Border collision bifurcations of stroboscopic maps in periodically driven spiking models

In this work we consider a general non-autonomous hybrid system based on the integrate-and-fire model, widely used as simplified version of neuronal models and other types of excitable systems. Our unique assumption is that the system is monotonic, possesses an attracting subthreshold equilibrium point and is forced by means of periodic pulsatile (square wave) function.\\ In contrast to classical methods, in our approach we use the stroboscopic map (time-$T$ return map) instead of the so-called firing-map. It becomes a discontinuous map potentially defined in an infinite number of partitions. By applying theory for piecewise-smooth systems, we avoid relying on particular computations and we develop a novel approach that can be easily extended to systems with other topologies (expansive dynamics) and higher dimensions.\\ More precisely, we rigorously study the bifurcation structure in the two-dimensional parameter space formed by the amplitude and the duty cycle of the pulse. We show that it is covered by regions of existence of periodic orbits given by period adding structures. They do not only completely describe all the possible spiking asymptotic dynamics but also the behavior of the firing rate, which is a devil's staircase as a function of the parameters

Deletion of myeloid-PTP1B decreases MHC Class I expression and peptide presentation through an IL-10 dependent mechanism in response to LPS challenge

Peer reviewedPublisher PD

Protein Tyrosine Phosphatase 1B (PTP1B) in the immune system

Journal not available online when checked 02/04/19. DOI: 10.14800/ics.965Peer reviewedPublisher PD

Finding the rarest objects in the universe: A new, efficient method for discovering BL Lacertae objects

We present a new, efficient method for discovering new BL Lac Objects based upon the results of the Einstein Extended Medium Sensitivity Survey (EMSS). We have found that all x-ray selected BL Lacs are radio emitters, and further, that in a 'color-color' diagram (radio/optical and optical/x-ray) the BL Lac Objects occupy an area distinct from both radio loud quasars and the radio quiet QSOs and Seyferts which dominate x-ray selected samples. After obtaining radio counterparts via VLA 'snapshot' observations of a large sample of unidentified x-ray sources, the list of candidates is reduced. These candidates then can be confirmed with optical spectroscopy and/or polarimetry. Since greater than 70 percent of these sources are expected to be BL Lacs, the optical observations are very efficient. We have tested this method using unidentified sources found in the Einstein Slew Survey. The 162 Slew Survey x-ray source positions were observed with the VLA in a mixed B/C configuration at 6 cm resulting in 60 detections within 1.5 position error circle radii. These x-ray/optical/radio sources were then plotted, and 40 BL Lac candidates were identified. To date, 10 candidates have been spectroscopically observed resulting in 10 new BL Lac objects! Radio flux, optical magnitude, and polarization statistics (obtained in white light with the Steward Observatory 2.3 m CCD polarimeter) for each are given

Lipopolysaccharide-primed heterotolerant dendritic cells suppress experimental autoimmune uveoretinitis by multiple mechanisms

Exposure of bone-marrow-derived dendritic cells (BMDC) to high-dose ultrapure lipopolysaccharide for 24 hr (LPS-primed BMDC) enhances their potency in preventing inter-photoreceptor retinoid binding protein: complete Freund's adjuvant-induced experimental autoimmune uveoretinitis (EAU). LPS-primed BMDC are refractory to further exposure to LPS (= endotoxin tolerance), evidenced here by decreased phosphorylation of TANK-binding kinase 1, interferon regulatory factor 3 (IRF3), c-Jun N-terminal kinase and p38 mitogen-activated protein kinase as well as impaired nuclear translocation of nuclear factor κB (NF-κB) and IRF3, resulting in reduced tumour necrosis factor-α (TNF-α), interleukin-6 (IL-6), IL-12 and interferon-β secretion. LPS-primed BMDC also show reduced surface expression of Toll-like receptor-4 and up-regulation of CD14, followed by increased apoptosis, mediated via nuclear factor of activated T cells (NFATc)-2 signalling. LPS-primed BMDC are not only homotolerant to LPS but are heterotolerant to alternative pathogen-associated molecular pattern ligands, such as mycobacterial protein extract (Mycobacterium tuberculosis). Specifically, while M. tuberculosis protein extract induces secretion of IL-1β, TNF-α and IL-6 in unprimed BMDC, LPS-primed BMDC fail to secrete these cytokines in response to M. tuberculosis. We propose that LPS priming of BMDC, by exposure to high doses of LPS for 24 hr, stabilizes their tolerogenicity rather than promoting immunogenicity, and does so by multiple mechanisms, namely (i) generation of tolerogenic apoptotic BMDC through CD14:NFATc signalling; (ii) reduction of NF-κB and IRF3 signalling and downstream pro-inflammatory cytokine production; and (iii) blockade of inflammasome activation

