The Asymptotic distribution of circles in the orbits of Kleinian groups

Let P be a locally finite circle packing in the plane invariant under a non-elementary Kleinian group Gamma and with finitely many Gamma-orbits. When Gamma is geometrically finite, we construct an explicit Borel measure on the plane which describes the asymptotic distribution of small circles in P, assuming that either the critical exponent of Gamma is strictly bigger than 1 or P does not contain an infinite bouquet of tangent circles glued at a parabolic fixed point of Gamma. Our construction also works for P invariant under a geometrically infinite group Gamma, provided Gamma admits a finite Bowen-Margulis-Sullivan measure and the Gamma-skinning size of P is finite. Some concrete circle packings to which our result applies include Apollonian circle packings, Sierpinski curves, Schottky dances, etc.Comment: 31 pages, 8 figures. Final version. To appear in Inventiones Mat

Transonic flutter analysis using a fully coupled density based solver for inviscid flow

This paper focuses on the coupling between the high fidelity aerodynamic model for the flow field and the modal analysis of a typical wing section to carry out flutter analysis. This coupled aeroelastic model is implemented in one of the most widely used open source CFD codes called OpenFOAM. The model is designed to calculate the structural displacement in the time domain based on the free vibration modes of the structure by constructing the numerical model directly from the modal analysis. Essentially a second order ordinary differential equation is solved for each mode as a function of the generalised coordinates. A density based solver using central difference scheme of Kurganov and Tadmor is used to model the flow field. Two main cases of transonic flow over NACA 64A010 are modelled for a forced pitching oscillation airfoil and a self-sustained aerofoil respectively. The self-sustained two degrees of freedom case is modelled for three different possibilities covering damped, neutral and divergent oscillations. Predicted results show very good agreement with the numerical and experimental data available in the literature

Random polytopes: Their definition, generation and aggregate properties

The definition of random polytope adopted in this paper restricts consideration to those probability measures satisfying two properties. First, the measure must induce an absolutely continuous distribution over the positions of the bounding hyperplanes of the random polytope; and second, it must result in every point in the space being equally as likely as any other point of lying within the random polytope. An efficient Monte Carlo method for their computer generation is presented together with analytical formulas characterizing their aggregate properties. In particular, it is shown that the expected number of extreme points for such random polytopes increases monotonically in the number of constraints to the limiting case of a polytope topologically equivalent to a hypercube. The implied upper bound of 2 n where n is the dimensionality of the space is significantly less than McMullen's attainable bound on the maximal number of vertices even for a moderate number of constraints.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47911/1/10107_2005_Article_BF01585093.pd

Dimethyl fumarate in patients admitted to hospital with COVID-19 (RECOVERY): a randomised, controlled, open-label, platform trial

Dimethyl fumarate (DMF) inhibits inflammasome-mediated inflammation and has been proposed as a treatment for patients hospitalised with COVID-19. This randomised, controlled, open-label platform trial (Randomised Evaluation of COVID-19 Therapy [RECOVERY]), is assessing multiple treatments in patients hospitalised for COVID-19 (NCT04381936, ISRCTN50189673). In this assessment of DMF performed at 27 UK hospitals, adults were randomly allocated (1:1) to either usual standard of care alone or usual standard of care plus DMF. The primary outcome was clinical status on day 5 measured on a seven-point ordinal scale. Secondary outcomes were time to sustained improvement in clinical status, time to discharge, day 5 peripheral blood oxygenation, day 5 C-reactive protein, and improvement in day 10 clinical status. Between 2 March 2021 and 18 November 2021, 713 patients were enroled in the DMF evaluation, of whom 356 were randomly allocated to receive usual care plus DMF, and 357 to usual care alone. 95% of patients received corticosteroids as part of routine care. There was no evidence of a beneficial effect of DMF on clinical status at day 5 (common odds ratio of unfavourable outcome 1.12; 95% CI 0.86-1.47; p = 0.40). There was no significant effect of DMF on any secondary outcome

Exercício de força ativa a via AKT/mTor pelo receptor de angiotensina II tipo I no músculo cardíaco de ratos Activation of AKT-mTor signaling pathways by angiotensin II receptor type 1 after a session of strength exercise in cardiac muscle of rats

