The heart of a convex body

We investigate some basic properties of the {\it heart} $\heartsuit(\mathcal{K})$ of a convex set $\mathcal{K}.$ It is a subset of $\mathcal{K},$ whose definition is based on mirror reflections of euclidean space, and is a non-local object. The main motivation of our interest for $\heartsuit(\mathcal{K})$ is that this gives an estimate of the location of the hot spot in a convex heat conductor with boundary temperature grounded at zero. Here, we investigate on the relation between $\heartsuit(\mathcal{K})$ and the mirror symmetries of $\mathcal{K};$ we show that $\heartsuit(\mathcal{K})$ contains many (geometrically and phisically) relevant points of $\mathcal{K};$ we prove a simple geometrical lower estimate for the diameter of $\heartsuit(\mathcal{K});$ we also prove an upper estimate for the area of $\heartsuit(\mathcal{K}),$ when $\mathcal{K}$ is a triangle.Comment: 15 pages, 3 figures. appears as "Geometric Properties for Parabolic and Elliptic PDE's", Springer INdAM Series Volume 2, 2013, pp 49-6

Using the Process Digital Twin as a tool for companies to evaluate the Return on Investment of manufacturing automation

The fourth industrial revolution is gaining momentum, but still lacks full realization. Several studies suggest that many companies around the world have begun the digital transformation undertaking, but most are still far from full adoption and yet fail to see the full economic potential, being stuck in what has been called "pilot purgatory”. Digitalization is largely recognized as an accelerator and enabler for full automation in manufacturing, but companies are still struggling to assess the return on investment and the impact on operational performance indicators. Therefore, companies, especially SMEs characterized by dynamic, high-value, high-mix, and low-volume contexts, are reluctant to invest further. By incorporating simulation, data analytics and behavioral models, digital twins may also be used to support automation solutions ramp-up, demonstrate their impact evaluation, usage scenarios, eliminating the need for physical prototypes, reducing development time, and improving quality. Few forward-thinking companies are pursuing the digital transformation path, while the majority are clipping the wings of a transformation that is essential for a sustainable manufacturing. This paper describes a theoretical approach to exploit the digital twin technology to gather insights towards a realistic economical assessment of full automation solutions, to back and encourage investments to realize the potential of the digital manufacturing transformation. The approach is being tested under the European Union’s Horizon 2020 research and innovation program under grant agreement No. 958363, which provides an opportunity to assess how the various components of the method are constructed, how complex they are, and what level of effort is required, using a practical example

Combining astrometry and JUICE -- Europa Clipper radio science to improve the ephemerides of the Galilean moons

The upcoming JUICE and Europa Clipper missions to Jupiter's Galilean satellites will provide radio science tracking measurements of both spacecraft. Such data are expected to significantly help estimating the moons' ephemerides and related dynamical parameters. However, the two missions will yield an imbalanced dataset, with no flybys planned at Io, condensed over less than six years. Current ephemerides' solutions for the Galilean moons, on the other hand, rely on ground-based astrometry collected over more than a century which, while being less accurate, bring very valuable constraints on the long-term dynamics of the system. An improved solution for the Galilean satellites' complex dynamics could however be achieved by exploiting the existing synergies between these different observation sets. To quantify this, we merged simulated JUICE and Clipper radio science data with existing ground-based astrometric and radar observations, and performed the inversion. Our study specifically focusses on the resulting formal uncertainties in the moons' states, as well as Io's and Jupiter's tidal dissipation parameters. Adding astrometry stabilises the moons' state solution, especially beyond the missions' timelines. It furthermore reduces the uncertainties in $1/Q$ (inverse of the tidal quality factor) by a factor two to four for Jupiter, and about 30-35\% for Io. Among all data types, classical astrometry data prior to 1960 proved particularly beneficial. We also show that ground observations of Io add the most to the solution, confirming that ground observations can fill the lack of radio science data for this specific moon. We obtained a noticeable solution improvement when exploiting the complementarity between all different observation sets. These promising simulation results thus motivate future efforts to achieve a global solution from actual JUICE and Clipper radio science data

Combining astrometry and JUICE-Europa Clipper radio science to improve the ephemerides of the Galilean moons

