Untrained shear strength is the main parameter in most problems concerned with short-term stability or total stress analysis states (TSA). Mechanism of soil deposit formation leads to inherent variability in soil strength and stiffness parameters.Inherent variability as the primary source of uncertainty in geotechnical problems consists of deterministic and stochastic components. In this paper, a generic deterministic trend is proposed by utilizing a good amount of well-documented in-situ test data. The new concept of transformation depth was introduced as the depth where it changes from a decreasing trend to an increasing one. Random Field Theory and local average subdivision (LAS) technique was employed in order to produce realization of untrained shear strength. Untrained shear strength was assumed to inherit a deterministic trend in vertical direction while preserving its stochastic behavior in horizontal direction.

In the case of problematic soils and tall buildings where the design requirements cannot be satisfied merely by a raft foundation, it is of common practice to improve the raft performance by adding a number of piles so that the ultimate load capacity and settlement behavior can be enhanced. In this study, the effect of spatial variability of soil parameters on the bearing capacity of piled raft foundation is investigated based on the Random Field Theory using the finite difference software of FLAC3D. The coefficient of variation (COV) of the soil’ s undrained shear strength, the ratio of standard deviation to the mean, was considered as a Random variable. Moreover, the effect of variation of this parameter on the bearing capacity of piled raft foundation in undrained clayey soils was studied taking the Monte Carlo simulation approach and the normal statistical distribution. According to the results, taking into account the soil heterogeneity generally results in more contribution of the raft in bearing capacity than that of the homogenous soils obtained by experimental relationships, which implies the significance of carrying out stochastic analyses where the soil properties are intensively variant.

Seismic waves caused by earthquakes undergo many changes when passing through different layers of soil. For this reason, the effects of soil parameters on the dynamic response of the ground should be considered. The parameters in a heterogeneous soil layer are affected by a set of uncertainties, which in this research is the inherent variability of the soil shear modulus parameter. In this research, using Random Field Theory and finite difference method in the framework of Monte Carlo simulations, the effect of two-dimensional spatial variability of the soil shear modulus parameter on the magnification factor of the maximum ground acceleration and the surface acceleration response spectrum has been investigated. In the conventional deterministic analysis, only a constant value of the average shear modulus is considered in the dynamic model, but in the stochastic analysis, the parameter of the soil shear modulus is considered as a Random variable. The results obtained from the analysis show that with the increase of heterogeneity and changes in the shear modulus of the soil, the values of the magnification factor of the maximum ground acceleration decrease. Also, with the increase in the coefficient of variation of the soil shear modulus and as a result of the increase in the heterogeneity of the soil profile, the acceleration response spectrum of the surface of the soil profile obtained from Random analyzes decreases.

The Gaussian Random Field is commonly used to analyze spatial data. One of the important features of this Random Field is having essential properties of the normal distribution family, such as closure under linear transformations, marginalization and conditioning, which makes the marginal consistency condition of the Kolmogorov extension theorem. Similarly, the skew-Gaussian Random Field is used to model skewed spatial data. Although the skew-normal distribution has many of the properties of the normal distribution, in some definitions of the skew-Gaussian Random Field, the marginal consistency property is not satisfied. This paper introduces a stationery skew-Gaussian Random Field, and its marginal consistency property is investigated. Then, the spatial correlation model of this skew Random Field is analyzed using an empirical variogram. Also, the likelihood analysis of the introduced Random Field parameters is expressed with a simulation study, and at the end, a discussion and conclusion are presented.

A Random walk on a lattice is one of the most fun-damental models in probability Theory. When the Random walk is inhomogenous and its inhomogeniety comes from an ergodic sta-tionary process, the walk is called a Random walk in a Random environment (RWRE). The basic questions such as the law of large numbers (LLN), the central limit theorem (CLT), and the large de-viation principle (LDP) are not fully understood for RWRE. Some known results in the case of LLN and LDP are reviewed. These results are closely related to the homogenization phenomenon for Hamilton-Jacobi-Bellman equations when both space and time are discretized.

