Darboux's Theorem, Lie series and the standardization of the Salerno and Ablowitz-Ladik models

In the framework of nonlinear Hamiltonian lattices, we revisit the proof of Moser-Darboux's Theorem, in order to present a general scheme for its constructive applicability to Hamiltonian models with non-standard symplectic structures. We take as a guiding example the Salerno and Ablowitz-Ladik (AL) models: we justify the form of a well-known change of coordinates which is adapted to the Gauge symmetry, by showing that it comes out in a natural way within the general strategy outlined in the proof. Moreover, the full or truncated Lie-series technique in the extended phase-space is used to transform the Salerno model, at leading orders in the Darboux coordinates: thus the dNLS Hamiltonian turns out to be a normal form of the Salerno and AL models; as a byproduct we also get estimates of the dynamics of these models by means of dNLS one. We also stress that, once it is cast into the perturbative approach, the method allows to deal with the cases where the explicit trasformation is not known, or even worse it is not writable in terms of elementary functions.Comment: 24 pages, 2 figure

On the continuation of degenerate periodic orbits via normal form: lower dimensional resonant tori

We consider the classical problem of the continuation of periodic orbits surviving to the breaking of invariant lower dimensional resonant tori in nearly integrable Hamiltonian systems. In particular we extend our previous results (presented in CNSNS, 61:198-224, 2018) for full dimensional resonant tori to lower dimensional ones. We develop a constructive normal form scheme that allows to identify and approximate the periodic orbits which continue to exist after the breaking of the resonant torus. A specific feature of our algorithm consists in the possibility of dealing with degenerate periodic orbits. Besides, under suitable hypothesis on the spectrum of the approximate periodic orbit, we obtain information on the linear stability of the periodic orbits feasible of continuation. A pedagogical example involving few degrees of freedom, but connected to the classical topic of discrete solitons in dNLS-lattices, is also provided.Comment: 28 page

Universities’ responses to crises : the influence of competition and reputation on tuition fees

Author's accepted manuscript.Available from 10/11/2021.This is a post-peer-review, pre-copyedit version of an article published in Higher Education. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10734-020-00622-2.acceptedVersio

a comparison of semg temporal and spatial information in the analysis of continuous movements

Abstract Much effort has recently been devoted to the analysis of continuous movements with the aim of promoting EMG signal acceptance in several fields of application. Moreover, several studies have been performed to optimize the temporal and spatial parameters in order to obtain a robust interpretation of EMG signals. Resulting from these perspectives, the investigation of the contribution of EMG temporal and spatial information has become a relevant aspect for signal interpretation. This paper aims to evaluate the effects of the two types of information on continuous motions analysis. In order to achieve this goal, the spatial and temporal information of EMG signals were separated and applied as input for an offline Template Making and Matching algorithm. Movement recognition was performed testing three different methods. In the first case (the Temporal approach) the RMS time series generated during movements was the only information employed. In the second case (the Spatial approach) the mean RMS amplitude measured on each channel was considered. Finally, in the third case (the Spatio-Temporal approach) a combination of the information from both the previous approaches was applied. The experimental protocol included 14 movements, which were different from each other in the muscular activation and the execution timing. Results show that the recognition of continuous movements cannot disregard the temporal information. Moreover, the temporal patterns seem to be relevant also for distinguishing movements which differ only in the muscular areas they activate

Deciphering the relative contribution of vascular inflammation and blood rheology in metastatic spreading

Vascular adhesion of circulating tumor cells (CTCs) is a key step in cancer spreading. If inflammation is recognized to favor the formation of vascular metastatic niches, little is known about the contribution of blood rheology to CTC deposition. Herein, a microfluidic chip, covered by a confluent monolayer of endothelial cells, is used for analyzing the adhesion and rolling of colorectal (HCT 15) and breast (MDA MB 231) cancer cells under different biophysical conditions. These include the analysis of cell transport in a physiological solution and whole blood; over a healthy and a TNF alpha inflamed endothelium; with a flow rate of 50 and 100 nL/min. Upon stimulation of the endothelial monolayer with TNF alpha (25 ng/mL), CTC adhesion increases by 2 to 4 times whilst cell rolling velocity only slightly reduces. Notably, whole blood also enhances cancer cell deposition by 2 to 3 times, but only on the unstimulated vasculature. For all tested conditions, no statistically significant difference is observed between the two cancer cell types. Finally, a computational model for CTC transport demonstrates that a rigid cell approximation reasonably predicts rolling velocities while cell deformability is needed to model adhesion. These results would suggest that, within microvascular networks, blood rheology and inflammation contribute similarly to CTC deposition thereby facilitating the formation of metastatic niches along the entire network, including the healthy endothelium. In microfluidic based assays, neglecting blood rheology would significantly underestimate the metastatic potential of cancer cells

Strong confinement-induced engineering of the g factor and lifetime of conduction electron spins in Ge quantum wells

Control of electron spin coherence via external fields is fundamental in spintronics. Its implementation demands a host material that accommodates the desirable but contrasting requirements of spin robustness against relaxation mechanisms and sizeable coupling between spin and orbital motion of the carriers. Here, we focus on Ge, which is a prominent candidate for shuttling spin quantum bits into the mainstream Si electronics. So far, however, the intrinsic spin-dependent phenomena of free electrons in conventional Ge/Si heterojunctions have proved to be elusive because of epitaxy constraints and an unfavourable band alignment. We overcome these fundamental limitations by investigating a two-dimensional electron gas in quantum wells of pure Ge grown on Si. These epitaxial systems demonstrate exceptionally long spin lifetimes. In particular, by fine-tuning quantum confinement we demonstrate that the electron Landé g factor can be engineered in our CMOS-compatible architecture over a range previously inaccessible for Si spintronics