The Stable Manifold Theorem for Stochastic Differential Equations

We formulate and prove a {\it Local Stable Manifold Theorem\/} for stochastic differential equations (sde's) that are driven by spatial Kunita-type semimartingales with stationary ergodic increments. Both Stratonovich and It\^o-type equations are treated. Starting with the existence of a stochastic flow for a sde, we introduce the notion of a hyperbolic stationary trajectory. We prove the existence of invariant random stable and unstable manifolds in the neighborhood of the hyperbolic stationary solution. For Stratonovich sde's, the stable and unstable manifolds are dynamically characterized using forward and backward solutions of the anticipating sde. The proof of the stable manifold theorem is based on Ruelle-Oseledec multiplicative ergodic theory

Performance Analysis of Best Relaying Protocol Selection with Interferences at Relays

In this paper, we investigate the performance of selecting the best protocol between amplify and forward (AF) and decode and forward (DF) in multiple relay networks with multiple interferences at relays. In the selection scheme, the best protocol between AF and DF is selected depending on the comparisons of signal-to-interference and noise ratio (SINR) for all source-relay links. All relays measure the received SINR to decide forwarding signal or not. When SINR is above a certain threshold then DF is used otherwise AF is used. Particularly, we develop an accurate mathematical model for best relaying protocol by considering the effect of interferences to our scheme. Firstly, we derive the asymptotic closed form expression for the symbol error rate (SER) for the system under study. Also we derive an upper and lower bound of symbol error rate and show how they were tight with exact SER. Furthermore an approximate expression for the outage probability is derived. Numerical results are finally presented to validate the theoretical analysis with a different number of relays

A framework for adapting deep brain stimulation using Parkinsonian state estimates

The mechanisms underlying the beneficial effects of deep brain stimulation (DBS) for Parkinson's disease (PD) remain poorly understood and are still under debate. This has hindered the development of adaptive DBS (aDBS). For further progress in aDBS, more insight into the dynamics of PD is needed, which can be obtained using machine learning models. This study presents an approach that uses generative and discriminative machine learning models to more accurately estimate the symptom severity of patients and adjust therapy accordingly. A support vector machine is used as the representative algorithm for discriminative machine learning models, and the Gaussian mixture model is used for the generative models. Therapy is effected using the state estimates obtained from the machine learning models together with a fuzzy controller in a critic-actor control approach. Both machine learning model configurations achieve PD suppression to desired state in 7 out of 9 cases; most of which settle in under 2 s

Modifying Plaque assay and Clearance test as tools in determination of phage typing for E. Coli bacterial interspecies

Bacteriophage of E. Coli interspecies from sewage samples were isolated , the phage particles were isolated from two different sewage samples . The first sample was collected from sewage sample of Baghdad university and the second sample was isolated from domestic sewage sample , first sample showed phages specialized for three E. Coli interspecies bacteria (first plate ) and two E. Coli interspecies bacteria (second plate ) , meanwhile second sample showed phage specialized for two E. Coli. interspeciesThe study of appearance of E coli phages from first sample showed three types of E. coli phages with different size of inhibition zone ( 1 , 0.7,0.5 )Cm respectively ( first plate ) , meanwhile E. Coli interspecies bacteria showed phages related with two interspecies with size of inhibition zone ( 0.5 ,0.4) Cm respectively ( second plate ), on other hand , the second sample showed also two interspecies E. coli with inhibition zone (1,0.8)Cm . experimental method has been designed which showed the modifying method of phage assay to determine phage typing assay . phage has been tested particles with different bacterial strains ( E. coli , shagilla and Serratia ) from different sources and the control was the host of each bacteriophages by taking the O.D for all the tests and controls , to setup new criteria for phage typing .:and this test is called ( Clearance Test ) The result showed that O.D for Test 1 , 2 , 3, was ( 1.6 , 1.2 . 1.7) for ( E. coli , shagilla and Serratia ) bacterial strains , meanwhile the control tests was ( 0.3 , 0.2, 0.4 ) for strains isolated from first sample (first and second plate ) and second samples with different interspecies respectively . This result can predict high specificity of phage strain and this method can be used to determine interspecies strains .So from this experiment we can identify only Clearance Test by measuring only O.D. of bacterial strain with different phages instead of going through plaque assay

An Efficient and Effective Pilot Space-Time Adaptive Algorithm for Mobile Communication Systems

In this paper we present a new adaptive space-time algorithm for mitigating the effects of CCI and ISI and minimizing the probability of error in mobile communication systems, and evaluate its performance for different mobile velocities. The proposed algorithm is computationally efficient and provides better performance than the conventional RLS algorithm

Simulation of Wireless Digital Communication Systems

Due to the explosive demands for high speed wireless services, such as wireless Internet, email and cellular video conferencing, digital wireless communications has become one of the most exciting research topics in electrical and electronic engineering field. The never-ending demand for such personal and multimedia services, however, demands technologies operating at higher data rates and broader bandwidths. In addition, the complexity of wireless communication and signal processing systems has grown considerably during the past decade. Therefore, powerful computer­aided techniques are required for the process of modeling, designing, analyzing and evaluating the performance of digital wireless communication systems. In this paper we discuss the basic propagation mechanisms affecting the performance of wireless communication systems, and present a simple, powerful and efficient way to simulate digital wireless communication systems using Matlab. The simulated results are compared with the theoretical analysis to validate the simulator. The simulator is useful in evaluating the performance of wireless multimedia services and the associated signal processing structures and algorithms for current and next generation wireless mobile communication systems

An Adaptive Block-Based Eigenvector Equalization for Time-Varying Multipath Fading Channels

In this paper we present an adaptive Block-Based EigenVector Algorithm (BBEVA) for blind equalization of time-varying multipath fading channels. In addition we assess the performance of the new algorithm for different configurations and compare the results with the least mean squares (LMS) algorithm. The new algorithm is evaluated in terms of intersymbol interference (ISI) suppression, mean squared error (MSE) and by examining the signal constellation at the output of the equalizer. Simulation results show that the BBEVA performs better than the non-blind LMS algorithm

New connection formulae for the q-orthogonal polynomials via a series expansion of the q-exponential

Using a realization of the q-exponential function as an infinite multiplicative sereis of the ordinary exponential functions we obtain new nonlinear connection formulae of the q-orthogonal polynomials such as q-Hermite, q-Laguerre and q-Gegenbauer polynomials in terms of their respective classical analogs.Comment: 14 page