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author[rvt]{Author1corref{cor1}}
ead{author1_Firstname@univ-jijel.dz}

author[rvt]{Author2}
ead{author2_Firstname@univ-jijel.dz}

%% fntext[label2]{}
cortext[cor1]{Coresponding author. Tel.: +225 095243621.}
address[rvt]{Non Destructive Testing Laboratory (NDT Lab), Automatic Department, Sciences and Technology Faculty, University , BP 98 street, 18000, City, country}

title{Title of the paper}


begin{abstract}
Based on clinical data collected using different brain imaging and recording techniques, brain researchers built mathematical models of the activity in the human brain. To test these models they simulate them by performing on those models a virtual brain experiment and compare the outputs from those with the real brain activity recordings. The models can be a basis for understanding what goes wrong in brain diseases and brain disorders and potentially help to create new drugs for these conditions. These models are often formulated in a continuous-discrete state space form. To fit these models to actual data, this require having suitable techniques that permits us to estimate both the hidden states and parameters of such models. The method proposed in this paper is a combination between the Square Root Cubature Kalman Filter (SCKF) and Maximum Likelihood Estimation (MLE). It uses gradient based optimization algorithms, for minimizing-maximizing the objective function. In the proposed method, it will be explained how the gradient can be calculated with a SCKF-like recursion. Numerical results obtained with simulated data are presented and discussed.
end{abstract}

begin{keyword}
FMRI sep Biophysical modelsep Stochastic Metabolic Hemodynamic Modelsep Maximum likelihood estimation sep Square-root Cubature Kalman Filter

end{keyword}

end{frontmatter}

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section{Introduction}
label{intro}
Functional magnetic resonance imaging (fMRI) represents one of the most powerful and noninvasive tools that has ever been developed, by virtue of its capability to image human brain function. The goal of research interest in fMRI is to understand the neural mechanism behind how we see, hear, think, feel and move. One of the most promising fields in which the fMRI was extensively used is the Cognitive Neuroscience, which focuses on the study of working memory, decision making, perception, sensation, reasoning, acquisition of knowledge and behavior.

begin{equation}
mathbf{x}(t+delta) = mathbf{x}(t)+delta mathbf{f}(t,mathbf{x}(t),mathbf{u}(t),theta)+sqrt{mathbf{Q}}mathbf{w}
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end{equation}

begin{equation}
mathbf{x}(t+delta) = mathbf{x}(t)+ mathbf{J_x}^{-1}[exp(delta mathbf{J_x}) - mathbf{I}]mathbf{f}(t,x(t),u(t),theta)
label{eq:Equat_7}
end{equation}

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