Context. The upcoming JUICE and Europa Clipper missions targeting Jupiter s Galilean satellites will provide radio science tracking measurements of both spacecraft. Such data are expected to significantly help estimating the moons ephemerides and related dynamical parameters (e.g. tidal dissipation parameters). However, the two missions will yield an imbalanced dataset, with no flybys planned at Io, condensed over less than six years. Current ephemerides solutions for the Galilean moons, on the other hand, rely on ground-based astrometry collected over more than a century which, while being less accurate, bring very valuable constraints on the long-term dynamics of the system. Aims. An improved solution for the Galilean satellites complex dynamics could however be achieved by exploiting the existing synergies between these different observation sets. Methods. To quantify this, we merged simulated radio science data from both JUICE and Europa Clipper spacecraft with existing ground-based astrometric and radar observations, and performed the inversion in different configurations: either adding all available ground observations or individually assessing the contribution of different data subsets. Our discussion specifically focusses on the resulting formal uncertainties in the moons states, as well as Io s and Jupiter s tidal dissipation parameters. Results. Adding astrometry stabilises the moons state solution, especially beyond the missions timelines. It furthermore reduces the uncertainties in 1/Q (inverse of the tidal quality factor) by a factor two to four for Jupiter, and about 30- 35% for Io. Among all data types, classical astrometry data prior to 1960 proved particularly beneficial. Overall, we also show that ground observations of Io add the most to the solution, confirming that ground observations can fill the lack of radio science data for this specific moon. Conclusions. We obtained a noticeable solution improvement when making use of the complementarity between all different observation sets. The promising results obtained with simulations thus motivate future efforts to achieve a global solution from actual JUICE and Clipper radio science measurements

Part Variation Modeling to Avoid Scrap Parts in Multi-stage Production Systems

Manufacturing systems for today's products are complex systems requiring a variety of different processes in order to be able to manufacture all necessary part features. This also applies to the production of rotating components, which have experienced increasing demand at the latest due to the growth in mobility. As in almost every manufacturing process, quality-reducing defects can occur due to deviations for example tool wear, which cannot always be avoided. Those, that have accumulated from previous process steps can cause the occurrence of superimposed defects. This leads to complex relationships between quality defects in the end product and the numerous parameters of the manufacturing processes. To remain competitive, production must be optimized in order to identify defects as early as possible, as well as their dependencies and variation patterns. The paper presents an approach to identify and model part variations within multi-stage production systems. Subsequently, based on a detected deviation, a downstream compensation strategy can be proposed at an early stage of the manufacturing process, which uses the capability of the overall system to fundamentally eliminate rejects

Long-term proactive management of psoriasis with calcipotriol and betamethasone dipropionate foam: an Italian consensus through a combined nominal group technique and Delphi approach

Background: Although long-term management of psoriasis is paramount, this approach is challenging in clinical practice. In the recent PSO-LONG trial, a fixed-dose combination of betamethasone dipropionate (BD) and calcipotriol (Cal) foam applied twice a week on non-consecutive days for 52 weeks (proactive treatment) reduced the risk of relapse. However, the role of Cal/BD foam in the long-term management of psoriasis needs further clarifications. The ProActive Management (PAM) program, a nationwide Italian project, aims at reaching a consensus on the role of proactive management of psoriasis. Methods: A steering committee generated some statements through the nominal group technique (NGT). The statements were voted by an expert panel in an adapted Delphi voting process. Results: Eighteen statements were proposed, and the majority of them (14/18) reached a consensus during the Delphi voting. The need to provide long-term proactive topical treatment to reduce the risk of relapse for the treatment of challenging diseases sites or in patients where phototherapy or systemic therapies are contraindicated/ineffective was widely recognized. A consensus was reached about the possibility to associate the proactive treatment with systemic and biological therapies, without the need for dose intensification, thus favoring a prolonged remission. Moreover, the proactive treatment was recognized as more effective than weekend therapy in increasing time free from relapses. Approaches to improve adherence, on the other hand, need further investigation. Conclusions: The inclusion in guidelines of a proactive strategy among the effective treatment options will be a fundamental step in the evolution of a mild-moderate psoriasis therapeutic approach

