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

Symmetric periodic orbits near heteroclinic loops at infinity for a class of polynomial vector fields

For polynomial vector fields in R3, in general, it is very difficult to detect the existence of an open set of periodic orbits in their phase portraits. Here, we characterize a class of polynomial vector fields of arbitrary even degree having an open set of periodic orbits. The main two tools for proving this result are, first, the existence in the phase portrait of a symmetry with respect to a plane and, second, the existence of two symmetric heteroclinic loops

The ESPERIA satellite project for detecting seismo-associated effects in the topside ionosphere. First instrumental tests in space

In recent times, ionospheric and magnetospheric perturbations constituted by radiation belt particle precipitations, variations of temperature and density of ionic and electronic components of ionospheric plasma as well as electric and magnetic field fluctuations have been detected on board of the LEO satellites and associated with earthquake preparation and occurrence. Several mechanisms have been suggested as justifying the seismoelectromagnetic phenomena observed in the upper lithosphere and in the topside ionosphere before, during and after an earthquake. Their propagation in these media has also been investigated, but physical knowledge of such processes is below standard. Consequently, coordinated space and ground-based observations based on data gathered simultaneously in space and at the Earth's surface are needed to investigate seismo-associated phenomena. To this end, the ESPERIA space mission project has been designed for the Italian Space Agency (ASI). To date, a few instruments of its payload have been built and tested in space. This paper reports on the justification, science background, and characteristics of the ESPERIA mission project as well as the description and testing of ESPERIA Instruments (ARINA and LAZIO-EGLE) in space

Cutting and Shuffling a Line Segment: Mixing by Interval Exchange Transformations

We present a computational study of finite-time mixing of a line segment by cutting and shuffling. A family of one-dimensional interval exchange transformations is constructed as a model system in which to study these types of mixing processes. Illustrative examples of the mixing behaviors, including pathological cases that violate the assumptions of the known governing theorems and lead to poor mixing, are shown. Since the mathematical theory applies as the number of iterations of the map goes to infinity, we introduce practical measures of mixing (the percent unmixed and the number of intermaterial interfaces) that can be computed over given (finite) numbers of iterations. We find that good mixing can be achieved after a finite number of iterations of a one-dimensional cutting and shuffling map, even though such a map cannot be considered chaotic in the usual sense and/or it may not fulfill the conditions of the ergodic theorems for interval exchange transformations. Specifically, good shuffling can occur with only six or seven intervals of roughly the same length, as long as the rearrangement order is an irreducible permutation. This study has implications for a number of mixing processes in which discontinuities arise either by construction or due to the underlying physics.Comment: 21 pages, 10 figures, ws-ijbc class; accepted for publication in International Journal of Bifurcation and Chao

Phenotypic, morphological, and metabolic characterization of vascular-spheres from human vascular mesenchymal stem cells

The ability to form spheroids under non-adherent conditions is a well-known property of human mesenchymal stem cells (hMSCs), in addition to stemness and multilineage differentiation features. In the present study, we tested the ability of hMSCs isolated from the vascular wall (hVW-MSCs) to grow as spheres, and provide a characterization of this 3D model. hVW-MSCs were isolated from femoral arteries through enzymatic digestion. Spheres were obtained using ultra-low attachment and hanging drop methods. Immunophenotype and pluripotent genes (SOX-2, OCT-4, NANOG) were analyzed by immunocytochemistry and real-time PCR, respectively. Spheres histological and ultrastructural architecture were examined. Cell viability and proliferative capacity were measured using LIVE/DEATH assay and ki-67 proliferation marker. Metabolomic profile was obtained with liquid chromatography–mass spectrometry. In 2D, hVW-MSCs were spindle-shaped, expressed mesenchymal antigens, and displayed mesengenic potential. 3D cultures of hVW-MSCs were CD44+, CD105low, CD90low, exhibited a low propensity to enter the cell cycle as indicated by low percentage of ki-67 expression and accumulated intermediate metabolites pointing to slowed metabolism. The 3D model of hVW-MSCs exhibits stemness, dormancy and slow metabolism, typically observed in stem cell niches. This culture strategy can represent an accurate model to investigate hMSCs features for future clinical applications in the vascular field

Volume-preserving normal forms of Hopf-zero singularity

A practical method is described for computing the unique generator of the algebra of first integrals associated with a large class of Hopf-zero singularity. The set of all volume-preserving classical normal forms of this singularity is introduced via a Lie algebra description. This is a maximal vector space of classical normal forms with first integral; this is whence our approach works. Systems with a non-zero condition on their quadratic parts are considered. The algebra of all first integrals for any such system has a unique (modulo scalar multiplication) generator. The infinite level volume-preserving parametric normal forms of any non-degenerate perturbation within the Lie algebra of any such system is computed, where it can have rich dynamics. The associated unique generator of the algebra of first integrals are derived. The symmetry group of the infinite level normal forms are also discussed. Some necessary formulas are derived and applied to appropriately modified R\"{o}ssler and generalized Kuramoto--Sivashinsky equations to demonstrate the applicability of our theoretical results. An approach (introduced by Iooss and Lombardi) is applied to find an optimal truncation for the first level normal forms of these examples with exponentially small remainders. The numerically suggested radius of convergence (for the first integral) associated with a hypernormalization step is discussed for the truncated first level normal forms of the examples. This is achieved by an efficient implementation of the results using Maple

Absence of RNA-binding protein FXR2P prevents prolonged phase of kainate-induced seizures.

Status epilepticus (SE) is a condition in which seizures are not self-terminating and thereby pose a serious threat to the patient's life. The molecular mechanisms underlying SE are likely heterogeneous and not well understood. Here, we reveal a role for the RNA-binding protein Fragile X-Related Protein 2 (FXR2P) in SE. Fxr2 KO mice display reduced sensitivity specifically to kainic acid-induced SE. Immunoprecipitation of FXR2P coupled to next-generation sequencing of associated mRNAs shows that FXR2P targets are enriched in genes that encode glutamatergic post-synaptic components. Of note, the FXR2P target transcriptome has a significant overlap with epilepsy and SE risk genes. In addition, Fxr2 KO mice fail to show sustained ERK1/2 phosphorylation induced by KA and present reduced burst activity in the hippocampus. Taken together, our findings show that the absence of FXR2P decreases the expression of glutamatergic proteins, and this decrease might prevent self-sustained seizures