Real-time areal precipitation determination from radar by means of statistical objective analysis

Precipitation measurement by radar allows for areal rainfall determination with a high spatial and temporal resolution. However, hydrological applications require an accuracy of the precipitation quantification which cannot be obtained by today’s weather radar devices. The quality of the radar-derived precipitation can be significantly improved with the aid of ground measurements. In this paper, a complete processing pipeline for real-time radar precipitation determination using a modified statistical objective analysis method is presented. Thereby, several additional algorithms, such as a dynamical use of Z–R relationships, a bias correction and an advection correction scheme are employed. The performance of the algorithms is tested for several case studies. For an error analysis, an eight months data set of X-band radar scans and rain gauge precipitation measurements is used. We show a reduction in the radar–rain gauge RMS difference of up to 59% for the optimal combination of the different algorithms

Adherent carbon film deposition by cathodic arc with implantation

A method of improving the adhesion of carbon thin films deposited using a cathodic vacuum arc by the use of implantation at energies up to 20 keV is described. A detailed analysis of carbon films deposited onto silicon in this way is carried out using complementary techniques of transmission electron microscopy and x-ray photoelectron spectroscopy (XPS) is presented. This analysis shows that an amorphous mixing layer consisting of carbon and silicon is formed between the grown pure carbon film and the crystalline silicon substrate. In the mixing layer, it is shown that some chemical bonding occurs between carbon and silicon. Damage to the underlying crystalline silicon substrate is observed and believed to be caused by interstitial implanted carbon atoms which XPS shows are not bonded to the silicon. The effectiveness of this technique is confirmed by scratch testing and by analysis with scanning electron microscopy which shows failure of the silicon substrate occurs before delamination of the carbon film

Topological Speed Limits to Network Synchronization

We study collective synchronization of pulse-coupled oscillators interacting on asymmetric random networks. We demonstrate that random matrix theory can be used to accurately predict the speed of synchronization in such networks in dependence on the dynamical and network parameters. Furthermore, we show that the speed of synchronization is limited by the network connectivity and stays finite, even if the coupling strength becomes infinite. In addition, our results indicate that synchrony is robust under structural perturbations of the network dynamics.Comment: 5 pages, 3 figure

Breaking Synchrony by Heterogeneity in Complex Networks

For networks of pulse-coupled oscillators with complex connectivity, we demonstrate that in the presence of coupling heterogeneity precisely timed periodic firing patterns replace the state of global synchrony that exists in homogenous networks only. With increasing disorder, these patterns persist until they reach a critical temporal extent that is of the order of the interaction delay. For stronger disorder these patterns cease to exist and only asynchronous, aperiodic states are observed. We derive self-consistency equations to predict the precise temporal structure of a pattern from the network heterogeneity. Moreover, we show how to design heterogenous coupling architectures to create an arbitrary prescribed pattern.Comment: 4 pages, 3 figure

Dynamical response of the Hodgkin-Huxley model in the high-input regime

The response of the Hodgkin-Huxley neuronal model subjected to stochastic uncorrelated spike trains originating from a large number of inhibitory and excitatory post-synaptic potentials is analyzed in detail. The model is examined in its three fundamental dynamical regimes: silence, bistability and repetitive firing. Its response is characterized in terms of statistical indicators (interspike-interval distributions and their first moments) as well as of dynamical indicators (autocorrelation functions and conditional entropies). In the silent regime, the coexistence of two different coherence resonances is revealed: one occurs at quite low noise and is related to the stimulation of subthreshold oscillations around the rest state; the second one (at intermediate noise variance) is associated with the regularization of the sequence of spikes emitted by the neuron. Bistability in the low noise limit can be interpreted in terms of jumping processes across barriers activated by stochastic fluctuations. In the repetitive firing regime a maximization of incoherence is observed at finite noise variance. Finally, the mechanisms responsible for spike triggering in the various regimes are clearly identified.Comment: 14 pages, 24 figures in eps, submitted to Physical Review

Comparison of Langevin and Markov channel noise models for neuronal signal generation

