Testing surface area with arbitrary accuracy

Recently, Kothari et al.\ gave an algorithm for testing the surface area of an arbitrary set $A \subset [0, 1]^n$. Specifically, they gave a randomized algorithm such that if $A$'s surface area is less than $S$ then the algorithm will accept with high probability, and if the algorithm accepts with high probability then there is some perturbation of $A$ with surface area at most $\kappa_n S$. Here, $\kappa_n$ is a dimension-dependent constant which is strictly larger than 1 if $n \ge 2$, and grows to $4/\pi$ as $n \to \infty$. We give an improved analysis of Kothari et al.'s algorithm. In doing so, we replace the constant $\kappa_n$ with $1 + \eta$ for $\eta > 0$ arbitrary. We also extend the algorithm to more general measures on Riemannian manifolds.Comment: 5 page

Upregulated wnt-11 and mir-21 expression trigger epithelial mesenchymal transition in aggressive prostate cancer cells

Prostate cancer (PCa) is the second-leading cause of cancer-related death among men. microRNAs have been identified as having potential roles in tumorigenesis. An oncomir, miR-21, is commonly highly upregulated in many cancers, including PCa, and showed correlation with the Wnt-signaling axis to increase invasion. Wnt-11 is a developmentally regulated gene and has been found to be upregulated in PCa, but its mechanism is unknown. The present study aimed to investigate the roles of miR-21 and Wnt-11 in PCa in vivo and in vitro. First, different Gleason score PCa tissue samples were used; both miR-21 and Wnt-11 expressions correlate with high Gleason scores in PCa patient tissues. This data then was confirmed with formalin-fixed paraffin cell blocks using PCa cell lines LNCaP and PC3. Cell survival and colony formation studies proved that miR-21 involves in cells’ behaviors, as well as the epithelial-mesenchymal transition. Consistent with the previous data, silencing miR-21 led to significant inhibition of cellular invasiveness. Overall, these results suggest that miR-21 plays a significant role related to Wnt-11 in the pathophysiology of PCa

New Frontiers in the Treatment of Perfectionism

Perfectionism can present as a clinical problem in its own right or it can interfere with the successful treatment of Axis I disorders. In the past 15 years, a cognitive behavioral analysis of “clinical perfectionism” has been proposed. This approach and the measurement of the construct of clinical perfectionism have proved controversial. Nevertheless, the approach has experimental support and clinical utility; the derived treatment has been shown to lead to significant improvement on both measures of perfectionism and Axis I disorders. The cognitive behavioral intervention for perfectionism has been evaluated in a range of formats (group, individual, face-to-face, and online) and all show promise. Further work is required to address clinically important questions such as when to treat clinical perfectionism if it occurs in the context of single and multiple Axis I disorders

Higher Order Decompositions of Ordered Operator Exponentials

We present a decomposition scheme based on Lie-Trotter-Suzuki product formulae to represent an ordered operator exponential as a product of ordinary operator exponentials. We provide a rigorous proof that does not use a time-displacement superoperator, and can be applied to non-analytic functions. Our proof provides explicit bounds on the error and includes cases where the functions are not infinitely differentiable. We show that Lie-Trotter-Suzuki product formulae can still be used for functions that are not infinitely differentiable, but that arbitrary order scaling may not be achieved.Comment: 16 pages, 1 figur

Professor DS Kotharis Reflections on the Parallelism between Epistemological Foundations of Modern Physics and Indian Philosophical Thought Part II: The Principle of complementarity and Syadvada

A favourite theme in Prof Kothari's talks and writings during his later years was the close parallelism between Bohr's principle of complementarity and Indian philosophical thought, in particular, the  Syadvada of J ain philosophy 1-6. In this part of the article , we have tried to summarize Prof Kothari's views on the subject

Laparoscopic management of right paraduodenal hernia along with the correction of malrotation in a pediatric patient: a case report

Paraduodenal hernias (PDH) are rare; however, they are the most common form of internal hernias. A 11-year-old boy presented to us with a history of intermittent abdominal pain since 1 year. His physical examination was normal. Plain abdominal radiographs and ultrasonography were inconclusive. Contrast-enhanced computed tomography of the abdomen reported a right subhepatic cecum. The patient underwent diagnostic laparoscopy followed by successful laparoscopic right PDH repair (excision of hernial sac, release of Ladd’s bands, and appendectomy). Ours is the sixth report to describe laparoscopic repair of a right PDH and the third in the pediatric age group. He was discharged home on postoperative day 1. He was completely asymptomatic at the 1-year follow-up. Keywords: laparoscopic, malrotation, paraduodenal hernia, pediatri

Prosthesis for a Case of Subtotal Orbital Exenteration

Aims and objectives: To rehabilitate a patient with subtotal orbital exenteration defect. Case description: A 32 year old male with history of carcinoma of ethmoid, treated surgically with subtotal orbital exenteration presented with a defect communicating with the pharynx. He was rehabilitated with a prosthetic eye. Conclusion: A two piece cast with a removable part containing the defect made it very easy to fabricate the prosthesis. Patient was happy with the appearance and expressed satisfaction.&nbsp