Conservation of resonant periodic solutions for the one-dimensional nonlinear Schroedinger equation

We consider the one-dimensional nonlinear Schr\"odinger equation with Dirichlet boundary conditions in the fully resonant case (absence of the zero-mass term). We investigate conservation of small amplitude periodic-solutions for a large set measure of frequencies. In particular we show that there are infinitely many periodic solutions which continue the linear ones involving an arbitrary number of resonant modes, provided the corresponding frequencies are large enough and close enough to each other (wave packets with large wave number)

Periodic solutions for the Schroedinger equation with nonlocal smoothing nonlinearities in higher dimension

We consider the nonlinear Schroedinger equation in higher dimension with Dirichlet boundary conditions and with a non-local smoothing nonlinearity. We prove the existence of small amplitude periodic solutions. In the fully resonant case we find solutions which at leading order are wave packets, in the sense that they continue linear solutions with an arbitrarily large number of resonant modes. The main difficulty in the proof consists in solving a "small divisor problem" which we do by using a renormalisation group approach.Comment: 60 pages 8 figure

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

Functional and structural characterization of HCMV complexes by dissecting molecular interactions

Human cytomegalovirus (HCMV) is a virus infecting the majority of adults worldwide. In healthy individuals, a strong immune response to HCMV is able to limit and contain the spread of the disease [1]. HCMV can infect a remarkably broad cell range within its host. The broad cell tropism of HCMV may reflect the abundance of distinct glycoprotein complexes in the virion envelope [10]. The core machinery for Herpesvirus entry comprises three highly conserved viral glycoproteins, glycoprotein B (gB), glycoprotein H (gH), and glycoprotein L (gL) [21]. In addition to gB and gH/gL, most Herpesviruses encode additional glycoproteins that are able to interact with gH/gL. For HCMV, this addition consist of the glycoprotein gO, to form gH/gL/gO complex, or the trimer UL128/UL130/UL131A (referred as “ULs”), to form a pentameric structure often designated as “Pentamer”. Viral entry into fibroblast or epithelial/endothelial and lymphoid cells relies on the presence of gH/gL/gO or Pentamer respectively [35, 40]. In an in vitro system, specific cysteines have been identified to stabilize these complexes and impairment of disulfide bonds formation abolishes complexes maturation and cellular trafficking [41]. Here we addressed the relevance of these disulfide bonds in the formation of HCMV entry complexes and on the infectivity of point mutated viruses. To this purpose, four recombinant Cys-mutated viruses, generated through mutagenesis of a Bacterial Artificial Chromosome (BAC) containing the entire genome of HCMV TR strain, were analysed for viral tropism on three different cell types. We also checked by Western blot the content of the pentameric proteins expressed by these mutants both in the extracts of infected fibroblasts and monocytic cells (HFF and THP-1, respectively) and in virions produced by infection of human fibroblasts. Surprisingly, results from our analysis showed that mutation on two specific cysteines involving gL disulfide bonds to gO or UL128 and to gH resulted in the loss of intracellular gL or expression level under the detection power of Wb. Two other Cys mutated viruses showed no differences in the levels of viral structural proteins compared to wt. These results suggest that the impairment of the disulfide bond involving binding of gL to UL128 or gO and gL to gH, cause instability of the gL protein with loss or reduced ability to form higher order complexes and likely cellular degradation. However, our results show that infectious viruses can achieve a complete life cycle in absence of a crucial protein like as gL but it also raise the question of which pattern of factors, likely interacting with gH, are necessary as “surrogate” gL

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

Development of a hierarchical fuzzy model for the evaluation of inherent safety

Inherent safety has been recognized as a design approach useful to remove or reduce hazards at the source instead of controlling them with add-on protective barriers. However, inherent safety is based on qualitative principles that cannot easily be evaluated and analyzed, and this is one of the major difficulties for the systematic application and quantification of inherent safety in plant design. The present research introduces the use of fuzzy logic for the measurement of inherent safety by proposing a hierarchical fuzzy model. This dissertation establishes a novel conceptual framework for the analysis of inherent safety and proposes a methodology that addresses several of the limitations of the methodologies available for current inherent safety analysis. This research proposes a methodology based on a hierarchical fuzzy model that analyzes the interaction of variables relevant for inherent safety and process safety in general. The use of fuzzy logic is helpful for modeling uncertainty and subjectivities implied in evaluation of certain variables and it is helpful for combining quantitative data with qualitative information. Fuzzy logic offers the advantage of being able to model numerical and heuristic expert knowledge by using fuzzy IF-THEN rules. Safety is traditionally considered a subjective issue because of the high uncertainty associated with its significant descriptors and parameters; however, this research recognizes that rather than subjective, "safety" is a vague problem. Vagueness derives from the fact that it is not possible to define sharp boundaries between safe and unsafe states; therefore the problem is a "matter of degree". The proposed method is computer-based and process simulator-oriented in order to reduce the time and expertise required for the analysis. It is expected that in the future, by linking the present approach to a process simulator, process engineers can develop safety analysis during the early stages of the design in a rapid and systematic way. Another important aspect of inherent safety, rarely addressed, is transportation of chemical substances; this dissertation includes the analysis of transportation hazard by truck using a fuzzy logic-based approach

