Second order differentiation formula on RCD∗(K;N) spaces

The aim of this paper is to prove a second order differentiation formula for H2;2 functions along geodesics in RCD∗(K;N) spaces with K ∈R and N < ∞. This formula is new even in the context of Alexandrov spaces, where second order differentiation is typically related to semiconvexity. We establish this result by showing that W2-geodesics can be approximated up to second order, in a sense which we shall make precise, by entropic interpolations. In turn this is achieved by proving new, even in the smooth setting, estimates concerning entropic interpolations which we believe are interesting on their own. In particular we obtain: • equiboundedness of densities along entropic interpolations, • local equi-Lipschitz continuity of Schrödinger potentials, • uniform weighted L2 control of the Hessian of such potentials. Finally, the techniques adopted in this paper can be used to show that in the RCD setting the viscous solution of the Hamilton-Jacobi equation can be obtained via a vanishing viscosity method, as in the smooth case. With respect to a previous version, where the space was assumed to be compact, in this paper the second order differentiation formula is proved in full generality

Insight into the WNT system and its drug related response.

The WNT signalling pathway is a complex system for transferring information for DNA expression from the cell surface receptors to cytoplasm and then to the nucleus. It is based on several proteins that work together as agonists and antagonists in order to maintain homeostasys and to promote anabolic processes. The WNT system acts on all cellular lines involved in bone resorption and formation. WNT pathway can mainly be triggered by two different signalling cascades. The first is well known and is the so-called WNT-beta catenin system (or the canonical pathway), the second is known as the non canonical WNT pathway. WNT proteins form a superfamily of secreted glycoproteins. The association with surface receptors, called Frizzled, that are members of the G protein-coupled receptors superfamily and co receptors like low-density lipoprotein receptor-related proteins 5 and 6 (LRP5/6) complete the WNT system. LRP5/6 show high affinity for WNT antagonists that modulate the activity of this pathway: DKK1 and sclerostin (SCL), that play a crucial role in modulating the WNT system. The WNT-pathway and in particular its antagonists SCL and DKK1 seems to play a key role in the regulation of bone remodeling during treatment with bone active agents such as bisphosphonates, but not only. Their effects become relevant especially in the course of long-term treatments

Extensive carrier testing and CF birth prevalence: evidence for a negative correlation

Aim of the study was to evaluate if extensive CF carrier testing may be connected with the progressive decrease of CF birth incidence recorded in North Eastern Italy. From 1993 to 2007 an average 52,000 newborns per year underwent Neonatal Screening (NS), and 198 newborns with CF were detected (1/3937). A time related contraction in birth prevalence was confirmed, with an average annual percent decrease of 0.15 per 10,000 neonates (Poisson regression analysis p 0.003). In the NS area two sections were identified: the Western Region (WR), where CF carrier testing is not offered to couples from the general population, and the Eastern Region (ER), where CF carrier testing is widely offered to couples from the general population. In ER from 1995 to 2007 such testing practice has been steadily expanding, with a total of 87,721 CF carrier tests performed, 3460 carriers identified, and 238 carrier couples detected (data collection in progress). The prevalence of CF decreased by time (p<0.001) but the rate of decrease was more enhanced in ER as suggested by the existence of a statistically significant (p = 0.014) interaction term between time and region in the Poisson regression model. The overall negative trend in North Eastern Italy is due to a contraction of CF births in its Eastern part. In ER a negative correlation was found between CF incidence and the number of carrier tests (p 0.012). Prenatal diagnosis data collection is in progress. These data support the hypothesis that carrier screening may modify the incidence of CF

Constraining the evolution of Newton's constant with slow inspirals observed from spaceborne gravitational-wave detectors

