Convexity Index Research Articles

Index of convexity: A novel liver function index using Tc-GSA scintigraphy

To investigate the clinical usefulness of a newly developed index, the "index of convexity (IOC)", for evaluating liver functional reserve using technetium-99m-diethylenetriaminepentaacetic acid-galactosyl-human serum albumin (Tc-GSA scintigraphy). In total, 349 patients underwent Tc-GSA scintigraphy. Dynamic planner images were obtained, and time activity curves of the liver and heart were generated and analyzed. Our focus was on the convex shape of the liver accumulation curve. We developed a method for evaluating the extent of convexity and calculated an index that we named the IOC. Clearance index and receptor index were also calculated. The correlations between each GSA index with other liver function tests and liver histopathology were evaluated. Among the 3 indices generated by Tc-GSA, the IOC had the highest correlation with all other liver function tests (indocyanine green R15, albumin, prothrombin time, cholinesterase level, platelet count, and total bilirubin level). IOC can also differentiate between normal liver, chronic hepatitis, and liver cirrhosis with highest F ratio among GSA indices as determined by one-way analysis of variance. Receiver operating characteristic analysis demonstrated high diagnostic performance of IOC in the diagnosis of cirrhosis. IOC is a very simple and reliable index for assessing liver functional reserve, which may prove to be useful in combination with the indocyanine green test for preoperative assessment of hepatic resection.

FCAW process optimization using the multivariate mean square error

Optimization of welding processes is not a trivial task, mainly due to the great number of required and desirable characteristics that must be analysed. Moreover, the optimization of a welding process with multiple characteristics without considering the variance–covariance structure may lead to inadequate optimum. To help with this task, a method of multi-objective optimization based on the multivariate mean square error applied in the study of multiple correlated characteristics of a flux-cored arc welding process is presented. This method characterized by a combined approach based on the response surface methodology, design of experiments, and principal components analysis consisted of an attempt to achieve the nearest values to specific targets, for each characteristic (penetration, deposition rate, deposition efficiency, convexity index of the weld bead, and dilution), considering the welding variables expressed as a result of welding voltage (V), wire feed speed (Va), and contact tip to workpiece distance (d). The results point, to a good adequacy of the proposed method.

Modeling and Analysis of Shape with Applications in Computer-Aided Diagnosis of Breast Cancer

Malignant tumors due to breast cancer and masses due to benign disease appear in mammograms with different shape characteristics: the former usually have rough, spiculated, or microlobulated contours, whereas the latter commonly have smooth, round, oval, or macrolobulated contours. Features that characterize shape roughness and complexity can assist in distinguishing between malignant tumors and benign masses. In spite of the established importance of shape factors in the analysis of breast tumors and masses, difficulties exist in obtaining accurate and artifact-free boundaries of the related regions from mammograms. Whereas manually drawn contours could contain artifacts related to hand tremor and are subject to intra-observer and inter-observer variations, automatically detected contours could contain noise and inaccuracies due to limitations or errors in the procedures for the detection and segmentation of the related regions. Modeling procedures are desired to eliminate the artifa ts in a given contour, while preserving the important and significant details present in the contour. This book presents polygonal modeling methods that reduce the influence of noise and artifacts while preserving the diagnostically relevant features, in particular the spicules and lobulations in the given contours. In order to facilitate the derivation of features that capture the characteristics of shape roughness of contours of breast masses, methods to derive a signature based on the turning angle function obtained from the polygonal model are described. Methods are also described to derive an index of spiculation, an index characterizing the presence of convex regions, an index characterizing the presence of concave regions, an index of convexity, and a measure of fractal dimension from the turning angle function. Results of testing the methods with a set of 111 contours of 65 benign masses and 46 malignant tumors are presented and discussed. It is shown that shape modeling and a alysis can lead to classification accuracy in discriminating between benign masses and malignant tumors, in terms of the area under the receiver operating characteristic curve, of up to 0.94. The methods have applications in modeling and analysis of the shape of various types of regions or objects in images, computer vision, computer graphics, and analysis of biomedical images, with particular significance in computer-aided diagnosis of breast cancer. Table of Contents: Analysis of Shape / Polygonal Modeling of Contours / Shape Factors for Pattern Classification / Classification of Breast Masses

The potential energy surface and chaos in 2D Hamiltonian systems

We provide a new insight into the relationship between the geometric property of the potential energy surface and chaotic behavior of 2D Hamiltonian dynamical systems, and give an indicator of chaos based on the geometric property of the potential energy surface by defining Mean Convex Index (MCI). We also discuss a model of unstable Hamiltonian in detail, and show our results in good agreement with HBLSL's (Horwitz, Ben Zion, Lewkowicz, Schiffer and Levitan) new Riemannian geometric criterion.

