Gauge Invariance, the Quantum Action Principle, and the Renormalization Group

If the Wilsonian renormalization group (RG) is formulated with a cutoff that breaks gauge invariance, then gauge invariance may be recovered only once the cutoff is removed and only once a set of effective Ward identities is imposed. We show that an effective Quantum Action Principle can be formulated in perturbation theory which enables the effective Ward identities to be solved order by order, even if the theory requires non-vanishing subtraction points. The difficulties encountered with non-perturbative approximations are briefly discussed.Comment: 11 pages, latex, no figures, one reference added, version to be published on Phys. Lett.

Minimal codewords in Norm-Trace codes

In this paper, we consider the affine variety codes obtained evaluating the polynomials $by=a_kx^k+\dots+a_1x+a_0$, $b,a_i\in\mathbb{F}_{q^r}$, at the affine \F_{q^r}-rational points of the Norm-Trace curve. In particular, we investigate the weight distribution and the set of minimal codewords. Our approach, which uses tools of algebraic geometry, is based on the study of the absolutely irreducibility of certain algebraic varieties

Minimal codewords in Norm-Trace codes

In this paper, we consider the affine variety codes obtained evaluating the polynomials $by=a_kx^k+\dots+a_1x+a_0$, $b,a_i\in\mathbb{F}_{q^r}$, at the affine \F_{q^r}-rational points of the Norm-Trace curve. In particular, we investigate the weight distribution and the set of minimal codewords. Our approach, which uses tools of algebraic geometry, is based on the study of the absolutely irreducibility of certain algebraic varieties

Acanthamoeba keratitis: perspectives for patients

Purpose: To unveil the long-term prognosis of Acanthamoeba keratitis based on clinical presentation and timing of diagnosis to better inform patients since the first visit regarding their length of treatment, quality of life, and visual function.Methods: Retrospective observational study enrolling patients with Acanthamoeba keratitis from 1994 to 2019. Patients with a complete eye examination and medical records were analyzed. The severity of the disease, the time from onset of symptoms to the appropriate therapeutic regimen, the time until clinical resolution, visual function, and long term follow-up was evaluated. Quality of life was assessed at the last follow-up visit by means of the VFQ-25 questionnaire.Results: Thirty-five patients (40 eyes) were assessed. The overall healing time of patients with Acanthamoeba keratitis was 12.5 ± 3.5 months, while patients with a severe corneal ulcer (stage III) had a significant longer healing time (16.2 ± 3.7 months) compared to patients with stage II (7.04 ± 0.7 months) or I (7.7 ± 1.5 months; p < .05). Patients who received a prompt therapy (<30 days form symptoms onset) had a reduced healing time compared to patients with a delayed diagnosis (p < .01). Quality of life was assessed after a mean of 11.7 ± 4.7 years and it was mildly reduced (86.6 ± 17). Patients that were diagnosed early (<30 days from onset) showed a lower reduction in quality of life than in patients that were diagnosed >30 days from onset. After resolution, 59% of the patients considered unnecessary any further proposed surgical intervention.Conclusions: Delayed diagnosis of Acanthamoeba keratitis and disease severity significantly increases healing time and duration of treatment. The time to diagnosis and disease stage at diagnosis predicts the duration of treatment, the final outcome, quality of life, and the requirement of surgery. These data would allow us to promptly inform patients about long-term disease timeline, future outcomes, improving disease acceptance, and quality of life

Metabolic and cardiovascular response to exercise in patients with type 1 diabetes

Physical activity is an effective therapeutic tool for cardiovascular risk prevention. However, exercise aerobic capacity of patients with type 1 diabetes (T1DM) has not been thoroughly investigated. Aim of the present study is to evaluate exercise aerobic capacity in patients with T1DM compared to a normal control population

Seismic and structural characterization of fluid escape pipes using 3D and partial stack seismic from the Loyal field (UK) : A multiphase and repeated intrusive mechanism

Acknowledgements We thank an anonymous reviewer for the several constructive comments. The seismic interpretation and image processing was carried out in the SeisLab facility at the University of Aberdeen (sponsored by BG BP and Chevron). Seismic imaging analysis was performed using GeoTeric® (ffA), and analysis of seismic amplitudes was performed in Petrel® 2016 (Schlumberger). We would like to thank the Tuscany PhD Regional program and the Erasmus+exchange for funding the Aberdeen permanence of one of us (D.M.). Gazprom for supporting A.J PhD., BP for the release of the Loyal field seismic dataset utilized in this research paper and also N.Vanden Beukel (BP) and M. Gorling (BP) and his colleagues for their assistance.Peer reviewedPostprin