Birkhoff Normal Form and Long Time Existence for Periodic Gravity Water Waves

We consider the gravity water waves system with a periodic one-dimensional interface in infinite depth and give a rigorous proof of a conjecture of Dyachenko-Zakharov [16] concerning the approximate integrability of these equations. More precisely, we prove a rigorous reduction of the water waves equations to its integrable Birkhoff normal form up to order 4. As a consequence, we also obtain a long-time stability result: periodic perturbations of a flat interface that are initially of size ε remain regular and small up to times of order (Formula presented.). This time scale is expected to be optimal. © 2022 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC

Randomized Intervention and Outpatient Follow-Up Lowers 30-D Readmissions for Patients With Hepatic Encephalopathy, Decompensated Cirrhosis

BACKGROUND: We previously reported national 30-d readmission rates of 27% in patients with decompensated cirrhosis (DC). AIM: To study prospective interventions to reduce early readmissions in DC at our tertiary center. METHODS: Adults with DC admitted July 2019 to December 2020 were enrolled and randomized into the intervention (INT) or standard of care (SOC) arms. Weekly phone calls for a month were completed. In the INT arm, case managers ensured outpatient follow-up, paracentesis, and medication compliance. Thirty-day readmission rates and reasons were compared. RESULTS: Calculated sample size was not achieved due to coronavirus disease 2019; 240 patients were randomized into INT and SOC arms. 30-d readmission rate was 33.75%, 35.83% in the INT CONCLUSION: Our 30-d readmission rate was higher than the national rate but reduced by interventions in patients with DC with HE and early outpatient follow-up. Development of interventions to reduce early readmission in patients with DC is needed

Aspects of the planetary Birkhoff normal form

The discovery in [G. Pinzari. PhD thesis. Univ. Roma Tre. 2009], [L. Chierchia and G. Pinzari, Invent. Math. 2011] of the Birkhoff normal form for the planetary many--body problem opened new insights and hopes for the comprehension of the dynamics of this problem. Remarkably, it allowed to give a {\sl direct} proof of the celebrated Arnold's Theorem [V. I. Arnold. Uspehi Math. Nauk. 1963] on the stability of planetary motions. In this paper, using a "ad hoc" set of symplectic variables, we develop an asymptotic formula for this normal form that may turn to be useful in applications. As an example, we provide two very simple applications to the three-body problem: we prove a conjecture by [V. I. Arnold. cit] on the "Kolmogorov set"of this problem and, using Nehoro{\v{s}}ev Theory [Nehoro{\v{s}}ev. Uspehi Math. Nauk. 1977], we prove, in the planar case, stability of all planetary actions over exponentially-long times, provided mean--motion resonances are excluded. We also briefly discuss perspectives and problems for full generalization of the results in the paper.Comment: 44 pages. Keywords: Averaging Theory, Birkhoff normal form, Nehoro{\v{s}}ev Theory, Planetary many--body problem, Arnold's Theorem on the stability of planetary motions, Properly--degenerate kam Theory, steepness. Revised version, including Reviewer's comments. Typos correcte

Early hemostatic responses to trauma identified with hierarchical clustering analysis

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/111900/1/jth12919.pd

The new Checklist of the Italian Fauna: marine Mollusca.

The mollusc fauna of the Mediterranean Sea is still considered as the best-known marine mollusc fauna in the world. The previous modern checklists of marine Mollusca were produced by joint teams of amateurs and professionals. During the last years the Italian Society of Malacology (Società Italiana di Malacologia – S.I.M.) maintained an updated version of the Mediterranean checklist, that served as the backbone for the development of the new Italian checklist. According to the current version (updated on April 1st, 2021), 1,777 recognised species of marine molluscs are present in the Italian Economic Exclusive Zone, including also the Tyrrhenian coasts of Corsica and the continental shelf of the Maltese archipelago. The new checklist shows an increase of 17% of the species reported in the 1995 Checklist. This is largely (yet not solely) due to the new wave of studies based on Integrative Taxonomy approaches. A total of 135 species (7.6%) are strictly endemic to the Italian waters; 44 species (2.5%) are alien and correspond to the 28% of the Mediterranean alien marine molluscs. All eight extant molluscan classes are represented. The families represented in the Italian fauna are 307, an increase of 14.6% from the first checklist, partly due to new records and partly to new phylogenetic systematics. Compared with the whole Mediterranean malacofauna, the Italian component represents 71% in species and 61% in families, which makes it a very remarkable part of the Mediterranean fauna

Failure of recombinant factor VIIa in a patient with severe polymicrobial sepsis and postoperative uncontrolled intraabdominal bleeding

<p>Abstract</p> <p>Background</p> <p>This report discusses a case of unsuccessful treatment with recombinant factor VIIa (rFVIIa) in off-label use. The need for international guidelines concerning the off-label use of rFVIIa is outlined as well as the need for methods to control the efficacy of rFVIIa objectively.</p> <p>Case presentation</p> <p>54 year old male with severe polymicrobial sepsis due to a perforated diverticulitis of the sigmoid colon and consecutive overt disseminated intravascular coagulation. He suffered severe intraabdominal bleeding after abdominal surgery despite conventional haemostatic support. Repeated applications of factor VIIa temporarily improved coagulation essays but did not stop clinical bleeding. The patient died in multiorgan failure due to septic and haemorrhagic shock.</p> <p>Conclusion</p> <p>Off-label use of rFVIIa could result in more side effects than could be expected from literature because of a publication bias. However for most off-label applications large prospective, randomised and controlled trials to confirm the positive findings are missing. For the future, not only guidelines concerning the off-label use of rFVIIa are urgently needed but also guidelines for monitoring the efficacy of rFVIIa.</p