The role of optical and virt ual colonoscopy in colorectal neoplasms

Purpose: High prevalence of colon carcinoma explains the continued high mortality rate of this disease.Utilizing a strategy of virtual colonoscopy (VC) in patients aged over 50 years with optical colonoscopy (OC) following-up for removal of detected adenomatous polyps may result in lowering the colon cancer death rate. However, VC diagnostic potential has not been widely recognized yet.Material and methods: This article reviews the currently available in diagnostic options in colorectal neoplasms and discusses their advantages and drawbacks.Results: VC has many advantages over the existing options and its several drawbacks can be mitigated so that it would become a valuable diagnostic modality. A strategy that utilizes VC for screening of patients over the age of 50 years and OC for screening high-risk individuals and those with positive VC findings would result in a significantly reduced colon cancer mortality rate.Conclusion: Both OC and VC (i.e., CTC and MRC) progress toward the clinical needs as new technologies are developed and applied to overcome the drawbacks of these diagnostic methods. Each of them plays a unique role for colon cancer prevention

Endoscopic radical treatment in early rectal cancer

Purpose: Standard radical treatment for early rectal cancer includes a removal of the tumour with total mesorectal excision. There are numerous new techniques for endoscopic treatment which could shift the strategy for obtaining the postoperative results.Material and methods: We report our radical endoscopic treatment of early rectal carcinoma by endoscopic submucosal dissection (ESD ). Forty-five patients with early-stage rectal cancer (carcinoma in situ, T1sm1 and T1sm2) were enrolled. All of them were staged by 3-D endorectal ultrasound. In 43 cases, the tumours were endoscopically removed. The postoperative results were analyzed and presented only. No oncological results were reported.Results: The mean lesion size was 31,0 mm (range, 19-82 mm), and the mean operating time was 86 min. (range, 48-131 min.). Forty-two lesions were resected en bloc with tumour-free margins with a successful rate of 97,33% (42/43). Three lesions were understaged or their localization in the rectum was not suitable for endoscopic treatment. The following complications were observed: perforation of the rectum in one patient (4%) treated conservatively, and major bleeding in four patients (10%) stopped by endoscopic hemostasis. Neither systematic complications, nor mortality were observed.Conclusion: ESD procedure for early-stage rectal cancers is safe and effective. It has the advantage of a shorter hospital recovery. The postoperative results are significantly better in comparison of radical surgical treatment such as transanal excision. The perioperative morbidity is of different kind and the postoperative period is shorter

Group Analysis of the Novikov Equation

We find the Lie point symmetries of the Novikov equation and demonstrate that it is strictly self-adjoint. Using the self-adjointness and the recent technique for constructing conserved vectors associated with symmetries of differential equations, we find the conservation law corresponding to the dilations symmetry and show that other symmetries do not provide nontrivial conservation laws. Then we investigat the invariant solutions

Conservation laws for self-adjoint first order evolution equations

In this work we consider the problem on group classification and conservation laws of the general first order evolution equations. We obtain the subclasses of these general equations which are quasi-self-adjoint and self-adjoint. By using the recent Ibragimov's Theorem on conservation laws, we establish the conservation laws of the equations admiting self-adjoint equations. We illustrate our results applying them to the inviscid Burgers' equation. In particular an infinite number of new symmetries of these equations are found and their corresponding conservation laws are established.Comment: This manuscript has been accepted for publication in Journal of Nonlinear Mathematical Physic

Numerical Ricci-flat metrics on K3

We develop numerical algorithms for solving the Einstein equation on Calabi-Yau manifolds at arbitrary values of their complex structure and Kahler parameters. We show that Kahler geometry can be exploited for significant gains in computational efficiency. As a proof of principle, we apply our methods to a one-parameter family of K3 surfaces constructed as blow-ups of the T^4/Z_2 orbifold with many discrete symmetries. High-resolution metrics may be obtained on a time scale of days using a desktop computer. We compute various geometric and spectral quantities from our numerical metrics. Using similar resources we expect our methods to practically extend to Calabi-Yau three-folds with a high degree of discrete symmetry, although we expect the general three-fold to remain a challenge due to memory requirements.Comment: 38 pages, 10 figures; program code and animations of figures downloadable from http://schwinger.harvard.edu/~wiseman/K3/ ; v2 minor corrections, references adde