From Canards of Folded Singularities to Torus Canards in a Forced van der Pol Equation

International audienceIn this article, we study canard solutions of the forced van der Pol equation in the relaxation limit for low-, intermediate-, and high-frequency periodic forcing. A central numerical observation made herein is that there are two branches of canards in parameter space which extend across all positive forcing frequencies. In the low-frequency forcing regime, we demonstrate the existence of primary maximal canards induced by folded saddle nodes of type I and establish explicit formulas for the parameter values at which the primary maximal canards and their folds exist. Then, we turn to the intermediate- and high-frequency forcing regimes and show that the forced van der Pol possesses torus canards instead. These torus canards consist of long segments near families of attracting and repelling limit cycles of the fast system, in alternation. We also derive explicit formulas for the parameter values at which the maximal torus canards and their folds exist. Primary maximal canards and maximal torus canards correspond geometrically to the situation in which the persistent manifolds near the family of attracting limit cycles coincide to all orders with the persistent manifolds that lie near the family of repelling limit cycles. The formulas derived for the folds of maximal canards in all three frequency regimes turn out to be representations of a single formula in the appropriate parameter regimes, and this unification confirms the central numerical observation that the folds of the maximal canards created in the low-frequency regime continue directly into the folds of the maximal torus canards that exist in the intermediate- and high-frequency regimes. In addition, we study the secondary canards induced by the folded singularities in the low-frequency regime and find that the fold curves of the secondary canards turn around in the intermediate-frequency regime, instead of continuing into the high-frequency regime. Also, we identify the mechanism responsible for this turning. Finally, we show that the forced van der Pol equation is a normal form-type equation for a class of single-frequency periodically driven slow/fast systems with two fast variables and one slow variable which possess a non-degenerate fold of limit cycles. The analytic techniques used herein rely on geometric desingularisation, invariant manifold theory, Melnikov theory, and normal form methods. The numerical methods used herein were developed in Desroches et al. (SIAM J Appl Dyn Syst 7:1131–1162, 2008, Nonlinearity 23:739–765 2010)

Aspidoscelis costatus costatus (Squamata, Teiidae): high elevation clutch production for a population of whiptail lizards

Artículo del tamaño de nidada en la lagartija Aspidoscelis costatus costatus.Clutch size and number of clutches per reproductive cycle are important life history traits that can be influenced by anatomical, physiological, evolutionary, and ecological factors. This report on the clutch size and number of clutches of an endemic Mexican whiptail lizard, Aspidoscelis costatus costatus (Cope, 1878), is based on a study of population at an unsually high elevation for a member of this genus. The study site is located in Ixtapan de la Sal, southeastern Estado de México, Central Mexico, at 2090 m a.s.l. Lizards were sampled in June 2006, and from May to July 2007, where females of Aspidoscelis costatus costatus were collected by hand along a drift fence. Female reproductive condition was evaluated based on abdominal palpation for presence of developing eggs; clutch size was determined by actual counts of either vitellogenic follicles or oviductal eggs. The smallest reproductive female was 77 mm snout vent length; females produced a minimum of two clutches during the breeding season, the mean clutch size of 6.5 eggs (n = 33) was one of the largest reported for the genus. However, both length and width of its eggs, and the relative clutch mass have not been diminished by development of a large clutch. Additionally, comparisons of clutch size were undertaken within the polytypic A. costatus complex, within the genus Aspidoscelis, and between certain genera of whiptail lizards. This apparently represents the first study of whiptail lizards (genus Aspidoscelis), assessing the aforementioned reproductive characteristics, in a population above 2000 m

The Period adding and incrementing bifurcations: from rotation theory to applications

International audienceThis survey article is concerned with the study of bifurcations of discontinuous piecewise-smooth maps, with a special focus on the one-dimensional case. We review the literature on circle maps and quasi-contractions and provide paths through this literature to prove sufficient conditions for the occurrence of two types of bifurcation scenarios involving rich dynamics. The first scenario consists of the appearance of periodic orbits whose symbolic sequences and “rotation” numbers follow a Farey tree structure; the periods of the periodic orbits are given by consecutive addition. This is called the period adding bifurcation, and the proof of its existence relies on results for maps on the circle. In the second scenario, symbolic sequences are obtained by consecutive attachment of a given symbolic block, and the periods of periodic orbits are incremented by a constant term. This is called the period incrementing bifurcation, and its proof relies on results for maps on the interval. We also discuss the expanding cases, as some of the partial results found in the literature also hold when these maps lose contractiveness. The higher-dimensional case is also discussed by means of quasi-contractions. We provide applied examples in control theory, power electronics, and neuroscience, where these results can be used to obtain precise descriptions of their dynamics