Tannaka-Krein duality for Hopf algebroids

We develop the Tannaka-Krein duality for monoidal functors with target in the categories of bimodules over a ring. The \coend of such a functor turns out to be a Hopf algebroid over this ring. Using the result of a previous paper we characterize a small abelian, locally finite rigid monoidal category as the category of rigid comodules over a transitive Hopf algebroid.Comment: 25 pages, final version, to appear in Israel Journal of Mathematic

The analysis of European lacquer : optimization of thermochemolysis temperature of natural resins

In order to optimize chromatographic analysis of European lacquer, thermochemolysis temperature was evaluated for the analysis of natural resins. Five main ingredients of lacquer were studied: sandarac, mastic, colophony, Manila copal and Congo copal. For each, five temperature programs were tested: four fixed temperatures (350, 480, 550, 650 degrees C) and one ultrafast thermal desorption (UFD), in which the temperature rises from 350 to 660 degrees C in 1 min. In total, the integrated signals of 27 molecules, partially characterizing the five resins, were monitored to compare the different methods. A compromise between detection of compounds released at low temperatures and compounds formed at high temperatures was searched. 650 degrees C is too high for both groups, 350 degrees C is best for the first, and 550 degrees C for the second. Fixed temperatures of 480 degrees C or UFD proved to be a consensus in order to detect most marker molecules. UFD was slightly better for the molecules released at low temperatures, while 480 degrees C showed best compounds formed at high temperatures

Divisive Gain Modulation with Dynamic Stimuli in Integrate-and-Fire Neurons

The modulation of the sensitivity, or gain, of neural responses to input is an important component of neural computation. It has been shown that divisive gain modulation of neural responses can result from a stochastic shunting from balanced (mixed excitation and inhibition) background activity. This gain control scheme was developed and explored with static inputs, where the membrane and spike train statistics were stationary in time. However, input statistics, such as the firing rates of pre-synaptic neurons, are often dynamic, varying on timescales comparable to typical membrane time constants. Using a population density approach for integrate-and-fire neurons with dynamic and temporally rich inputs, we find that the same fluctuation-induced divisive gain modulation is operative for dynamic inputs driving nonequilibrium responses. Moreover, the degree of divisive scaling of the dynamic response is quantitatively the same as the steady-state responses—thus, gain modulation via balanced conductance fluctuations generalizes in a straight-forward way to a dynamic setting

Balanced Synaptic Input Shapes the Correlation between Neural Spike Trains

Stimulus properties, attention, and behavioral context influence correlations between the spike times produced by a pair of neurons. However, the biophysical mechanisms that modulate these correlations are poorly understood. With a combined theoretical and experimental approach, we show that the rate of balanced excitatory and inhibitory synaptic input modulates the magnitude and timescale of pairwise spike train correlation. High rate synaptic inputs promote spike time synchrony rather than long timescale spike rate correlations, while low rate synaptic inputs produce opposite results. This correlation shaping is due to a combination of enhanced high frequency input transfer and reduced firing rate gain in the high input rate state compared to the low state. Our study extends neural modulation from single neuron responses to population activity, a necessary step in understanding how the dynamics and processing of neural activity change across distinct brain states