On the Whitham hierarchy: dressing scheme, string equations and additional symmetrie

A new description of the universal Whitham hierarchy in terms of a factorization problem in the Lie group of canonical transformations is provided. This scheme allows us to give a natural description of dressing transformations, string equations and additional symmetries for the Whitham hierarchy. We show how to dress any given solution and prove that any solution of the hierarchy may be undressed, and therefore comes from a factorization of a canonical transformation. A particulary important function, related to the $\tau$-function, appears as a potential of the hierarchy. We introduce a class of string equations which extends and contains previous classes of string equations considered by Krichever and by Takasaki and Takebe. The scheme is also applied for an convenient derivation of additional symmetries. Moreover, new functional symmetries of the Zakharov extension of the Benney gas equations are given and the action of additional symmetries over the potential in terms of linear PDEs is characterized

On the Whitham hierarchy: dressing scheme, string equations and additional symmetrie

A new description of the universal Whitham hierarchy in terms of a factorization problem in the Lie group of canonical transformations is provided. This scheme allows us to give a natural description of dressing transformations, string equations and additional symmetries for the Whitham hierarchy. We show how to dress any given solution and prove that any solution of the hierarchy may be undressed, and therefore comes from a factorization of a canonical transformation. A particulary important function, related to the $\tau$-function, appears as a potential of the hierarchy. We introduce a class of string equations which extends and contains previous classes of string equations considered by Krichever and by Takasaki and Takebe. The scheme is also applied for an convenient derivation of additional symmetries. Moreover, new functional symmetries of the Zakharov extension of the Benney gas equations are given and the action of additional symmetries over the potential in terms of linear PDEs is characterized

L1CAM binds ErbB receptors through Ig-like domains coupling cell adhesion and neuregulin signalling.

During nervous system development different cell-to-cell communication mechanisms operate in parallel guiding migrating neurons and growing axons to generate complex arrays of neural circuits. How such a system works in coordination is not well understood. Cross-regulatory interactions between different signalling pathways and redundancy between them can increase precision and fidelity of guidance systems. Immunoglobulin superfamily proteins of the NCAM and L1 families couple specific substrate recognition and cell adhesion with the activation of receptor tyrosine kinases. Thus it has been shown that L1CAM-mediated cell adhesion promotes the activation of the EGFR (erbB1) from Drosophila to humans. Here we explore the specificity of the molecular interaction between L1CAM and the erbB receptor family. We show that L1CAM binds physically erbB receptors in both heterologous systems and the mammalian developing brain. Different Ig-like domains located in the extracellular part of L1CAM can support this interaction. Interestingly, binding of L1CAM to erbB enhances its response to neuregulins. During development this may synergize with the activation of erbB receptors through L1CAM homophilic interactions, conferring diffusible neuregulins specificity for cells or axons that interact with the substrate through L1CAM

`Interpolating' differential reductions of multidimensional integrable hierarchies

We transfer the scheme of constructing differential reductions, developed recently for the case of the Manakov-Santini hierarchy, to the general multidimensional case. We consider in more detail the four-dimensional case, connected with the second heavenly equation and its generalization proposed by Dunajski. We give a characterization of differential reductions in terms of the Lax-Sato equations as well as in the framework of the dressing method based on nonlinear Riemann-Hilbert problem.Comment: Based on the talk at NLPVI, Gallipoli, 15 page

Integrable Deformations of Algebraic Curves

A general scheme for determining and studying integrable deformations of algebraic curves, based on the use of Lenard relations, is presented. We emphasize the use of several types of dynamical variables : branches, power sums and potentials.Comment: 10 Pages, Proceedings Workshop-Nonlinear Physics: Theory and Experiment, Gallipoli 200

Fluctuation induced hopping and spin polaron transport

We study the motion of free magnetic polarons in a paramagnetic background of fluctuating local moments. The polaron can tunnel only to nearby regions of local moments when these fluctuate into alignment. We propose this fluctuation induced hopping as a new transport mechanism for the spin polaron. We calculate the diffusion constant for fluctuation induced hopping from the rate at which local moments fluctuate into alignment. The electrical resistivity is then obtained via the Einstein relation. We suggest that the proposed transport mechanism is relevant in the high temperature phase of the Mn pyrochlore colossal magneto resistance compounds and Europium hexaboride.Comment: 8 pages, 3 figure

