Weighted Lp{L^p}-Liouville Theorems for Hypoelliptic Partial Differential Operators on Lie Groups

We prove weighted $L^p$-Liouville theorems for a class of second order hypoelliptic partial differential operators $\mathcal{L}$ on Lie groups $\mathbb{G}$ whose underlying manifold is $n$-dimensional space. We show that a natural weight is the right-invariant measure $\check{H}$ of $\mathbb{G}$. We also prove Liouville-type theorems for $C^2$ subsolutions in $L^p(\mathbb{G},\check{H})$. We provide examples of operators to which our results apply, jointly with an application to the uniqueness for the Cauchy problem for the evolution operator $\mathcal{L}-\partial_t$

Multivariate Asset Models Using Levy Processes and Applications

In this paper we propose a multivariate asset model based on L´evy processes for pricing of products written on more than one underlying asset. Our construction is based on a two factor representation of the dynamics of the asset log-returns. We investigate the properties of the model and introduce a multivariate generalization of some processes which are quite common in financial applications, such as subordinated Brownian motions, jump diffusion processes and time changed L´evy processes. Finally, we explore the issue of model calibration for the proposed setting and illustrate its robustness on a number of numerical examples

The role of fundamental solution in Potential and Regularity Theory for subelliptic PDE

In this survey we consider a general Hormander type operator, represented as a sum of squares of vector fields plus a drift and we outline the central role of the fundamental solution in developing Potential and Regularity Theory for solutions of related PDEs. After recalling the Gaussian behavior at infinity of the kernel, we show some mean value formulas on the level sets of the fundamental solution, which are the starting point to obtain a comprehensive parallel of the classical Potential Theory. Then we show that a precise knowledge of the fundamental solution leads to global regularity results, namely estimates at the boundary or on the whole space. Finally in the problem of regularity of non linear differential equations we need an ad hoc modification of the parametrix method, based on the properties of the fundamental solution of an approximating problem

Approximations of Sobolev norms in Carnot groups

This paper deals with a notion of Sobolev space $W^{1,p}$ introduced by J.Bourgain, H.Brezis and P.Mironescu by means of a seminorm involving local averages of finite differences. This seminorm was subsequently used by A.Ponce to obtain a Poincar\'e-type inequality. The main results that we present are a generalization of these two works to a non-Euclidean setting, namely that of Carnot groups. We show that the seminorm expressd in terms of the intrinsic distance is equivalent to the $L^p$ norm of the intrinsic gradient, and provide a Poincar\'e-type inequality on Carnot groups by means of a constructive approach which relies on one-dimensional estimates. Self-improving properties are also studied for some cases of interest

Parents' Use of Social Media for Health Information Before and After a Consultation With Health Care Professionals: Australian Cross-Sectional Study.

BACKGROUND: Social media is a crucial source of health information for many parents due to its integration into modern life, raising critical concerns for public health. Parents use various social media platforms to find health information for their children, with most information created and shared by parents with no medical or health training. The extent to which parents seek health information from social media before and after a consultation and their motivations for doing so remain underresearched. OBJECTIVE: This study aimed to investigate Australian parents' use of social media for health information for their children, aged between 6 months and 5 years, before and after consulting with health care professionals. METHODS: A representative cross-sectional survey of 1000 Australian parents with children aged 6 months to 5 years was conducted between November and December 2021. Data were cleaned and analyzed using IBM SPSS software. The primary outcomes were (1) parental motivation and prevalence of social media use for health information and (2) parental motivation for using social media before and after a consultation with their child's health care professional. RESULTS: Of the 1000 parents surveyed, 82.2% (n=822) reported using social media for health information for their child. Parents were more likely to consult social media before and after a health consultation if they were aged 30-39 or ≥50 years and born in Australia. Parents with higher levels of education were less likely to consult social media. Parents were motivated to seek health information before a consultation for a variety of reasons, including exchanging opinions and experiences (639/767, 83.3%), having information that is available 24/7 (622/767, 81.1%), receiving emotional support (599/767, 78.1%), having previous positive experiences (597/767, 77.8%), and having friends and family that use social media for health information (577/767, 75.2%). Parents sought information after a consultation to connect with parents with similar experiences (546/794, 68.8%), seek a second opinion (505/794, 63.6%), fact-check information provided by their health care professional (483/794, 60.8%), and look for other treatment options (353/794, 44.5%). CONCLUSIONS: Using social media for child health information is part of the modern parenting experience. It can be challenging to discern the quality of health information on social media, leaving parents open to incorrect information and misinformation. Although access to immediate social support is a welcomed feature of social media, receiving incorrect health information can have unwanted consequences for the child, family, health provider, and wider community. The upskilling of parental health literacy to navigate the unique health literacy challenges that social media brings, alongside the creation and delivery of accessible, evidence-based information in varying formats, is urgently required. The provision of this information is the responsibility of every level of the health system, not just the treating health care professional