Spaceborne gravitational-wave (GW) detectors observing at milli-Hz and deci-Hz frequencies are expected to detect large numbers of quasi-monochromatic signals. The first and second time-derivative of the GW frequency ($\dot f_0$ and $\ddot f_0$) can be measured for the most favourable sources and used to look for negative post-Newtonian corrections, which can be induced by the source's environment or modifications of general relativity. We present an analytical, Fisher-matrix-based approach to estimate how precisely such corrections can be constrained. We use this method to estimate the bounds attainable on the time evolution of the gravitational constant $G(t)$ with different classes of quasi-monochromatic sources observable with LISA and DECIGO, two representative spaceborne detectors for milli-Hz and deci-Hz GW frequencies. We find that the most constraining source among a simulated population of LISA galactic binaries could yield $\dot G/G_0 \lesssim 10^{-6}\text{yr}^{-1}$, while the best currently known verification binary will reach $\dot G/G_0 \lesssim 10^{-4}\text{yr}^{-1}$. We also perform Monte-Carlo simulations using quasi-monochromatic waveforms to check the validity of our Fisher-matrix approach, as well as inspiralling waveforms to analyse binaries that do not satisfy the quasi-monochromatic assumption. We find that our analytical Fisher matrix produces good order-of-magnitude constraints even for sources well beyond its regime of validity. Monte-Carlo investigations also show that chirping stellar-mass compact binaries detected by DECIGO-like detectors at cosmological distances of tens of Mpc can yield constraints as tight as $\dot G/G_0 \lesssim 10^{-11}\text{yr}^{-1}$.Comment: 10 pages, 3 figure

Constraining the evolution of Newton's constant with slow inspirals observed from spaceborne gravitational-wave detectors

Spaceborne gravitational-wave (GW) detectors observing at milli-Hz and deci-Hz frequencies are expected to detect large numbers of quasi-monochromatic signals. The first and second time-derivative of the GW frequency ($\dot f_0$ and $\ddot f_0$) can be measured for the most favourable sources and used to look for negative post-Newtonian corrections, which can be induced by the source's environment or modifications of general relativity. We present an analytical, Fisher-matrix-based approach to estimate how precisely such corrections can be constrained. We use this method to estimate the bounds attainable on the time evolution of the gravitational constant $G(t)$ with different classes of quasi-monochromatic sources observable with LISA and DECIGO, two representative spaceborne detectors for milli-Hz and deci-Hz GW frequencies. We find that the most constraining source among a simulated population of LISA galactic binaries could yield $\dot G/G_0 \lesssim 10^{-6}\text{yr}^{-1}$, while the best currently known verification binary will reach $\dot G/G_0 \lesssim 10^{-4}\text{yr}^{-1}$. We also perform Monte-Carlo simulations using quasi-monochromatic waveforms to check the validity of our Fisher-matrix approach, as well as inspiralling waveforms to analyse binaries that do not satisfy the quasi-monochromatic assumption. We find that our analytical Fisher matrix produces good order-of-magnitude constraints even for sources well beyond its regime of validity. Monte-Carlo investigations also show that chirping stellar-mass compact binaries detected by DECIGO-like detectors at cosmological distances of tens of Mpc can yield constraints as tight as $\dot G/G_0 \lesssim 10^{-11}\text{yr}^{-1}$

Análise da prevalência e fatores associados à incontinência urinária entre idosos do Município de São Paulo, Brasil: Estudo SABE (Saúde, Bem-Estar e Envelhecimento)

