How spiking neurons give rise to a temporal-feature map

A temporal-feature map is a topographic neuronal representation of temporal attributes of phenomena or objects that occur in the outside world. We explain the evolution of such maps by means of a spike-based Hebbian learning rule in conjunction with a presynaptically unspecific contribution in that, if a synapse changes, then all other synapses connected to the same axon change by a small fraction as well. The learning equation is solved for the case of an array of Poisson neurons. We discuss the evolution of a temporal-feature map and the synchronization of the single cells’ synaptic structures, in dependence upon the strength of presynaptic unspecific learning. We also give an upper bound for the magnitude of the presynaptic interaction by estimating its impact on the noise level of synaptic growth. Finally, we compare the results with those obtained from a learning equation for nonlinear neurons and show that synaptic structure formation may profit from the nonlinearity

Contributors to the March Issue/Notes

Notes by John A. Berry, Joseph P. Judge, Paul Kempter, Joseph A. McCabe, William T. Kirby, Granville P. Ziegler, and Donald F. Wise

Entropy Drives Calcium Carbonate Ion Association

The understanding of the molecular mechanisms underlying the early stages of crystallisation is still incomplete. In the case of calcium carbonate, experimental and computational evidence suggests that phase separation relies on so-called pre-nucleation clusters (PNCs). A thorough thermodynamic analysis of the enthalpic and entropic contributions to the overall free energy of PNC formation derived from three independent methods demonstrates that solute clustering is driven by entropy. This can be quantitatively rationalised by the release of water molecules from ion hydration layers, explaining why ion association is not limited to simple ion pairing. The key role of water release in this process suggests that PNC formation should be a common phenomenon in aqueous solutions

Analysis of the intraspinal calcium dynamics and its implications on the plasticity of spiking neurons

The influx of calcium ions into the dendritic spines through the N-metyl-D-aspartate (NMDA) channels is believed to be the primary trigger for various forms of synaptic plasticity. In this paper, the authors calculate analytically the mean values of the calcium transients elicited by a spiking neuron undergoing a simple model of ionic currents and back-propagating action potentials. The relative variability of these transients, due to the stochastic nature of synaptic transmission, is further considered using a simple Markov model of NMDA receptos. One finds that both the mean value and the variability depend on the timing between pre- and postsynaptic action-potentials. These results could have implications on the expected form of synaptic-plasticity curve and can form a basis for a unified theory of spike time-dependent, and rate based plasticity.Comment: 14 pages, 10 figures. A few changes in section IV and addition of a new figur

PULSED DOPPLER FROM THE SUPRASTERNAL NOTCH SYSTEMATICALLY UNDERESTIMATES MEAN BLOOD FLOW VELOCITY IN THE ASCENDING AORTA COMPARED TO PHASE CONTRAST MRI

Background Continuous pulsed-wave Doppler readings of flow velocity in the ascending aorta from the suprasternal position (sCD) are widely used in estimating stroke volume, particularly during physiological challenge maneuvers such as head-up tilt testing. Stroke volume is derived from velocity time integrals and vessel area. We compared the sCD against an established gold standard. Methods In 12 healthy women and men, we obtained 2D cross sectional, velocity encoded phase contrast MRI of the ascending aorta (2DMRI) and sCD to measure mean blood flow velocity (Vmean) at the ascending aorta. We compared sCD insonation depth to the distance between Doppler probe and sinotubular junction measured by MRI. Within an aortic 4D-Flow dataset, allowing flow measurements in every anatomical point along the ascending aorta, Vmean was determined at the sCD measurement point for comparison. Results sCD significantly underestimated Vmean compared with 2DMRI at the sinotubular junction (Vmean 2DMRI – Vmean sCD = 24.42 cm/s ± 12.55 cm/s, p = <0.001). Moreover, sCD sampled flow velocities 21.8 mm ± 7mm (p = <0.001) or 26% off the sinotubular junction. Yet, depth and velocity differences between sCD and 2DMRI were not correlated with each other (Pearson r = -0.147; p = 0.648). When we applied 4DMRI to assess flow velocity at the sCD measurement site, the Vmean difference between methodologies was reduced to 9.1 cm/s ± 12.38 cm/s (p = 0.035). Conclusion sCD profoundly underestimates Vmean in the ascending aorta compared to 4DMRI. The methodology has important limitations in accessing the ideal position for aortic flow measurements and precise information regarding the position of data acquisition for vessel area quantification cannot be ascertained. Overall, sCD is of limited utility in measuring absolute stroke volum

