Towards a More General Type of Univariate Constrained Interpolation With Fractal Splines

Recently, in [Electronic Transaction on Numerical Analysis, 41 (2014), pp. 420-442] authors introduced a new class of rational cubic fractal interpolation functions with linear denominators via fractal perturbation of traditional nonrecursive rational cubic splines and investigated their basic shape preserving properties. The main goal of the current article is to embark on univariate constrained fractal interpolation that is more general than what was considered so far. To this end, we propose some strategies for selecting the parameters of the rational fractal spline so that the interpolating curves lie strictly above or below a prescribed linear or a quadratic spline function. Approximation property of the proposed rational cubic fractal spine is broached by using the Peano kernel theorem as an interlude. The paper also provides an illustration of background theory, veined by examples.Comment: 7 pages, 6 figure

Limits on the time variation of the electromagnetic fine-structure constant in the low energy limit from absorption lines in the spectra of distant quasars

Most of the successful physical theories rely on the constancy of few fundamental quantities (such as the speed of light, $c$, the fine-structure constant, \alpha, the proton to electron mass ratio, \mu, etc), and constraining the possible time variations of these fundamental quantities is an important step toward a complete physical theory. Time variation of \alpha can be accurately probed using absorption lines seen in the spectra of distant quasars. Here, we present the results of a detailed many-multiplet analysis performed on a new sample of Mg II systems observed in high quality quasar spectra obtained using the Very Large Telescope. The weighted mean value of the variation in \alpha derived from our analysis over the redshift range 0.4<z<2.3 is \Delta\alpha/\alpha = (-0.06+/-0.06) x 10^{-5}. The median redshift of our sample (z=1.55) corresponds to a look-back time of 9.7 Gyr in the most favored cosmological model today. This gives a 3\sigma limit, -2.5 x 10^{-16} yr^-1 <(\Delta\alpha/\alpha\Delta t) <+1.2x10^{-16} yr^-1, for the time variation of \alpha, that forms the strongest constraint obtained based on high redshift quasar absorption line systems.Comment: uses revtex, 4 pages 3 figures. Accepted for publication in Physical Review Letter

Systematic review of prognostic importance of extramural venous invasion in rectal cancer

AIM: To systematically review the survival outcomes relating to extramural venous invasion in rectal cancer. METHODS: A systematic review was conducted using PRISMA guidelines. An electronic search was carried out using MEDLINE, EMBASE, CINAHL, Cochrane library databases, Google scholar and Pubmed until October 2014. Search terms were used in combination to yield articles on extramural venous invasion in rectal cancer. Outcome measures included prevalence and 5-year survival rates. These were graphically displayed using Forest plots. Statistical analysis of the data was carried out. RESULTS: Fourteen studies reported the prevalence of extramural venous invasion (EMVI) positive patients. Prevalence ranged from 9%-61%. The pooled prevalence of EMVI positivity was 26% [Random effects: Event rate 0.26 (0.18, 0.36)]. Most studies showed that EMVI related to worse oncological outcomes. The pooled overall survival was 39.5% [Random effects: Event rate 0.395 (0.29, 0.51)]. CONCLUSION: Historically, there has been huge variation in the prevalence of EMVI through inconsistent reporting. However the presence of EMVI clearly leads to worse survival outcomes. As detection rates become more consistent, EMVI may be considered as part of risk-stratification in rectal cancer. Standardised histopathological definitions and the use of magnetic resonance imaging to identify EMVI will improve detection rates in the future

Performance of FEC codes over AWGN channel for efficient use in Polymer Optical Fiber links

Volume 1 Issue 7 (September 2013

Phase diagram and upper critical field of homogenously disordered epitaxial 3-dimensional NbN films

We report the evolution of superconducting properties with disorder, in 3-dimensional homogeneously disordered epitaxial NbN thin films. The effective disorder in NbN is controlled from moderately clean limit down to Anderson metal-insulator transition by changing the deposition conditions. We propose a phase diagram for NbN in temperature-disorder plane. With increasing disorder we observe that as kFl-->1 the superconducting transition temperature (Tc) and minimum conductivity (sigma_0) go to zero. The phase diagram shows that in homogeneously disordered 3-D NbN films, the metal-insulator transition and the superconductor-insulator transition occur at a single quantum critical point at kFl~1.Comment: To appear in Journal of Superconductivity and Novel Magnetism (ICSM2010 proceedings

Sexual dysfunction following rectal cancer surgery

INTRODUCTION: Sexual and urological problems after surgery for rectal cancer are common, multifactorial, inadequately discussed, and untreated. The urogenital function is dependent on dual autonomic sympathetic and parasympathetic innervation, and four key danger zones exist that are at risk for nerve damage during colorectal surgery: one of these sites is in the abdomen and three are in the pelvis. The aim of this study is to systematically review the epidemiology of sexual dysfunction following rectal cancer surgery, to describe the anatomical basis of autonomic nerve-preserving techniques, and to explore the scientific evidence available to support the laparoscopic or robotic approach over open surgery. METHODS: According to the PRISMA guidelines, a comprehensive literature search of studies evaluating sexual function in patients undergoing rectal surgery for cancer was performed in Medline, Scopus, Web of Science, Embase, and Cochrane Central Register of controlled trials. RESULTS: An increasing number of studies assessing the incidence and prevalence of sexual dysfunction following multimodality treatment for rectal cancer has been published over the last 30 years. Significant heterogeneity in the prevalence of sexual dysfunction is reported in the literature, with rates between 5 and 90%. CONCLUSIONS: There is no evidence to date in favor of any surgical approach (open vs laparoscopic vs robotic). Standardized diagnostic tools should be routinely used to prospectively assess sexual function in patients undergoing rectal surgery

Extramural venous invasion is a potential imaging predictive biomarker of neoadjuvant treatment in rectal cancer

BACKGROUND: Extramural venous invasion (EMVI) is a poor prognostic factor in rectal cancer and identified on magnetic resonance imaging (MRI) (mrEMVI). The clinical relevance of improvement in mrEMVI following neoadjuvant therapy is unknown. This study aimed to demonstrate that regression of mrEMVI following neoadjuvant chemoradiotherapy (CRT) results in improved outcomes and mrEMVI can be used as an imaging biomarker METHODS: Retrospective analysis of prospectively collected data was conducted examining the staging and post-treatment MRIs of patients who had presented with EMVI-positive rectal cancer. All patients had undergone neoadjuvant CRT and curative surgery. Changes in mrEMVI were graded with a new MRI-based TRG scale–mr-vTRG; and related to disease-free survival (DFS). The study fulfilled Reporting Recommendations for Tumour Marker Prognostic Studies criteria for biomarkers. RESULTS: Sixty-two patients were included. Thirty-five patients showed more than 50% fibrosis of mrEMVI (mr-vTRG 1-3); 3-year DFS 87.8% and 9% recurrence. Twenty-seven patients showed less than 50% fibrosis (mr-vTRG 4-5); 3-year DFS 45.8% with 44% recurrence – P<0.0001. On multivariate Cox-regression, only mr-vTRG 4-5 increased risk of disease recurrence – HR=5.748. CONCLUSION: Patients in whom there has been a significant response of EMVI to CRT show improved DFS. Those patients with poor response should be considered for intensive treatment. As an imaging biomarker in rectal cancer, mrEMVI can be used