Multilayer adaptive networks in neuronal processing

The connectome is a wiring diagram mapping all the neural connections in the brain. At the cellular level, it provides a map of the neurons and synapses within a part or all of the brain of an organism. In recent years, significant advances have been made in the study of the connectome via network science and graph theory. This analysis is fundamental to understand neurotransmission (fast synaptic transmission) networks. However, neurons use other forms of communication as neuromodulation that, instead of conveying excitation or inhibition, change neuronal and synaptic properties. This additional neuromodulatory layers condition and reconfigure the connectome. In this paper, we propose that multilayer adaptive networks, in which different synaptic and neurochemical layers interact, are the appropriate framework to explain neuronal processing. Then, we describe a simplified multilayer adaptive network model that accounts for these extra-layers of interaction and analyse the emergence of interesting computational capabilities.     

Stochastic resonance in mammalian neuronal networks

We present stochastic resonance observed in the dynamics of neuronal networks from mammalian brain. Both sinusoidal signals and random noise were superimposed into an applied electric field. As the amplitude of the noise component was increased, an optimization (increase then decrease) in the signal-to-noise ratio of the network response to the sinusoidal signal was observed. The relationship between the measures used to characterize the dynamics is discussed. Finally, a computational model of these neuronal networks that includes the neuronal interactions with the electric field is presented to illustrate the physics behind the essential features of the experiment. (c) 1998 American Institute of Physics.     

Hidden neuronal correlations in cultured networks

Utilization of a clustering algorithm on neuronal spatiotemporal correlation matrices recorded during a spontaneous activity of in vitro networks revealed the existence of hidden correlations: the sequence of synchronized bursting events (SBEs) is composed of statistically distinguishable subgroups each with its own distinct pattern of interneuron spatiotemporal correlations. These findings hint that each of the SBE subgroups can serve as a template for coding, storage, and retrieval of a specific information.     

Long term variations of solar radius

Total and annular eclipses allow us to measure the angular solar diameter at unit distance up to an accuracy of some hundredths of arcsecond. Data of lunar limb features from Japanese mission Kaguya will be useful to detect also the solar oblateness signal, relevant from a General Relativistic point of view. Useful eclipse data are available for 1567, 1715, 1869, 1925 and from 1966 to 2009 with uneven sampling: only these data can allow a study of solar diameter evolution with significant resolution on secular basis.     

Bursting synchronization in clustered neuronal networks

Neuronal networks in the brain exhibit the modular (clustered) property, i.e., they are composed of certain subnetworks with differential internal and external connectivity. We investigate bursting synchronization in a clustered neuronal network. A transition to mutual-phase synchronization takes place on the bursting time scale of coupled neurons, while on the spiking time scale, they behave asynchronously. This synchronization transition can be induced by the variations of inter- and intra- coupling strengths, as well as the probability of random links between different subnetworks. Considering that some pathological conditions are related with the synchronization of bursting neurons in the brain, we analyze the control of bursting synchronization by using a time-periodic external signal in the clustered neuronal network. Simulation results show a frequency locking tongue in the driving parameter plane, where bursting synchronization is maintained, even in the presence of external driving. Hence, effective synchronization suppression can be realized with the driving parameters outside the frequency locking region.     

Self-regulated complexity in cultured neuronal networks

New quantified observables of complexity are identified and utilized to study sequences (time series) recorded during the spontaneous activity of different size cultured networks. The sequence is mapped into a tiled time-frequency domain that maximizes the information about local time-frequency resolutions. The sequence regularity is associated with the domain homogeneity and its complexity with its local and global variations. Shuffling the recorded sequence lowers its complexity down to artificially constructed ones. The new observables are utilized to identify self-regulation motifs in observed complex network activity.     

