Synchronization of Integrate and Fire oscillators with global coupling

In this article we study the behavior of globally coupled assemblies of a large number of Integrate and Fire oscillators with excitatory pulse-like interactions. On some simple models we show that the additive effects of pulses on the state of Integrate and Fire oscillators are sufficient for the synchronization of the relaxations of all the oscillators. This synchronization occurs in two forms depending on the system: either the oscillators evolve ``en bloc'' at the same phase and therefore relax together or the oscillators do not remain in phase but their relaxations occur always in stable avalanches. We prove that synchronization can occur independently of the convexity or concavity of the oscillators evolution function. Furthermore the presence of disorder, up to some level, is not only compatible with synchronization, but removes some possible degeneracy of identical systems and allows new mechanisms towards this state.Comment: 37 pages, 19 postscript figures, Latex 2

Energy loss of pions and electrons of 1 to 6 GeV/c in drift chambers operated with Xe,CO2(15%)

We present measurements of the energy loss of pions and electrons in drift chambers operated with a Xe,CO2(15%) mixture. The measurements are carried out for particle momenta from 1 to 6 GeV/c using prototype drift chambers for the ALICE TRD. Microscopic calculations are performed using input parameters calculated with GEANT3. These calculations reproduce well the measured average and most probable values for pions, but a higher Fermi plateau is required in order to reproduce our electron data. The widths of the measured distributions are smaller for data compared to the calculations. The electron/pion identification performance using the energy loss is also presented.Comment: 15 pages, 10 figures, accepted for publication in Nucl.Instrum.Meth.

Cell-attached measurements of the firing threshold of rat hippocampal neurones

The cell-attached configuration of the patch-clamp technique was used to assess resting membrane potential and firing threshold of CA1 pyramidal cells and interneurones of rat hippocampal slices.Resting potential was inferred from the reversal potential of voltage-gated K+ currents with symmetrical intracellular and pipette K+ concentrations. Its mean value was −74 ± 9 mV for silent interneurones (mean ± s.d.; n = 17) and −84 ± 7 mV for silent pyramidal cells (n = 8). Spontaneous action currents occurred in thirteen out of thirty-two interneurones and two out of ten pyramidal cells. In active cells, membrane potential values fluctuated by up to 20 mV, due in part to the large hyperpolarizations that followed an action current.Membrane potential values determined from K+ current reversal were 13 ± 6 mV more hyperpolarized than those measured in whole-cell recordings from the same neurones (n = 8), probably due to a Donnan equilibrium potential between pipette and cytoplasm.Firing threshold of silent cells was determined by elevating external K+ until action currents were generated, while membrane potential was monitored from the cell-attached K+ current reversal. Spike threshold was attained at −49 ± 8 mV for interneurones (n = 17) and at −60 ± 8 mV for pyramidal cells (n = 8). Increasing external Ca2+ from 2 to 4 mM shifted the neuronal voltage threshold by +5 mV, without affecting resting potential.For comparison with these values, we examined how the rate of membrane polarization influenced firing threshold in whole-cell records. Ramp current injections, of duration 15–1500 ms, revealed that current threshold followed a classical strength-duration relationship. In contrast voltage threshold, determined from current injection or by elevating extracellular K+, varied little with the rate of membrane polarization.The state of activation and inactivation of Na+ and K+ currents might contribute to the stability of the voltage threshold. Cell-attached records showed that 79 ± 10 % of Na+ channels and 64 ± 10 % of K+ channels were available for activation at resting potential in silent cells (n = 8). As cells were depolarized to threshold, Na+ current availability was reduced to 23 ± 10 %, and K+ current availability to 31 ± 12 %.The speed of transition into the inactivated states also appears to contribute to the invariance of threshold for all but the fastest depolarizations. At potentials close to threshold, the rate of inactivation of Na+ and K+ followed a double exponential time course, such that Na+ currents were 62 % inactivated and K+ currents were 63 % inactivated within 15 ms

Stable and Rapid Recurrent Processing in Realistic Autoassociative Memories

It is shown that in those autoassociative memories that learn by storing multiple patterns of activity on their recurrent collateral connections, there is a fundamental conflict between dynamical stability and storage capacity. It is then found that the network can nevertheless retrieve many different memory patterns, as predicted by nondynamical analyses, if its firing is regulated by inhibition that is sufficiently multiplicative in nature. Simulations of a model network with integrate-and-fire units confirm that this is a realistic solution to the conflict. The simulations also confirm the earlier analytical result that cued-elicited memory retrieval, which follows an exponential time course, occurs in a time linearly related to the time constant for synaptic conductance inactivation and relatively independent of neuronal time constants and firing levels