Otimização do processo de soldagem FCAW usando o erro quadrático médio multivariado

Encontrar um conjunto ótimo de parâmetros para um processo de soldagem é uma tarefa pouco trivial, face às múltiplas características exigíveis ou desejáveis que devem ser analisadas. Além disso, a negligência da estrutura de variância-covariância destas características na otimização pode conduzir a ótimos inadequados. Com o intuito de auxiliar na busca desses parâmetros, um método para otimização multiobjetiva, desenvolvido para o estudo do processo de soldagem FCAW (do inglês Flux Cored Arc Welding), utilizando-se arames tubulares, baseado no conceito de Erro Quadrático Médio Multivariado, será apresentado. Trata-se de uma abordagem combinada da Metodologia de Superfície de Resposta, Projeto de Experimentos e Análise de Componentes Principais, na tentativa de localizar valores próximos a alvos especificados, para cada uma das características estudadas (Penetração, Taxa de deposição, Rendimento, Índice de convexidade e Diluição), considerando-se as variáveis de processo expressas em função da tensão (V), velocidade de alimentação do arame (Va) e da distância do bico de contato-peça (d). Os resultados obtidos apontam para uma boa adequação desta proposta.

Predicting oak tree mortality caused by the ambrosia beetle Platypus quercivorus in a cool‐temperate forest

AbstractMass mortality of fagaceous trees due to wilt disease, which has been spreading throughout Japan since the 1980s, is caused by the ambrosia beetle Platypus quercivorus. Quercus crispula is one of the species most susceptible to the disease. Previous studies have examined this disease in secondary forests, where fagaceous trees are dominant and are considered to be distributed uniformly. We examined whether the uneven distribution of Q. crispula in a natural forest affects the spread of this disease. We determined its distribution using Morisita’s index of dispersion (Iδ), and then predicted the probability of mortality using a generalized linear model with topographic variables (altitude and index of convexity), tree size (diameter at breast height, DBH), and basal areas of Q. crispula and Cryptomeria japonica (the dominant species at the study site) per 0.01, 0.09, and 0.25 ha as explanatory variables. The site included 310 Q. crispula within a 14 ha plot in a cool‐temperate forest of Japan with no signs of beetle infestation in 2003. The calculated index of dispersion showed a clumped distribution of Q. crispula with an estimated clump size of 0.08 ha. At the end of 2007, 36 Q. crispula in the study site were dead, and DBH and basal area of Q. crispula per 0.09 ha had significant positive effects on the probability of mortality. The basal area of C. japonica, a non‐host conifer species for P. quercivorus, per 0.09 ha also had a positive effect on the probability of mortality. These results suggest that P. quercivorus first flew to a cluster of Q. crispula aggregated in about a 0.1 ha area where the density of C. japonica is high, and then DBH played a role in determining the target trees.

Optimization of the FCAW process by weld bead geometry analysis

The flux cored arc welding process has grown in use in recent times as a function of its characteristics of high rate of deposition, associated with suitable mechanical properties in the welded joint. However, many aspects still remain obscure in regard to greater utilization of this process. As a result, the intention of this work is the analysis and optimization of the voltage, wire feed speed and contact tip part distance welding parameters, in a process using tubular wire with shielding gas, on the penetration and convex index of the weld. By means of statistical techniques, a mathematical model was developed with subsequent optimization of the responses. Based on the results obtained, the strong influence of the wire feed speed on the process was seen, followed by the voltage and, with less intensity, the contact tip to workpiece distance (CTWD). Statistical analyses indicated that the best condition for the parameters analysed was obtained with voltage values between 32 and 34 V, associated with a wire feed speed of 12 m/min and a CTWD of 20 mm. On the other hand, tensions at around 36 V caused surface defects that prejudiced the quality of the weld. Later tests showed an acceptable forecast of the results of the mathematical models when compared to the actual results.

On twice differentiable direct and indirect utility functions and the monotonicity of the demand

This article investigates the relationships between the Hessians of the direct and indirect utility function and the Jacobian of the demand correspondence. The monotonicity of the demand is analysed thanks to the convexity indices of the function and the monotonicity index of the demand.