Long transients dynamics in biochemical networks

Summary  A Coupled Map Lattice, which simulates gene expression dynamics inside cells and cellular interactions on a regular lattice, shows a complex pattern of temporal behaviour. The model is represented as a network of genes interacting through their products in space and time in a lattice of genetically identical cells. Despite the fact that the system is described through a step function that imposes a simple repertoire of constant or oscillatory steady states, the dynamics over the lattice are extremely complex. One of the main feature of the asymptotic dynamics is the appearance of long transients in certain regions of parameter space, before the attainment of the final stable attractor. These dynamics, that can grow linearly or exponentially with lattice size, can become the only dynamics computationally observable. The study of the global dynamics-i.e. the average value of the variable over the lattice-shows a qualitative different behaviour depending on the region of the parameter space observed. In the case of the linear transient-growth region the system shows an average that falls quickly on a periodic attractor. In the exponential region values of the average quantities show a behaviour that has stochastic properties. At the boundary of these two regimes the system has an average that shows a complex behaviour before attainment of the final attractor. The possible implications of these results for the study of the dynamical aspects of gene regulation, biochemical pathways and in signal transduction in experimental systems are discussed. This work has been partially supported by CNR grant No. 95.01751.CT14 “Studio analitico della dinamica della regolazione genica e della morfogenesi#x201C;, and by funds from the National Ministry of Public Health. FB and RL would like to thank I.S.I., Torino, for the kind hospitality during the workshop of the EEC Network “Complexity and Chaos#x201D;, contract No. ERBCHRX-CT940546, in 1995 and 1996, during which part of this research has been done.     

Long chaotic transients in complex networks

We show that long chaotic transients dominate the dynamics of randomly diluted networks of pulse-coupled oscillators. This contrasts with the rapid convergence towards limit cycle attractors found in networks of globally coupled units. The lengths of the transients strongly depend on the network connectivity and vary by several orders of magnitude, with maximum transient lengths at intermediate connectivities. The dynamics of the transients exhibit a novel form of robust synchronization. An approximation to the largest Lyapunov exponent characterizing the chaotic nature of the transient dynamics is calculated analytically.     

Learning and structure of neuronal networks

We study the effect of learning dynamics on network topology. Firstly, a network of discrete dynamical systems is considered for this purpose and the coupling strengths are made to evolve according to a temporal learning rule that is based on the paradigm of spike-time-dependent plasticity (STDP). This incorporates necessary competition between different edges. The final network we obtain is robust and has a broad degree distribution. Then we study the dynamics of the structure of a formal neural network. For properly chosen input signals, there exists a steady state with a residual network. We compare the motif profile of such a network with that of the real neural network of C. elegans and identify robust qualitative similarities. In particular, our extensive numerical simulations show that this STDP-driven resulting network is robust under variations of model parameters.     

Long term wave hindcast in the Adriatic Sea

Summary We have carried out a long term hindcast of the wave conditions in the Adriatic Sea. The results have been validated against wave data recorded in the Northern Adriatic Sea and then used for the extremes statistics in this area.     

Stochastic resonance in hybrid scale-free neuronal networks

We study the phenomenon of stochastic resonance in a system of coupled neurons that are globally excited by a weak periodic input signal. We make the realistic assumption that the chemical and electrical synapses interact in the same neuronal network, hence constituting a hybrid network. By considering a hybrid coupling scheme embedded in the scale-free topology, we show that the electrical synapses are more efficient than chemical synapses in promoting the best correlation between the weak input signal and the response of the system. We also demonstrate that the average degree of neurons within the hybrid scale-free network significantly influences the optimal amount of noise for the occurrence of stochastic resonance, indicating that there also exists an optimal topology for the amplification of the response to the weak input signal. Lastly, we verify that the presented results are robust to variations of the system size.     

Bifurcation in neuronal networks with hub structure

We investigate bifurcations in neuronal networks with a hub structure. It is known that hubs play a leading role in characterizing the network dynamical behavior. However, the dynamics of hubs or star-coupled systems is not well understood. Here, we study rather subnetworks with a star-like configuration. This coupled system is an important motif in complex networks. Thus, our study is a basic step for understanding structure formation in large networks. We use the Morris-Lecar neuron with class I and class II excitabilities as a node. Homogeneous (coupling the same class neurons) and heterogeneous (coupling different class neurons) cases are considered for both excitatory and inhibitory coupling. For the homogeneous system class II neurons are suitable for achieving both complete and cluster synchronization in excitatory and inhibitory coupling, respectively. For the heterogeneous system with inhibitory coupling, the class I hub neuron has a wider parameter region of synchronous firings than the class II hub. Moreover, the class I hub neuron with the excitatory synapse gives rise to bifurcations of synchronized states and multi-stability (coexistence of a few different states) is observed.     

