Rigid systems of second-order linear differential equations

We say that a system of differential equations d^2x(t)/dt^2=Adx(t)/dt+Bx(t)+Cu(t), in which A and B are m-by-m complex matrices and C is an m-by-n complex matrix, is rigid if it can be reduced by substitutions x(t)=Sy(t), u(t)=Udy(t)/dt+Vy(t)+Pv(t) with nonsingular S and P to each system obtained from it by a small enough perturbation of its matrices A,B,C. We prove that there exists a rigid system if and only if m<n(1+square_root{5})/2, and describe all rigid systems.Comment: 22 page

Mòduls locals de sistemes dinàmics lineals amb coeficients constants

La present memòria estudia l'estabilitat estructural de ternes de matrius. Es ben conegut que els sistemes dinàmic lineals amb coeficients constants poden venir definits per ternes de matrius, d'aquí l'interès d'aquest estudi. En particular es donen a la memòria diferents condicions necessàries i suficients per que una terna de matrius sigui estructuralment estable respecte d'una relació d'equivalència prèviament introduïda en l'espai de ternes de matrius, bé a partir de la seva forma reduïda canònica, bé per altres mètodes. En aquest estudi s'utilitzen de forma bàsica les deformacions miniversals de ternes de matrius, la qual cosa és possible ja que es veu la relació d'equivalència considerada en l'espai de ternes de matrius com l'induïda per l'acció d'un grup de LIE en la varietat diferenciable del espai de ternes de matrius. L'estudi dels casos de ternes de matrius no estructuralment estables per a les quals la dimensió de la deformació miniversal és inferior o igual a tres suggereix una nova partició de l'espai de ternes de matrius (que es demostra que és una estratificació) i una nova relació d'equivalència, l'associada a aquesta darrera partició. Es caracteritzen també les ternes de matrius estructuralment estables respecte d'aquesta nova relació d'equivalència. Finalment, s'estudien els casos de les ternes que no són estructuralment estables respecte d'aquesta darrera relació en els casos que la dimensió d'una família minitransversal a l'estrat té dimensió inferior o igual a tres, família que ha estat prèviament trobada. A tot l'estudi realitzat s'utilitza un nou sistema complet d'invariants per a una terna de matrius, la principal característica dels quals és tot els invariants discrets del sistema venen donats en funció del rang d'unes certes matrius associades a les matrius que composen la terna. La definició d'aquestes matrius i la demostració de que és una sistema complet d'invariants constitueix la primera part de la memòria.-RESUMEN La presente memoria estudia la estabilidad estructural de ternas de matrices. Es bien conocido que los sistemas dinamicos lineales con coeficientes constantes pueden venir definidos por ternas de matrices, de ahi el interes de este estudio. En particular, se dan en la memoria distintas condiciones necesarias y suficientes para que una terna de matrices sea estructuralmente estable con respecto de una relacion de equivalencia previamente introducida en el espacio de ternas de matrices, bien a partir de su forma reducida canonica, bien por otros metodos. En este estudio se utilizan de forma basica las deformaciones miniversales de ternas de matrices, lo cual es posible puesto que se ve la relacion de equivalencia considerada en el espacio de ternas de matrices como la inducida por la accion de un grupo de lie en la variedad diferenciable del espacio de ternas de matrices. El estudio de los casos de ternas de matrices no estructuralmente estables para las cuales la dimension de la deformacion miniversal es inferior o igual a tres sugiere una nueva particion del espacio de ternas de matrices (que se demuestra que es una estratificacion) y una nueva relacion de equivalencia, la asociada a esta ultima particion. Se caracterizan tambien las ternas de matrices estructuralmente estables respecto de esta nueva relacion de equivalencia. Finalmente, se estudian los casos de las ternas que no son estructuralmente estables respecto de esta ultima relacion en los casos en que la dimension de una familia minitransversal al estrato tiene dimension inferior o igual a tres, familia que ha sido previamente encontrada. En todo el estudio realizado se utiliza un nuevo sistema completo de invariantes para una terna de matrices, cuya principal caracteristica es que todos los invariantes discretos del sistema vienen dados en funcion del rango de unas ciertas matrices asociadas a las matrices que componen la terna. La definicion de estas matrices y la demostracion de que es un sistema completo de invariantes constituye la primera parte de la memoria

Impact of non-invasive mechanical ventilation (niv) in critical patients with influenza (H1N1) PDM09

The use of non-invasive mechanical ventilation (NIV) in patients with influenza A (H1N1)pdm09 admitted to intensive care units (ICU) has been controversial

Combinations of β-lactam or aminoglycoside antibiotics with plectasin are synergistic against methicillin-sensitive and methicillin-resistant Staphylococcus aureus.

