Non-polynomial Worst-Case Analysis of Recursive Programs

We study the problem of developing efficient approaches for proving worst-case bounds of non-deterministic recursive programs. Ranking functions are sound and complete for proving termination and worst-case bounds of nonrecursive programs. First, we apply ranking functions to recursion, resulting in measure functions. We show that measure functions provide a sound and complete approach to prove worst-case bounds of non-deterministic recursive programs. Our second contribution is the synthesis of measure functions in nonpolynomial forms. We show that non-polynomial measure functions with logarithm and exponentiation can be synthesized through abstraction of logarithmic or exponentiation terms, Farkas' Lemma, and Handelman's Theorem using linear programming. While previous methods obtain worst-case polynomial bounds, our approach can synthesize bounds of the form $\mathcal{O}(n\log n)$ as well as $\mathcal{O}(n^r)$ where $r$ is not an integer. We present experimental results to demonstrate that our approach can obtain efficiently worst-case bounds of classical recursive algorithms such as (i) Merge-Sort, the divide-and-conquer algorithm for the Closest-Pair problem, where we obtain $\mathcal{O}(n \log n)$ worst-case bound, and (ii) Karatsuba's algorithm for polynomial multiplication and Strassen's algorithm for matrix multiplication, where we obtain $\mathcal{O}(n^r)$ bound such that $r$ is not an integer and close to the best-known bounds for the respective algorithms.Comment: 54 Pages, Full Version to CAV 201

The Hall Technique; a randomized controlled clinical trial of a novel method of managing carious primary molars in general dental practice: acceptability of the technique and outcomes at 23 months

<p>Abstract</p> <p>Background</p> <p>Scotland has high levels of untreated dental caries in primary teeth. The Hall Technique is a simplified method of managing carious primary molars using preformed metal crowns (PMCs) cemented with no local anaesthesia, caries removal or tooth preparation. This study compared the acceptability of the Hall Technique for children, their carers, and dentists, and clinical outcomes for the technique, with conventional restorations.</p> <p>Methods</p> <p>General dental practice based, split mouth, randomized controlled trial (132 children, aged 3–10). General dental practitioners (GDPs, n = 17) in Tayside, Scotland (dmft 2.7) placed conventional (Control) restorations in carious primary molars, and Hall Technique PMCs on the contralateral molar (matched clinically and radiographically). Dentists ranked the degree of discomfort they felt the child experienced for each procedure; then children, their carers and dentists stated which technique they preferred. The teeth were followed up clinically and radiographically.</p> <p>Results</p> <p>128 conventional restorations were placed on 132 control teeth, and 128 PMCs on 132 intervention teeth. Using a 5 point scale, 118 Hall PMCs (89%) were rated as no apparent discomfort up to mild, not significant; for Control restorations the figure was 103 (78%). Significant, unacceptable discomfort was recorded for two Hall PMCs (1.5%) and six Control restorations (4.5%). 77% of children, 83% of carers and 81% of dentists who expressed a preference, preferred the Hall technique, and this was significant (Chi square, p < 0.0001). There were 124 children (94% of the initial sample) with a minimum follow-up of 23 months. The Hall PMCs outperformed the Control restorations:</p> <p>a) 'Major' failures (signs and symptoms of irreversible pulpal disease): 19 Control restorations (15%); three Hall PMCs (2%) (P < 0.000);</p> <p>b) 'Minor' failures (loss of restoration, caries progression): 57 Control restorations (46%); six Hall PMCs (5%) (P < 0.000)</p> <p>c) Pain: 13 Control restorations (11%); two Hall PMCs (2%) (P = 0.003).</p> <p>Conclusion</p> <p>The Hall Technique was preferred to conventional restorations by the majority of children, carers and GDPs. After two years, Hall PMCs showed more favourable outcomes for pulpal health and restoration longevity than conventional restorations. The Hall Technique appears to offer an effective treatment option for carious primary molar teeth.</p> <p>Trial registration number</p> <p>Current Controlled Trials ISRCTN47267892 – A randomized controlled trial in primary care of a novel method of using preformed metal crowns to manage decay in primary molar teeth: the Hall technique.</p

The role of the carotenoids, lutein and zeaxanthin, in protecting against age-related macular degeneration: A review based on controversial evidence