A common scientific purpose in spatial data analysis is prediction of a Random Field in unmeasured sites based on measured data in some sample sites. If the Random Field is Gaussian with parametric mean and covariance functions, optimal predictor and its mean square error can be determined. But in some applications, the data give evidence of non-Gausian features. In this case, if a nonlinear transformation of the Random Field is Gaussian, the spatial prediction is carried out. When the transformation is unknown, we assumed that it is belong to a certain parametric family of transformations. If the maximum likelihood estimators of the model parameters is determined and plugged in optimal predictor, optimality of the obtained predictor is doubt and often, we can't determine its MSE. Instead, in this paper, using the Bayesian approach, we determine the optimal predictor and its MSE. In a numerical example our method is used to deriving the Bayesian spatial prediction of rainfall at a given site.

Image segmentation is an important task in image processing and computer vision which attract many researchers attention. There are a couple of information sets pixels in an image: statistical and structural information which refer to the feature value of pixel data and local correlation of pixel data, respectively. Markov Random Field (MRF) is a tool for modeling statistical and structural information at the same time. Fuzzy Markov Random Field (FMRF) is a MRF in fuzzy space which handles fuzziness and Randomness of data simultaneously. This paper propose a new method called FMRFC which is model clustering using FMRF and applying it in application of image segmentation. Due to the similarity of FMRF model structure and image neighbourhood structure, exploiting FMRF in image segmentation makes results in acceptable levels. One of the important tools is Cellular learning automata (CLA) for suitable initial labelling of FMRF. The reason for choosing this tool is the similarity of CLA to FMRF and image structure. We compared the proposed method with several approaches such as Kmeans, FCM, and MRF and results demonstratably show the good performance of our method in terms of tanimoto, mean square error and energy minimization metrics.

Although strong ground motion networks are expanding, near-source strong motion recordings are still sparse .In this article it is planned to characterize the level and variability of strong ground motion in near Field of large earthquakes due to source effects. We have developed a stochastic rupture model that characterizes the variability and spatial complexity of slip as observed in past earthquakes. We model slip heterogeneity on the fault plane as a spatial Random Field for 21 near source earthquakes. The data follows a von Karman autocorrelation function (ACF), for which the correlation lengths (a) increase with the source dimensions .These stochastic slip distributions are used to develop the temporal behavior of slip using physically consistent with stochastic-dynamic earthquake source models .It means that we can use this model to simulate realistic strong ground motion in order to characterize the variability of source effects in the near-Field of large earthquakes. For earthquakes with large fault aspect ratios, we observe substantial differences of the correlation length in the along-strike (ax) and downdip (az) directions. Increasing correlation length with increasing magnitude can be understood using concepts of dynamic rupture propagation. The power spectrum of the slip distribution can also be well described with a  fractal distribution in which the fractal dimension D remains scale invariant, accounting for larger ‘‘asperities ’’ for large-magnitude events.Our stochastic slip model can be used to generate scenario earthquakes for near-source ground motion simulations.

One of the factors that can be the link between our intentions and actions and their external consequences is human agency, which indicates the conscious design and intentional execution of actions by the individual in order to influence future events.Objective and Method: This research with a developmental approach of psychometric method and method 1, examines the psychometric indices of the Human Factor Characteristics Scale using the classical Theory of test score measurement and the graduated question-answer Theory. The purpose of this study, which included high school students in Tehran, was selected by cluster sampling of 500 people as a sample size and statistical analysis was performed on 481 data. To collect the data, the ion Human Agent Characteristics Scale (2011) was used and the research questions were evaluated using IRTPRO and SPSS software.Results:The assumption of local independence based on Pearson x2 index was established by applying Simjima's calibrated question-answer Theory and the assumption of being one-dimensional based on the analysis of multidimensional question-answer Theory. Diagnosis parameters with question-answer approach and classical approach Test score Both item 25 approach had the lowest and item 2 had the highest diagnosis parameter. The answer thresholds for all the questions were so far apart that no option was covered by the other option, and the options were independently selected by individuals at intervals of theta. The total scale was calculated with Cronbach's alpha of 0.945, intentionality of 0.894, foresight of 0.780, self-reactivity of 0.871 and rethinking of 0.762. Also, the role of each item in internal consistency was investigated by the loop method, which all questions had a favorable role in internal consistency of this scale. The value of the validity coefficient obtained from the question-answer Theory was obtained by marginal method for intentionality 0.92, forethought 0.85, self-reaction 0.91, rethinking 0.83..