Estimate on the Pathwise Lyapunov Exponent of the Linear Stochastic Differential Equations with Constant Coefficients

, M.Sc. Thesis Sharif University of Technology Yazdanbakhsh, Proshat (Author) ; Zohuri Zangeneh, Bijan (Supervisor)

Abstract

The application of Stochastic Differential Equations in branches like nonlinear control,robatic systems, financial mathematics and etc. has grown impressively nowadays. In this thesis, we are going to introduce this equations and study their stability. First, we will present methods to check the stability of nonlinear systems dx(t) = f(x(t); t)dt using Lyapunov’s theorem.Then we will study stability of autonomous systems using it’s results. In the case of instability, we will study the possibility of stabilizing the stochastic equations dx(t) = Ax(t)dt + Σn i=1 Bix(t)dWi(t) by using Brownian motions and these methods. In the end, we will study the stabilizablity conditions of instable...

Study of CNT/ZnO/PANI Nanocomposite Biosensors

, M.Sc. Thesis Sharif University of Technology Yazdanbakhsh Sorkhabi, Khashayar (Author) ; Dolati, Abolghasem (Supervisor)

Abstract

For application as a biosensor electrode, Aligned Carbon Nanotubes (CNTs) were produced on Stainless Steel 304 substrate by optimizing the CVD method. For better performance, Zinc Oxide (ZnO) nanoparticles were coated on CNTs, using electrochemical deposition method at room temperature and process variables were optimized to acquire discrete particles with a narrow distribution. After that, Polyaniline, which is a conductive polymer, was electropolymerized on CNT/ZnO composite to further improve the electrocatalytic abilities of the electrode. The produced electrode was then used to detect glucose by Cyclic Voltammetry and Amperometry methods. This electrode shows a linear relationship...

New attractor states for synchronous activity in synfire chains with excitatory and inhibitory coupling

, Article Biological Cybernetics ; Volume 86, Issue 5 , 2002 , Pages 367-378 ; 03401200 (ISSN) Yazdanbakhsh, A ; Babadi, B ; Rouhani, S ; Arabzadeh, E ; Abbassian, A ; Sharif University of Technology

2002

Abstract

In a feedforward network of integrate-and-fire neurons, where the firing of each layer is synchronous (synfire chain), the final firing state of the network converges to two attractor states: either a full activation or complete fading of the tailing layers. In this article, we analyze various modes of pattern propagation in a synfire chain with random connection weights and delta-type postsynaptic currents. We predict analytically that when the input is fully synchronized and the network is noise free, varying the characteristics of the weights distribution would result in modes of behavior that are different from those described in the literature. These are convergence to fixed points,...