KAM theory in configuration space and cancellations in the Lindstedt series

The KAM theorem for analytic quasi-integrable anisochronous Hamiltonian systems yields that the perturbation expansion (Lindstedt series) for quasi-periodic solutions with Diophantine frequency vector converges. If one studies the Lindstedt series, one finds that convergence is ultimately related to the presence of cancellations between contributions of the same perturbation order. In turn, this is due to symmetries in the problem. Such symmetries are easily visualised in action-angle coordinates, where KAM theorem is usually formulated, by exploiting the analogy between Lindstedt series and perturbation expansions in quantum field theory and, in particular, the possibility of expressing the solutions in terms of tree graphs, which are the analogue of Feynman diagrams. If the unperturbed system is isochronous, Moser's modifying terms theorem ensures that an analytic quasi-periodic solution with the same Diophantine frequency vector as the unperturbed Hamiltonian exists for the system obtained by adding a suitable constant (counterterm) to the vector field. Also in this case, one can follow the alternative approach of studying the perturbation expansion for both the solution and the counterterm, and again convergence of the two series is obtained as a consequence of deep cancellations between contributions of the same order. We revisit Moser's theorem, by studying the perturbation expansion one obtains by working in Cartesian coordinates. We investigate the symmetries giving rise to the cancellations which makes possible the convergence of the series. We find that the cancellation mechanism works in a completely different way in Cartesian coordinates. The interpretation of the underlying symmetries in terms of tree graphs is much more subtle than in the case of action-angle coordinates.Comment: 38 pages, 18 fugure

Almost-periodic solutions to the NLS equation with smooth convolution potentials

We consider the one-dimensional NLS equation with a convolution potential and a quintic nonlinearity. We prove that, for most choices of potentials with polynomially decreasing Fourier coefficients, there exist almost-periodic solutions in the Gevrey class with frequency satisfying a Bryuno non-resonance condition. This allows convolution potentials of class $C^p$, for any integer $p$: as far as we know this is the first result where the regularity of the potential is arbitrarily large and not compensated by a corresponding smoothing of the nonlinearity.Comment: 140 pages, 32 figure

A KAM result on compact Lie groups

We describe some recent results on existence of quasi-periodic solutions of Hamiltonian PDEs on compact manifolds. We prove a linear stability result for the non-linear Schr\"odinger equation in the case of $SU(2)$ and $SO(3)$.Comment: 20 pages, 1 figur

Almost-periodic Response Solutions for a forced quasi-linear Airy equation

We prove the existence of almost-periodic solutions for quasi-linear perturbations of the Airy equation. This is the first result about the existence of this type of solutions for a quasi-linear PDE. The solutions turn out to be analytic in time and space. To prove our result we use a Craig-Wayne approach combined with a KAM reducibility scheme and pseudo-differential calculus on ${\mathbb T}^\infty$

Untangling sustainability reporting: theoretical approaches informing non-financial disclosure

This study analyses different theoretical frameworks used in the literature to explain corporate social and environmental sustainability (SES) reporting. A systematic literature review of 232 scientific articles published in top-tier journals was performed through bibliometric visualizations, quantitative statistics and narrative analyses. Results highlight that legitimacy, institutional, and stakeholder theories most commonly inform studies on SES reporting. Recent works also show the use of theoretical approaches less frequently employed in accounting and management that usually distinguish other research fields, such as sociology, psychology, and communication, highlighting crossfertilization among different research areas. This systematic literature review specifically focuses on the many theories related to SES reporting and offers an extensive overview of theoretical frameworks underpinning thirty years of studies on non-financial disclosure. Moreover, encourages scholars to engage with critical and emerging theories in the study of SES reporting following multidimensional and multidisciplinary perspectives

Stem Cells and Innate Immunity in Aquatic Invertebrates: Bridging Two Seemingly Disparate Disciplines for New Discoveries in Biology

The scopes related to the interplay between stem cells and the immune system are broad and range from the basic understanding of organism's physiology and ecology to translational studies, further contributing to (eco)toxicology, biotechnology, and medicine as well as regulatory and ethical aspects. Stem cells originate immune cells through hematopoiesis, and the interplay between the two cell types is required in processes like regeneration. In addition, stem and immune cell anomalies directly affect the organism's functions, its ability to cope with environmental changes and, indirectly, its role in ecosystem services. However, stem cells and immune cells continue to be considered parts of two branches of biological research with few interconnections between them. This review aims to bridge these two seemingly disparate disciplines towards much more integrative and transformative approaches with examples deriving mainly from aquatic invertebrates. We discuss the current understanding of cross-disciplinary collaborative and emerging issues, raising novel hypotheses and comments. We also discuss the problems and perspectives of the two disciplines and how to integrate their conceptual frameworks to address basic equations in biology in a new, innovative way

