Canard Cycles and Poincar\'e Index of Non-Smooth Vector Fields on the Plane

This paper is concerned with closed orbits of non-smooth vector fields on the plane. For a subclass of non-smooth vector fields we provide necessary and sufficient conditions for the existence of canard kind solutions. By means of a regularization we prove that the canard cycles are singular orbits of singular perturbation problems which are limit periodic sets of a sequence of limit cycles. Moreover, we generalize the Poincar\'e Index for non-smooth vector fields.Comment: 20 pages, 25 figure

The regularized visible fold revisited

The planar visible fold is a simple singularity in piecewise smooth systems. In this paper, we consider singularly perturbed systems that limit to this piecewise smooth bifurcation as the singular perturbation parameter $\epsilon\rightarrow 0$. Alternatively, these singularly perturbed systems can be thought of as regularizations of their piecewise counterparts. The main contribution of the paper is to demonstrate the use of consecutive blowup transformations in this setting, allowing us to obtain detailed information about a transition map near the fold under very general assumptions. We apply this information to prove, for the first time, the existence of a locally unique saddle-node bifurcation in the case where a limit cycle, in the singular limit $\epsilon\rightarrow 0$, grazes the discontinuity set. We apply this result to a mass-spring system on a moving belt described by a Stribeck-type friction law

Antidromic vasodilatation and the migraine mechanism

Despite the fact that an unprecedented series of new discoveries in neurochemistry, neuroimaging, genetics and clinical pharmacology accumulated over the last 20 years has significantly increased our current knowledge, the underlying mechanism of the migraine headache remains elusive. The present review article addresses, from early evidence that emerged at the end of the nineteenth century, the role of ‘antidromic vasodilatation’ as part of the more general phenomenon, currently defined as neurogenic inflammation, in the unique type of pain reported by patients suffering from migraine headaches. The present paper describes distinctive orthodromic and antidromic properties of a subset of somatosensory neurons, the vascular- and neurobiology of peptides contained in these neurons, and the clinical–pharmacological data obtained in recent investigations using provocation tests in experimental animals and human beings. Altogether, previous and recent data underscore that antidromic vasodilatation, originating from the activation of peptidergic somatosensory neurons, cannot yet be discarded as a major contributing mechanism of the throbbing head pain and hyperalgesia of migraine

Defining Kawasaki disease and pediatric inflammatory multisystem syndrome-temporally associated to SARS-CoV-2 infection during SARS-CoV-2 epidemic in Italy: results from a national, multicenter survey

Background: There is mounting evidence on the existence of a Pediatric Inflammatory Multisystem Syndrome-temporally associated to SARS-CoV-2 infection (PIMS-TS), sharing similarities with Kawasaki Disease (KD). The main outcome of the study were to better characterize the clinical features and the treatment response of PIMS-TS and to explore its relationship with KD determining whether KD and PIMS are two distinct entities. Methods: The Rheumatology Study Group of the Italian Pediatric Society launched a survey to enroll patients diagnosed with KD (Kawasaki Disease Group - KDG) or KD-like (Kawacovid Group - KCG) disease between February 1st 2020, and May 31st 2020. Demographic, clinical, laboratory data, treatment information, and patients' outcome were collected in an online anonymized database (RedCAP®). Relationship between clinical presentation and SARS-CoV-2 infection was also taken into account. Moreover, clinical characteristics of KDG during SARS-CoV-2 epidemic (KDG-CoV2) were compared to Kawasaki Disease patients (KDG-Historical) seen in three different Italian tertiary pediatric hospitals (Institute for Maternal and Child Health, IRCCS "Burlo Garofolo", Trieste; AOU Meyer, Florence; IRCCS Istituto Giannina Gaslini, Genoa) from January 1st 2000 to December 31st 2019. Chi square test or exact Fisher test and non-parametric Wilcoxon Mann-Whitney test were used to study differences between two groups. Results: One-hundred-forty-nine cases were enrolled, (96 KDG and 53 KCG). KCG children were significantly older and presented more frequently from gastrointestinal and respiratory involvement. Cardiac involvement was more common in KCG, with 60,4% of patients with myocarditis. 37,8% of patients among KCG presented hypotension/non-cardiogenic shock. Coronary artery abnormalities (CAA) were more common in the KDG. The risk of ICU admission were higher in KCG. Lymphopenia, higher CRP levels, elevated ferritin and troponin-T characterized KCG. KDG received more frequently immunoglobulins (IVIG) and acetylsalicylic acid (ASA) (81,3% vs 66%; p = 0.04 and 71,9% vs 43,4%; p = 0.001 respectively) as KCG more often received glucocorticoids (56,6% vs 14,6%; p < 0.0001). SARS-CoV-2 assay more often resulted positive in KCG than in KDG (75,5% vs 20%; p < 0.0001). Short-term follow data showed minor complications. Comparing KDG with a KD-Historical Italian cohort (598 patients), no statistical difference was found in terms of clinical manifestations and laboratory data. Conclusion: Our study suggests that SARS-CoV-2 infection might determine two distinct inflammatory diseases in children: KD and PIMS-TS. Older age at onset and clinical peculiarities like the occurrence of myocarditis characterize this multi-inflammatory syndrome. Our patients had an optimal response to treatments and a good outcome, with few complications and no deaths

