Dynamics from seconds to hours in Hodgkin-Huxley model with time-dependent ion concentrations and buffer reservoirs

The classical Hodgkin--Huxley (HH) model neglects the time-dependence of ion concentrations in spiking dynamics. The dynamics is therefore limited to a time scale of milliseconds, which is determined by the membrane capacitance multiplied by the resistance of the ion channels, and by the gating time constants. We study slow dynamics in an extended HH framework that includes time-dependent ion concentrations, pumps, and buffers. Fluxes across the neuronal membrane change intra- and extracellular ion concentrations, whereby the latter can also change through contact to reservoirs in the surroundings. Ion gain and loss of the system is identified as a bifurcation parameter whose essential importance was not realized in earlier studies. Our systematic study of the bifurcation structure and thus the phase space structure helps to understand activation and inhibition of a new excitability in ion homeostasis which emerges in such extended models. Also modulatory mechanisms that regulate the spiking rate can be explained by bifurcations. The dynamics on three distinct slow times scales is determined by the cell volume-to-surface-area ratio and the membrane permeability (seconds), the buffer time constants (tens of seconds), and the slower backward buffering (minutes to hours). The modulatory dynamics and the newly emerging excitable dynamics corresponds to pathological conditions observed in epileptiform burst activity, and spreading depression in migraine aura and stroke, respectively.Comment: 18 pages, 11 figure

Surprise volume and heteroskedasticity in equity market returns

Heterosedasticity in returns may be explainable by trading volume. We use different volume variables, including surprise volume - i.e. unexpected above-avergae trading activity - which is derived from uncorrelated volume innovations. Assuming eakly exogenous volume, we extend the Lamoureux and Lastrapes (1990) model by an asymmetric GARCH in-mean specification following Golstein et al. (1993). Model estimation for the U.S. as well as six large equity markets shows that surprise volume superior model fit and helps to explain volatility persistence as well as excess kurtosis. Surprise volume reveals a significant positive market risk premium, asymmetry, and a surprise volume effect in conditional variance. The findings suggest that, e.g., a surprise volume shock (breakdown) - i.e. large (small) contemporaneous and small (large) lagged surprise volume - relates to increased (decreased) conditional market variance and return. --ARCH,trading volume,return volume dependence,asymmetric volatility,market risk premium,leverage effect

Surprise Volume and Heteroskedasticity in Equity Market Returns

Heteroskedasticity in returns may be explainable by trading volume. We use different volume variables, including surprise volume---i.e. unexpected above-average trading activity---which is derived from uncorrelated volume innovations. Assuming weakly exogenous volume, we extend the Lamoureux and Lastrapes (1990) model by an asymmetric GARCH in-mean specification following Golsten et al. (1993). Model estimation for the U.S. as well as six large equity markets shows that surprise volume provides superior model fit and helps to explain volatility persistence as well as excess kurtosis. Surprise volume reveals a significant positive market risk premium, asymmetry, and a surprise volume effect in conditional variance. The findings suggest that, e.g., a surprise volume shock (breakdown)---i.e. large (small) contemporaneous and small (large) lagged surprise volume---relates to increased (decreased) conditional market variance and return.ARCH, trading volume, return volume dependence, asymmetric volatility, market risk premium, leverage effect

On the stability of projection methods for the incompressible Navier-Stokes equations based on high-order discontinuous Galerkin discretizations

The present paper deals with the numerical solution of the incompressible Navier-Stokes equations using high-order discontinuous Galerkin (DG) methods for discretization in space. For DG methods applied to the dual splitting projection method, instabilities have recently been reported that occur for coarse spatial resolutions and small time step sizes. By means of numerical investigation we give evidence that these instabilities are related to the discontinuous Galerkin formulation of the velocity divergence term and the pressure gradient term that couple velocity and pressure. Integration by parts of these terms with a suitable definition of boundary conditions is required in order to obtain a stable and robust method. Since the intermediate velocity field does not fulfill the boundary conditions prescribed for the velocity, a consistent boundary condition is derived from the convective step of the dual splitting scheme to ensure high-order accuracy with respect to the temporal discretization. This new formulation is stable in the limit of small time steps for both equal-order and mixed-order polynomial approximations. Although the dual splitting scheme itself includes inf-sup stabilizing contributions, we demonstrate that spurious pressure oscillations appear for equal-order polynomials and small time steps highlighting the necessity to consider inf-sup stability explicitly.Comment: 31 page

Bistable dynamics underlying excitability of ion homeostasis in neuron models

When neurons fire action potentials, dissipation of free energy is usually not directly considered, because the change in free energy is often negligible compared to the immense reservoir stored in neural transmembrane ion gradients and the long-term energy requirements are met through chemical energy, i.e., metabolism. However, these gradients can temporarily nearly vanish in neurological diseases, such as migraine and stroke, and in traumatic brain injury from concussions to severe injuries. We study biophysical neuron models based on the Hodgkin-Huxley (HH) formalism extended to include time-dependent ion concentrations inside and outside the cell and metabolic energy-driven pumps. We reveal the basic mechanism of a state of free energy-starvation (FES) with bifurcation analyses showing that ion dynamics is for a large range of pump rates bistable without contact to an ion bath. This is interpreted as a threshold reduction of a new fundamental mechanism of 'ionic excitability' that causes a long-lasting but transient FES as observed in pathological states. We can in particular conclude that a coupling of extracellular ion concentrations to a large glial-vascular bath can take a role as an inhibitory mechanism crucial in ion homeostasis, while the Na$^+$/K$^+$ pumps alone are insufficient to recover from FES. Our results provide the missing link between the HH formalism and activator-inhibitor models that have been successfully used for modeling migraine phenotypes, and therefore will allow us to validate the hypothesis that migraine symptoms are explained by disturbed function in ion channel subunits, Na$^+$/K$^+$ pumps, and other proteins that regulate ion homeostasis.Comment: 14 pages, 8 figures, 4 table

Thermal neutron image intensifier tube provides brightly visible radiographic pattern

Vacuum-type neutron image intensifier tube improves image detection in thermal neutron radiographic inspection. This system converts images to an electron image, and with electron acceleration and demagnification between the input target and output screen, produces a bright image viewed through a closed circuit television system