? Very small glass fragments arise during various accidents and criminal offences, and could be carried on the clothes, shoes and hair of participants. It is therefore necessary to obtain information on their physicochemical composition in order to solve the classification problem. Scanning Electron Microscopy coupled with an Energy Dispersive X-ray Spectrometer and the Glass Refractive Index Measurement method are routinely used in many forensic institutes for the investigation of glass. A natural form of glass evidence evaluation for forensic purposes is the likelihood ratio—LR = p(E|H1)/p(E|H2). The main aim of this paper was to study the performance of LR models for glass object classification which considered one or two sources of data variability, i.e. between-glass-object variability and(or) within-glass-object variability. Within the proposed model a multivariate kernel density approach was adopted for modelling the between-object distribution and a multivariate normal distribution was adopted for modelling within-object distributions. Moreover, a graphical method of estimating the dependence structure was employed to reduce the highly multivariate problem to several lower-dimensional problems. The performed analysis showed that the best likelihood model was the one which allows to include information about between and within-object variability, and with variables derived from elemental compositions measured by SEM-EDX, and refractive values determined before (RIb) and after (RIa) the annealing process, in the form of dRI=log10|RIa −RIb|. This model gave better results than the model with only between-object variability considered. In addition, when dRI and variables derived from elemental compositions were used, this model outperformed two other classification methods in classifying test set observations into car or building windows. [Copyright &y& Elsevier]

Based on graphical method, this paper proposed the necessary condition of zero liquid discharge (ZLD) and optimized the corresponding regenerated water flowrate and regeneration concentration for single contaminant water system with fixed mass load. As far as the water system without water loss is concerned, ZLD can be accomplished when the post-regeneration concentration is not higher than the minimum limiting inlet concentration of all the operations. Moreover, considering the water system with water loss, the formulations for calculating the optimal targets (the optimal regenerated water flowrate and the optimal regeneration concentration) for ZLD are deduced. The maximum post-regeneration concentration for ZLD is defined. If the post-regeneration concentration is not higher than it, ZLD is feasible. The optimal zero discharge water network is constructed with a given post-regeneration concentration. [ABSTRACT FROM AUTHOR]

The Mohr diagram is one of the most powerful and efficient graphical methods in stress/strain analysis and structural design. However, it cannot be used to determine the direction of the shear stress or shear strain for three-dimensional states. In this paper, a three-dimensional figure is given to describe the variation of normal and shear stress on different inclined planes at one point. Based on a mathematical formulation, the direction of the total shear stress is determined, and a graphical method is proposed to represent both the magnitude and the direction of the normal stress and shear stress together. [Copyright &y& Elsevier]

This paper presents theory and applications of a simple graphical method, called hazard plotting, for the analysis of multiply censored life data consisting of failure times of failed units intermixed with running times on unfailed units. Applications of the method are given for multiply censored data on service life of equipment, for strength data on an item with different failure modes, and for biological data multiply censored on both sides from paired comparisons. Theory for the hazard plotting method, which is based on the hazard function of a distribution, is developed from the properties of order statistics from Type II multiply censored samples. [ABSTRACT FROM AUTHOR]

A graphical method is proposed to display a number of point estimates while allowing for their differing standard errors. More generally, it can be viewed as a representation of interval estimates by points on a bivariate plot. The method exploits a familiar connection between standardized estimates and regression through the origin and has several advantages over some alternative plots used in the literature. It is particularly useful when there may be a mixture of parameters, as illustrated by the problem of "mixed ages" in fission track dating. [ABSTRACT FROM AUTHOR]

Presents a graphical method for selecting power-law transformation. Applicability of nonparametric procedure; Provision of graphical perspective on different approaches to symmetric data; Suitability for exploratory data analysis.

This paper presents theory and applications of a simple graphical method, called hazard plotting, for the analysis of multiply censored life data consisting of failure times of failed units intermixed with running times on unfailed units. Applications of the method are given for multiply censored data on service life of equipment, for strength data on an item with different failure modes, and for biological data multiply censored on both sides from paired comparisons. Theory for the hazard plotting method, which is based on the hazard function of a distribution, is developed from the properties of order statistics from Type II multiply censored samples. [ABSTRACT FROM AUTHOR]

Integration of Earth system data from various sources is a challenging task. Except for their qualitative heterogeneity, different data records exist for describing similar Earth system processes at different spatiotemporal scales. Data inter-comparison and validation are usually performed at a single spatial or temporal scale, which could hamper the identification of potential discrepancies in other scales. Here, we propose a simple, yet efficient, graphical method for synthesizing and comparing observed and modelled data across a range of spatiotemporal scales. Instead of focusing at specific scales, such as annual means or original grid resolution, we examine how their statistical properties change across spatiotemporal continuum. The proposed cross-scale framework for integrating multi-source data in Earth system sciences is already developed as a stand-alone R package that is freely available to download. • A cross-scale framework for comparing datasets from different sources in all space and time scales. • Comes with a simple, yet efficient, graphical tool in R that can be useful in data validation and integration studies. • An example with climatic data coming from ground stations, radars, satellites and model simulations is presented. [ABSTRACT FROM AUTHOR]

A new functional ANOVA test, with a graphical interpretation of the result, is presented. The test is an extension of the global envelope test introduced by Myllymäki et al. (2017, Global envelope tests for spatial processes, J. R. Statist. Soc. B 79, 381{404, doi: 10.1111/rssb.12172). The graphical interpretation is realized by a global envelope which is drawn jointly for all samples of functions. If a mean function computed from the empirical data is out of the given envelope, the null hypothesis is rejected with the predetermined significance level α. The advantages of the proposed one-way functional ANOVA are that it identifies the domains of the functions which are responsible for the potential rejection. We introduce two versions of this test: the first gives a graphical interpretation of the test results in the original space of the functions and the second immediately offers a post-hoc test by identifying the significant pair-wise differences between groups. The proposed tests rely on discretization of the functions, therefore the tests are also applicable in the multidimensional ANOVA problem. In the empirical part of the article, we demonstrate the use of the method by analyzing fiscal decentralization in European countries. [ABSTRACT FROM AUTHOR]

Evaluates the use of the computer software STATA. Characteristics of the software; Efficiency on statistic use; Applicability on graphical method of statistics.