Approximation of Z2-cocycles and shift dynamical systems

Let G = G{n,, n, 1 n,+,, t >- 0} be a subgroup of all roots of unity generated by exp(21ri/n, ), t >- 0, and le_t r: (X, B, ji) C) be an ergodic transformation with pure point spectrum G. Given a cocycle P , SO:Xza , admitting an approximation with speed 0(l/nl+', e > 0) there exista a Morse cocycle 0 such that the corresponding transformations r and -ro are relatively isomorphic. An effective way of a construction of the Morse cocycle 0 is given. There is a cocycle p oddly approximated with an arbitrarily high speed and without roots. This note delivers examples of <p's admitting an arbitrarily high speed of approximation and such that the power multiplicity function of rn is equal to one and the power rank function is oscillatory. Finally, we also prove that if (p is a Morse cocycle then each proper factor of r,p is rigid. In particular continuous substitutions on two symbols cannot be factors of Morse dynamical systems

Approximation of Z2-cocycles and shift dynamical systems

Let G = G{n,, n, 1 n,+,, t >- 0} be a subgroup of all roots of unity generated by exp(21ri/n, ), t >- 0, and le_t r: (X, B, ji) C) be an ergodic transformation with pure point spectrum G. Given a cocycle P , SO:Xza , admitting an approximation with speed 0(l/nl+', e > 0) there exista a Morse cocycle 0 such that the corresponding transformations r and -ro are relatively isomorphic. An effective way of a construction of the Morse cocycle 0 is given. There is a cocycle p oddly approximated with an arbitrarily high speed and without roots. This note delivers examples of <p's admitting an arbitrarily high speed of approximation and such that the power multiplicity function of rn is equal to one and the power rank function is oscillatory. Finally, we also prove that if (p is a Morse cocycle then each proper factor of r,p is rigid. In particular continuous substitutions on two symbols cannot be factors of Morse dynamical systems

Combined forest and soil management after a catastrophic event

At the end of October 2018, a storm of unprecedented strength severely damaged the forests of the eastern sector of the Italian Alps. The affected forest area covers 42,500 ha. The president of one of the damaged regions asked for help from the University of Padua. After eight months of discussion, the authors of this article wrote a consensus text. The sometimes asper debate brought to light some crucial aspects: 1) even experienced specialists may have various opinions based on scientific knowledge that lead to conflicting proposals for action. For some of them there is evidence that to restore a destroyed natural environment it is more judicious to do nothing; 2) the soil corresponds to a living structure and every ecosystem\u2019s management should be based on it; 3) faced with a catastrophe, people and politicians find themselves unarmed, also because they rarely have the scientific background to understand natural processes. Yet politicians are the only persons who make the key decisions that drive the economy in play and therefore determine the near future of our planet. This article is an attempt to respond directly to a governor with a degree in animal production science, who formally and prudently asked a university department called \u201cLand, Environment, Agriculture and Forestry\u201d for help before taking decisions; 4) the authors also propose an artistic interpretation of facts (uncontrolled storm) and conclusions (listen to the soil). Briefly, the authors identify the soil as an indispensable source for the renewal of the destroyed forest, give indications on how to prepare a map of the soils of the damaged region, and suggest to anchor on this soil map a series of silvicultural and soil management actions that will promote the soil conservation and the faster recovery of the natural dynamic stability and resilience

Rivaroxaban versus enoxaparin for thromboprophylaxis after hip arthroplasty

BACKGROUND: This phase 3 trial compared the efficacy and safety of rivaroxaban, an oral direct inhibitor of factor Xa, with those of enoxaparin for extended thromboprophylaxis in patients undergoing total hip arthroplasty. METHODS: In this randomized, double-blind study, we assigned 4541 patients to receive either 10 mg of oral rivaroxaban once daily, beginning after surgery, or 40 mg of enoxaparin subcutaneously once daily, beginning the evening before surgery, plus a placebo tablet or injection. The primary efficacy outcome was the composite of deep-vein thrombosis (either symptomatic or detected by bilateral venography if the patient was asymptomatic), nonfatal pulmonary embolism, or death from any cause at 36 days (range, 30 to 42). The main secondary efficacy outcome was major venous thromboembolism (proximal deep-vein thrombosis, nonfatal pulmonary embolism, or death from venous thromboembolism). The primary safety outcome was major bleeding. RESULTS: A total of 3153 patients were included in the superiority analysis (after 1388 exclusions), and 4433 were included in the safety analysis (after 108 exclusions). The primary efficacy outcome occurred in 18 of 1595 patients (1.1%) in the rivaroxaban group and in 58 of 1558 patients (3.7%) in the enoxaparin group (absolute risk reduction, 2.6%; 95% confidence interval [CI], 1.5 to 3.7; P<0.001). Major venous thromboembolism occurred in 4 of 1686 patients (0.2%) in the rivaroxaban group and in 33 of 1678 patients (2.0%) in the enoxaparin group (absolute risk reduction, 1.7%; 95% CI, 1.0 to 2.5; P<0.001). Major bleeding occurred in 6 of 2209 patients (0.3%) in the rivaroxaban group and in 2 of 2224 patients (0.1%) in the enoxaparin group (P=0.18). CONCLUSIONS: A once-daily, 10-mg oral dose of rivaroxaban was significantly more effective for extended thromboprophylaxis than a once-daily, 40-mg subcutaneous dose of enoxaparin in patients undergoing elective total hip arthroplasty. The two drugs had similar safety profiles. (ClinicalTrials.gov number, NCT00329628