Periodic solutions for planar autonomous systems with nonsmooth periodic perturbations

In this paper we consider a class of planar autonomous systems having an isolated limit cycle x_0 of smallest period T>0 such that the associated linearized system around it has only one characteristic multiplier with absolute value 1. We consider two functions, defined by means of the eigenfunctions of the adjoint of the linearized system, and we formulate conditions in terms of them in order to have the existence of two geometrically distinct families of T-periodic solutions of the autonomous system when it is perturbed by nonsmooth T-periodic nonlinear terms of small amplitude. We also show the convergence of these periodic solutions to x_0 as the perturbation disappears and we provide an estimation of the rate of convergence. The employed methods are mainly based on the theory of topological degree and its properties that allow less regularity on the data than that required by the approach, commonly employed in the existing literature on this subject, based on various versions of the implicit function theorem.Comment: To appear in J. Math. Anal. App

Ventricular arrhythmias in young competitive athletes: Prevalence, determinants, and underlying substrate

Whether ventricular arrhythmias (VAs) represent a feature of the adaptive changes of the athlete's heart remains elusive. We aimed to assess the prevalence, determinants, and underlying substrates of VAs in young competitive athletes.Background--Whether ventricular arrhythmias (VAs) represent a feature of the adaptive changes of the athlete's heart remains elusive. We aimed to assess the prevalence, determinants, and underlying substrates of VAs in young competitive athletes. Method and Results--We studied 288 competitive athletes (age range, 16-35 years; median age, 21 years) and 144 sedentary individuals matched for age and sex who underwent 12-lead 24-hour ambulatory electrocardiographic monitoring. VAs were evaluated in terms of number, complexity (ie, couplet, triplet, or nonsustained ventricular tachycardia), exercise inducibility, and morphologic features. Twenty-eight athletes (10%) and 13 sedentary individuals (11%) showed > 10 isolated premature ventricular beats (PVBs) or 651 complex VA (P=0.81). Athletes with > 10 isolated PVBs or 651 complex VA were older (median age, 26 versus 20 years; P=0.008) but did not differ with regard to type of sport, hours of training, and years of activity compared with the remaining athletes. All athletes with > 10 isolated PVBs or 651 complex VA had a normal echocardiographic examination; 17 of them showing > 500 isolated PVBs, exercise-induced PVBs, and/or complex VA underwent additional cardiac magnetic resonance, which demonstrated nonischemic left ventricular late gadolinium enhancement in 3 athletes with right bundle branch block PVBs morphologic features. Conclusions--The prevalence of > 10 isolated PVBs or 651 complex VA at 24-hour ambulatory electrocardiographic monitoring did not differ between young competitive athletes and sedentary individuals and was unrelated to type, intensity, and years of sports practice. An underlying myocardial substrate was uncommon and distinctively associated with right bundle branch block VA morphologic features

On complex and real identifiability of tensors

We report about the state of the art on complex and real generic identifiability of tensors, we describe some of our recent results obtained in [6] and we present perspectives on the subject.Comment: To appear on Rivista di Matematica dell'Universit\`a di Parma, Volume 8, Number 2, 2017, pages 367-37

Waring-like decompositions of polynomials - 1

Let $F$ be a homogeneous form of degree $d$ in $n$ variables. A Waring decomposition of $F$ is a way to express $F$ as a sum of $d^{th}$ powers of linear forms. In this paper we consider the decompositions of a form as a sum of expressions, each of which is a fixed monomial evaluated at linear forms.Comment: 12 pages; Section 5 added in this versio

Collaboration in Social Networks

The very notion of social network implies that linked individuals interact repeatedly with each other. This allows them not only to learn successful strategies and adapt to them, but also to condition their own behavior on the behavior of others, in a strategic forward looking manner. Game theory of repeated games shows that these circumstances are conducive to the emergence of collaboration in simple games of two players. We investigate the extension of this concept to the case where players are engaged in a local contribution game and show that rationality and credibility of threats identify a class of Nash equilibria -- that we call "collaborative equilibria" -- that have a precise interpretation in terms of sub-graphs of the social network. For large network games, the number of such equilibria is exponentially large in the number of players. When incentives to defect are small, equilibria are supported by local structures whereas when incentives exceed a threshold they acquire a non-local nature, which requires a "critical mass" of more than a given fraction of the players to collaborate. Therefore, when incentives are high, an individual deviation typically causes the collapse of collaboration across the whole system. At the same time, higher incentives to defect typically support equilibria with a higher density of collaborators. The resulting picture conforms with several results in sociology and in the experimental literature on game theory, such as the prevalence of collaboration in denser groups and in the structural hubs of sparse networks

Inhibition of Hedgehog-dependent tumors and cancer stem cells by a newly identified naturally occurring chemotype