Feature Extraction from a Signature Based on the Turning Angle Function for the Classification of Breast Tumors

Malignant breast tumors and benign masses appear in mammograms with different shape characteristics: the former usually have rough, spiculated, or microlobulated contours, whereas the latter commonly have smooth, round, oval, or macrolobulated contours. Features that characterize shape roughness and complexity can assist in distinguishing between malignant tumors and benign masses. Signatures of contours may be used to analyze their shapes. We propose to use a signature based on the turning angle function of contours of breast masses to derive features that capture the characteristics of shape roughness as described above. We propose methods to derive an index of the presence of convex regions (XR ( TA )), an index of the presence of concave regions (VR ( TA )), an index of convexity (CX ( TA )), and two measures of fractal dimension (FD ( TA ) and FDd ( TA )) from the turning angle function. The methods were tested with a set of 111 contours of 65 benign masses and 46 malignant tumors with different parameters. The best classification accuracies in discriminating between benign masses and malignant tumors, obtained for XR ( TA ), VR ( TA ), CX ( TA ), FD ( TA ), and FDd ( TA ) in terms of the area under the receiver operating characteristics curve, were 0.92, 0.92, 0.93, 0.93, and, 0.92, respectively.

Prediction of bead geometry in pulsed GMA welding using back propagation neural network

This paper presents the development of a back propagation neural network model for the prediction of weld bead geometry in pulsed gas metal arc welding process. The model is based on experimental data. The thickness of the plate, pulse frequency, wire feed rate, wire feed rate/travel speed ratio, and peak current have been considered as the input parameters and the bead penetration depth and the convexity index of the bead as output parameters to develop the model. The developed model is then compared with experimental results and it is found that the results obtained from neural network model are accurate in predicting the weld bead geometry.

Effect of aging and degeneration on disc volume and shape: A quantitative study in asymptomatic volunteers

Debate continues on the effect of disc degeneration and aging on disc volume and shape. So far, no quantitative in vivo MRI data is available on the factors influencing disc volume and shape. The objective of this MRI study was to quantitatively investigate changes in disc height, volume, and shape as a result of aging and/or degeneration omitting pathologic (i.e., painful) disc alterations. Seventy asymptomatic volunteers (20-78 years) were investigated with sagittal T1- and T2-weighted MR-images encompassing the whole lumbar spine. Disc height was determined by the Dabbs method and the Farfan index. Disc volume was calculated by the Cavalieri method. For the disc shape the "disc convexity index" was calculated by the ratio of central disc height and mean anterior/posterior disc height. Disc height, disc volume, and the disc convexity index measurements were corrected for disc level and the individuals age, weight, height, and sex in a multilevel regression analysis. Multilevel regression analysis showed that disc volume was negatively influenced by disc degeneration (p < 0.001) and positively correlated with body height (p < 0.001) and age (p < 0.01). Mean disc height and the disc convexity index were negatively influenced by disc degeneration but not by gender, weight, and height. Disc height was positively correlated with age (p < 0.01). From the results of this study, it can be concluded that disc degeneration generally results in a decrease of disc height and volume as well as a less convex disc shape. In the absence of disc degeneration, however, age tends to result in an inverse relationship on disc height, volume, and shape.

Diagnosis of lung nodule using semivariogram and geometric measures in computerized tomography images

This paper uses the geostatistical function - semivariogram and a set of 3D geometric measures - sphericity index, convexity index, extrinsic and intrinsic curvature index and surface type, to characterize lung nodules as malignant or benign in computerized tomography images. Based on a sample of 31 nodules, 25 benign and 6 malignant, these methods are first analyzed individually and then jointly, with techniques for classification and analysis (stepwise discriminant analysis, leave-one-out and ROC curve). We have concluded that the individual measures and their combinations produce good results in the diagnosis of lung nodules.

Convexity index in photosynthetic light response curve of seven species of deciduous broad-leaved tree

Convexity index in photosynthetic light response curve of seven species of deciduous broad-leaved tree

An approach to checking link conflicts in the mapping of uniform dependence algorithms into lower dimensional processor arrays

In this paper, we propose an enumeration method to check link conflicts in the mapping of n-dimensional uniform dependence algorithms with arbitrary convex index sets into k-dimensional processor arrays. Previous methods on checking the link conflicts had to examine either the whole index set or the I/O spaces whose size are O(N/sup 2n/) or O(N/sup n-1/), respectively, where N is the problem size of the n-dimensional uniform dependence algorithm. In our approach, checking the link conflicts is done by enumerating integer solutions of a mixed integer linear program. In order to enumerate integer solutions efficiently, a representation of the integer solutions is devised so that the size of the space enumerated is O((2N)/sup n-k/). Thus, our approach to checking link conflicts has better performance than previous methods, especially for larger k. For the special case k=n-2, we show that link conflicts can be checked by solving two linear programs in one variable.

