Journal title

Semiparametric bootstrap prediction intervals in time series

Nasrollah Iranpanah

One of the main goals in studying the time series is estimation of prediction interval based on an observed sample path of the process. In recent years, different semiparametric bootstrap methods have been proposed to find the prediction intervals without any assumption of error distribution. In semiparametric bootstrap methods, a linear process is approximated by a autoregressive process. Then the bootstrap samples are generated by resampling from the residuals.

In this paper, at first these sieve bootstrap methods are defined and then, in a simulation study sieve bootstrap prediction intervals are compared with a Standard Gaussian prediction interval. at last these methods are used to find the prediction intervals for weather data of Isfahan.
One of the main goals in studying the time series is estimation of prediction interval based on an observed sample path of the process. In recent years, different semiparametric bootstrap methods have been proposed to find the prediction intervals without any assumption of error distribution. In semiparametric bootstrap methods, a linear process is approximated by a autoregressive process. Then the bootstrap samples are generated by resampling from the residuals.

In this paper, at first these sieve bootstrap methods are defined and then, in a simulation study sieve bootstrap prediction intervals are compared with a Standard Gaussian prediction interval. at last these methods are used to find the prediction intervals for weather data of Isfahan.

A Stream Cipher based on chaotic permutations

Amir Daneshgar

In this paper we introduce a word based stream cipher consisting of a chaotic part operating as a chaotic permutation and a linear part, both of which designed on a finite field. We will show that this system can operate in both synchronized and self-synchronized modes. In particular, we show that in the self-synchronized mode the stream cipher has a receiver operating as an unknown input observer.
In addition we evaluate the statistical uniformity of the output and we also show that the system in the self-synchronized mode is much faster and lighter for implementation compared to similar self-synchronized systems with equal key size.

On Statistical Studying two Diffusion Processes on Torus and Their Applications

Mousa Golalizadeh

Diffusion Processes such as Brownian motions and Ornstein-Uhlenbeck processes are the classes of stochastic processes that have been under considerations of the researchers in various scientific disciplines including biological sciences. It is usually assumed that the outcomes of these processes
are lied on the Euclidean spaces. However, some data are appeared in physical, chemical and biological phenomena that cannot be considered as the observations in Euclidean spaces due to various features
such as the periodicity of the data. Hence, we cannot analysis them using the common mathematical methods available in Euclidean spaces. In addition, studying and analyzing them using common linear statistics are not possible. One of these typical data is the dihedral angles that are utilized to identifying, modeling and predicting the proteins backbones. Because these angles are representatives of points on the surface of torus, it seems that proper statistical modeling of diffusion processes on the torus could be of a great help for the research activities on dynamic molecular simulations in predicting the proteins backbones. In this article, using the Riemannian distance on the torus, the stochastic differential equations to describe the Brownian motions and Ornstein-Uhlenbeck processes on this geometrical objects will be derived. Then, in order to evaluate the proposed models, the statistical simulations will be performed using the equilibrium distributions of aforementioned stochastic processes. Moreover, the link between the gained results with the available concepts in the non-linear statistics will be highlighted.

Stabilization of Nonlinear Control Systems bu using Zobov's Theorem and Neural Networks

Azhdar Soleymanpour Bakefayat

In this paper, We Stabilize a subclass of nonlinear control systems by using neural networks and Zobov's theorem. Zobov’s Theorem is one of the theorems which indicates the conditions for the stability of a nonlinear systems with specific attraction region. We applied neural networks to approximate some functions mentioned in Zobov’s theorem, So as to find the controller of a nonlinear controlled system which is difficult task to find its law in mathematic manner. also we apply nelder meed optimization method to learning neural network. Finally, the effectiveness and the applicability of the proposed method are demonstrated by using some numerical examples.

The stability of non-standard finite difference scheme for solution of partial differential equations of fractional order

Fractional derivatives and integrals are new concepts of derivatives and integrals of arbitrary order. Partial differential equations whose derivatives can be of fractional order, are called fractional partial differential equations (FPDEs). Recently, these equations have been under special attentions due to their most practical usages. In this paper, we survey a rather general case of FPDE, to obtain a numerical scheme, the fractional derivatives in the equation are replaced by common definitions such as Grundwald-Letnikov, Riemann-Liouville and Caputo, to improve the numerical solution, partial derivatives inside the equation are discrete using non-standard finite difference scheme. Then, we survey the stability of numerical scheme and prove that the proposed method is unconditionally stable. Eventually, in order to approve the theoretical results, we use presented technique to solve wave equation with fractional-order that is very practical and widely used in physics and its branches. Numerical results confirm the findings of the theory and show that this technique is effective.

a mathematical analysis of new L-curve to estimate the parameters of Regularization in TSVD method

Alireza Keshvari

A new technique to find the optimization parameter in TSVD regularization method based on a curve which is drawn against the residual norm [5]. Since the TSVD regularization is a method with discrete regularization parameter then the above-mentioned curve is also discrete. In this paper we present a mathematical analysis of this curve, showing that the curve has L-shaped path very similar to that of the classical L-curve and its corner point can represent the optimization regularization parameter very well. In order to find the corner point of the L-curve (optimization parameter), two methods are applied: pruning and triangle. Numerical results show that in the considered test problems the new curve is better than the classical L-curve.

Bayesian Melding of Deterministic Models and Kriging For Analysis of Spatially Correlated Data

Mohsen Mohammadzadeh

Linking between geographic information systems and decision making approach own the invention and development of spatial data melding methods. Data melding methods combine the data, to achieve a better result and their aim is, to detect the information available in the data set in order to enhance the ability of interpreting data and increase the accuracy of the data analysis. In this paper, Bayesian melding method has been studied for combination of measurements, outputs of deterministic models and kriging methods. By spatial Bayesian melding and kriging an attempted is made to spatial prediction of ozone data in Tehran and results are validated and compared using the mean square error criterion.