ADVANCES IN MATHEMATICAL MODELING
Year:2015 | Volume:4 | Issue:2|Papers Count:6

In time of natural and man-made disasters, the supplies of some commodities, which are directly related to human life, are very critical. In the real world, supply systems are exposed to various disruptions in their facilities, these disruptions can essentially affect systems performance and can lead to shortage in the supply, and importance of this subject is much more expressed in the blood supply case. In this paper, a multi– objective mathematical model is proposed for the collection of temporary blood facilities and allocation of blood donators to these places. The goals of the model are to minimize the maximum blood shortage in the blood bank and to minimize the total cost in the worst case scenario in disruptions. In order to demonstrate the applicability of the proposed model, the epsilon constraint method is solved and analyzed on numerical examples.

The present study evaluates the portfolio optimization problem (as one of the fundamental problems in the field of investments) with respect to the concepts of risk based on credibility theory. So that, a possibilistic portfolio optimization model (Zadeh 1965-1978) associates a new probabilistic portfolio optimization model, and The latter model, which actually comes in the form of a passive investment approach, formed around a portfolio of active equity mutual funds in the Tehran Stock Exchange from 2011 until the end of January of 2013 puts. The results of the implementation of the approach by use of genetic algorithms, suggesting a similar performance composed of a portfolio of mutual funds (based on the Sharpe index) with the market.

Identifiablity is a necessary property for the adequacy of a statistical model. When a model is not identifiable, no amount of data cannot determine true parameter. In this article, well-known concept of identifiablity and its properties is reviewed. Moreover, since non-identifiably problem in linear mixed effects models and generalized linear models with random effects is very common, our main focus is on these models. On the other hand, statistical software, after fitting non-identifiable models, don’t usually indicate the problem and show invalid outputs. Consequently, it is useful to have a way to check model identifiability before fitting. In this regard, some new theorems to check identifiability in generalized linear models with random effects are presented. data from non-identifiable models are simulated and problems with model non-identifiablity are listed for showing advantages of the mentioned theorems.

Directional statistics are very useful tools to model the phenomenon that are characterized by the angles. Recently, various disciplines including biology, astronomy, meteorology and bioinformatics have paid attention to use these distributions. Particularly, it was shown in biological researches that there are two pair angles describing, relatively, the complete geometrical and spatial structures of a protein in the three dimensional space. There is a distribution, called bivariate Von-Mises, to represent the position of the atoms based upon the values of these angles in a probabilistic manner. In this paper, considering an especial case of this density (cosine model), the properties of distribution including the numbers of modes and its approximation by the bivariate normal distribution are first studied. Then, to estimate the parameters using the pseudo-likelihood method is described. The theoretical materials are evaluated in simulation studies and the application of the cosine model in a real example is presented.

Let CF (X) be the socle of C (X) and LCF (X)={FÎC (X):`SF=X}, where SF is the union of all open subsets U in X such that | U\ Z (f) |< ¥, LCF (X) is called the locally socle of C (X) and it is a z-ideal of C (X) containing CF (X)…

One of the most widely used models for fitting survival data is Cox proportional hazards model that is based on homogeneity, independence and equi-distributed of survival data. However, in many cases, hazards of statistical units are different and the assumption of population homogeneity is not established. One of the reasons for such deference is the unknown or unobserved risk factors, which may lead to some misleading models if there is no concern for them or some models such as Cox proportional hazard models have to be implemented. In such cases, regarding the unknown risk factors, frailty models are used. In this paper, the performances of the Cox and frailty models for survival and spatial survival data with unknown risk factors are considered. The efficiency of these models whilst the source of unknown risk factors is the spatial correlation of survival data is also examined.