Dispersionless scalar integrable hierarchies, Whitham hierarchy and the quasi-classical dbar-dressing method

The quasi-classical limit of the scalar nonlocal dbar-problem is derived and a quasi-classical version of the dbar-dressing method is presented. Dispersionless KP, mKP and 2DTL hierarchies are discussed as illustrative examples. It is shown that the universal Whitham hierarchy it is nothing but the ring of symmetries for the quasi-classical dbar-problem. The reduction problem is discussed and, in particular, the d2DTL equation of B type is derived.Comment: LaTex file,19 page

AMoDSim: An Efficient and Modular Simulation Framework for Autonomous Mobility on Demand

Urban transportation of next decade is expected to be disrupted by Autonomous Mobility on Demand (AMoD): AMoD providers will collect ride requests from users and will dispatch a fleet of autonomous vehicles to satisfy requests in the most efficient way. Differently from current ride sharing systems, in which driver behavior has a clear impact on the system, AMoD systems will be exclusively determined by the dispatching logic. As a consequence, a recent interest in the Operations Research and Computer Science communities has focused on this control logic. The new propositions and methodologies are generally evaluated via simulation. Unfortunately, there is no simulation platform that has emerged as reference, with the consequence that each author uses her own custom-made simulator, applicable only in her specific study, with no aim of generalization and without public release. This slows down the progress in the area as researchers cannot build on each other's work and cannot share, reproduce and verify the results. The goal of this paper is to present AMoDSim, an open-source simulation platform aimed to fill this gap and accelerate research in future ride sharing systems

Effect of Exercise on Inflammation in Hemodialysis Patients: A Systematic Review

Background: In recent years, physical exercise has been investigated for its potential as a therapeutic tool in patients with end-stage renal disease (ESRD) undergoing hemodialysis maintenance treatment (HD). It has been shown that regular practice of moderate-intensity exercise can improve certain aspects of immune function and exert anti-inflammatory effects, having been associated with low levels of pro-inflammatory cytokines and high levels of anti-inflammatory cytokines. Purpose: The aim of this review is to examine the studies carried out in this population that analyzed the effect of intradialytic exercise on the inflammatory state and evaluate which exercise modality is most effective. Methods: The search was carried out in the MEDLINE, CINAHL Web of Science and Cochrane Central Register of Controlled Trials databases from inception to June 2022. The PEDro scale was used to assess methodological quality, and the Cochrane Risk of Bias Tool and MINORS were used to evaluate the risk of bias. The quality of evidence was assessed with GRADE scale. The outcome measures were systemic inflammation biomarkers. Results: Mixed results were found in terms of improving inflammation biomarkers, such as CRP, IL-6 or TNFα, after exercise. Aerobic exercise seems to improve systemic inflammation when performed at medium intensity while resistance training produced better outcomes when performed at high intensity. However, some studies reported no differences after exercise and these results should be taken with caution. Conclusions: The low quality of the evidence suggests that aerobic and resistance exercise during HD treatment improves systemic inflammation biomarkers in patients with ESRD. In any case, interventions that increase physical activity in patients with ESRD are of vital importance as sedentary behaviors are associated with mortality. More studies are needed to affirm solid conclusions and to make intervention parameters, such as modality, dose, intensity or duration, sufficiently clear

Line Broadening in Field Metal-poor Red Giant and Red Horizontal Branch Stars

We report 349 radial velocities for 45 metal-poor field red giant and red horizontal branch stars. We have have identified one new spectroscopic binary, HD 4306, and one possible such system, HD 184711. We also report 57 radial velocities for 11 of the 91 stars reported on previously by Carney et al. (2003). As was found in the previous study, radial velocity "jitter" is present in many of the most luminous stars. Excluding stars showing spectroscopic binary orbital motion, all 7 of the red giants with M(V) <= -2.0 display jitter, as well as 3 of the 14 stars with -2.0 <= M(V) <= -1.4. We have also measured line broadening in all of the new spectra, using synthetic spectra as templates. The most luminous red giants show significant line broadening, as do many of the red horizontal branch stars, and we discuss briefly possible causes.Comment: To appear in the Astronomical Journa