The Lex-Plus-Power inequality for local cohomology modules

We prove an inequality between Hilbert functions of local cohomology modules supported in the homogeneous maximal ideal of standard graded algebras over a field, within the framework of embeddings of posets of Hilbert functions. As a main application, we obtain a positive answer to an analogous of Evans’ Lex-Plus-Power Conjecture for local cohomology and also to some cases of the classical Lex-Plus-Power Conjecture for Betti numbers

Estudio experimental comparativo de la estabilidad de distintos tutores externos

Se investigó la rigidez de 11 diferentes montajes de tutores externos usando un modelo experimental con tibias cadavéricas a las cuales se realizaba una osteotomía transversal mediodiafisaria perpendicular al eje longitudinal del hueso, creando entre ambos segmentos una brecha de 35 mm, simulando una fractura. Mediante dispositivos de medición diseñados y construidos especialmente para este estudio se logró cuantificar los desplazamientos que se producen en el foco de fractura ante cargas de compresión axial, torsión y flexiones anteroposterior y mediolateral. Se determinó en cada ensayo la carga segura y carga máxima previamente definidas. La mayor rigidez a la compresión axial se observó en el tutor Orthofix a la torsión y a la flexión anteroposterior en el Kronner biplanar y a la flexión mediolateral en el tutor AO triangulado. Se determina la rigidez total porcentual de cada montaje como índice que representa el funcionamiento promedio del mismo en todas las modalidades de carga. Se consideran las indicaciones, ventajas, complicaciones y fundamentalmente la biología de la consolidación ósea en referencia a los fijadores externos. Se concluye sobre el cuidado con que debe ser conducida la carga de un miembro con fractura inestable, ya que la mayoría de los montajes permiten más de 1 mm de movimiento en la brecha de la fractura con una carga axial baja.The stiffness of 11 different device configurations of external fixation was investigated in an experimental model using human cadaveric tibia. After application of the different devices, a diaphyseal osteotomy allowing removal of a 35 mm bone segment was performed in the specimens. Displacements of the bone fragments at the osteotomy site induced by compresion loading, torsion, and both anteroposterior and mediolateral flexion were measured with dispositives designed for this experiment. Maximal load and that required for inducing 1 mm displacement were recorded. The higher stiffness corresponded to the Orthofix fixator in axial compression, the Kronner biplanar device in anteroposterior flexion, and the triangular configuration of the AO device in mediolateral flexion. A total stiffness index of each configuration as an average of the behavior against all loading modahties was obtained. The indications, advantages, complications and the biology of bone consolidation wien regards to external fixation are considered. As conclusion, progressive loading of the extremity with unstable fracture requires a close monitorization, since most of the device configurations analyzed allow more than 1 mm displacement of bone fragments at the fracture site, even with low axial loading

Epitaxial growth and thermodynamic stability of SrIrO3/SrTiO3 heterostructures

Obtaining high-quality thin films of 5d transition metal oxides is essential to explore the exotic semimetallic and topological phases predicted to arise from the combination of strong electron correlations and spin-orbit coupling. Here, we show that the transport properties of SrIrO3 thin films, grown by pulsed laser deposition, can be optimized by considering the effect of laser-induced modification of the SrIrO3 target surface. We further demonstrate that bare SrIrO3 thin films are subject to degradation in air and are highly sensitive to lithographic processing. A crystalline SrTiO3 cap layer deposited in-situ is effective in preserving the film quality, allowing us to measure metallic transport behavior in films with thicknesses down to 4 unit cells. In addition, the SrTiO3 encapsulation enables the fabrication of devices such as Hall bars without altering the film properties, allowing precise (magneto)transport measurements on micro- and nanoscale devices.Comment: 5 pages, 3 figure

The Impact of Dysmetabolic Sarcopenia Among Insulin Sensitive Tissues: A Narrative Review

Sarcopenia is a common muscular affection among elderly individuals. More recently, it has been recognized as the skeletal muscle (SM) expression of the metabolic syndrome. The prevalence of sarcopenia is increasing along with visceral obesity, to which it is tightly associated. Nonetheless, it is a still underreported entity by clinicians, despite the worsening in disease burden and reduced patient quality of life. Recognition of sarcopenia is clinically challenging, and variability in study populations and diagnostic methods across the clinical studies makes it hard to reach a strong evidence. Impaired insulin activity in SM is responsible for the altered molecular pathways and clinical manifestations of sarcopenia, which is morphologically expressed by myosteatosis. Lipotoxicity, oxidative stress and adipose tissue-derived inflammation lead to both alterations in glucose disposal and protein synthesis in SM, with raising insulin resistance (IR) and SM atrophy. In particular, hyperleptinemia and leptin resistance interfere directly with SM activity, but also with the release of Growth Hormone from the hypohysis, leading to a lack in its anabolic effect on SM. Moreover, sarcopenia is independently associated to liver fibrosis in Non-Alcoholic Fatty Liver Disease (NAFLD), which in turn worsens SM functionality through the secretion of proinflammatory heptokines. The cross-talk between the liver and SM in the IR setting is of crucial relevance, given the high prevalence of NAFLD and the reciprocal impact of insulin-sensitive tissues on the overall disease burden. Along with the efforts of non-invasive diagnostic approaches, irisin and myostatin are two myokines currently evaluated as potential biomarkers for diagnosis and prognostication. Decreased irisin levels seem to be potentially associated to sarcopenia, whereas increased myostatin has shown to negatively impact on sarcopenia in pre-clinical studies. Gene variants in irisin have been explored with regard to the impact on the liver disease phenotype, with conflicting results. The gut-muscle axis has gain relevance with the evidence that insulin resistance-derived gut dysbiosis is responsible for increased endotoxemia and reduction in short-chain free fatty acids, directly affecting and predisposing to sarcopenia. Based on the current evidence, more efforts are needed to increase awareness and improve the management of sarcopenic patients

Regularity of prime ideals

We answer several natural questions which arise from a recent paper of McCullough and Peeva providing counterexamples to the Eisenbud\u2013Goto Regularity Conjecture. We give counterexamples using Rees algebras, and also construct counterexamples that do not rely on the Mayr\u2013Meyer construction. Furthermore, examples of prime ideals for which the difference between the maximal degree of a minimal generator and the maximal degree of a minimal first syzygy can be made arbitrarily large are given. Using a result of Ananyan-Hochster we show that there exists an upper bound on regularity of prime ideals in terms of the multiplicity alone

Bimodal Phase Diagram of the Superfluid Density in LaAlO3/SrTiO3 Revealed by an Interfacial Waveguide Resonator

We explore the superconducting phase diagram of the two-dimensional electron system at the LaAlO3/SrTiO3 interface by monitoring the frequencies of the cavity modes of a coplanar waveguide resonator fabricated in the interface itself. We determine the phase diagram of the superconducting transition as a function of temperature and electrostatic gating, finding that both the superfluid density and the transition temperature follow a dome shape, but that the two are not monotonically related. The ground state of this 2DES is interpreted as a Josephson junction array, where a transition from long- to short-range order occurs as a function of the electronic doping. The synergy between correlated oxides and superconducting circuits is revealed to be a promising route to investigate these exotic compounds, complementary to standard magneto-transport measurements.Comment: 5 pages, 4 figures and 10 pages of supplementary materia