R-matrix for a geodesic flow associated with a new integrable peakon equation

We use the r-matrix formulation to show the integrability of geodesic flow on an $N$-dimensional space with coordinates $q_k$, with $k=1,...,N$, equipped with the co-metric $g^{ij}=e^{-|q_i-q_j|}\big(2-e^{-|q_i-q_j|}\big)$. This flow is generated by a symmetry of the integrable partial differential equation (pde) $m_t+um_x+3mu_x=0, m=u-\alpha^2u_{xx}$ (\al is a constant). This equation -- called the Degasperis-Procesi (DP) equation -- was recently proven to be completely integrable and possess peakon solutions by Degasperis, Holm and Hone (DHH[2002]). The isospectral eigenvalue problem associated with the integrable DP equation is used to find a new $L$-matrix, called the Lax matrix, for the geodesic dynamical flow. By employing this Lax matrix we obtain the $r$-matrix for the integrable geodesic flow.Comment: This paper has some crucial technical errors in $r$-matrix formula derivatio

Iontophoretic drug delivery models

Iontophoresis relies on active transportation of the charged medication agent within an electric field and delivers medication transdermally. It uses electric current to ionize drug molecules and propel them through the skin. It is a kind of transdermal drug delivery method, and hence the method has to handle the variability in skin characteristics of a patient. In this paper, a preliminary study based on the different models of the skin impedance is carried out. The purpose is to examine several skin models for iontophoretic drug delivery. This paper carries out a simulation study based on three different skin impedance models. © 2011 IEEE.published_or_final_versionThe 1st Middle East Conference on Biomedical Engineering (MECBME 2011), Sharjah, UAE, 21-24 February 2011. In Proceedings of the 1st MECBME, 2011, p. 331-33

An iteratively Reweighted Least Square algorithm for RSS-based sensor network localization

In this article, we give a new algorithm for localization based on RSS measurement. There are many measurement methods for localizing the unknown nodes in a sensor network. RSS is the most popular one due to its simple and cheap hardware requirement. However, accurate algorithm based on RSS is needed to obtain the positions of unknown nodes. Recent algorithms such as MDS(Multi-Dimensional Scaling)-MAP, PDM (Proximity Distance Matrix) cannot give accurate results based on RSS as the RSS signals always have large variations. Besides, recent algorithms on sensor network localization ignore the received signal strength (RSS) and thus get a disappointing accuracy. This is because they are mostly focused on the difference between the estimated distance and the real distance. This paper introduces a target function - signal-based maximum likelihood (SML), which uses the maximum likelihood based on the directly measured RSS signal. Inspired by the SMACOF (Scaling by Majorizing A COmplicated Function) algorithm, an iteration surrogate algorithm named IRLS (Iteratively Reweighted Least Square) is introduced to solve the SML. From the simulation results, the IRLS algorithm can give accurate results for RSS positioning. When compared with other popular algorithms such as MDS-MAP, PDM, and SMACOF, the error (distance between the estimated position and the actual position) calculated by IRLS is less than all the other algorithms. In anisotropic network, IRLS also has good performance. © 2011 IEEE.published_or_final_versionThe 2011 IEEE International Conference on Mechatronics and Automation (ICMA 2011), Beijing, China, 7-10 August 2011. In Proceedings of ICMA, 2011, p. 1085-109

Solutions for connectivity-based sensor network localization

This paper compares the solutions obtained by various methods in the literature for sensor network localization based on connectivity. The deficiencies of some of those solutions are discussed. It is argued that the actual problem should be represented as an optimization problem with both convex and non-convex constraints. A new method is proposed which utilizes multi-dimensional scaling (MDS) to provide an initial solution on the location of the unknown nodes and then searches for a solution to satisfy all the constraints of the problem. The final solution can reach the most suitable configuration of the unknown nodes because all the information on the constraints (convex and non-convex) related to connectivity will have been used. Compared with other constraint models that only consider the nodes that have connections, this method considers not only the connection constraints, but also the disconnection constraints. Simulation results have shown that better solution can be obtained through the use of this method when compared with those produced by other methods. © 2011 IEEE.published_or_final_versionThe 2011 IEEE International Conference on Mechatronics and Automation (ICMA 2011), Beijing, China, 7-10 August 2011. In Proceedings of ICMA, 2011, p. 1056-106

Localization in wireless sensor networks with gradient descent

In this article, we present two distance-based sensor network localization algorithms. The location of the sensors is unknown initially and we can estimate the relative locations of sensors by using knowledge of inter-sensor distance measurements. Together with the knowledge of the absolute locations of three or more sensors, we can also determine the locations of all the sensors in the wireless network. The proposed algorithms make use of gradient descent to achieve excellent localization accuracy. The two gradient descent algorithms are iterative in nature and result is obtained when there is no further improvement on the accuracy. Simulation results have shown that the proposed algorithms have better performance than existing localization algorithms. A comparison of different methods is given in the paper. © 2011 IEEE.published_or_final_versionThe 2011 IEEE Pacific Rim Conference on Communications, Computers and Signal Processing (PacRim), Victoria, B.C., 23-26 August 2011. In IEEE PacRim Conference Proceedings, 2011, p. 91-9