Bacterial infections remain the leading killer worldwide which is worsened by the continuous emergence of antibiotic resistance. In particular, methicillin-sensitive (MSSA) and methicillin-resistant Staphylococcus aureus (MRSA) are prevalent and the latter can be difficult to treat. The traditional strategy of novel therapeutic drug development inevitably leads to emergence of resistant strains, rendering the new drugs ineffective. Therefore, rejuvenating the therapeutic potentials of existing antibiotics offers an attractive novel strategy. Plectasin, a defensin antimicrobial peptide, potentiates the activities of other antibiotics such as β-lactams, aminoglycosides and glycopeptides against MSSA and MRSA. We performed in vitro and in vivo investigations to test against genetically diverse clinical isolates of MSSA (n = 101) and MRSA (n = 115). Minimum inhibitory concentrations (MIC) were determined by the broth microdilution method. The effects of combining plectasin with β-lactams, aminoglycosides and glycopeptides were examined using the chequerboard method and time kill curves. A murine neutropenic thigh model and a murine peritoneal infection model were used to test the effect of combination in vivo. Determined by factional inhibitory concentration index (FICI), plectasin in combination with aminoglycosides (gentamicin, neomycin or amikacin) displayed synergistic effects in 76-78% of MSSA and MRSA. A similar synergistic response was observed when plectasin was combined with β-lactams (penicillin, amoxicillin or flucloxacillin) in 87-89% of MSSA and MRSA. Interestingly, no such interaction was observed when plectasin was paired with vancomycin. Time kill analysis also demonstrated significant synergistic activities when plectasin was combined with amoxicillin, gentamicin or neomycin. In the murine models, plectasin at doses as low as 8 mg/kg augmented the activities of amoxicillin and gentamicin in successful treatment of MSSA and MRSA infections. We demonstrated that plectasin strongly rejuvenates the therapeutic potencies of existing antibiotics in vitro and in vivo. This is a novel strategy that can have major clinical implications in our fight against bacterial infections

Environmental changes during the onset of the Late Pliensbachian Event (Early Jurassic) in the Cardigan Bay Basin, Wales

The Late Pliensbachian Event (LPE), in the Early Jurassic, is associated with a perturbation in the global carbon cycle (positive carbon isotope excursion (CIE) of ∼2 ‰), cooling of ∼5 ∘C, and the deposition of widespread regressive facies. Cooling during the late Pliensbachian has been linked to enhanced organic matter burial and/or disruption of thermohaline ocean circulation due to a sea level lowstand of at least regional extent. Orbital forcing had a strong influence on the Pliensbachian environments and recent studies show that the terrestrial realm and the marine realm in and around the Cardigan Bay Basin, UK, were strongly influenced by orbital climate forcing. In the present study we build on the previously published data for long eccentricity cycle E459 ± 1 and extend the palaeoenvironmental record to include E458 ± 1. We explore the environmental and depositional changes on orbital timescales for the Llanbedr (Mochras Farm) core during the onset of the LPE. Clay mineralogy, X-ray fluorescence (XRF) elemental analysis, isotope ratio mass spectrometry, and palynology are combined to resolve systematic changes in erosion, weathering, fire, grain size, and riverine influx. Our results indicate distinctively different environments before and after the onset of the LPE positive CIE and show increased physical erosion relative to chemical weathering. We also identify five swings in the climate, in tandem with the 405 kyr eccentricity minima and maxima. Eccentricity maxima are linked to precessionally repeated occurrences of a semi-arid monsoonal climate with high fire activity and relatively coarser sediment from terrestrial runoff. In contrast, 405 kyr minima in the Mochras core are linked to a more persistent, annually wet climate, low fire activity, and relatively finer-grained deposits across multiple precession cycles. The onset of the LPE positive CIE did not impact the expression of the 405 kyr cycle in the proxy records; however, during the second pulse of heavier carbon (13C) enrichment, the clay minerals record a change from dominant chemical weathering to dominant physical erosion