Italian guidelines for primary headaches: 2012 revised version

The first edition of the Italian diagnostic and therapeutic guidelines for primary headaches in adults was published in J Headache Pain 2(Suppl. 1):105–190 (2001). Ten years later, the guideline committee of the Italian Society for the Study of Headaches (SISC) decided it was time to update therapeutic guidelines. A literature search was carried out on Medline database, and all articles on primary headache treatments in English, German, French and Italian published from February 2001 to December 2011 were taken into account. Only randomized controlled trials (RCT) and meta-analyses were analysed for each drug. If RCT were lacking, open studies and case series were also examined. According to the previous edition, four levels of recommendation were defined on the basis of levels of evidence, scientific strength of evidence and clinical effectiveness. Recommendations for symptomatic and prophylactic treatment of migraine and cluster headache were therefore revised with respect to previous 2001 guidelines and a section was dedicated to non-pharmacological treatment. This article reports a summary of the revised version published in extenso in an Italian version

Gaia Early Data Release 3: Summary of the contents and survey properties

ABSTRACT: Context. We present the early installment of the third Gaia data release, Gaia EDR3, consisting of astrometry and photometry for 1.8 billion sources brighter than magnitude 21, complemented with the list of radial velocities from Gaia DR2. Aims. A summary of the contents of Gaia EDR3 is presented, accompanied by a discussion on the differences with respect to Gaia DR2 and an overview of the main limitations which are present in the survey. Recommendations are made on the responsible use of Gaia EDR3 results. Methods. The raw data collected with the Gaia instruments during the first 34 months of the mission have been processed by the Gaia Data Processing and Analysis Consortium and turned into this early third data release, which represents a major advance with respect to Gaia DR2 in terms of astrometric and photometric precision, accuracy, and homogeneity. Results. Gaia EDR3 contains celestial positions and the apparent brightness in G for approximately 1.8 billion sources. For 1.5 billion of those sources, parallaxes, proper motions, and the (GBP ? GRP) colour are also available. The passbands for G, GBP, and GRP are provided as part of the release. For ease of use, the 7 million radial velocities from Gaia DR2 are included in this release, after the removal of a small number of spurious values. New radial velocities will appear as part of Gaia DR3. Finally, Gaia EDR3 represents an updated materialisation of the celestial reference frame (CRF) in the optical, the Gaia-CRF3, which is based solely on extragalactic sources. The creation of the source list for Gaia EDR3 includes enhancements that make it more robust with respect to high proper motion stars, and the disturbing effects of spurious and partially resolved sources. The source list is largely the same as that for Gaia DR2, but it does feature new sources and there are some notable changes. The source list will not change for Gaia DR3. Conclusions. Gaia EDR3 represents a significant advance over Gaia DR2, with parallax precisions increased by 30 per cent, proper motion precisions increased by a factor of 2, and the systematic errors in the astrometry suppressed by 30-40% for the parallaxes and by a factor ~2.5 for the proper motions. The photometry also features increased precision, but above all much better homogeneity across colour, magnitude, and celestial position. A single passband for G, GBP, and GRP is valid over the entire magnitude and colour range, with no systematics above the 1% levelThe Gaia mission and data processing have financially been supported by ; the Spanish Ministry of Economy (MINECO/FEDER, UE) through grants ESP2016-80079-C2-1-R, ESP2016-80079-C2-2-R, RTI2018-095076-B-C21, RTI2018-095076-B-C22, BES-2016-078499, and BES-2017-083126 and the Juan de la Cierva formación 2015 grant FJCI-2015-2671, the Spanish Ministry of Education, Culture, and Sports through grant FPU16/03827, the Spanish Ministry of Science and Innovation (MICINN) through grant AYA2017-89841P for project “Estudio de las propiedades de los fósiles estelares en el entorno del Grupo Local” and through grant TIN2015-65316-P for project “Computación de Altas Prestaciones VII

