Cantor Spectrum for Schr\"odinger Operators with Potentials arising from Generalized Skew-shifts

We consider continuous $SL(2,\mathbb{R})$-cocycles over a strictly ergodic homeomorphism which fibers over an almost periodic dynamical system (generalized skew-shifts). We prove that any cocycle which is not uniformly hyperbolic can be approximated by one which is conjugate to an $SO(2,\mathbb{R})$-cocycle. Using this, we show that if a cocycle's homotopy class does not display a certain obstruction to uniform hyperbolicity, then it can be $C^0$-perturbed to become uniformly hyperbolic. For cocycles arising from Schr\"odinger operators, the obstruction vanishes and we conclude that uniform hyperbolicity is dense, which implies that for a generic continuous potential, the spectrum of the corresponding Schr\"odinger operator is a Cantor set.Comment: Final version. To appear in Duke Mathematical Journa

The Structure on Invariant Measures of C1C^1 generic diffeomorphisms

Let $\Lambda$ be an isolated non-trival transitive set of a $C^1$ generic diffeomorphism f\in\Diff(M). We show that the space of invariant measures supported on $\Lambda$ coincides with the space of accumulation measures of time averages on one orbit. Moreover, the set of points having this property is residual in $\Lambda$ (which implies the set of irregular$^+$ points is also residual in $\Lambda$). As an application, we show that the non-uniform hyperbolicity of irregular$^+$ points in $\Lambda$ with totally 0 measure (resp., the non-uniform hyperbolicity of a generic subset in $\Lambda$) determines the uniform hyperbolicity of $\Lambda$

Mechanical ventilation in patients with acute ischaemic stroke: From pathophysiology to clinical practice

Most patients with ischaemic stroke are managed on the ward or in specialty stroke units, but a significant number requires higher-acuity care and, consequently, admission to the intensive care unit. Mechanical ventilation is frequently performed in these patients due to swallowing dysfunction and airway or respiratory system compromise. Experimental studies have focused on stroke-induced immunosuppression and brain-lung crosstalk, leading to increased pulmonary damage and inflammation, as well as reduced alveolar macrophage phagocytic capability, which may increase the risk of infection. Pulmonary complications, such as respiratory failure, pneumonia, pleural effusions, acute respiratory distress syndrome, lung oedema, and pulmonary embolism from venous thromboembolism, are common and found to be among the major causes of death in this group of patients. Furthermore, over the past two decades, tracheostomy use has increased among stroke patients, who can have unique indications for this procedure - depending on the location and type of stroke - when compared to the general population. However, the optimal mechanical ventilator strategy remains unclear in this population. Although a high tidal volume (V T) strategy has been used for many years, the latest evidence suggests that a protective ventilatory strategy (V T = 6-8 mL/kg predicted body weight, positive end-expiratory pressure and rescue recruitment manoeuvres) may also have a role in brain-damaged patients, including those with stroke. The aim of this narrative review is to explore the pathophysiology of brain-lung interactions after acute ischaemic stroke and the management of mechanical ventilation in these patients

Dominated Splitting and Pesin's Entropy Formula

Let $M$ be a compact manifold and $f:\,M\to M$ be a $C^1$ diffeomorphism on $M$. If $\mu$ is an $f$-invariant probability measure which is absolutely continuous relative to Lebesgue measure and for $\mu$ $a.\,\,e.\,\,x\in M,$ there is a dominated splitting $T_{orb(x)}M=E\oplus F$ on its orbit $orb(x)$, then we give an estimation through Lyapunov characteristic exponents from below in Pesin's entropy formula, i.e., the metric entropy $h_\mu(f)$ satisfies $$h_{\mu}(f)\geq\int \chi(x)d\mu,$$ where $\chi(x)=\sum_{i=1}^{dim\,F(x)}\lambda_i(x)$ and $\lambda_1(x)\geq\lambda_2(x)\geq...\geq\lambda_{dim\,M}(x)$ are the Lyapunov exponents at $x$ with respect to $\mu.$ Consequently, by using a dichotomy for generic volume-preserving diffeomorphism we show that Pesin's entropy formula holds for generic volume-preserving diffeomorphisms, which generalizes a result of Tahzibi in dimension 2

Do We Really Need Quantum Mechanics to Describe Plasmonic Properties of Metal Nanostructures?