O receptor de angiotensina II tipo I (AT1) tem uma importante participação no desenvolvimento da hipertrofia cardíaca. Em um trabalho publicado anteriormente, por nosso grupo, demonstramos que o bloqueio do receptor AT1 durante o treinamento de força inibiu a hipertrofia cardíaca em ratos. Por isso, o objetivo deste trabalho foi estudar a participação do receptor AT1 na ativação de vias de sinalização intracelular relacionadas com o aumento da síntese de proteína em ratos submetidos a uma sessão de exercício de força. Para isso, realizamos um experimento com seis grupos de animais (n = 6; cada): controle (Con), exercitado e sacrificado cinco minutos após o exercício (Exe 5), exercitado e sacrificado 30 minutos após o exercício (Exe 30), controle tratado com losartan (Con Los), tratado com losartan, exercitado e sacrificado cinco minutos após o exercício (Exe 5 Los), tratado com losartan, exercitado e sacrificado 30 minutos após o exercício (Exe 30 Los). Os resultados mostram que no grupo Exe 5 e Exe 30 ocorreu um aumento de 63% (P < 0,05) e 62% (P < 0,05), respectivamente, na fosforilação da proteína AKT comparado com o grupo controle. Enquanto a fosforilação da mTor foi aumentada 65% (P < 0,05) somente no grupo Exe 30 comparado com o grupo controle, sendo estes efeitos bloqueados pelo uso do losartan nos grupos Exe 5 Los e Exe 30 Los. Portanto, esses resultados, juntamente com nossos resultados prévios, demonstram que o receptor AT1 tem participação na ativação da AKT e mTOR após uma sessão de exercício de força.<br>The angiotensin II type I (AT1) receptor has an important participation in the development of cardiac hypertrophy. Previously, we have shown that AT1 receptor participates in the cardiac hypertrophy induced by resistance training in rats. Here, we studied the involvement of AT1 receptor in the activation of intracellular signaling pathways related to the concentric HC in rats submitted to a session of strength exercise. Male Wistar rats were divided into 6 groups (n= 6 each): control (Con); exercised and killed 5 minutes after exercise (Exe 5); exercised and killed 30 minutes after exercise (Exe 30); control treated with Losartan (Con Los); treated with Losartan, exercised and killed 5 minutes after the exercise (Exe Los 5); treated with Losartan, exercised and killed 30 minutes after training (Exe Los 30). The results show that phosphorylation activity of AKT in group Exe 5 and Exe 30 increased 63% (P < 0.05) and 62% (P < 0.05), respectively, compared with Con. Whereas the phosphorylation of mTOR was increased 65% (P < 0.05), compared to Con, only in the group Exe 30. Furthermore, these effects were blocked by losartan treatment in groups Exe Los 5 and Exe Los 30. These results, together with ours previous data shows that the AT1 receptor has an role in the activation of AKT and mTOR pathway after a session of strength exercise

Enhanced cardiac phosphoinositide 3-kinase (p110α) using gene therapy attenuates cardiac remodeling in type 2 diabetic mice

Diabetic cardiomyopathy is a distinct form of heart disease that represents a major cause of death and disability in diabetic patients, particularly the more prevalent type-2 diabetic population. In the current study, we investigated administration of recombinant adeno-associated viral vectors carrying a constitutively-active PI3K(p110α) construct (rAAV6-caPI3K) at a clinically-relevant time point attenuates diabetic cardiomyopathy in a pre-clinical type-2 diabetes (T2D) model. T2D was induced by a combination of high-fat diet and low-dose streptozotocin, and confirmed by increased body weight, hyperglycemia, and impaired glucose tolerance. After 18 weeks of untreated diabetes, impaired left ventricular (LV) systolic dysfunction was evident, as confirmed by echocardiography. A single tail vein injection of rAAV6-caPI3K gene therapy was then administered. Mice were followed for an additional 8 weeks before end-point. Administration of cardiac targeted rAAV6-caPI3K attenuates diabetes-induced cardiac remodeling by limiting cardiac fibrosis and cardiomyocyte hypertrophy. The diabetes-induced LV systolic dysfunction was reversed with rAAV6-caPI3K as demonstrated by improved fractional shortening and velocity of circumferential fiber shortening. This cardioprotection occurred in combination with reduced LV ROS levels and an associated decrease in markers of endoplasmic reticulum stress. Together, the findings demonstrate that cardiac-selective increases in PI3K(p110α), via rAAV6-caPI3K, attenuates diabetic cardiomyopathy in a mouse model of T2D.Darnel Prakoso, Miles J. De Blasio, Mitchel Tate, Helen Kiriazis, Daniel G. Donner, Hongwei Qian ... et al