Variational derivatives in locally Lagrangian field theories and Noether--Bessel-Hagen currents

The variational Lie derivative of classes of forms in the Krupka's variational sequence is defined as a variational Cartan formula at any degree, in particular for degrees lesser than the dimension of the basis manifold. As an example of application we determine the condition for a Noether--Bessel-Hagen current, associated with a generalized symmetry, to be variationally equivalent to a Noether current for an invariant Lagrangian. We show that, if it exists, this Noether current is exact on-shell and generates a canonical conserved quantity.Comment: 20 page

From PDEs to Pfaffian fibrations

We explain how to encode the essential data of a PDE on jet bundle into a more intrinsic object called Pfaffian fibration. We provide motivations to study this new notion and show how prolongations, integrability and linearisations of PDEs generalise to this setting.Comment: 49 pages; v3 several sections rewritten, section 3.4 adde

Variational derivatives in locally Lagrangian field theories and Noether-Bessel-Hagen currents

The variational Lie derivative of classes of forms in the Krupka's variational sequence is defined as a variational Cartan formula at any degree, in particular for degrees lesser than the dimension of the basis manifold. As an example of application, we determine the condition for a Noether-Bessel-Hagen current, associated with a generalized symmetry, to be variationally equivalent to a Noether current for an invariant Lagrangian. We show that, if it exists, this Noether current is exact on-shell and generates a canonical conserved quantity

Spontaneous erectile function recovery among young men with erectile dysfunction taking tadalafil 5 mg once a day

Daily (once a day [OaD]) tadalafil intake is a valuable option for men favoring spontaneous over scheduled sexual intercourse.BACKGROUNDDaily (once a day [OaD]) tadalafil intake is a valuable option for men favoring spontaneous over scheduled sexual intercourse.The study sought to assess the rate of and the clinical factors associated with spontaneous, medication-free erectile function (EF) recovery after discontinuation of tadalafil 5 mg OaD in a cohort of young men seeking first medical help for psychogenic erectile dysfunction (ED) as their primary complaint.AIMThe study sought to assess the rate of and the clinical factors associated with spontaneous, medication-free erectile function (EF) recovery after discontinuation of tadalafil 5 mg OaD in a cohort of young men seeking first medical help for psychogenic erectile dysfunction (ED) as their primary complaint.Data from 96 consecutive patients 22 after tadalafil discontinuation, prompting cessation of follow-up. Descriptive statistics compared tadalafil OaD responders and nonresponders. Cox regression hazard models explored the association between baseline characteristics and EF recovery risk post-drug discontinuation. Kaplan-Meier analyses estimated EF recovery probability over time.METHODSData from 96 consecutive patients 22 after tadalafil discontinuation, prompting cessation of follow-up. Descriptive statistics compared tadalafil OaD responders and nonresponders. Cox regression hazard models explored the association between baseline characteristics and EF recovery risk post-drug discontinuation. Kaplan-Meier analyses estimated EF recovery probability over time.The primary outcome was EF recovery after discontinuation of tadalafil 5 mg OaD.OUTCOMESThe primary outcome was EF recovery after discontinuation of tadalafil 5 mg OaD.Overall, median age was 39 (interquartile range [IQR], 32-45) years. Of all, 82 (85.4%) patients achieved EF recovery after tadalafil OaD discontinuation, while 14 (14.6%) patients were identified as nonresponders. Median tadalafil usage time (from beginning to discontinuation) was 3 (IQR, 2-11) months. The most common treatment-emergent adverse event was headache in 9 (9.4%) patients. Nonresponders were older (43 [IQR, 42-45] years vs 38 [IQR, 31-44] years; P = .03), had higher body mass index (25.5 [IQR, 23.4-29.9] kg/m2 vs 23.6 [IQR, 21.8-25.9] kg/m2; P = .04), and reported lower baseline IIEF EF domain scores (12 [IQR, 7-15] vs 15 [IQR, 10-22]; P = .02) than responders. Nonresponders and responders did not differ in terms of baseline ED severity, Charlson comorbidity index, smoking, alcohol consumption, regular physical exercise, and color Doppler ultrasound parameters. Upon Cox regression analysis, younger age (hazard ratio, 0.95; 95% confidence interval, 0.92-0.99; P = .01) was associated to EF recovery, after adjusting for baseline ED severity, body mass index, smoking, and Charlson comorbidity index ≥1. The Kaplan-Meier analysis displays the probability of EF recovery over time, indicating rates of 43%, 60%, and 72% at 3-, 6-, and 12-month follow-up intervals, respectively.RESULTSOverall, median age was 39 (interquartile range [IQR], 32-45) years. Of all, 82 (85.4%) patients achieved EF recovery after tadalafil OaD discontinuation, while 14 (14.6%) patients were identified as nonresponders. Median tadalafil usage time (from beginning to discontinuation) was 3 (IQR, 2-11) months. The most common treatment-emergent adverse event was headache in 9 (9.4%) patients. Nonresponders were older (43 [IQR, 42-45] years vs 38 [IQR, 31-44] years; P = .03), had higher body mass index (25.5 [IQR, 23.4-29.9] kg/m2 vs 23.6 [IQR, 21.8-25.9] kg/m2; P = .04), and reported lower baseline IIEF EF domain scores (12 [IQR, 7-15] vs 15 [IQR, 10-22]; P = .02) than responders. Nonresponders and responders did not differ in terms of baseline ED severity, Charlson comorbidity index, smoking, alcohol consumption, regular physical exercise, and color Doppler ultrasound parameters. Upon Cox regression analysis, younger age (hazard ratio, 0.95; 95% confidence interval, 0.92-0.99; P = .01) was associated to EF recovery, after adjusting for baseline ED severity, body mass index, smoking, and Charlson comorbidity index ≥1. The Kaplan-Meier analysis displays the probability of EF recovery over time, indicating rates of 43%, 60%, and 72% at 3-, 6-, and 12-month follow-up intervals, respectively.Tadalafil 5 mg OaD is an effective short-term treatment for psychogenic ED, allowing its discontinuation after achieving a normal medication-free EF.CLINICAL IMPLICATIONSTadalafil 5 mg OaD is an effective short-term treatment for psychogenic ED, allowing its discontinuation after achieving a normal medication-free EF.The main limitations are the limited number of participants and the potential neglect of confounding factors.STRENGTHS AND LIMITATIONSThe main limitations are the limited number of participants and the potential neglect of confounding factors.Almost 1 out of 2 young men with primary psychogenic ED who were prescribed with tadalafil 5 mg OaD recovered spontaneous medication-free EF after 3 months of treatment. Overall, the younger the patient was, the higher the chance there was of spontaneous EF recovery after drug discontinuation.CONCLUSIONAlmost 1 out of 2 young men with primary psychogenic ED who were prescribed with tadalafil 5 mg OaD recovered spontaneous medication-free EF after 3 months of treatment. Overall, the younger the patient was, the higher the chance there was of spontaneous EF recovery after drug discontinuation