Josephson effect in two-band superconductors

We study theoretically the Josephson effect between two time-reversal two-band superconductors, where we assume the equal-time spin-singlet $s$-wave pair potential in each conduction band. %as well as the band asymmetry and the band hybridization in the normal state. The superconducting phase at the first band $\varphi_1$ and that at the second band $\varphi_2$ characterize a two-band superconducting state. We consider a Josephson junction where an insulating barrier separates two such two-band superconductors. By applying the tunnel Hamiltonian description, the Josephson current is calculated in terms of the anomalous Green's function on either side of the junction. We find that the Josephson current consists of three components which depend on three types of phase differences across the junction: the phase difference at the first band $\delta\varphi_1$, the phase difference at the second band $\delta\varphi_2$, and the difference at the center-of-mass phase $\delta(\varphi_1+\varphi_2)/2$. A Cooper pairs generated by the band hybridization carries the last current component. In some cases, the current-phase relationship deviates from the sinusoidal function as a result of time-reversal symmetry breaking down.Comment: 6 page, 2 figure

Design for a Darwinian Brain: Part 1. Philosophy and Neuroscience

Physical symbol systems are needed for open-ended cognition. A good way to understand physical symbol systems is by comparison of thought to chemistry. Both have systematicity, productivity and compositionality. The state of the art in cognitive architectures for open-ended cognition is critically assessed. I conclude that a cognitive architecture that evolves symbol structures in the brain is a promising candidate to explain open-ended cognition. Part 2 of the paper presents such a cognitive architecture.Comment: Darwinian Neurodynamics. Submitted as a two part paper to Living Machines 2013 Natural History Museum, Londo

Universal features of correlated bursty behaviour

Inhomogeneous temporal processes, like those appearing in human communications, neuron spike trains, and seismic signals, consist of high-activity bursty intervals alternating with long low-activity periods. In recent studies such bursty behavior has been characterized by a fat-tailed inter-event time distribution, while temporal correlations were measured by the autocorrelation function. However, these characteristic functions are not capable to fully characterize temporally correlated heterogenous behavior. Here we show that the distribution of the number of events in a bursty period serves as a good indicator of the dependencies, leading to the universal observation of power-law distribution in a broad class of phenomena. We find that the correlations in these quite different systems can be commonly interpreted by memory effects and described by a simple phenomenological model, which displays temporal behavior qualitatively similar to that in real systems

Theory of Interaction of Memory Patterns in Layered Associative Networks

A synfire chain is a network that can generate repeated spike patterns with millisecond precision. Although synfire chains with only one activity propagation mode have been intensively analyzed with several neuron models, those with several stable propagation modes have not been thoroughly investigated. By using the leaky integrate-and-fire neuron model, we constructed a layered associative network embedded with memory patterns. We analyzed the network dynamics with the Fokker-Planck equation. First, we addressed the stability of one memory pattern as a propagating spike volley. We showed that memory patterns propagate as pulse packets. Second, we investigated the activity when we activated two different memory patterns. Simultaneous activation of two memory patterns with the same strength led the propagating pattern to a mixed state. In contrast, when the activations had different strengths, the pulse packet converged to a two-peak state. Finally, we studied the effect of the preceding pulse packet on the following pulse packet. The following pulse packet was modified from its original activated memory pattern, and it converged to a two-peak state, mixed state or non-spike state depending on the time interval

Sparse and Dense Encoding in Layered Associative Network of Spiking Neurons

A synfire chain is a simple neural network model which can propagate stable synchronous spikes called a pulse packet and widely researched. However how synfire chains coexist in one network remains to be elucidated. We have studied the activity of a layered associative network of Leaky Integrate-and-Fire neurons in which connection we embed memory patterns by the Hebbian Learning. We analyzed their activity by the Fokker-Planck method. In our previous report, when a half of neurons belongs to each memory pattern (memory pattern rate $F=0.5$), the temporal profiles of the network activity is split into temporally clustered groups called sublattices under certain input conditions. In this study, we show that when the network is sparsely connected ($F<0.5$), synchronous firings of the memory pattern are promoted. On the contrary, the densely connected network ($F>0.5$) inhibit synchronous firings. The sparseness and denseness also effect the basin of attraction and the storage capacity of the embedded memory patterns. We show that the sparsely(densely) connected networks enlarge(shrink) the basion of attraction and increase(decrease) the storage capacity