Effects and Mechanisms of Cognitive, Aerobic Exercise, and Combined Training on Cognition, Health, and Brain Outcomes in Physically Inactive Older Adults : The Projecte Moviment Protocol

Altres ajuts: It has also been rewarded with three pre-doctoral fellowships ( FPU014/01460, FI-2016, and FI-2018).Introduction: Age-related health, brain, and cognitive impairment is a great challenge in current society. Cognitive training, aerobic exercise and their combination have been shown to benefit health, brain, cognition and psychological status in healthy older adults. Inconsistent results across studies may be related to several variables. We need to better identify cognitive changes, individual variables that may predict the effect of these interventions, and changes in structural and functional brain outcomes as well as physiological molecular correlates that may be mediating these effects. Projecte Moviment is a multi-domain randomized trial examining the effect of these interventions applied 5 days per week for 3 months compared to a passive control group. The aim of this paper is to describe the sample, procedures and planned analyses. Methods: One hundred and forty healthy physically inactive older adults will be randomly assigned to computerized cognitive training (CCT), aerobic exercise (AE), combined training (COMB), or a control group. The intervention consists of a 3 month home-based program 5 days per week in sessions of 45 min. Data from cognitive, physical, and psychological tests, cardiovascular risk factors, structural and functional brain scans, and blood samples will be obtained before and after the intervention. Results: Effects of the interventions on cognitive outcomes will be described in intention-to-treat and per protocol analyses. We will also analyze potential genetic, demographic, brain, and physiological molecular correlates that may predict the effects of intervention, as well as the association between cognitive effects and changes in these variables using the per protocol sample. Discussion: Projecte Moviment is a multi-domain intervention trial based on prior evidence that aims to understand the effects of CCT, AE, and COMB on cognitive and psychological outcomes compared to a passive control group, and to determine related biological correlates and predictors of the intervention effects. Clinical Trial Registration: www.ClinicalTrials.gov, identifier NCT03123900

Petrological and geochemical characterisation of the sarsen stones at Stonehenge.

Little is known of the properties of the sarsen stones (or silcretes) that comprise the main architecture of Stonehenge. The only studies of rock struck from the monument date from the 19th century, while 20th century investigations have focussed on excavated debris without demonstrating a link to specific megaliths. Here, we present the first comprehensive analysis of sarsen samples taken directly from a Stonehenge megalith (Stone 58, in the centrally placed trilithon horseshoe). We apply state-of-the-art petrographic, mineralogical and geochemical techniques to two cores drilled from the stone during conservation work in 1958. Petrographic analyses demonstrate that Stone 58 is a highly indurated, grain-supported, structureless and texturally mature groundwater silcrete, comprising fine-to-medium grained quartz sand cemented by optically-continuous syntaxial quartz overgrowths. In addition to detrital quartz, trace quantities of silica-rich rock fragments, Fe-oxides/hydroxides and other minerals are present. Cathodoluminescence analyses show that the quartz cement developed as an initial <10 μm thick zone of non-luminescing quartz followed by ~16 separate quartz cement growth zones. Late-stage Fe-oxides/hydroxides and Ti-oxides line and/or infill some pores. Automated mineralogical analyses indicate that the sarsen preserves 7.2 to 9.2 area % porosity as a moderately-connected intergranular network. Geochemical data show that the sarsen is chemically pure, comprising 99.7 wt. % SiO2. The major and trace element chemistry is highly consistent within the stone, with the only magnitude variations being observed in Fe content. Non-quartz accessory minerals within the silcrete host sediments impart a trace element signature distinct from standard sedimentary and other crustal materials. 143Nd/144Nd isotope analyses suggest that these host sediments were likely derived from eroded Mesozoic rocks, and that these Mesozoic rocks incorporated much older Mesoproterozoic material. The chemistry of Stone 58 has been identified recently as representative of 50 of the 52 remaining sarsens at Stonehenge. These results are therefore representative of the main stone type used to build what is arguably the most important Late Neolithic monument in Europe