PURPOSE: A review of the role of the carotenoids, lutein and zeaxanthin, and their function in altering the pathogenesis of age-related macular degeneration (AMD). METHODS: Medline and Embase search. RESULTS: Recent evidence introduces the possibility that lutein and zeaxanthin, carotenoids found in a variety of fruits and vegetables may protect against the common eye disease of macular degeneration. This potential and the lack to slow the progression of macular degeneration, has fueled high public interest in the health benefits of these carotenoids and prompted their inclusion in various supplements. The body of evidence supporting a role in this disease ranges from basic studies in experimental animals to various other clinical and epidemiological studies. Whilst some epidemiological studies suggest a beneficial role for carotenoids in the prevention of AMD, others are found to be unrelated to it. Results of some clinical studies indicate that the risk for AMD is reduced when levels of the carotenoids are elevated in the serum or diet, but this correlation is not observed in other studies. Published data concerning the toxicity of the carotenoids or the optimum dosage of these supplements is lacking. CONCLUSION: An intake of dietary supplied nutrients rich in the carotenoids, lutein and zeaxanthin, appears to be beneficial in protecting retinal tissues, but this is not proven. Until scientifically sound knowledge is available we recommend for patients judged to be at risk for AMD to: alter their diet to more dark green leafy vegetables, wear UV protective lenses and a hat when outdoors. Future investigations on the role of nutrition, light exposure, genetics, and combinations of photodynamic therapy with intravitreal steroid (triamcinolone-acetonide) injections hold potential for future treatment possibilities

Root length and alveolar bone level of impacted canines and adjacent teeth after orthodontic traction: a long-term evaluation

Abstract Objective The aim of this retrospective study was to evaluate the long-term effects of orthodontic traction on root length and alveolar bone level in impacted canines and adjacent teeth. Material and Methods Sample consisted of 16 patients (nine males and seven females), mean initial age 11 years and 8 months presenting with unilaterally maxillary impacted canines, palatally displaced, treated with the same surgical and orthodontic approach. Teeth from the impacted-canine side were assigned as Group I (GI), and contralateral teeth as control, Group II (GII). The mean age of patients at the end of orthodontic treatment was 14 years and 2 months and the mean post-treatment time was 5 years and 11 months. Both contralateral erupted maxillary canines and adjacent teeth served as control. Root length and alveolar bone level (buccal and palatal) were evaluated on cone-beam computed tomography (CBCT) images. The comparison of root length and alveolar bone level changes between groups were assessed by applying paired t-test, at a significance level of 5% (p<0.05). Results There were no statistically significant differences in root length and buccal and palatal bone levels of canines and adjacent teeth among groups. Conclusions Impacted canine treatment by closed-eruption technique associated with canine crown perforation, has a minimal effect on root length and buccal and palatal alveolar bone level in both canine and adjacent teeth, demonstrating that this treatment protocol has a good long-term prognosis

Iron Behaving Badly: Inappropriate Iron Chelation as a Major Contributor to the Aetiology of Vascular and Other Progressive Inflammatory and Degenerative Diseases

The production of peroxide and superoxide is an inevitable consequence of aerobic metabolism, and while these particular "reactive oxygen species" (ROSs) can exhibit a number of biological effects, they are not of themselves excessively reactive and thus they are not especially damaging at physiological concentrations. However, their reactions with poorly liganded iron species can lead to the catalytic production of the very reactive and dangerous hydroxyl radical, which is exceptionally damaging, and a major cause of chronic inflammation. We review the considerable and wide-ranging evidence for the involvement of this combination of (su)peroxide and poorly liganded iron in a large number of physiological and indeed pathological processes and inflammatory disorders, especially those involving the progressive degradation of cellular and organismal performance. These diseases share a great many similarities and thus might be considered to have a common cause (i.e. iron-catalysed free radical and especially hydroxyl radical generation). The studies reviewed include those focused on a series of cardiovascular, metabolic and neurological diseases, where iron can be found at the sites of plaques and lesions, as well as studies showing the significance of iron to aging and longevity. The effective chelation of iron by natural or synthetic ligands is thus of major physiological (and potentially therapeutic) importance. As systems properties, we need to recognise that physiological observables have multiple molecular causes, and studying them in isolation leads to inconsistent patterns of apparent causality when it is the simultaneous combination of multiple factors that is responsible. This explains, for instance, the decidedly mixed effects of antioxidants that have been observed, etc...Comment: 159 pages, including 9 Figs and 2184 reference