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The study aims to determine a mathematical model that can be used to describe the growth of the Adana pigeon. Since pigeons have only one breeding season, just one or two pairs of baby pigeons are raised per year. Hatchlings sometimes die before reaching adulthood. For this reason, measurements can be taken for 10, 15 and 60 days periods. Related with this issue, only 43-days measurements of 68 pigeons are used over a 6-year period. The study is modelled by taking the day-to-day average of the data (43 days) of 68 pigeons. The study was conducted on 68 Adana pigeons in the interval between the age of 1 and 43 days. The growth of pigeon cub was measured by daily live weight until 1 to 43 days. The estimation is carried out by writing the specific Matlab codes. Classical growth functions used in animals are in nonlinear form. Various numerical methods have been developed to estimate parameters in nonlinear functions. Special program routines have been developed to implement these methods. In these nonlinear models, there are more than one parameter to be estimated. Therefore, the number of mathematical operations in estimating the parameters is large. The most used models in the literature are Brody, Bertalanffy, Logistic, Generalized Logistic, Gompertz, Richards, Negative Exponential, Stevens, and Tanaka. However, as far as is known, there is no published article for Adana pigeons that uses all of these models and compares which one is better. These models are Brody, Bertalanffy, Logistic, Generalized Logistic, Gompertz, Richards, Negative Exponential, Stevens, and Tanaka. The best analysis was done by the Richards model in terms of both the Mean Squared Error (MSE), mean absolute percentage error (MAPE) and (Coefficient of Determination) R2 .

In this work, Adaptive Extended Kalman Filter (AEKF) is introduced and its use for oscillation of an object connected to the end of a spring is shown. As a new approach, an AEKF is used as a nonlinear estimation tool for online estimation of the states and parameters of an oscillating object attached to the end of a spring model. Parameter states that do not change with time were examined. The simulation results revealed that with proper selection of initial values of AEKF, AEKF is a very useful tool for this particular application.

In this study, sleep electroencephalography (EEG) which is frequently used in statistical modelling has been modelled with the autoregressive (AR) time-series model and what kind of a structure the variance of the term white noise included in the model represented in different sleep stages has been observed. Taking all of the stages scored in accordance with Rechtschaffen and Kales criterion into account separately, epoches in each stage have been modelled with the AR and the variance of the term white noise in this model has been monitored. The study has evaluated the sleep EEG variances of a subject. In accordance with the results, the heterogeneity at Stage 2 was thought to be the reason why the objective differences appeared in scoring. It is thought that this data pointed out a necessity that the period in Rechtschaffen and Kales scoring which is called Stage 2 must be revised.

In this study, theemergences of postsynaptic action potentials are investigated using simulationstudy which is depended on the statistical model of acetylcholine (Ach) quantalrelease theory at motor end-plate. It is supposed that the end-plate potentials(EPP) are sum of miniature end-plate potentials (MEPP) which are released asquantal and random in number (N). By the hypothesis that N number has a Poissonand MEPPs have a Gaussian distribution, EPPsare obtained by simulating distributions parameters. Our study suggests thatthe simulation of the EPPs are aconvenient tool in understanding bothphysiological process of synaptic transmission and pathological process of neuromuscular junction.

The Extended Kalman Filter (EKF) is the often used filtering algorithm for nonlinear systems. But it does not usually produce desirable results. Recently a new nonlinear filtering algorithm named as Unscented Kalman Filter (UKF) is introduced. In this paper, we propose a new modified Unscented Kalman Filter (MUKF) algorithm for nonlinear stochastic systems that are linear in some components. These nonlinear systems can be considered as having linear subsystems with parameters and aim is to estimate the system parameters. In simulation study, performance of the EKF, its known variant Modified Extended Kalman Filter (MEKF), UKF and the proposed MUKF is demonstrated for a nonlinear system that is linear in some components. The results show that MUKF gives the best solution for parameter identification problem