Fibers and global geometry of functions

Since the seminal work of Ambrosetti and Prodi, the study of global folds was enriched by geometric concepts and extensions accomodating new examples. We present the advantages of considering fibers, a construction dating to Berger and Podolak's view of the original theorem. A description of folds in terms of properties of fibers gives new perspective to the usual hypotheses in the subject. The text is intended as a guide, outlining arguments and stating results which will be detailed elsewhere

The Italian National Registry for FSHD: an enhanced data integration and an analytics framework towards Smart Health Care and Precision Medicine for a rare disease

Background: The Italian Clinical network for FSHD (ICNF) has established the Italian National Registry for FSHD (INRF), collecting data from patients affected by Facioscapulohumeral dystrophy (FSHD) and their relatives. The INRF has gathered data from molecular analysis, clinical evaluation, anamnestic information, and family history from more than 3500 participants. Methods: A data management framework, called Mediator Environment for Multiple Information Sources (MOMIS) FSHD Web Platform, has been developed to provide charts, maps and search tools customized for specific needs. Patients’ samples and their clinical information derives from the Italian Clinical network for FSHD (ICNF), a consortium consisting of fourteen neuromuscular clinics distributed across Italy. The tools used to collect, integrate, and visualize clinical, molecular and natural history information about patients affected by FSHD and their relatives are described. Results: The INRF collected the molecular data regarding FSHD diagnosis conducted on 7197 subjects and identified 3362 individuals carrying a D4Z4 Reduced Allele (DRA): 1634 were unrelated index cases. In 1032 cases the molecular testing has been extended to 3747 relatives, 1728 carrying a DRA. Since 2009 molecular analysis has been accompanied by clinical evaluation based standardized evaluation protocols. In the period 2009–2020, 3577 clinical forms have been collected, 2059 follow the Comprehensive Clinical Evaluation form (CCEF). The integration of standardized clinical information and molecular data has made possible to demonstrate the wide phenotypic variability of FSHD. The MOMIS (Mediator Environment for Multiple Information Sources) data integration framework allowed performing genotype–phenotype correlation studies, and generated information of medical importance either for clinical practice or genetic counseling. Conclusion: The platform implemented for the FSHD Registry data collection based on OpenClinica meets the requirement to integrate patient/disease information, as well as the need to adapt dynamically to security and privacy concerns. Our results indicate that the quality of data collection in a multi-integrated approach is fundamental for clinical and epidemiological research in a rare disease and may have great value in allowing us to redefine diagnostic criteria and disease markers for FSHD. By extending the use of the MOMIS data integration framework to other countries and the longitudinal systematic collection of standardized clinical data will facilitate the understanding of disease natural history and offer valuable inputs towards trial readiness. This approach is of high significance to FSHD medical community and also to rare disease research in general

Subsurface hydrothermal processes and the bioenergetics of chemolithoautotrophy at the shallow-sea vents off Panarea Island (Italy)

The subsurface evolution of shallow-sea hydrothermal fluids is a function of many factors including fluid-mineral equilibria, phase separation, magmatic inputs, and mineral precipitation, all of which influence discharging fluid chemistry and consequently associated seafloor microbial communities. Shallow-sea vent systems, however, are understudied in this regard. In order to investigate subsurface processes in a shallow-sea hydrothermal vent, and determine how these physical and chemical parameters influence the metabolic potential of the microbial communities, three shallow-sea hydrothermal vents associated with Panarea Island (Italy) were characterized. Vent fluids, pore fluids and gases at the three sites were sampled and analyzed for major and minor elements, redox-sensitive compounds, free gas compositions, and strontium isotopes. The corresponding data were used to 1) describe the subsurface geochemical evolution of the fluids and 2) to evaluate the catabolic potential of 61 inorganic redox reactions for in situ microbial communities. Generally, the vent fluids can be hot (up to 135 °C), acidic (pH 1.9-5.7), and sulfidic (up to 2.5 mM H2S). Three distinct types of hydrothermal fluids were identified, each with higher temperatures and lower pH, Mg2 + and SO42 -, relative to seawater. Type 1 was consistently more saline than Type 2, and both were more saline than seawater. Type 3 fluids were similar to or slightly depleted in most major ions relative to seawater. End-member calculations of conservative elements indicate that Type 1 and Type 2 fluids are derived from two different sources, most likely 1) a deeper, higher salinity reservoir and 2) a shallower, lower salinity reservoir, respectively, in a layered hydrothermal system. The deeper reservoir records some of the highest end-member Cl concentrations to date, and developed as a result of recirculation of brine fluids with long term loss of steam and volatiles due to past phase separation. No strong evidence for ongoing phase separation is observed. Type 3 fluids are suggested to be mostly influenced by degassing of volatiles and subsequently dissolution of CO2, H2S, and other gases into the aqueous phase. Gibbs energies (ΔGr) of redox reactions that couple potential terminal electron acceptors (O2, NO3-, MnIV, FeIII, SO42 -, S0, CO2,) with potential electron donors (H2, NH4+, Fe2 +, Mn2 +, H2S, CH4) were evaluated at in situ temperatures and compositions for each site and by fluid type. When Gibbs energies of reaction are normalized per kilogram of hydrothermal fluid, sulfur oxidation reactions are the most exergonic, while the oxidation of Fe2 +, NH4+, CH4, and Mn2 + are moderately energy yielding. The energetics calculations indicate that the most robust microbial communities in the Panarea hot springs combine H2S from deep water-rock-gas interactions with O2 that is entrained via seawater mixing to fuel their activities, regardless of site location or fluid type

Non-radial maximizers for functionals with exponential non-linearity in R-2

We consider the functional F:H-0(1)(B(0,1))-> R F(u)=integral(B(0,1)) vertical bar x vertical bar(alpha)(e(p vertical bar u vertical bar gamma)-1-p vertical bar u vertical bar(gamma))dx where alpha>0, p>0, 1<= 2, and B(0,1) is the unit ball in R-2. We prove that for any p>0, 1<2 and 0<4 pi, gamma=2 no maximizer of F(u) on the unit ball in H-0(1) is radially symmetric provided that alpha is large enough. This extends a result of Smets, Su and Willem concerning the existence of non-radial ground state solutions for the Rayleigh quotient related to the Henon equation with Dirichlet boundary conditions