To investigate the prevalence of urinary incontinence among elderly people living in São Paulo, Brazil and their associated risk factors. The Pan-American Health Organization and World Health Organization coordinated a multicenter study named Health, Wellbeing and Aging (SABE Study) in elderly people (over 60 years old) living in seven countries in Latin America and the Caribbean. In Brazil, the study was carried out in São Paulo in the year 2000. The total Brazilian sample included 2,143 people. The prevalence of self reported urinary incontinence was 11.8% among men and 26.2% for women. It was verified that among those reporting urinary incontinence, 37% also reported stroke and 34% depression. It was found that the greater the dependence that the elderly people presented, the greater the prevalence of urinary incontinence. The associated factors found were depression (odds ratio = 2.49), female (2.42), advanced age (2.35), important functional limitation (2.01). Urinary incontinence is a highly prevalent symptom among the elderly population of the municipality of São Paulo, especially among women. The adoption of preventive measures can reduce the negative effects of urinary incontinence.Investigar a prevalência de incontinência urinária entre idosos de São Paulo, Brasil, e fatores associados e de risco. A Organização Pan-Americana da Saúde e a Organização Mundial da Saúde coordenaram estudo multicêntrico denominado Saúde, Bem-Estar e Envelhecimento (Estudo SABE) em pessoas idosas (60 anos ou mais) que vivem em sete países da América Latina e Caribe. No Brasil, o estudo populacional foi realizado no Município de São Paulo no ano 2000. A amostra total brasileira foi de 2.143 pessoas. A prevalência da incontinência urinária auto-referida foi de 11,8% entre homens e 26,2% entre mulheres. Verificou-se que entre aqueles que relataram incontinência urinária, 37% também relataram acidente vascular cerebral e 34%, depressão. Observou-se que quanto maior a dependência do idoso, maior era a prevalência de incontinência urinária. Os fatores associados encontrados foram depressão (OR = 2,49), sexo feminino (2,42), idade avançada (2,35), limitação funcional (2,01). Incontinência urinária é um sintoma altamente prevalente entre a população idosa do Município de São Paulo, especialmente entre as mulheres. A adoção de medidas preventivas pode reduzir os efeitos negativos da incontinência urinária

The Jang equation reduction of the spacetime positive energy theorem in dimensions less than eight

We extend the Jang equation proof of the positive energy theorem due to R. Schoen and S.-T. Yau from dimension $n=3$ to dimensions $3 \leq n <8$. This requires us to address several technical difficulties that are not present when $n=3$. The regularity and decay assumptions for the initial data sets to which our argument applies are weaker than those of R. Schoen and S.-T. Yau. In recent joint work with L.-H. Huang, D. Lee, and R. Schoen we have given a different proof of the full positive mass theorem in dimensions $3 \leq n < 8$. We pointed out that this theorem can alternatively be derived from our density argument and the positive energy theorem of the present paper.Comment: All comments welcome! Final version to appear in Comm. Math. Phy

Observing GW190521-like binary black holes and their environment with LISA

Binaries of relatively massive black holes like GW190521 have been proposed to form in dense gas environments, such as the disks of Active Galactic Nuclei (AGNs), and they might be associated with transient electromagnetic counterparts. The interactions of this putative environment with the binary could leave a significant imprint at the low gravitational wave frequencies observable with the Laser Interferometer Space Antenna (LISA). We show that LISA will be able to detect up to ten GW190521-like black hole binaries, with sky position errors $\lesssim1$ deg$^2$. Moreover, it will measure directly various effects due to the orbital motion around the supermassive black hole at the center of the AGN, especially the Doppler modulation and the Shapiro time delay. Thanks to a careful treatment of their frequency domain signal, we were able to perform the full parameter estimation of Doppler and Shapiro-modulated binaries as seen by LISA. We find that the Doppler and Shapiro effects will allow for measuring the AGN parameters (radius and inclination of the orbit around the AGN, central black hole mass) with up to percent-level precision. Properly modeling these low-frequency environmental effects is crucial to determine the binary formation history, as well as to avoid biases in the reconstruction of the source parameters and in tests of general relativity with gravitational waves. <br

Duration of treatment for osteoporosis

Many treatments for postmenopausal osteoporosis with proven efficacy in lowering fracture risk had become available since many years now. In the last few years the issue about treatment duration has become a matter of importance. In this paper the pivotal trials for alendronate, risedronate, zoledronate and other anti reabsorptive drugs such as denosumab are revised with particular attention to the extension studies aimed to verify the effect of drug discontinuation. The results of the review highlight differences among the available drugs and the practical clinical consequences also in terms of cost-effectiveness

Pharmacological Modulators of Sphingolipid Metabolism for the Treatment of Cystic Fibrosis Lung Inflammation

