7,081 research outputs found

    Fenchel Conjugate of Set-Valued Mappings

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    In this paper, we present a novel concept of the Fenchel conjugate for set-valued mappings and investigate its properties in finite and infinite dimensions. After establishing the fundamental properties of the Fenchel conjugate for set-valued mappings, we derive its main calculus rules in various settings. Our approach is geometric and draws inspiration from the successful application of this method by B.~S.~Mordukhovich and coauthors in variational and convex analysis. Subsequently, we demonstrate that our new findings for the Fenchel conjugate of set-valued mappings can be utilized to obtain many established calculus rules of convex generalized differentiation in both finite and infinite dimensions

    Are topical nitrates safe and effective for upper extremity tendinopathies?

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    Q. Are topical nitrates safe and effective for upper extremity tendinopathies? A. Topical nitrates provide short-term relief with some side effects, especially headache. Topical nitroglycerin (NTG) patches improve subjective pain scores by about 30% and range of motion over 3 days in patients with acute shoulder tendinopathy (strength of recommendation [SOR]: C, small randomized controlled trial [RCT] with no methodologic flaws). NTG patches, when combined with tendon rehabilitation, improve subjective pain ratings by about 30% and shoulder strength by about 10% in patients with chronic shoulder tendinopathy over 3 to 6 months, but not in the long term (SOR: C, RCTs with methodologic flaws). They improve pain and strength 15% to 50% for chronic extensor tendinosis of the elbow over a 6-month period (SOR: C, small RCT with methodologic flaws). NTG patches used without tendon rehabilitation don't improve pain or strength in chronic lateral epicondylitis over 8 weeks (SOR: C, RCT). Topical NTG patches commonly produce headaches and rashes (SOR: B, multiple RCTs)

    Paclitaxel Drug Elution from a Biodegradable Stent

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    Recently, drug-eluting stents have become a common treatment for coronary heart disease. These stents are usually loaded with a drug that prevents restenosis. Unfortunately, there are risks associated with the placement of these metallic structures in the body. Stent thrombosis is one such problem, and can lead to restenosis despite the presence of drug. Advances in biomaterials have led to the development of biodegradable stents, which can reduce the risks associated with stents. However, since it is a relatively new technology, it is not known to what degree the biodegradability affects the drug releasing properties of the stent. We hope to characterize these effects and to determine if the biodegradability reduces the efficacy of the stent when compared to normal non-degradable stents. To accomplish this, we modeled a stent that diminished in size over time using COMSOL Multiphysics, and monitored the drug concentration in the nearby tissue. We established that our model was a viable predictor of actual stent behavior by comparing our simulated results with previous studies. We were then able to determine the optimal initial loading stent concentration of our modeled drug, paclitaxel, to ensure therapeutic levels in the tissue. Lastly, we found that drug concentrations in the tissue were not substantially different between the degradable and non-degradable models. This affirms the effectiveness of using biodegradable stents, showing them as a viable alternative to traditional metal stents

    Fenchel-Rockafellar Theorem in Infinite Dimensions via Generalized Relative Interiors

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    In this paper we provide further studies of the Fenchel duality theory in the general frame work of locally convex topological vector (LCTV) spaces. We prove the validity of the Fenchel strong duality under some qualification conditions via generalized relative interiors imposed on the epigraphs and the domains of the functions involved. Our results directly generalize the classical Fenchel-Rockafellar theorem on strong duality from finite dimensions to LCTV spaces.Comment: arXiv admin note: text overlap with arXiv:1812.0060

    Inferring behavioral specifications from large-scale repositories by leveraging collective intelligence

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    Despite their proven benefits, useful, comprehensible, and efficiently checkable specifications are not widely available. This is primarily because writing useful, non-trivial specifications from scratch is too hard, time consuming, and requires expertise that is not broadly available. Furthermore, the lack of specifications for widely-used libraries and frameworks, caused by the high cost of writing specifications, tends to have a snowball effect. Core libraries lack specifications, which makes specifying applications that use them expensive. To contain the skyrocketing development and maintenance costs of high assurance systems, this self-perpetuating cycle must be broken. The labor cost of specifying programs can be significantly decreased via advances in specification inference and synthesis, and this has been attempted several times, but with limited success. We believe that practical specification inference and synthesis is an idea whose time has come. Fundamental breakthroughs in this area can be achieved by leveraging the collective intelligence available in software artifacts from millions of open source projects. Finegrained access to such data sets has been unprecedented, but is now easily available. We identify research directions and report our preliminary results on advances in specification inference that can be had by using such data sets to infer specifications
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