The stochastic opening and closing of voltage-gated ion channels produces noise in neurons. The effect of this noise on the neuronal performance has been modelled using either approximate or Langevin model, based on stochastic differential equations or an exact model, based on a Markov process model of channel gating. Yet whether the Langevin model accurately reproduces the channel noise produced by the Markov model remains unclear. Here we present a comparison between Langevin and Markov models of channel noise in neurons using single compartment Hodgkin-Huxley models containing either $Na^{+}$ and $K^{+}$, or only $K^{+}$ voltage-gated ion channels. The performance of the Langevin and Markov models was quantified over a range of stimulus statistics, membrane areas and channel numbers. We find that in comparison to the Markov model, the Langevin model underestimates the noise contributed by voltage-gated ion channels, overestimating information rates for both spiking and non-spiking membranes. Even with increasing numbers of channels the difference between the two models persists. This suggests that the Langevin model may not be suitable for accurately simulating channel noise in neurons, even in simulations with large numbers of ion channels

A comparative study of different integrate-and-fire neurons: spontaneous activity, dynamical response, and stimulus-induced correlation

Stochastic integrate-and-fire (IF) neuron models have found widespread applications in computational neuroscience. Here we present results on the white-noise-driven perfect, leaky, and quadratic IF models, focusing on the spectral statistics (power spectra, cross spectra, and coherence functions) in different dynamical regimes (noise-induced and tonic firing regimes with low or moderate noise). We make the models comparable by tuning parameters such that the mean value and the coefficient of variation of the interspike interval match for all of them. We find that, under these conditions, the power spectrum under white-noise stimulation is often very similar while the response characteristics, described by the cross spectrum between a fraction of the input noise and the output spike train, can differ drastically. We also investigate how the spike trains of two neurons of the same kind (e.g. two leaky IF neurons) correlate if they share a common noise input. We show that, depending on the dynamical regime, either two quadratic IF models or two leaky IFs are more strongly correlated. Our results suggest that, when choosing among simple IF models for network simulations, the details of the model have a strong effect on correlation and regularity of the output.Comment: 12 page

Derivation of Hebb's rule

On the basis of the general form for the energy needed to adapt the connection strengths of a network in which learning takes place, a local learning rule is found for the changes of the weights. This biologically realizable learning rule turns out to comply with Hebb's neuro-physiological postulate, but is not of the form of any of the learning rules proposed in the literature. It is shown that, if a finite set of the same patterns is presented over and over again to the network, the weights of the synapses converge to finite values. Furthermore, it is proved that the final values found in this biologically realizable limit are the same as those found via a mathematical approach to the problem of finding the weights of a partially connected neural network that can store a collection of patterns. The mathematical solution is obtained via a modified version of the so-called method of the pseudo-inverse, and has the inverse of a reduced correlation matrix, rather than the usual correlation matrix, as its basic ingredient. Thus, a biological network might realize the final results of the mathematician by the energetically economic rule for the adaption of the synapses found in this article.Comment: 29 pages, LaTeX, 3 figure

A Markovian event-based framework for stochastic spiking neural networks

In spiking neural networks, the information is conveyed by the spike times, that depend on the intrinsic dynamics of each neuron, the input they receive and on the connections between neurons. In this article we study the Markovian nature of the sequence of spike times in stochastic neural networks, and in particular the ability to deduce from a spike train the next spike time, and therefore produce a description of the network activity only based on the spike times regardless of the membrane potential process. To study this question in a rigorous manner, we introduce and study an event-based description of networks of noisy integrate-and-fire neurons, i.e. that is based on the computation of the spike times. We show that the firing times of the neurons in the networks constitute a Markov chain, whose transition probability is related to the probability distribution of the interspike interval of the neurons in the network. In the cases where the Markovian model can be developed, the transition probability is explicitly derived in such classical cases of neural networks as the linear integrate-and-fire neuron models with excitatory and inhibitory interactions, for different types of synapses, possibly featuring noisy synaptic integration, transmission delays and absolute and relative refractory period. This covers most of the cases that have been investigated in the event-based description of spiking deterministic neural networks

Noise Induced Coherence in Neural Networks

We investigate numerically the dynamics of large networks of $N$ globally pulse-coupled integrate and fire neurons in a noise-induced synchronized state. The powerspectrum of an individual element within the network is shown to exhibit in the thermodynamic limit ($N\to \infty$) a broadband peak and an additional delta-function peak that is absent from the powerspectrum of an isolated element. The powerspectrum of the mean output signal only exhibits the delta-function peak. These results are explained analytically in an exactly soluble oscillator model with global phase coupling.Comment: 4 pages ReVTeX and 3 postscript figure