Period-adding bifurcations and chaos in a periodically stimulated excitable neural relaxation oscillator

This is a pre-print. The definitive version: COOMBES, S. and OSBALDESTIN, A.H., 2000. Period-adding bifurcations and chaos in a periodically stimulated excitable neural relaxation oscillator. Physical Review E, 62(3), pp.4057-4066 Part B.The response of an excitable neuron to trains of electrical spikes is relevant to the understanding of the neural code. In this paper we study a neurobiologically motivated relaxation oscillator, with appropriately identified fast and slow coordinates, that admits an explicit mathematical analysis. An application of geometric singular perturbation theory shows the existence of an attracting invariant manifold which is used to construct the Fenichel normal form for the system. This facilitates the calculation of the response of the system to pulsatile stimulation and allows the construction of a so-called extended isochronal map. The isochronal map is shown to have a single discontinuity and be of a type that can admit three types of response: mode-locked, quasi-periodic and chaotic. The bifurcation structure of the system is seen to be extremely rich and supports period-adding bifurcations separated by windows of both chaos and periodicity. A bifurcation analysis of the isochronal map is presented in conjunction with a description of the various routes to chaos in this system

Modeling Brain Resonance Phenomena Using a Neural Mass Model

Stimulation with rhythmic light flicker (photic driving) plays an important role in the diagnosis of schizophrenia, mood disorder, migraine, and epilepsy. In particular, the adjustment of spontaneous brain rhythms to the stimulus frequency (entrainment) is used to assess the functional flexibility of the brain. We aim to gain deeper understanding of the mechanisms underlying this technique and to predict the effects of stimulus frequency and intensity. For this purpose, a modified Jansen and Rit neural mass model (NMM) of a cortical circuit is used. This mean field model has been designed to strike a balance between mathematical simplicity and biological plausibility. We reproduced the entrainment phenomenon observed in EEG during a photic driving experiment. More generally, we demonstrate that such a single area model can already yield very complex dynamics, including chaos, for biologically plausible parameter ranges. We chart the entire parameter space by means of characteristic Lyapunov spectra and Kaplan-Yorke dimension as well as time series and power spectra. Rhythmic and chaotic brain states were found virtually next to each other, such that small parameter changes can give rise to switching from one to another. Strikingly, this characteristic pattern of unpredictability generated by the model was matched to the experimental data with reasonable accuracy. These findings confirm that the NMM is a useful model of brain dynamics during photic driving. In this context, it can be used to study the mechanisms of, for example, perception and epileptic seizure generation. In particular, it enabled us to make predictions regarding the stimulus amplitude in further experiments for improving the entrainment effect

Small bowtie systems: an enumeration

There exist 3 near bowtie systems of order 7, 12 bowtie systems of order 9, and 1,411,422 balanced bowtie systems of order 13

Leak rate analysis of the Westinghouse Reactor Coolant Pump

An independent analysis was performed by ETEC to determine what the seal leakage rates would be for the Westinghouse Reactor Coolant Pump (RCP) during a postulated station blackout resulting from loss of ac electric power. The object of the study was to determine leakage rates for the following conditions: Case 1: All three seals function. Case 2: No. 1 seal fails open while Nos. 2 and 3 seals function. Case 3: All three seals fail open. The ETEC analysis confirmed Westinghouse calculations on RCP seal performance for the conditions investigated. The leak rates predicted by ETEC were slightly lower than those predicted by Westinghouse for each of the three cases as summarized below. Case 1: ETEC predicted 19.6 gpm, Westinghouse predicted 21.1 gpm. Case 2: ETEC predicted 64.7 gpm, Westinghouse predicted 75.6 gpm. Case 3: ETEC predicted 422 gpm, Westinghouse predicted 480 gpm. 3 refs., 22 figs., 6 tabs

Challenges in sub-100 nm Dual Damascene Etch of Porous Oxycarbosilane Ultra Low-k Dielectrics for BEOL Integration

International audienc

Content, Methodology, and Design Selections in Counselor Education Dissertations

This study explored the content, methodology, and design trends present in counselor education dissertations. The dissertations examined were drawn from a random selection of CACREP-accredited doctoral programs located at Carnegie-classified research universities. In descending order, the three content areas most selected were: (a) counselor education, (b) school counseling, and (c) multicultural counseling. The majority of the dissertations reviewed made use of quantitative methods (64%). With quantitative studies, observational designs were the most-employed category (89%)

Molecularly Reinforced Sol-gel Glasses: Preparation, Characterization and Integration Studies

International audienc

Role of Dorsal Striatum Histone Deacetylase 5 in Incubation of Methamphetamine Craving

BACKGROUND: Methamphetamine (meth) seeking progressively increases after withdrawal (incubation of meth craving). We previously demonstrated an association between histone deacetylase 5 (HDAC5) gene expression in the rat dorsal striatum and incubation of meth craving. Here we used viral constructs to study the causal role of dorsal striatum HDAC5 in this incubation. METHODS: In experiment 1 (overexpression), we injected an adeno-associated virus bilaterally into dorsal striatum to express either green fluorescent protein (control) or a mutant form of HDAC5, which strongly localized to the nucleus. After training rats to self-administer meth (10 days, 9 hours/day), we tested the rats for relapse to meth seeking on withdrawal days 2 and 30. In experiment 2 (knockdown), we injected an adeno-associated virus bilaterally into the dorsal striatum to express a short hairpin RNA either against luciferase (control) or against HDAC5. After training rats to self-administer meth, we tested the rats for relapse on withdrawal days 2 and 30. We also measured gene expression of other HDACs and potential HDAC5 downstream targets. RESULTS: We found that HDAC5 overexpression in dorsal striatum increased meth seeking on withdrawal day 30 but not day 2. In contrast, HDAC5 knockdown in the dorsal striatum decreased meth seeking on withdrawal day 30 but not on day 2; this manipulation also altered other HDACs (Hdac1 and Hdac4) and potential HDAC5 targets (Gnb4 and Suv39h1). CONCLUSIONS: Results demonstrate a novel role of dorsal striatum HDAC5 in incubation of meth craving. These findings also set up future work to identify HDAC5 targets that mediate this incubation