On the number of distinct prime factors of a sum of super-powers

Given k,ℓ∈N+, let xi,j be, for 1≤i≤k and 0≤j≤ℓ some fixed integers, and define, for every n∈N+, sn:=∑i=1 k∏j=0 ℓxi,j n. We prove that the following are equivalent: (a) There are a real θ>1 and infinitely many indices n for which the number of distinct prime factors of sn is greater than the super-logarithm of n to base θ.(b) There do not exist non-zero integers a0,b0,…,aℓ,bℓ such that s2n=∏i=0 ℓai (2n) and s2n−1=∏i=0 ℓbi (2n−1) for all n.We will give two different proofs of this result, one based on a theorem of Evertse (yielding, for a fixed finite set of primes S, an effective bound on the number of non-degenerate solutions of an S-unit equation in k variables over the rationals) and the other using only elementary methods. As a corollary, we find that, for fixed c1,x1,…,ck,xk∈N+, the number of distinct prime factors of c1x1 n+⋯+ckxk n is bounded, as n ranges over N+, if and only if x1=⋯=xk

Enhancing the significance of gravitational wave bursts through signal classification

The quest to observe gravitational waves challenges our ability to discriminate signals from detector noise. This issue is especially relevant for transient gravitational waves searches with a robust eyes wide open approach, the so called all- sky burst searches. Here we show how signal classification methods inspired by broad astrophysical characteristics can be implemented in all-sky burst searches preserving their generality. In our case study, we apply a multivariate analyses based on artificial neural networks to classify waves emitted in compact binary coalescences. We enhance by orders of magnitude the significance of signals belonging to this broad astrophysical class against the noise background. Alternatively, at a given level of mis-classification of noise events, we can detect about 1/4 more of the total signal population. We also show that a more general strategy of signal classification can actually be performed, by testing the ability of artificial neural networks in discriminating different signal classes. The possible impact on future observations by the LIGO-Virgo network of detectors is discussed by analysing recoloured noise from previous LIGO-Virgo data with coherent WaveBurst, one of the flagship pipelines dedicated to all-sky searches for transient gravitational waves

Diffusion of biosimilar hemopoietic growth factors use in oncology practice: an Italian experience

Background: Biosimilars of hemopoietic growth factors present an important saving opportunity in oncology. However, while pharmacologists are aware of their potential benefits, biosimilars are still under-used in Italy. Improved information and guided clinical experience may help to increase the clinical acceptance of these drugs. To this aim, a collaborative educational project was set between an Hospital Oncology Unit and the Local Health Care Authority in Pavia, Italy. Methods: The project lasted 12 months. The strategy included an education-information seminar at startup, a reporting meeting at +6$+6$ months, electronic prescription monitoring and implementation of pharmacovigilance. The target was set to reach 90% of all naïve patients treated with biosimilars. Results: At the end of the study (2013), a dramatic relative increase in the prescription of biosimilar drugs was noted, with virtually 100% of new patients receiving biosimilar drugs during the last 4 months, with a positive impact on average per capita drug expenses. Active pharmacovigilance did not report any serious adverse drug reactions. An anonymous questionnaire showed that oncologists judged the experience quite positively, acquired a positive attitude toward these drugs and considered biosimilars a relevant saving opportunity, while adherence to prescription guidelines was maintained. Analysis of the year following the end of the project, 2014, showed a persistent prescription change. Conclusions: Results from this local experience suggests that specifically designed pragmatic interventions focused on information-education and monitoring may help in promoting the use and acceptance of biosimilar drugs in the real clinical setting

Corrigendum: Effects of a 3-week inpatient multidisciplinary body weight reduction program on body composition and physical capabilities in adolescents and adults with obesity

A correction has been made to Funding. The correct Funding statement is: “Research funded by the Italian Ministry of Health.” The authors apologize for this error and state that this does not change the scientific conclusions of the article in any way. The original article has been updated

Integrated socio-hydrogeological approach to tackle nitrate contamination in groundwater resources. The case of Grombalia Basin (Tunisia)

Nitrate contamination still remains one of the main groundwater quality issues in several aquifers worldwide, despite the perduring efforts of the international scientific community to effectively tackle this problem. The classical hydrogeological and isotopic investigations are obviously of paramount importance for the characterization of contaminant sources, but are clearly not sufficient for the correct and long-term protection of groundwater resources. This paper aims at demonstrating the effectiveness of the socio-hydrogeological approach as the best tool to tackle groundwater quality issues, while contributing bridging the gap between science and society. An integrated survey, including land use, hydrochemical (physicochemical parameters and major ions) and isotopic (delta N-15(No3) and delta O-18(No3)) analyses, coupled to capacity building and participatory activities was carried out to correctly attribute the nitrate origin in groundwater from the Grombalia Basin (North Tunisia), a region where only synthetic fertilizers have been generally identified as the main source of such pollution. Results demonstrates that the basin is characterized by high nitrate concentrations, often exceeding the statutory limits for drinking water, in both the shallow and deep aquifers, whereas sources are associated to both agricultural and urban activities