Role of spatial contiguity in quail chicks' responsiveness to multimodal maternal cues

We provide a new insight into the relationship between the geometric property of the potential energy surface and chaotic behavior of 2D Hamiltonian dynamical systems, and give an indicator of chaos based on the geometric property of the potential energy surface by defining Mean Convex Index (MCI). We also discuss a model of unstable Hamiltonian in detail, and show our results in good agreement with HBLSL's (Horwitz, Ben Zion, Lewkowicz, Schiffer and Levitan) new Riemannian geometric criterion.

Maximum principle for the optimal control of a hyperbolic equation in one space dimension, part 1: Theory

A maximum principle is developed for a class of problems involving the optimal control of a damped-parameter system governed by a linear hyperbolic equation in one space dimension that is not necessarily separable. A convex index of performance is formulated, which consists of functionals of the state variable, its first- and second-order space derivatives, its first-order time derivative, and a penalty functional involving the open-loop control force. The solution of the optimal control problem is shown to be unique. The adjoint operator is determined, and a maximum principle relating the control function to the adjoint variable is stated. The proof of the maximum principle is given with the help of convexity arguments. The maximum principle can be used to compute the optimal control function and is particularly suitable for problems involving the active control of structural elements for vibration suppression.

A NEW APPROACH TO FINDING OPTIMAL LINEAR SCHEDULES FOR UNIFORM DEPENDENCE ALGORITHMS†

A uniform dependence algorithm can be represented by an index set of index points and a finite set of data dependence vectors. Usually, the convex hull R of the index set is a nondegenerated convex polytope in R n, In this paper, we show that finding an optimal linear schedule for a uniform dependence algorithm with an arbitrary bounded convex index set is equivalent to finding a vector of smallest norm, where the vector norm is defined on a symmetric convex set R∗ (which is the dual of difference body R − R). A linear programming problem is derived for finding the smallest vector. This problem can be solved in the empirical average time complexity O(36n 3 + 12an 2 + a), where a is the number of the linear inequalities defining the convex hull R and n is the dimension of the index set. This time complexity is better than those of the existing methods.

Korovkin inequalities for stochastic processes

The rate of convergence of a sequence of positive linear stochastic operators { T j } j ∈ n to the unit operator I on spaces of stochastic processes X is studied. This is mainly done for stochastic processes that are smooth over a compact and convex index set Q ⊂ R k, k ⩾ 1. Nearly best upper bounds are given for ¦E(T jX)(x 0) − (EX)(x 0)¦, x 0 ϵ Q , where E is the expectation operator and T j are E-commutative. These lead to strong and elegant inequalities many times sharp, which involve the first modulus of continuity of EX α, where X α is a (partial) derivative of X. The case of Q being a compact convex subset of a real normed vector space is also met and there the upper bound is the best possible.

Maximum principle for optimal control of distributed-parameter systems with singular mass matrix

A maximum principle for the open-loop optimal control of a vibrating system relative to a given convex index of performance is investigated. Though maximum principles have been studied by many people (see, e.g., Refs. 1–5), the principle derived in this paper is of particular use for control problems involving mechanical structures. The state variable satisfies general initial conditions as well as a self-adjoint system of partial differential equations together with a homogeneous system of boundary conditions. The mass matrix is diagonal, constant, and singular, and the viscous damping matrix is diagonal. The maximum principle relates the optimal control with the solution of the homogeneous adjoint equation in which terminal conditions are prescribed in terms of the terminal values of the optimal state variable. An application of this theory to a structural vibrating system is given in a companion paper (Ref. 6).

On the convexity of integrals of multivalued mappings: Applications in control theory

Using the notion of the local convexity index, we characterize in a quantitative way the local convexity of a set in then-dimensional Euclidean space, defined by an integral of a multivalued mapping. We estimate the rate of convergence of the conditional gradient method for solving an abstract optimization problem by means of the convexity index of the constraining set at the solution point. These results are applied to the qualitative analysis of the solutions of time-optimal and Mayer problems for linear control systems, as well as for estimating the convergence rate of algorithms solving these problems.