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

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

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

Constraining a possible time variation of the gravitational constant G with terrestrial nuclear laboratory data

Testing the constancy of the gravitational constant G has been a longstanding fundamental question in natural science. As first suggested by Jofr\'{e}, Reisenegger and Fern\'{a}ndez [1], Dirac's hypothesis of a decreasing gravitational constant $G$ with time due to the expansion of the Universe would induce changes in the composition of neutron stars, causing dissipation and internal heating. Eventually, neutron stars reach their quasi-stationary states where cooling due to neutrino and photon emissions balances the internal heating. The correlation of surface temperatures and radii of some old neutron stars may thus carry useful information about the changing rate of G. Using the density dependence of the nuclear symmetry energy constrained by recent terrestrial laboratory data on isospin diffusion in heavy-ion reactions at intermediate energies and the size of neutron skin in $^{208}Pb$ within the gravitochemical heating formalism, we obtain an upper limit of the relative changing rate of $|\dot{G}/G|\le4\times 10^{-12}yr^{-1}$ consistent with the best available estimates in the literature.Comment: 27 pages, 11 figures, and 2 tables. Accepted version to appear in PRC (2007

Oncological safety of stromal vascular fraction enriched fat grafting in two-stage breast reconstruction after nipple sparing mastectomy: long-term results of a prospective study

OBJECTIVE: Autologous fat transfer (AFT) is commonly used to treat implant palpability and prevent fibrosis and thinning in mastectomy skin flaps. A major limit to this procedure is volume retention over time, leading to the introduction of fat enrichment with stromal vascular fraction (SVF+AFT). Oncological concerns have been raised over the injection of an increased concentration of progenitors cells (ASCs) in the SVF. The aim of the study is to evaluate the long-term cancer recurrence risk of SVF+AFT cases compared to AFT, in patients undergoing Nipple Sparing Mastectomy (NSM). PATIENTS AND METHODS: A prospective study was designed to compare three groups of patients undergoing NSM followed by SVF+AFT, AFT or none (control group), after a two-stage breast reconstruction. Patients were strictly followed-up for at least 5-years from the second stage reconstructive procedure. Loco-regional and systemic recurrence rate were evaluated over time as the primary outcome. Logistic regression was used to investigate which factors were associated with recurrence events and independent variables of interest were: surgical technique, age above 50 years old, lympho-vascular invasion, oncological stage, adjuvant or neoadjuvant chemotherapy, adjuvant radiotherapy and adjuvant hormone therapy. RESULTS: 41 women were included in G1 (SVF+AFT), 64 in G2 (AFT), and 64 in G3 (control group). Loco-regional recurrence rate was 2.4% for G1, 4.7% for G2, and 1.6% for G3. Systemic recurrence was 7.3%, 3.1%, and 3.1%, respectively. Among the variables included, there were no significant risk factors influencing a recurrence event, either loco-regional or systemic. In particular, SVF+AFT (G1) did not increase the oncological recurrence. CONCLUSIONS: Our data suggest that both centrifuged and SVF-enhanced fat transfer have a similar safety level in comparison to patients who did not undergo fat grafting in breast reconstruction after NSM

Training emergency services’ dispatchers to recognise stroke: an interrupted time-series analysis

Background: Stroke is a time-dependent medical emergency in which early presentation to specialist care reduces death and dependency. Up to 70% of all stroke patients obtain first medical contact from the Emergency Medical Services (EMS). Identifying ‘true stroke’ from an EMS call is challenging, with over 50% of strokes being misclassified. The aim of this study was to evaluate the impact of the training package on the recognition of stroke by Emergency Medical Dispatchers (EMDs). Methods: This study took place in an ambulance service and a hospital in England using an interrupted time-series design. Suspected stroke patients were identified in one week blocks, every three weeks over an 18 month period, during which time the training was implemented. Patients were included if they had a diagnosis of stroke (EMS or hospital). The effect of the intervention on the accuracy of dispatch diagnosis was investigated using binomial (grouped) logistic regression. Results: In the Pre-implementation period EMDs correctly identified 63% of stroke patients; this increased to 80% Post-implementation. This change was significant (p=0.003), reflecting an improvement in identifying stroke patients relative to the Pre-implementation period both the During-implementation (OR=4.10 [95% CI 1.58 to 10.66]) and Post-implementation (OR=2.30 [95% CI 1.07 to 4.92]) periods. For patients with a final diagnosis of stroke who had been dispatched as stroke there was a marginally non-significant 2.8 minutes (95% CI −0.2 to 5.9 minutes, p=0.068)reduction between Pre- and Post-implementation periods from call to arrival of the ambulance at scene. Conclusions: This is the first study to develop, implement and evaluate the impact of a training package for EMDs with the aim of improving the recognition of stroke. Training led to a significant increase in the proportion of stroke patients dispatched as such by EMDs; a small reduction in time from call to arrival at scene by the ambulance also appeared likely. The training package has been endorsed by the UK Stroke Forum Education and Training, and is free to access on-line