Siciak-Zahariuta extremal functions, analytic discs and polynomial hulls

We prove two disc formulas for the Siciak-Zahariuta extremal function of an arbitrary open subset of complex affine space. We use these formulas to characterize the polynomial hull of an arbitrary compact subset of complex affine space in terms of analytic discs. Similar results in previous work of ours required the subsets to be connected

Optimal deployment of components of cloud-hosted application for guaranteeing multitenancy isolation

One of the challenges of deploying multitenant cloud-hosted services that are designed to use (or be integrated with) several components is how to implement the required degree of isolation between the components when there is a change in the workload. Achieving the highest degree of isolation implies deploying a component exclusively for one tenant; which leads to high resource consumption and running cost per component. A low degree of isolation allows sharing of resources which could possibly reduce cost, but with known limitations of performance and security interference. This paper presents a model-based algorithm together with four variants of a metaheuristic that can be used with it, to provide near-optimal solutions for deploying components of a cloud-hosted application in a way that guarantees multitenancy isolation. When the workload changes, the model based algorithm solves an open multiclass QN model to determine the average number of requests that can access the components and then uses a metaheuristic to provide near-optimal solutions for deploying the components. Performance evaluation showed that the obtained solutions had low variability and percent deviation when compared to the reference/optimal solution. We also provide recommendations and best practice guidelines for deploying components in a way that guarantees the required degree of isolation

Design of a randomized controlled double-blind crossover clinical trial to assess the effects of saliva substitutes on bovine enamel and dentin in situ

<p>Abstract</p> <p>Background</p> <p>Hyposalivation is caused by various syndromes, diabetes, drugs, inflammation, infection, or radiotherapy of the salivary glands. Patients with hyposalivation often show an increased caries incidence. Moreover, hyposalivation is frequently accompanied by oral discomfort and impaired oral functions, and saliva substitutes are widely used to alleviate oral symptoms. However, preference of saliva substitutes due to taste, handling, and relief of oral symptoms has been discussed controversially. Some of the marketed products have shown demineralizing effects on dental hard tissues <it>in vitro</it>. This demineralizing potential is attributed to the undersaturation with respect to calcium phosphates. Therefore, it is important to modify the mineralizing potential of saliva substitutes to prevent carious lesions. Thus, the aim of the present study was to evaluate the effects of a possible remineralizing saliva substitute (SN; modified Saliva natura) compared to a demineralizing one (G; Glandosane) on mineral parameters of sound bovine dentin and enamel as well as on artificially demineralized enamel specimens <it>in situ</it>. Moreover, oral well-being after use of each saliva substitute was recorded.</p> <p>Methods/Design</p> <p>Using a randomized, double-blind, crossover, phase II/III <it>in situ </it>trial, volunteers with hyposalivation utilize removable dentures containing bovine specimens during the experimental period. The volunteers are divided into two groups, and are required to apply both saliva substitutes for seven weeks each. After both test periods, differences in mineral loss and lesion depth between values before and after exposure are evaluated based on microradiographs. The oral well-being of the volunteers before and after therapy is determined using questionnaires. With respect to the microradiographic analysis, equal mineral losses and lesion depths of enamel and dentin specimens during treatment with SN and G, and no differences in patients' experienced oral comfort after SN compared to G usage are expected (H₀).</p> <p>Discussion</p> <p>Up to now, 14 patients have been included in the study, and no reasons for early termination of the trial have been identified. The design seems suitable for determining the effects of saliva substitutes on dental hard tissues <it>in situ</it>, and should provide detailed information on the oral well-being after use of different saliva substitutes in patients with hyposalivation.</p> <p>Trial registration</p> <p><b>ClinicalTrials.gov ID. </b><a href="http://www.clinicaltrials.gov/ct2/show/NCT01165970">NCT01165970</a></p