Optical properties of metal nanostructures are the basis of several scientific and technological applications. When the nanostructure characteristic size is of the order of few nm or less, it is generally accepted that only a description that explicitly describes electrons by quantum mechanics can reproduce faithfully its optical response. For example, the plasmon resonance shift upon shrinking the nanostructure size (red-shift for simple metals, blue-shift for d-metals such as gold and silver) is universally accepted to originate from the quantum nature of the system. Here we show instead that an atomistic approach based on classical physics, ωFQFμ (frequency dependent fluctuating charges and fluctuating dipoles), is able to reproduce all the typical “quantum” size effects, such as the sign and the magnitude of the plasmon shift, the progressive loss of the plasmon resonance for gold, the atomistically detailed features in the induced electron density, and the non local effects in the nanoparticle response. To support our findings, we compare the ωFQFμ results for Ag and Au with literature time-dependent DFT simulations, showing the capability of fully classical physics to reproduce these TDDFT results. Only electron tunneling between nanostructures emerges as a genuine quantum mechanical effect, that we had to include in the model by an ad hoc term

ArCo: the Italian Cultural Heritage Knowledge Graph

ArCo is the Italian Cultural Heritage knowledge graph, consisting of a network of seven vocabularies and 169 million triples about 820 thousand cultural entities. It is distributed jointly with a SPARQL endpoint, a software for converting catalogue records to RDF, and a rich suite of documentation material (testing, evaluation, how-to, examples, etc.). ArCo is based on the official General Catalogue of the Italian Ministry of Cultural Heritage and Activities (MiBAC) - and its associated encoding regulations - which collects and validates the catalogue records of (ideally) all Italian Cultural Heritage properties (excluding libraries and archives), contributed by CH administrators from all over Italy. We present its structure, design methods and tools, its growing community, and delineate its importance, quality, and impact

The Complexity of Reasoning for Fragments of Default Logic

Default logic was introduced by Reiter in 1980. In 1992, Gottlob classified the complexity of the extension existence problem for propositional default logic as \SigmaPtwo-complete, and the complexity of the credulous and skeptical reasoning problem as SigmaP2-complete, resp. PiP2-complete. Additionally, he investigated restrictions on the default rules, i.e., semi-normal default rules. Selman made in 1992 a similar approach with disjunction-free and unary default rules. In this paper we systematically restrict the set of allowed propositional connectives. We give a complete complexity classification for all sets of Boolean functions in the meaning of Post's lattice for all three common decision problems for propositional default logic. We show that the complexity is a hexachotomy (SigmaP2-, DeltaP2-, NP-, P-, NL-complete, trivial) for the extension existence problem, while for the credulous and skeptical reasoning problem we obtain similar classifications without trivial cases.Comment: Corrected versio

High H2O content in Pyroxenes of residual mantle Peridotites at a Mid Atlantic ridge segment

Global correlations of mid-ocean-ridges basalt chemistry, axial depth and crustal thickness have been ascribed to mantle temperature variations affecting degree of melting. However, mantle H2O content and elemental composition may also play a role. How H2O is distributed in the oceanic upper mantle remains poorly constrained. We tackled this problem by determining the H2O content of orthopyroxenes (opx) and clinopyroxenes (cpx) of peridotites from a continuous lithospheric section created during 26 Ma at a 11°N Mid-Atlantic Ridge segment, and exposed along the Vema Transform. The H2O content of opx ranges from 119 ppm to 383 ppm; that of cpx from 407 ppm to 1072 ppm. We found anomalous H2O-enriched peridotites with their H2O content not correlating inversely with their degree of melting, although H2O is assumed to be incompatible during melting. Inverse correlation of H2O with Ce, another highly incompatible component, suggests post-melting H2O enrichment. We attribute a major role to post-melting temperature-dependent diffusion of hydrogen occurring above the melting region, where water-rich melt flows faster than residual peridotites through dunitic conduits cross-cutting the uprising mantle. Accordingly, estimates of the H2O content of the MORB mantle source based on H2O in abyssal peridotites can be affected by strong uncertainties

Resilience of community food systems (CFS): co-design as a long-term viable pathway to face crises in neglected territories?

The COVID-19 pandemic has brought on a global crisis, with impacts an ongoing food security and nutrition, exposing the vulnerabilities of our society. However, it can be a time for reflection and an opportunity to propose and stimulate initiatives that are ready to facilitate resilience within the food system. The food to fork must be shortened and diversified where it is viable and feasible, while made affordable for all societal levels. To face these challengers, the community food systems (CFS) approach has a crucial role, since it copes with relevant principles, including the necessities of low-income societies from areas particularly marginalized from mainstream food systems, of which those land areas also can pose as additional insurance just in case of occurrence of whatever crises. Systematizing the components and contributions of CFS can facilitate the advance of strategies to better deal with crises and increase resilience. Therefore, in this paper, through key elements of CFS, we propose a theoretical framework that can be applied by decision makers as a conceptual guide for combating threats to food systems in neglected territories