Periodic solutions for completely resonant nonlinear wave equations

We consider the nonlinear string equation with Dirichlet boundary conditions $u_{xx}-u_{tt}=\phi(u)$, with $\phi(u)=\Phi u^{3} + O(u^{5})$ odd and analytic, $\Phi\neq0$, and we construct small amplitude periodic solutions with frequency \o for a large Lebesgue measure set of \o close to 1. This extends previous results where only a zero-measure set of frequencies could be treated (the ones for which no small divisors appear). The proof is based on combining the Lyapunov-Schmidt decomposition, which leads to two separate sets of equations dealing with the resonant and nonresonant Fourier components, respectively the Q and the P equations, with resummation techniques of divergent powers series, allowing us to control the small divisors problem. The main difficulty with respect the nonlinear wave equations $u_{xx}-u_{tt}+ M u = \phi(u)$, $M\neq0$, is that not only the P equation but also the Q equation is infinite-dimensiona

Periodic solutions for a class of nonlinear partial differential equations in higher dimension

We prove the existence of periodic solutions in a class of nonlinear partial differential equations, including the nonlinear Schroedinger equation, the nonlinear wave equation, and the nonlinear beam equation, in higher dimension. Our result covers cases where the bifurcation equation is infinite-dimensional, such as the nonlinear Schroedinger equation with zero mass, for which solutions which at leading order are wave packets are shown to exist.Comment: 34 page

COVID-19 pneumonia and pulmonary microembolism in a patient with B-thalassemia major

We think that thalassemia is not necessarily a cause of aggravation of the clinical course in COVID-19; however, certain key factors must be considered, such as the anemic condition, the likely pathogenic role of the virus on hemoglobin, and the hypercoagulable state to prevent any complications

Anxiety, Depression, and Body Weight in Children and Adolescents With Migraine

Background: There is a lack of studies that explore the possible association between body weight, psychological symptoms, and migraine severity in pediatric populations. The purpose of the study was to explore: (1) the association between body weight and the frequency of migraine attacks, (2) the possible differences in anxiety and depression symptoms according to the frequency of attacks and body weight, and (3) the possible mediating role of anxiety and/or depression in the association between body weight and frequency of migraine attacks in children.Methods: One hundred and eleven children/adolescents with migraine were included (47 boys and 64 girls; mean age 11.7; +/- 2.4 years). The patients were classified as: (1) high frequency patients, reporting from weekly to daily episodes and (2) low frequency patients, with <= 3 episodes per month. According to their body mass index percentiles, the patients were divided in "Normal weight" (from >= 5 to <85 percentile), "Overweight" (from >= 85 to <95 percentile), and "Obese" (>= 95 percentile). Given the low number of obese patients, the overweight and obese groups were considered together in the "Overweight" group. Anxiety and depression symptoms were assessed by the Self-Administered Psychiatric Scales for Children and Adolescents (SAFA).Results: Fifty-four patients were normal in weight (49.6%), while 56 patients (50.4%) were overweight. The overweight patients showed a higher frequency of migraine attacks (64.7%; p < 0.05). Patients with a high frequency of attacks reported higher scores in all SAFA-Anxiety subscales (SAFA-A Tot: F = 15.107; p = 0.000). Overweight patients showed a significantly higher score in the "Separation anxiety" subscale (F = 7.855; p = 0.006). We found a mediating role between the overweight and high frequency for total anxiety (z = 2.11 +/- 0.03; p < 0.05) and social anxiety (z = 2.04 +/- 0.03; p < 0.05).Conclusions: Our results suggest that, among the children suffering from migraine, the overweight status is associated with a higher frequency of attacks and separation anxiety symptoms. In particular, our study provides the first evidence of the role of anxiety in linking overweight and the frequency of migraine attacks in children and adolescents