The classification of Shape data is a significant challenge in the statistical analysis of Shapes and machine learning. In this paper, we introduce a multinomial logistic regression model based on Shape descriptors for classifying labeled configurations. In this model, the explanatory variables include a set of geometric descriptors such as area, elongation, convexity, and circularity, while the response variable represents the category of each configuration. The inclusion of these descriptors preserves essential geometric information and enhances classification accuracy. We evaluate the proposed model using both simulated data and real datasets, and the results demonstrate its effective performance. Additionally, the proposed method was compared with one of the existing methods in the literature, and the results indicated its superiority in terms of both classification accuracy and computational simplicity.

Introduction Statistical Shape analysis is one of the fields of multivariate statistics, where the main focus is on the geometric structures of objects. This analysis method is widely used in many scientific fields, such as medicine and morphology. One of the tools for diagnosing diseases or determining animal species is the images and the Shapes extracted from them. Introducing methods of classifying Shapes can be a solution to determine the class of each observation. Usually, in regression modelling, explanatory and dependent variables are quantitative. However, one may want to measure the relationship between an explanatory variable (with continuous values) and a dependent variable with qualitative values. One option is to use the multinomial logistic regression model. Therefore, a semiparametric multinomial logistic regression model to classify Shape data is introduced in this paper. Material and Methods The power-divergence criterion is a measure for hypothesis testing in multinomial data. This criterion is used to define the kernel function of explanatory variables. The model is a multinomial logistic regression model based on kernel function as a function of explanatory variables and an intercept. Since the Shapes’,geometric structure and size play a key role in the classification of Shapes, the kernel function is determined based on the Shape distances. The smoothing parameter was estimated using the least square cross-validation method. Also, the estimation of model parameters was done using the neural network method. Results and Discussion The Shape space is a manifold, but most of the methods presented in the literature for classifying Shapes were done in the Shape tangent space or used linear transformations. Since mapping from the manifold to linear space decreases data information, applying tangent space and linear spaces will reduce classification accuracy. Therefore, the Shape space is used to classify the Shape data. The performance of the model in a simulation study and two real data sets were investigated in the paper. The two real data sets used in this paper are taken from the Shape package in R software. The first data set is related to schizophrenia patients and people as control, and the second one is associated with the skull of three species of apes of two sexes. The classification of these data showed an accuracy of 82% and 84%, respectively. Also, a comparison was made with the previous methods based on a real data set, which showed the proper performance of our approach compared to the other two techniques. Conclusion Since in the nonparametric kernel function, suitable distances of the Shape space were used, the introduced method performs better than those based on Euclidean spaces. Also, the ability to use other Shape distances, such as partial, full Procrustes and Riemannian distances, makes the model more flexible in classifying different types of Shape data. On the other hand, sizeand-Shape distance can be used in the kernel function to classify data whose size plays a key role in their geometric structure. Furthermore, since few statistical distributions have been introduced in the Shape space, nonparametric methods can be helpful in the analysis of Shape data. However, using nonparametric methods in the Shape space is time-consuming from the point of view of computer calculations.

Recently, some statistical studies have been done using the Shape data. One of these studies is clustering Shape data, which is the main topic of this paper. We are going to study some clustering algorithms on Shape data and then introduce the best algorithm based on accuracy, speed, and scalability criteria. In addition, we propose a method for representing the Shape data that facilitates and speeds up the Shape clustering algorithms. Although the mentioned method is not very accurate, it is fast; therefore, it is useful for datasets with a high number of landmarks or observations, which take a long time to be clustered by means of other algorithms. It should be noted that this method is not new, but in this article we apply it in Shape data analysis.

The neoclassical growth model is tested by use of panel data procedure in this research. In the econometric test, simoultanously time series and cross detection will be compared on the basis of panel data method through which their observed points increase and consequently the estimation efficiency will be increased. The examination of neoclassical growth theory has been done with reference to external & internal factors of 52 selected countries from 1960 to 2000. The independent variable of model has been selected on the basis of the result of previous research which explains the result in three separate models: developed countries, developing countries, and whole countries. These factors are such as: Gross National Products with lag of period, work force age, growth rate, education level, the change of capital accumulation and economic trade volum. The consequences of this research is that: neoclassical growth model can explain the major part of economic growth of the countries with use of internal variables. Also with the use of panel procedure of fixed effect, we can see the fundamental differences and structure of the growth process for different countries; and show how the economic, and social conditions affect on the growth.

