Human Papilloma Virus Related Head and Neck Squamous Cell Carcinoma-an updated review

Human papilloma virus (HPV) related head and neck squamous cell cancer (HNSCC) has varying etiology, genetic as well as environmental factors involved and differential clinicicopathological features. HNSCC came in the limelight recently due to increased incidence rate and insufficient diagnostic methods. This review will comprehensively focus on the characteristics of HPV associated HNSCC.  It will provide an updated review of our understanding of HPV role in Oral squamous cell carcinoma (OSCC) known to date. Curruntly, three vaccines are available (Gardasil, Gardasil 9 and Cervarix). These vaccines prevent infections with HPV types 16 and 18 HPV-16 is most common type associated with HNSCC. HPV related HNSCC has better prognosis, does not mutate  but inactivatestumor suppressor genes and therefore has comparatively better treatment options. However, there is still a need to improve our methods of sampling, HPV molecular assay and type of specimen to be used.

Haar Wavelet Approach for Numerical Solution of Three-Dimensional Patial Differential Equations

In this dissertation new algorithms have been presented for the numerical solution of three-dimensional elliptic and parabolic partial differential equa- tions subject to Dirichlet boundary conditions. A numerical method based on Haar wavelet collocation technique(HWCT) is being formulated for numer- ical solution of 3D elliptic partial di erential equations(PDEs) and systems involving such equations. The newly developed numerical technique is ap- plied to both linear and nonlinear 3D elliptic PDEs and systems involving such PDEs. The proposed numerical is also applied to the time-invariant fully nonlinear Navier-Stoke''s model equations. In case of solving linear el- liptic PDEs, the resulting algebraic system of equations is solved by using Gauss elimination method. Whereas for nonlinear elliptic PDEs we used Newton''s or Broyden''s method. A hybrid numerical method based onnite di erence method and 3D HWCT is developed for the numerical solution of 3D parabolic PDEs and systems involving such PDEs. This hybrid numerical technique is applied to both linear and nonlinear parabolic PDEs including systems. In case of non- linear parabolic PDEs quasilinearization technique was applied to linearize the nonlinear terms. The time derivatives involved in parabolic PDEs is ap- proximated by thefinite difference method. The numerical simulations of all newly developed numerical techniques are performed using MATLAB. The efficiency and accuracy of the proposed numerical methods is vali- dated via various linear and nonlinear test problems including systems from the literature. The numerical results of these test problems are compared with the exact solutions as well as with the existent methods in literature. The maximum absolute errors and experimental rate of convergence have been calculated for different number of collocation points. The numerical re- sults shows better accuracy, efficiency and simple applicability of the newly developed numerical methods.