Hedgehog (Hh) inhibitors have emerged as valid tools in the treatment of a wide range of cancers. Indeed, aberrant activation of the Hh pathway occurring either by ligand-dependent or -independent mechanisms is a key driver in tumorigenesis. The smoothened (Smo) receptor is one of the main upstream transducers of the Hh signaling and is a validated target for the development of anticancer compounds, as underlined by the FDA-approved Smo antagonist Vismodegib (GDC-0449/Erivedge) for the treatment of basal cell carcinoma. However, Smo mutations that confer constitutive activity and drug resistance have emerged during treatment with Vismodegib. For this reason, the development of new effective Hh inhibitors represents a major challenge for cancer therapy. Natural products have always represented a unique source of lead structures in drug discovery, and in recent years have been used to modulate the Hh pathway at multiple levels. Here, starting from an in house library of natural compounds and their derivatives, we discovered novel chemotypes of Hh inhibitors by mean of virtual screening against the crystallographic structure of Smo. Hh functional based assay identified the chalcone derivative 12 as the most effective Hh inhibitor within the test set. The chalcone 12 binds the Smo receptor and promotes the displacement of Bodipy-Cyclopamine in both Smo WT and drug-resistant Smo mutant. Our molecule stands as a promising Smo antagonist able to specifically impair the growth of Hh-dependent tumor cells in vitro and in vivo and medulloblastoma stem-like cells and potentially overcome the associated drug resistance

Performance of the TOTEM Detectors at the LHC

The TOTEM Experiment is designed to measure the total proton-proton cross-section with the luminosity-independent method and to study elastic and diffractive pp scattering at the LHC. To achieve optimum forward coverage for charged particles emitted by the pp collisions in the interaction point IP5, two tracking telescopes, T1 and T2, are installed on each side of the IP in the pseudorapidity region 3.1 < = |eta | < = 6.5, and special movable beam-pipe insertions - called Roman Pots (RP) - are placed at distances of +- 147 m and +- 220 m from IP5. This article describes in detail the working of the TOTEM detector to produce physics results in the first three years of operation and data taking at the LHC.Comment: 40 pages, 31 figures, submitted to Int. J. Mod. Phys.

Search for GeV Gamma-ray Counterparts of Gravitational Wave Events by CALET

We present results on searches for gamma-ray counterparts of the LIGO/Virgo gravitational-wave events using CALorimetric Electron Telescope ({\sl CALET}) observations. The main instrument of {\sl CALET}, CALorimeter (CAL), observes gamma-rays from $\sim1$ GeV up to 10 TeV with a field of view of nearly 2 sr. In addition, the {\sl CALET} gamma-ray burst monitor (CGBM) views $\sim$3 sr and $\sim2\pi$ sr of the sky in the 7 keV -- 1 MeV and the 40 keV -- 20 MeV bands, respectively, by using two different crystal scintillators. The {\sl CALET} observations on the International Space Station started in October 2015, and here we report analyses of events associated with the following gravitational wave events: GW151226, GW170104, GW170608, GW170814 and GW170817. Although only upper limits on gamma-ray emission are obtained, they correspond to a luminosity of $10^{49}\sim10^{53}$ erg s$^{-1}$ in the GeV energy band depending on the distance and the assumed time duration of each event, which is approximately the order of luminosity of typical short gamma-ray bursts. This implies there will be a favorable opportunity to detect high-energy gamma-ray emission in further observations if additional gravitational wave events with favorable geometry will occur within our field-of-view. We also show the sensitivity of {\sl CALET} for gamma-ray transient events which is the order of $10^{-7}$~erg\,cm$^{-2}$\,s$^{-1}$ for an observation of 100~s duration.Comment: 12 pages, 8 figures, 1 table. Accepted for publication in Astrophysical Journa

Search for Chargino-Neutralino Associated Production at the Fermilab Tevatron Collider

We have searched in $p \bar{p}$ collisions at $\sqrt{s}$ = 1.8 TeV for events with three charged leptons and missing transverse energy. In the Minimal Supersymmetric Standard Model, we expect trilepton events from chargino-neutralino (\chione \chitwo) pair production, with subsequent decay into leptons. We observe no candidate $e^+e^-e^\pm$, $e^+e^-\mu^\pm$, $e^\pm\mu^+\mu^-$ or $\mu^+\mu^-\mu^\pm$ events in 106 pb$^{-1}$ integrated luminosity. We present limits on the sum of the branching ratios times cross section for the four channels: \sigma_{\chione\chitwo}\cdot BR(\chione\chitwo\to 3\ell+X) 81.5 \mgev\sp and M_\chitwo > 82.2 \mgev\sp for $\tan\beta=2$, $\mu =-600$~\mgev\sp and M_\squark= M_\gluino.Comment: 9 pages and 3 figure

Measurement of the Dipion Mass Spectrum in X(3872) -> J/Psi Pi+ Pi- Decays

We measure the dipion mass spectrum in X(3872)--> J/Psi Pi+ Pi- decays using 360 pb-1 of pbar-p collisions at 1.96 TeV collected with the CDF II detector. The spectrum is fit with predictions for odd C-parity (3S1, 1P1, and 3DJ) charmonia decaying to J/Psi Pi+ Pi-, as well as even C-parity states in which the pions are from Rho0 decay. The latter case also encompasses exotic interpretations, such as a D0-D*0Bar molecule. Only the 3S1 and J/Psi Rho hypotheses are compatible with our data. Since 3S1 is untenable on other grounds, decay via J/Psi Rho is favored, which implies C=+1 for the X(3872). Models for different J/Psi-Rho angular momenta L are considered. Flexibility in the models, especially the introduction of Rho-Omega interference, enable good descriptions of our data for both L=0 and 1.Comment: 7 pages, 4 figures -- Submitted to Phys. Rev. Let