Cystic Fibrosis (CF) lung disease is characterised by progressive chronic infection and inflammation of the airways. This prolonged airway inflammatory response leads to irreversible lung damage and fibrosis which is believed to be driven by two distinct, coordinated events: a) a defective cystic fibrosis transmembrane regulator (CFTR) causes airway surface dehydration and increased mucus viscosity leading to chronic colonization with Pseudomonas aeruginosa (P.aeruginosa) (Boucher, 2007); b) mutated CFTR triggers the generation of pro-inflammatory and chemotactic cytokines orchestrated by bronchial epithelial cells, independently of infection (Rubin, 2007; Elizur et al., 2008). The chemokine IL-8, abundantly expressed at sites of chronic inflammation, seems to play a major role in driving the formation of neutrophil (PMN)-rich exudates into the lung of CF patients (Khan et al., 1995; Noah et al., 1997; DiMango et al., 1998; Puchelle et al., 2001; Joseph et al., 2005; Perez et al., 2007). Therefore, reduction of the exaggerated production of IL-8 is key therapeutic target in CF. Anti-inflammatory drugs are an attractive therapeutic tool in CF aimed to decrease the rate of decline in lung function. However, the inherent complexity of the inflammatory response combined with the obvious dependency on this response to contain infection and the side effect profiles of common anti-inflammatories, have made identifying the most suitable therapy a major priority. Consensus is growing on sphingolipids (SLs) as novel targets to cure pulmonary disorders including CF, since modulation of cellular ceramide reduces lung inflammation (Lahiri and Futerman, 2007; Uhlig and Gulbins, 2008). The results in the area of ceramide and CF pathophysiology are very interesting, although contradicting due to the animal models used and methods of ceramide detection (Wojewodka , 2011). The accumulation of ceramide has been identified as one of the key regulators of inflammation in CF airways in different CFTR-/- mouse models (Teichgraber, 2008). On the contrary, decreased ceramide levels have been shown in CFTR ko mice (Guibault, 2008). The possible explanation for this discrepancy seems to be the special diet required for CFTR ko mice, that severely affects the concentration of SLs. Other possible causes, such as genetic determinants, could influence individual levels of SLs (Hicks, 2009). In a different study, no significant difference has been found in basal ceramide levels in immortalised CF bronchial epithelial cells and lung homogenate from CFTR ko mice compared to wild type cells and mice (Yu, 2009). Very importantly, ceramide has been demonstrated to accumulate in the lower airways of CF patients and to be positively associated with neutrophilic inflammation (Brodlie, 2010), supporting the hypothesis that reduction of ceramide may be a therapeutic target for CF lung inflammation. Extending our previous study (Dechecchi, 2008), we have recently demonstrated that the iminosugar N-butyldeoxynojirimycin (miglustat), an inhibitor of the first step in glycosphingolipid (GSL) biosynthesis, reducing the P.aeruginosa induced immunoreactive ceramide expression, produces an anti-inflammatory effect in human bronchial epithelial cells in vitro and down-regulates the neutrophil chemotaxis in murine lungs in vivo (Dechecchi, 2011). These findings strengthen the notion that the metabolism of SLs can be manipulated as a therapeutic option for CF lung disease. With regard to new treatments for CF lung pathology, miglustat deserves great attention since it restores CFTR function in respiratory and pancreatic cells in vitro (Norez, 2006; Dechecchi, 2008) and in CF mice (Lubamba, 2009) and produces an anti-inflammatory effect in vitro and in vivo Dechecchi, 2011). Notably, miglustat is a FDA-approved and EMA−designated orally bioavailable orphan drug, used in Europe and USA for the treatment of Gaucher disease and other GSL storage diseases. In this chapter we review the pre-clinical evidence on the anti-inflammatory effect of miglustat in comparative effectiveness studies with the SL inhibitor amitriptyline and the glucocorticoid (GC) dexamethasone. Importance will be placed on the efficacy of each anti-inflammatory molecule to balance between the anti-inflammatory activity and possible impairment of the host defence