Fabrication and Characterisation of 3D Diamond Pixel Detectors With Timing Capabilities

Diamond sensors provide a promising radiation hard solution to the challenges posed by the future experiments at hadron machines. A 3D geometry with thin columnar resistive electrodes orthogonal to the diamond surface, obtained by laser nanofabrication, is expected to provide significantly better time resolution with respect to the extensively studied planar diamond sensors. We report on the development, production, and characterisation of innovative 3D diamond sensors achieving 30% improvement in both space and time resolution with respect to sensors from the previous generation. This is the first complete characterisation of the time resolution of 3D diamond sensors and combines results from tests with laser, beta rays and high energy particle beams. Plans and strategies for further improvement in the fabrication technology and readout systems are also discussed

Contributions of symptomatic osteoarthritis and physical function to incident cardiovascular disease

Abstract Background Osteoarthritis (OA) is associated with worsening physical function and a high prevalence of comorbid health conditions. In particular, cardiovascular disease (CVD) risk is higher in individuals with OA than the general population. Limitations in physical function may be one pathway to the development of CVD among individuals with OA. This study evaluated associations of symptomatic knee OA (sxKOA), baseline physical function and worsening of function over time with self-reported incident CVD in a community-based cohort. Methods Our sample consisted of individuals from the Johnston County Osteoarthritis Project who did not report having CVD at baseline. Variables used to evaluate physical function were the Health Assessment Questionnaire (HAQ), time to complete 5 chair stands, and the 8-ft walk. Worsening function for these variables was defined based on previous literature and cutoffs from our sample. Logistic regression analyses examined associations of sxKOA, baseline function and worsening of function over time with self-reported incident CVD, unadjusted and adjusted for relevant demographic and clinical characteristics. Results Among 1709 participants included in these analyses, the mean age was 59.5 ± 9.5 years, 63.6% were women, 15% had sxKOA, and the follow up time was 5.9 ± 1.2 years. About a third of participants reported worsening HAQ score, about two-fifths had worsened chair stand time, half had worsened walking speed during the 8-ft walk, and 16% self-reported incident CVD. In unadjusted analyses, sxKOA, baseline function, and worsening function were all associated with self-reported incident CVD. In multivariable models including all of these variables, sxKOA was not associated with incident CVD, but worsening function was significantly associated with increased CVD risk, for all three functional measures: HAQ odds ratio (OR) = 2.49 (95% confidence interval (CI) 1.90–3.25), chair stands OR = 1.58 (95% CI 1.20–2.08), 8-ft walk OR = 1.53 (95%CI 1.15–2.04). These associations for worsening function remained in models additionally adjusted for demographic and clinical characteristics related to CVD risk. Conclusions The association between symptomatic knee osteoarthritis and cardiovascular disease risk was explained by measures of physical function. This highlights the importance of physical activity and other strategies to prevent functional loss among individuals with symptomatic knee osteoarthritis

Study of ferritin self-assembly and heteropolymer formation by the use of Fluorescence Resonance Energy Transfer (FRET) technology

The high stability and strong self-assembly properties made ferritins the most used proteins for nanotechnological applications. Human ferritins are made of 24 subunits of the H- and L-type that coassemble in an almost spherical nanocage 12 nm across, delimiting a large cavity. The mechanism and kinetics of ferritin self-assembly and why H/L heteropolymers formation is favored over the homopolymers remain unclarified. In order to study this, we used the Fluorescence Resonance Energy Transfer (FRET) tool by binding multiple donor or acceptor Alexa Fluor fluorophores on the outer surface of human H and L ferritins and then denaturing and reassembling them in different proportions and conditions. The FRET efficiency increase from 0.7 in the assembled allowed to study the assembly kinetics. We found that their assembly was complete in about one hour, and that the initial rate of self-assembly of H/L heteropolymers was slightly faster than that of the H/H homopolymers. Then, by adding various proportions of unlabeled H or L-chains to the FRET system we found that the presence of the L-chains displaced the formation of H-H dimers more efficiently than that of the H-chains. This favored formation of H/L heterodimers, which is the initial step in ferritin self-assembly, contributes to explain the preferred formation of H/L heteropolymers over the H or L homopolymers. Moreover, we found that the H-chains arrange at distant positions on the heteropolymeric shell until they reach a number above eight, when they start to co-localize.This work was partially supported by MIUR grant PRIN10-11 to PA, and by Telethon grant GGP15064 to PA. FC was recipient of a Post-Doc Fellowship from University of Brescia, and was partially supported by CIB (Consorzio Italiano di Biotecnologie)

Position Paper of the Italian Association of Medical Oncology on Early Palliative Care in Oncology Practice (Simultaneous Care)

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