Pulsations in main sequence OBAF-type stars

CONTEXT: The third Gaia data release provides photometric time series covering 34 months for about 10 million stars. For many of those stars, a characterisation in Fourier space and their variability classification are also provided. This paper focuses on intermediate- to high-mass (IHM) main sequence pulsators (M ≥  1.3 M⊙) of spectral types O, B, A, or F, known as β Cep, slowly pulsating B (SPB), δ Sct, and γ Dor stars. These stars are often multi-periodic and display low amplitudes, making them challenging targets to analyse with sparse time series. AIMS: We investigate the extent to which the sparse Gaia DR3 data can be used to detect OBAF-type pulsators and discriminate them from other types of variables. We aim to probe the empirical instability strips and compare them with theoretical predictions. The most populated variability class is that of the δ Sct variables. For these stars, we aim to confirm their empirical period-luminosity (PL) relation, and verify the relation between their oscillation amplitude and rotation. METHODS: All datasets used in this analysis are part of the Gaia DR3 data release. The photometric time series were used to perform a Fourier analysis, while the global astrophysical parameters necessary for the empirical instability strips were taken from the Gaia DR3 gspphot tables, and the v sin i data were taken from the Gaia DR3 esphs tables. The δ Sct PL relation was derived using the same photometric parallax method as the one recently used to establish the PL relation for classical Cepheids using Gaia data. RESULTS: We show that for nearby OBAF-type pulsators, the Gaia DR3 data are precise and accurate enough to pinpoint them in the Hertzsprung-Russell (HR) diagram. We find empirical instability strips covering broader regions than theoretically predicted. In particular, our study reveals the presence of fast rotating gravity-mode pulsators outside the strips, as well as the co-existence of rotationally modulated variables inside the strips as reported before in the literature. We derive an extensive period–luminosity relation for δ Sct stars and provide evidence that the relation features different regimes depending on the oscillation period. We demonstrate how stellar rotation attenuates the amplitude of the dominant oscillation mode of δ Sct stars. CONCLUSIONS: The Gaia DR3 time-series photometry already allows for the detection of the dominant (non-)radial oscillation mode in about 100 000 intermediate- and high-mass dwarfs across the entire sky. This detection capability will increase as the time series becomes longer, allowing the additional delivery of frequencies and amplitudes of secondary pulsation modes

Gaia Data Release 3: Mapping the asymmetric disc of the Milky Way

With the most recent Gaia data release the number of sources with complete 6D phase space information (position and velocity) has increased to well over 33 million stars, while stellar astrophysical parameters are provided for more than 470 million sources, in addition to the identification of over 11 million variable stars. Using the astrophysical parameters and variability classifications provided in Gaia DR3, we select various stellar populations to explore and identify non-axisymmetric features in the disc of the Milky Way in both configuration and velocity space. Using more about 580 thousand sources identified as hot OB stars, together with 988 known open clusters younger than 100 million years, we map the spiral structure associated with star formation 4-5 kpc from the Sun. We select over 2800 Classical Cepheids younger than 200 million years, which show spiral features extending as far as 10 kpc from the Sun in the outer disc. We also identify more than 8.7 million sources on the red giant branch (RGB), of which 5.7 million have line-of-sight velocities, allowing the velocity field of the Milky Way to be mapped as far as 8 kpc from the Sun, including the inner disc. The spiral structure revealed by the young populations is consistent with recent results using Gaia EDR3 astrometry and source lists based on near infrared photometry, showing the Local (Orion) arm to be at least 8 kpc long, and an outer arm consistent with what is seen in HI surveys, which seems to be a continuation of the Perseus arm into the third quadrant. Meanwhile, the subset of RGB stars with velocities clearly reveals the large scale kinematic signature of the bar in the inner disc, as well as evidence of streaming motions in the outer disc that might be associated with spiral arms or bar resonances. (abridged

What is the role of the placebo effect for pain relief in neurorehabilitation? Clinical implications from the Italian Consensus Conference on Pain in Neurorehabilitation

Background: It is increasingly acknowledged that the outcomes of medical treatments are influenced by the context of the clinical encounter through the mechanisms of the placebo effect. The phenomenon of placebo analgesia might be exploited to maximize the efficacy of neurorehabilitation treatments. Since its intensity varies across neurological disorders, the Italian Consensus Conference on Pain in Neurorehabilitation (ICCP) summarized the studies on this field to provide guidance on its use. Methods: A review of the existing reviews and meta-analyses was performed to assess the magnitude of the placebo effect in disorders that may undergo neurorehabilitation treatment. The search was performed on Pubmed using placebo, pain, and the names of neurological disorders as keywords. Methodological quality was assessed using a pre-existing checklist. Data about the magnitude of the placebo effect were extracted from the included reviews and were commented in a narrative form. Results: 11 articles were included in this review. Placebo treatments showed weak effects in central neuropathic pain (pain reduction from 0.44 to 0.66 on a 0-10 scale) and moderate effects in postherpetic neuralgia (1.16), in diabetic peripheral neuropathy (1.45), and in pain associated to HIV (1.82). Moderate effects were also found on pain due to fibromyalgia and migraine; only weak short-term effects were found in complex regional pain syndrome. Confounding variables might have influenced these results. Clinical implications: These estimates should be interpreted with caution, but underscore that the placebo effect can be exploited in neurorehabilitation programs. It is not necessary to conceal its use from the patient. Knowledge of placebo mechanisms can be used to shape the doctor-patient relationship, to reduce the use of analgesic drugs and to train the patient to become an active agent of the therapy