Investigations on offshore wind turbine inflow modelling using numerical weather prediction coupled with local-scale computational fluid dynamics

The computational power available nowadays to industry and research paves the way to increasingly more accurate systems for the wind resource prediction. A promising approach is to support the mesoscale numerical weather prediction (NWP) with high fidelity computational fluid dynamics (CFD). This approach aims at increasing the spatial resolution of the wind prediction by not only accounting for the complex and multiphysics aspects of the atmosphere over a large geographical region, but also including the effects of the fine scale turbulence and the interaction of the wind flow with the sea surface. In this work, we test a set of model setups for both the mesoscale (NWP) and local scale (CFD) simulations employed in a multi-scale modelling framework. The method comprises a one-way coupling interface to define boundary conditions for the local scale simulation (based on the Reynolds Averaged Navier–Stokes equations) using the mesoscale wind given by the NWP system. The wind prediction in an offshore site is compared with LiDAR measurements, testing a set of mesoscale planetary boundary layer schemes, and different model choices for the local scale simulation, which include steady and unsteady approaches for simulation and boundary conditions, different turbulence closure constants, and the effect of the wave motion of the sea surface. The resulting wind is then used for the simulation of a large wind turbine, showing how a realistic wind profile and an ideal exponential law profile lead to different predictions of wind turbine rotor performance and loads

Utilization of a population health survey in policy and practice: a case study

BackgroundThere is growing interest by funding bodies and researchers in assessing the impact of research on real world policy and practice. Population health monitoring surveys provide an important source of data on the prevalence and patterns of health problems, but few empirical studies have explored if and how such data is used to influence policy or practice decisions. Here we provide a case study analysis of how the findings from an Australian population monitoring survey series of children&rsquo;s weight and weight-related behaviors (Schools Physical Activity and Nutrition Survey (SPANS)) have been used, and the key facilitators and barriers to their utilization.MethodsData collection included semi-structured interviews with the chief investigators (n = 3) and end-users (n = 9) of SPANS data to explore if, how and under what circumstances the survey findings had been used, bibliometric analysis and verification using documentary evidence. Data analysis involved thematic coding of interview data and triangulation with other data sources to produce case summaries of policy and practice impacts for each of the three survey years (1997, 2004, 2010). Case summaries were then reviewed and discussed by the authors to distil key themes on if, how and why the SPANS findings had been used to guide policy and practice.ResultsWe found that the survey findings were used for agenda setting (raising awareness of issues), identifying areas and target groups for interventions, informing new policies, and supporting and justifying existing policies and programs across a range of sectors. Reported factors influencing use of the findings were: i) the perceived credibility of survey findings; ii) dissemination strategies used; and, iii) a range of contextual factors.ConclusionsUsing a novel approach, our case study provides important new insights into how and under what circumstances population health monitoring data can be used to influence real world policy and practice. The findings highlight the importance of population monitoring programs being conducted by independent credible agencies, researchers engaging end-users from the inception of survey programs and utilizing existing policy networks and structures, and using a range of strategies to disseminate the findings that go beyond traditional peer review publications.<br /

Pooling job physical exposure data from multiple independent studies in a consortium study of carpal tunnel syndrome

Pooling data from different epidemiological studies of musculoskeletal disorders (MSDs) is necessary to improve statistical power and to more precisely quantify exposure–response relationships for MSDs. The pooling process is difficult and time-consuming, and small methodological differences could lead to different exposure–response relationships. A subcommittee of a six-study research consortium studying carpal tunnel syndrome: (i) visited each study site, (ii) documented methods used to collect physical exposure data and (iii) determined compatibility of exposure variables across studies. Certain measures of force, frequency of exertion and duty cycle were collected by all studies and were largely compatible. A portion of studies had detailed data to investigate simultaneous combinations of force, frequency and duration of exertions. Limited compatibility was found for hand/wrist posture. Only two studies could calculate compatible Strain Index scores, but Threshold Limit Value for Hand Activity Level could be determined for all studies. Challenges of pooling data, resources required and recommendations for future researchers are discussed