The least-square minimization approaches for determination of depth, Shape and amplitude coefficient expressed by Abdolrahman et al. (2001) for sphere and horizontal cylinder is used for rectangular prisms as synthetic models with and without random noises. The method is also applied for real sources producing micro-gravity data .The capability of the method is tested and discussed in this paper.

Introduction: In most survival studies for parametric analysis of data is used the weibull model because it is flexibility. In most cases for weibull model is assumed that the Shape parameter is constant, although this assumption for some of the data is wrong.Aim: In this study, we present interval censored method for weibull distribution when the Shape parameter isn' t constant.Materials and Methods: With simulation of Monte Carlo, we will present advantages of this approach respect to situation that Shape parameter is constant. Then in a practical example we would show that how estimates are determined.Results: Estimation of model coefficient, DIC and Hazard ratio were calculated in model with constant and nonconstant Shape parameter then were compared. The results indicated that if the Shape parameter of distribution isn' t constant. The estimation of covariates coefficients has less bias, more appropriate fit and the results is different respect to Shape parameter is constant.Conclusion: Based on the results is better than the saturated model is selected in such a way that does not assume constant Shape parameter to be fixed parameter used as the test model, using appropriate criteria to select fit model.

Todays gamma knife radiosurgery is used widely for treatment of very small brain tumors. In order to investigate accuracy of dosimetry and treatment planning calculations, using Monte Carlo simulation with dedicated code named as beamnrc including non-CT data and CT data options is necessary. The aim of this study is choosing the best options in order to have an accurate tools based on their advantages and disadvantages. In this study, gamma knife unit 4C along with standard water equivalent phantom and EBT3 films were used to obtain dose distributions. Monte Carlo simulation was done with non-CT data and CT data options of the code and their resulting dose were compared. Comparison the calculated and measured dose distributions at X, Y and Z axis showed gamma value below 1 which verified Monte Carlo simulations. Also comparing the dose distributions from both non-CT data and CT data with each other implies that there is no significant difference between two methods. Based on the obtained results using non-CT data and CT data results in the same dose distribution. So for simplicity, using non CT data for regular phantom Shapes is preferred.

Aim: New technology has already changed our interpretation of Persian house. Theory of integration in the high-performance architecture theory shows that the different elements of Iranian house enjoy unity, despite their differences. The research aims to study the most important elements of Persian house based on Islamic-Iranian life style based on a holistic approach. Methods: The purposive sampling method is developed among the case from the central parts of Iran such as Isfahan, Kashan, Yazd and Ardakan; in order to calculate the area, the module and the period of building the house. Research tool was scientific documentation and survey. The data analysis is based on descriptive-analytical understanding of mathematical space syntax. Findings: Comparison of the principles considered in the selected samples by the syntactic tools of space, showed that these principles always exist in the spatial structure of Iranian housing. Furthermore, the results of the research emphasize on the highperformance architecture theory principles such as: 1-hierarchy, 2-privacy, 3-transparency and 4-centralization. Conclusion: The spatial structure of Persian house and Iranian housing is a manifestation of the theory of integration, which is arranges around a central courtyard. The essence of Persian house is depending on the climate as an influential factor, shows different appearance. The Persian house is a technologic-climatic interpretation of Iranian-Islamic lifestyle.

In this research work a Shape from shading (SFS) technique which incorporates a Lambertian model is implemented for the automatic generation of a digital terrain model (DTM) using a single view aerial image. The developed algorithm is tested on both simulated and real data. The estimated accuracy of the generated DTM from the simulated data, which has a bilinear surface, is about ±3 cm. The real data is a scanned aerial photograph taken over a low texture hilly terrain. The generated DTM by the SFS technique is compared with a DTM acquired by the manual measurement of the stereo image of the same area using a photogram metric plotter. The estimated rimes of the discrepancies between the grid nodes of the measured and the automatically generated DTM is about ±4 meters. The unsuccessful reconstruction of the terrain surface for the real data is due to the fact that a simple Lambertian model does not take into account, in a perfect way, different nondeterministic influential factors such as the terrain alb Edo variations and the random noise. The influence of the latter case was reduced by a low pass filter applied as a preprocessing stage.