Excitable neurons, firing threshold manifolds and canards

We investigate firing threshold manifolds in a mathematical model of an excitable neuron. The model analyzed investigates the phenomenon of post-inhibitory rebound spiking due to propofol anesthesia and is adapted from McCarthy et al. (SIAM J. Appl. Dyn. Syst. 11(4):1674-1697, 2012). Propofol modulates the decay time-scale of an inhibitory GABAa synaptic current. Interestingly, this system gives rise to rebound spiking within a specific range of propofol doses. Using techniques from geometric singular perturbation theory, we identify geometric structures, known as canards of folded saddle-type, which form the firing threshold manifolds. We find that the position and orientation of the canard separatrix is propofol dependent. Thus, the speeds of relevant slow synaptic processes are encoded within this geometric structure. We show that this behavior cannot be understood using a static, inhibitory current step protocol, which can provide a single threshold for rebound spiking but cannot explain the observed cessation of spiking for higher propofol doses. We then compare the analyses of dynamic and static synaptic inhibition, showing how the firing threshold manifolds of each relate, and why a current step approach is unable to fully capture the behavior of this model

Spielst du noch oder lernst du schon? Der Einfluss des Framings auf Unterhaltung und Inhaltsrezeption bei Game-based Learning

Der Umgang mit Lernspielen kann entweder spielerische oder ernste Züge tragen. Dieser Beitrag fragt danach, inwiefern sich aus einer solchen Rahmung Konsequenzen für das pädagogische Potenzial von Game-based Learning ergeben. Es wurde vermutet, dass es gerade die Abgrenzung des Spiels zum Ernst des Alltags ist, die es so unterhaltsam und motivierend macht, dass andererseits aber die Scheinhaftigkeit des Spiels womöglich die Bereitschaft der Adressaten zur Übernahme der Lernspielinhalte in ihr Wissensrepertoire reduziert. Ein und dasselbe Lernspiel könnte somit, abhängig von der Definition der Situation, als mehr oder weniger unterhaltsam, aber komplementär auch als mehr oder weniger informativ erachtet werden. In einem experimentellen Setting mit Realschüler/innen der 8. Klasse (n = 54) wurden diese Hypothesen empirisch geprüft. Versuchspersonen aus zwei unabhängigen Stichproben bearbeiteten das gleiche Lernspiel, den einen wurde jedoch suggeriert, es handle sich um eine Lernsoftware für den Unterricht, den anderen, es sei ein reines Computerspiel für die Freizeit. Im Anschluss wurden per Fragebogen die Unterhaltung und die Bereitschaft zur Übernahme der Medieninhalte erfasst. Der Bezugsrahmen allein hatte zwar nicht den erwarteten unmittelbaren Einfluss auf Unterhaltung und Rezeptionsbereitschaft, es ergaben sich aber in deskriptiver und teils auch inferenzstatistischer Hinsicht Interaktionen mit dem Bezugsrahmen und dem Geschlecht der Versuchspersonen bzw. ihrer Präferenz für Lernspiel

Mixed mode oscillations in a conceptual climate model

Much work has been done on relaxation oscillations and other simple oscillators in conceptual climate models. However, the oscillatory patterns in climate data are often more complicated than what can be described by such mechanisms. This paper examines complex oscillatory behavior in climate data through the lens of mixed-mode oscillations. As a case study, a conceptual climate model with governing equations for global mean temperature, atmospheric carbon, and oceanic carbon is analyzed. The nondimensionalized model is a fast/slow system with one fast variable (corresponding to ice volume) and two slow variables (corresponding to the two carbon stores). Geometric singular perturbation theory is used to demonstrate the existence of a folded node singularity. A parameter regime is found in which (singular) trajectories that pass through the folded node are returned to the singular funnel in the limiting case where $\epsilon = 0$. In this parameter regime, the model has a stable periodic orbit of type $1^s$ for some $s>0$. To our knowledge, it is the first conceptual climate model demonstrated to have the capability to produce an MMO pattern.Comment: 28 pages, 11 figure

Bečani i njihova rivijera

The exhibition Austrian Riviera – Vienna Reveals the Sea (Österreichische Riviera – Wien entdeckt das Meer) was opened in the Vienna City Museum in the middle of November 2013. The exhibition is a historical journey to favourite destinations of the Austrian-Hungarian Monarchy. Approximately 450 exhibits chronologically leads visitors from the opening of the Vienna – Trieste railway in 1857 to the great exhibition Adria in Prater in 1913. The „Austrian Riviera“ was in full tourist bloom in during precisely that period (1890–1914). It was helped by opening of the Monarhy’s railway network which connected Rijeka, Opatija and the Kvarner Gulf to Vienna in 1873. Traffic connections and suitable climate accelerated the development of health, family, fashion and art tourism. Larger Dalmatian cities (Split, Dubrovnik, Budva) were encompassed in addition to the Northern littoral. Numerous regional museums (from Trieste, Rijeka, Split, Opatija, etc.) provided their materials for the exhibition.Sredinom studenoga 2013. u Muzeju grada Beča otvorena je izložba Austrijska rivijera –Beč otkriva more (Österreichische Riviera – Wien entdeckt das Meer) Povijesno je to putovanje u omiljene destinacije Austro-Ugarske Monarhije. Oko 450 izloženih objekata kronološki vodi posjetioce od otvaranja željezničke poveznice Beč – Trst 1857. pa do velike izložbe Adria u Prateru 1913. Upravo u tom razdoblju (1890–1914), gotovo četvrt stoljeća, "Austrijska rivijera" je u punom turističkom cvatu. Tome je pripomoglo otvaranje željezničke mreže Monarhije koja 1873. godine Rijeku, Opatiju i Kvarnersku uvalu približava Beču. Prometne veze i pogodna klima utječu na brzi razvoj zdravstvenog, obiteljskog, modnog i umjetničkog turizma. Osim sjevernog priobalja obuhvaćeni su i veći gradovi Dalmacije (Split, Dubrovnik, Budva). Mnogobrojni muzeji regije (Trst, Rijeka, Split, Opatija, itd.) dali su izložbi na raspolaganje svoje materijale

Numerical computation of an Evans function for travelling waves

We demonstrate a geometrically inspired technique for computing Evans functions for the linearised operators about travelling waves. Using the examples of the F-KPP equation and a Keller-Segel model of bacterial chemotaxis, we produce an Evans function which is computable through several orders of magnitude in the spectral parameter and show how such a function can naturally be extended into the continuous spectrum. In both examples, we use this function to numerically verify the absence of eigenvalues in a large region of the right half of the spectral plane. We also include a new proof of spectral stability in the appropriate weighted space of travelling waves of speed $c \geq 2 \sqrt{\delta}$ in the F-KPP equation.Comment: 37 pages, 11 figure

Multiple timescales and the parametrisation method in geometric singular perturbation theory

We present a novel method for computing slow manifolds and their fast fibre bundles in geometric singular perturbation problems. This coordinate-independent method simultaneously computes parametrisations of these objects and the dynamics on them. It does so by iteratively solving a so-called conjugacy equation, yielding approximations with arbitrarily high degrees of accuracy. We show the power of this top-down method for the study of systems with multiple (i.e., three or more) timescales. In particular, we highlight the emergence of hidden timescales and show how our method can uncover these surprising multiple timescale structures. We also apply our parametrisation method to several reaction network problems.Comment: 33 pages, 5 figure