Smoothness-Increasing Accuracy-Conserving (SIAC) filtering and quasi interpolation: A unified view

Filtering plays a crucial role in postprocessing and analyzing data in scientific and engineering applications. Various application-specific filtering schemes have been proposed based on particular design criteria. In this paper, we focus on establishing the theoretical connection between quasi-interpolation and a class of kernels (based on B-splines) that are specifically designed for the postprocessing of the discontinuous Galerkin (DG) method called Smoothness-Increasing Accuracy-Conserving (SIAC) filtering. SIAC filtering, as the name suggests, aims to increase the smoothness of the DG approximation while conserving the inherent accuracy of the DG solution (superconvergence). Superconvergence properties of SIAC filtering has been studied in the literature. In this paper, we present the theoretical results that establish the connection between SIAC filtering to long-standing concepts in approximation theory such as quasi-interpolation and polynomial reproduction. This connection bridges the gap between the two related disciplines and provides a decisive advancement in designing new filters and mathematical analysis of their properties. In particular, we derive a closed formulation for convolution of SIAC kernels with polynomials. We also compare and contrast cardinal spline functions as an example of filters designed for image processing applications with SIAC filters of the same order, and study their properties

Finite quantum tomography via semidefinite programming

Using the the convex semidefinite programming method and superoperator formalism we obtain the finite quantum tomography of some mixed quantum states such as: qudit tomography, N-qubit tomography, phase tomography and coherent spin state tomography, where that obtained results are in agreement with those of References \cite{schack,Pegg,Barnett,Buzek,Weigert}.Comment: 25 page

One-Sided Position-Dependent Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering Over Uniform and Non-Uniform Meshes

In this paper, we introduce a new position-dependent Smoothness-Increasing Accuracy-Conserving (SIAC) filter that retains the benefits of position dependence while ameliorating some of its shortcomings. As in the previous position-dependent filter, our new filter can be applied near domain boundaries, near a discontinuity in the solution, or at the interface of different mesh sizes; and as before, in general, it numerically enhances the accuracy and increases the smoothness of approximations obtained using the discontinuous Galerkin (dG) method. However, the previously proposed position-dependent one-sided filter had two significant disadvantages: (1) increased computational cost (in terms of function evaluations), brought about by the use of $4k+1$ central B-splines near a boundary (leading to increased kernel support) and (2) increased numerical conditioning issues that necessitated the use of quadruple precision for polynomial degrees of $k\ge 3$ for the reported accuracy benefits to be realizable numerically. Our new filter addresses both of these issues --- maintaining the same support size and with similar function evaluation characteristicsas the symmetric filter in a way that has better numerical conditioning --- making it, unlike its predecessor, amenable for GPU computing. Our new filter was conceived by revisiting the original error analysis for superconvergence of SIAC filters and by examining the role of the B-splines and their weights in the SIAC filtering kernel. We demonstrate, in the uniform mesh case, that our new filter is globally superconvergent for $k=1$ and superconvergent in the interior (e.g., region excluding the boundary) for $k\ge2$. Furthermore, we present the first theoretical proof of superconvergence for postprocessing over smoothly varying meshes, and explain the accuracy-order conserving nature of this new filter when applied to certain non-uniform meshes cases. We provide numerical examples supporting our theoretical results and demonstrating that our new filter, in general, enhances the smoothness and accuracy of the solution. Numerical results are presented for solutions of both linear and nonlinear equation solved on both uniform and non-uniform one- and two-dimensional meshes

Developing Ontologies withing Decentralized Settings

This chapter addresses two research questions: “How should a well-engineered methodology facilitate the development of ontologies within communities of practice?” and “What methodology should be used?” If ontologies are to be developed by communities then the ontology development life cycle should be better understood within this context. This chapter presents the Melting Point (MP), a proposed new methodology for developing ontologies within decentralised settings. It describes how MP was developed by taking best practices from other methodologies, provides details on recommended steps and recommended processes, and compares MP with alternatives. The methodology presented here is the product of direct first-hand experience and observation of biological communities of practice in which some of the authors have been involved. The Melting Point is a methodology engineered for decentralised communities of practice for which the designers of technology and the users may be the same group. As such, MP provides a potential foundation for the establishment of standard practices for ontology engineering

Randomized control trial:Comparison of Triple Therapy plus Probiotic Yogurt vs. Standard Triple Therapy on Helicobacter Pylori Eradication

BACKGROUND: Treatment of Helicobacter pylori (H. pylori) as a major cause of gastric diseases is of utmost concern.We aimed to assess efficacy of triple therapy (amoxicillin, clarithromycin and pantoprazole) plus probiotic yogurt (PY) on eradication of H.pylori. METHODS: Total 102 H. pylori positive patients were divided to 3 groups equally and randomly. For treatment of each group Amoxicillin, clarithromycin and pantoprazole were used. Group A had additional PY, Group B ordinary low fat yogurt and Group C just had triple therapy in their regimen as well. These groups were compared regarding treatment success. RESULTS: Total number of 88 patients finished the treatment course. The most common experienced side effects were dysgeusia in groups A and B (25.8% and 32.3%, respectively), and dysgeusia with diarrhea and abdominal pain (30.8%) in group C. Eradication rate was, respectively, 61.3%, 64.5% and 71.3% in group A, B and C of which difference was not statistically significant (P> 0.05). However, the difference between 3 groups in regard to education level was statistically significant (P=0.005). CONCLUSION: PY enriched triple therapy has decreased side effects of antibiotics consumption; however, this has no impact on eradication of Hpylori. PY and triple therapy can be used concomitantly to increase the patient tolerance