Statistical Significance of Precisely Repeated Intracellular Synaptic Patterns

Can neuronal networks produce patterns of activity with millisecond accuracy? It may seem unlikely, considering the probabilistic nature of synaptic transmission. However, some theories of brain function predict that such precision is feasible and can emerge from the non-linearity of the action potential generation in circuits of connected neurons. Several studies have presented evidence for and against this hypothesis. Our earlier work supported the precision hypothesis, based on results demonstrating that precise patterns of synaptic inputs could be found in intracellular recordings from neurons in brain slices and in vivo. To test this hypothesis, we devised a method for finding precise repeats of activity and compared repeats found in the data to those found in surrogate datasets made by shuffling the original data. Because more repeats were found in the original data than in the surrogate data sets, we argued that repeats were not due to chance occurrence. Mokeichev et al. (2007) challenged these conclusions, arguing that the generation of surrogate data was insufficiently rigorous. We have now reanalyzed our previous data with the methods introduced from Mokeichev et al. (2007). Our reanalysis reveals that repeats are statistically significant, thus supporting our earlier conclusions, while also supporting many conclusions that Mokeichev et al. (2007) drew from their recent in vivo recordings. Moreover, we also show that the conditions under which the membrane potential is recorded contributes significantly to the ability to detect repeats and may explain conflicting results. In conclusion, our reevaluation resolves the methodological contradictions between Ikegaya et al. (2004) and Mokeichev et al. (2007), but demonstrates the validity of our previous conclusion that spontaneous network activity is non-randomly organized

Adaptive and Phase Selective Spike Timing Dependent Plasticity in Synaptically Coupled Neuronal Oscillators

We consider and analyze the influence of spike-timing dependent plasticity (STDP) on homeostatic states in synaptically coupled neuronal oscillators. In contrast to conventional models of STDP in which spike-timing affects weights of synaptic connections, we consider a model of STDP in which the time lags between pre- and/or post-synaptic spikes change internal state of pre- and/or post-synaptic neurons respectively. The analysis reveals that STDP processes of this type, modeled by a single ordinary differential equation, may ensure efficient, yet coarse, phase-locking of spikes in the system to a given reference phase. Precision of the phase locking, i.e. the amplitude of relative phase deviations from the reference, depends on the values of natural frequencies of oscillators and, additionally, on parameters of the STDP law. These deviations can be optimized by appropriate tuning of gains (i.e. sensitivity to spike-timing mismatches) of the STDP mechanism. However, as we demonstrate, such deviations can not be made arbitrarily small neither by mere tuning of STDP gains nor by adjusting synaptic weights. Thus if accurate phase-locking in the system is required then an additional tuning mechanism is generally needed. We found that adding a very simple adaptation dynamics in the form of slow fluctuations of the base line in the STDP mechanism enables accurate phase tuning in the system with arbitrary high precision. Adaptation operating at a slow time scale may be associated with extracellular matter such as matrix and glia. Thus the findings may suggest a possible role of the latter in regulating synaptic transmission in neuronal circuits

On How Network Architecture Determines the Dominant Patterns of Spontaneous Neural Activity

In the absence of sensory stimulation, neocortical circuits display complex patterns of neural activity. These patterns are thought to reflect relevant properties of the network, including anatomical features like its modularity. It is also assumed that the synaptic connections of the network constrain the repertoire of emergent, spontaneous patterns. Although the link between network architecture and network activity has been extensively investigated in the last few years from different perspectives, our understanding of the relationship between the network connectivity and the structure of its spontaneous activity is still incomplete. Using a general mathematical model of neural dynamics we have studied the link between spontaneous activity and the underlying network architecture. In particular, here we show mathematically how the synaptic connections between neurons determine the repertoire of spatial patterns displayed in the spontaneous activity. To test our theoretical result, we have also used the model to simulate spontaneous activity of a neural network, whose architecture is inspired by the patchy organization of horizontal connections between cortical columns in the neocortex of primates and other mammals. The dominant spatial patterns of the spontaneous activity, calculated as its principal components, coincide remarkably well with those patterns predicted from the network connectivity using our theory. The equivalence between the concept of dominant pattern and the concept of attractor of the network dynamics is also demonstrated. This in turn suggests new ways of investigating encoding and storage capabilities of neural networks