A Fokker-Planck formalism for diffusion with finite increments and absorbing boundaries

Gaussian white noise is frequently used to model fluctuations in physical systems. In Fokker-Planck theory, this leads to a vanishing probability density near the absorbing boundary of threshold models. Here we derive the boundary condition for the stationary density of a first-order stochastic differential equation for additive finite-grained Poisson noise and show that the response properties of threshold units are qualitatively altered. Applied to the integrate-and-fire neuron model, the response turns out to be instantaneous rather than exhibiting low-pass characteristics, highly non-linear, and asymmetric for excitation and inhibition. The novel mechanism is exhibited on the network level and is a generic property of pulse-coupled systems of threshold units.Comment: Consists of two parts: main article (3 figures) plus supplementary text (3 extra figures

Linear stability analysis of retrieval state in associative memory neural networks of spiking neurons

We study associative memory neural networks of the Hodgkin-Huxley type of spiking neurons in which multiple periodic spatio-temporal patterns of spike timing are memorized as limit-cycle-type attractors. In encoding the spatio-temporal patterns, we assume the spike-timing-dependent synaptic plasticity with the asymmetric time window. Analysis for periodic solution of retrieval state reveals that if the area of the negative part of the time window is equivalent to the positive part, then crosstalk among encoded patterns vanishes. Phase transition due to the loss of the stability of periodic solution is observed when we assume fast alpha-function for direct interaction among neurons. In order to evaluate the critical point of this phase transition, we employ Floquet theory in which the stability problem of the infinite number of spiking neurons interacting with alpha-function is reduced into the eigenvalue problem with the finite size of matrix. Numerical integration of the single-body dynamics yields the explicit value of the matrix, which enables us to determine the critical point of the phase transition with a high degree of precision.Comment: Accepted for publication in Phys. Rev.

Markov analysis of stochastic resonance in a periodically driven integrate-fire neuron

We model the dynamics of the leaky integrate-fire neuron under periodic stimulation as a Markov process with respect to the stimulus phase. This avoids the unrealistic assumption of a stimulus reset after each spike made in earlier work and thus solves the long-standing reset problem. The neuron exhibits stochastic resonance, both with respect to input noise intensity and stimulus frequency. The latter resonance arises by matching the stimulus frequency to the refractory time of the neuron. The Markov approach can be generalized to other periodically driven stochastic processes containing a reset mechanism.Comment: 23 pages, 10 figure

An associative memory of Hodgkin-Huxley neuron networks with Willshaw-type synaptic couplings

An associative memory has been discussed of neural networks consisting of spiking N (=100) Hodgkin-Huxley (HH) neurons with time-delayed couplings, which memorize P patterns in their synaptic weights. In addition to excitatory synapses whose strengths are modified after the Willshaw-type learning rule with the 0/1 code for quiescent/active states, the network includes uniform inhibitory synapses which are introduced to reduce cross-talk noises. Our simulations of the HH neuron network for the noise-free state have shown to yield a fairly good performance with the storage capacity of $\alpha_c = P_{\rm max}/N \sim 0.4 - 2.4$ for the low neuron activity of $f \sim 0.04-0.10$. This storage capacity of our temporal-code network is comparable to that of the rate-code model with the Willshaw-type synapses. Our HH neuron network is realized not to be vulnerable to the distribution of time delays in couplings. The variability of interspace interval (ISI) of output spike trains in the process of retrieving stored patterns is also discussed.Comment: 15 pages, 3 figures, changed Titl