Effects of combined training or moderate intensity continuous training during a 3-week multidisciplinary body weight reduction program on cardiorespiratory fitness, body composition, and substrate oxidation rate in adolescents with obesity

This study aimed to investigate the effects of combined training (COMB, a combination of moderate-intensity continuous training-MICT and high-intensity interval training-HIIT) vs. continuous MICT administered during a 3-week in-hospital body weight reduction program (BWRP) on body composition, physical capacities, and substrate oxidation in adolescents with obesity. The 3-week in-hospital BWRP entailed moderate energy restriction, nutritional education, psychological counseling, and two different protocols of physical exercise. Twenty-one male adolescents with obesity (mean age: 16.1 ± 1.5 years; mean body mass index [BMI] 37.8 ± 4.5 kg m−2) participated in this randomized control trial study (n:10 for COMB, n:11 MICT), attending ~ 30 training sessions. The COMB group performed 3 repetitions of 2 min at 95% of peak oxygen uptake (V′O2 peak) (e.g., HIIT ≤ 20%), followed by 30 min at 60% of V′O2 peak (e.g., MICT ≥ 80%). Body composition, V′O2 peak, basal metabolic rate (BMR), energy expenditure, and substrate oxidation rate were measured during the first week (W0) and at the end of three weeks of training (W3). The two training programs were equivalent in caloric expenditure. At W3, body mass (BM) and fat mass (FM) decreased significantly in both groups, although the decrease in BM was significantly greater in the MICT group than in the COMB group (BM: − 5.0 ± 1.2 vs. − 8.4 ± 1.5, P < 0.05; FM: − 4.3 ± 3.0 vs. − 4.2 ± 1.9 kg, P < 0.05). V′O2 peak increased only in the COMB by a mean of 0.28 ± 0.22 L min−1 (P < 0.05). The maximal fat oxidation rate (MFO) increased only in the COMB group by 0.04 ± 0.03 g min−1 (P < 0.05). COMB training represents a viable alternative to MICT for improving anthropometric characteristics, physical capacities, and MFO in adolescents with obesity during a 3-week in-hospital BWRP

External Validation of Equations to Estimate Resting Energy Expenditure in 2037 Children and Adolescents with and 389 without Obesity : a Cross-Sectional Study

We performed an external cross-validation study of 10 equations to estimate resting energy expenditure (REE) in 2037 children with and 389 without obesity. Inclusion criteria were Caucasian ethnicity, age 64 18 years, and availability of REE. REE was measured using indirect calorimetry. The correct classification fraction (CCF) of an equation was defined as the fraction of subjects whose estimated REE was within 10% of measured REE. The Moln\ue1r equation was the most accurate REE prediction equation with CCFs of 0.70 (95% CI 0.65 to 0.76) in girls without obesity, 0.64 (95% CI 0.61 to 0.66) in girls with obesity, 0.76 (95% CI 0.67 to 0.83) in boys without obesity, and 0.66 (95% CI 0.63 to 0.69) in boys with obesity. The Mifflin equation was the second most accurate equation with CCFs of 0.67 (95% CI 0.61 to 0.73) in girls without obesity, 0.61 (95% CI 0.58 to 0.64) in girls with obesity, 0.75 (95% CI 0.66 to 0.82) in boys without obesity, and 0.66 (95% CI 0.63 to 0.69) in boys with obesity

Safety and feasibility of thullium laser transurethral resection of prostate for the treatment of benign prostatic enlargement in overweight patients

Objective: We aimed to determine safety and feasibility of thulium laser transurethral vapoenucleation of prostate (ThuVEP) for treatment of obese patients affected by benign prostatic hyperplasia (BPH). Methods: We retrospectively analysed data of 452 patients with BPH who underwent ThuVEP from February 2012 to March 2016 in a single center. Patients were divided into three groups according to body mass index (BMI, kg/m2): Normal weight (18.5 64 BMI &lt; 25; Group A), overweight (25 64 BMI &lt; 30; Group B) and obese (BMI 65 30; Group C), for a total of 412 patients evaluable for this study. Preoperative total serum prostate-specific antigen (PSA), digital rectal examination of the prostate, transrectal ultrasound (TRUS), renal ultrasound, urine culture, uroflowmetry, International Prostate Symptoms Score (IPSS), and Quality of Life (QoL) score were analyzed. Post-operative complications, hospital stay and days of catheterization, questionnaires and uroflowmetry at 1 and 3 months after surgery were evaluated. Preoperative data, surgical outcomes, complication rate and clinical outcomes were compared between groups. Results: The median age of patients was 69 years (Interquartile Range [IQR 10]). The preoperative median IPSS among groups was 19 (IQR 8.75), 20 (IQR 10), and 18 (IQR 10) respectively. At 1 and 3 months of follow-up, this value was 8 (IQR 7), 8 (IQR 4), 7 (IQR 5) and 5 (IQR 6.25), 5 (IQR 6), 6 (IQR 5), respectively (all p between groups &gt; 0.05). There was no statistically significant difference among three groups as for hospital stay and days of catheterization (p &gt; 0.05). Conclusion: Our results showed that ThuVEP was safe and feasible even in overweight patients with substantially enlarged prostate