Breast cancer "tailored follow-up" in Italian oncology units: a web-based survey

urpose: Breast cancer follow-up procedures after primary treatment are still a controversial issue. Aim of this study was to investigate, through a web-based survey, surveillance methodologies selected by Italian oncologists in everyday clinical practice. Methods: Referents of Italian medical oncology units were invited to participate to the study via e-mail through the SurveyMonkey website. Participants were asked how, in their institution, exams of disease staging and follow-up are planned in asymptomatic women and if surveillance continues beyond the 5th year. Results: Between February and May 2013, 125 out of 233 (53.6%) invited referents of Italian medical oncology units agreed to participate in the survey. Ninety-seven (77.6%) referents state that modalities of breast cancer follow-up are planned according to the risk of disease progression at diagnosis and only 12 (9.6%) oncology units apply the minimal follow-up procedures according to international guidelines. Minimal follow-up is never applied in high risk asymptomatic women. Ninety-eight (78.4%) oncology units continue follow-up in all patients beyond 5 years. Conclusions: Our survey shows that 90.4% of participating Italian oncology units declare they do not apply the minimal breast cancer follow-up procedures after primary treatment in asymptomatic women, as suggested by national and international guidelines. Interestingly, about 80.0% of interviewed referents performs the so called "tailored follow-up", high intensity for high risk, low intensity for low risk patients. There is an urgent need of randomized clinical trials able to determine the effectiveness of risk-based follow-up modalities, their ideal frequency and persistence in time

HIV prevalence among female sex workers, drug users and men who have sex with men in Brazil: A Systematic Review and Meta-analysis

<p>Abstract</p> <p>Background</p> <p>The Brazilian response towards AIDS epidemic is well known, but the absence of a systematic review of vulnerable populations ─ men who have sex with men (MSM), female sex workers (FSW), and drug users (DU) remains a main gap in the available literature. Our goal was to conduct a systematic review and meta-analysis of studies assessing HIV prevalence among MSM, FSW and DU, calculating a combined pooled prevalence and summarizing factors associated the pooled prevalence for each group.</p> <p>Methods</p> <p>Nine electronic databases (MEDLINE via PubMed, EMBASE, Cochrane CENTRAL, AIDSLINE, AMED, CINAHL, TOXNET, SciELO, and ISI-Web of Science) were searched for peer-reviewed papers published in English, French, Spanish or Portuguese, from 1999 to 2009. To be included in the review, studies had to measure HIV prevalence and/or incidence as the primary outcome among at least one specific population under analysis.</p> <p>Results</p> <p>The studies targeting the three populations analyzed mostly young participants aged 30 years or less. Among FSW, eight studies were selected (3,625 participants), consistently identifying higher condom use with sexual clients than with occasional and stable partners. The combined HIV prevalence for FSW was 6.2 (95% CI: 4.4-8.3). Ten studies targeting MSM were identified (6,475 participants). Unprotected anal intercourse was commonly reported on those studies, but with great variability according to the nature of the relationship - stable vs. occasional sex partners - and sexual practice - receptive vs. insertive anal sex. Pooled HIV prevalence for MSM was 13.6 (95% CI: 8.2-20.2). Twenty nine studies targeting DU were identified (13,063 participants). Those studies consistently identified injection drug use and syringe/needle sharing as key predictors of HIV-infection, as well as engagement in sex work and male-to-male sex. The combined HIV prevalence across studies targeting DU was 23.1 (95% CI: 16.7-30.2).</p> <p>Conclusions</p> <p>FSW, MSM and DU from Brazil have a much risk of acquiring HIV infection compared to the general population, among which HIV prevalence has been relatively low (~0.6%). Those vulnerable populations should be targeted by focused prevention strategies that provide accurate information, counseling and testing, as well as concrete means to foster behavior change (e.g. access to condoms, drug abuse treatment, and clean syringes in the case of active injecting drug users), tailored to gender and culture-specific needs. Programs that provide these services need to be implemented on public health services throughout the country, in order to decrease the vulnerability of those populations to HIV infection.</p