Connectivities and synchronous firing in cortical neuronal networks

Network connectivities ((-)k) of cortical neural cultures are studied by synchronized firing and determined from measured correlations between fluorescence intensities of firing neurons. The bursting frequency (f) during synchronized firing of the networks is found to be an increasing function of (-)k. With f taken to be proportional to (-)k, a simple random model with a (-)k dependent connection probability p((-)k).has been constructed to explain our experimental findings successfully.     

Long term memory in extreme returns of financial time series

It is well known that while daily price returns of financial markets are uncorrelated, their absolute values (‘volatility’) are long-term correlated. Here we provide evidence that certain subsequences of the returns themselves also exhibit long-term memory. These subsequences consist of maxima (or minima) of returns in consecutive time windows of R days. Our analysis shows that for both stocks and currency exchange rates, long-term correlations are significant for R≥4. We argue that this long-term memory which is similar to that observed in volatility clustering sheds further insight on price dynamics that might be used for risk estimation.     

Minimal attractors in digraph system models of neuronal networks

We study a class of discrete dynamical systems models of neuronal networks. In these models, each neuron is represented by a finite number of states and there are rules for how a neuron transitions from one state to another. In particular, the rules determine when a neuron fires and how this affects the state of other neurons. In an earlier paper [D. Terman, S. Ahn, X. Wang, W. Just, Reducing neuronal networks to discrete dynamics, Physica D 237 (2008) 324-338], we demonstrate that a general class of excitatory-inhibitory networks can, in fact, be rigorously reduced to the discrete model. In the present paper, we analyze how the connectivity of the network influences the dynamics of the discrete model. For randomly connected networks, we find two major phase transitions. If the connection probability is above the second but below the first phase transition, then starting in a generic initial state, most but not all cells will fire at all times along the trajectory as soon as they reach the end of their refractory period. Above the first phase transition, this will be true for all cells in a typical initial state; thus most states will belong to a minimal attractor of oscillatory behavior (in a sense that is defined precisely in the paper). The exact positions of the phase transitions depend on intrinsic properties of the cells including the lengths of the cells’ refractory periods and the thresholds for firing. Existence of these phase transitions is both rigorously proved for sufficiently large networks and corroborated by numerical experiments on networks of moderate size.     

Power-law statistics of synchronous transition in inhibitory neuronal networks

We investigate the relationship between the synchronous transition and the power law behavior in spiking networks which are composed of inhibitory neurons and balanced by dc current. In the region of the synchronous transition, the avalanche size and duration distribution obey a power law distribution. We demonstrate the robustness of the power law for event sizes at different parameters and multiple time scales. Importantly, the exponent of the event size and duration distribution can satisfy the critical scaling relation. By changing the network structure parameters in the parameter region of transition, quasicriticality is observed, that is, critical exponents depart away from the criticality while still hold approximately to a dynamical scaling relation. The results suggest that power law statistics can emerge in networks composed of inhibitory neurons when the networks are balanced by external driving signal.     

Economic small-world behavior in weighted networks

The small-world phenomenon has been already the subject of a huge variety of papers, showing its appeareance in a variety of systems. However, some big holes still remain to be filled, as the commonly adopted mathematical formulation is valid only for topological networks. In this paper we propose a generalization of the theory of small worlds based on two leading concepts, efficiency and cost, and valid also for weighted networks. Efficiency measures how well information propagates over the network, and cost measures how expensive it is to build a network. The combination of these factors leads us to introduce the concept of economic small worlds, that formalizes the idea of networks that are “cheap” to build, and nevertheless efficient in propagating information, both at global and local scale. In this way we provide an adequate tool to quantitatively analyze the behaviour of complex networks in the real world. Various complex systems are studied, ranging from the realm of neural networks, to social sciences, to communication and transportation networks. In each case, economic small worlds are found. Moreover, using the economic small-world framework, the construction principles of these networks can be quantitatively analyzed and compared, giving good insights on how efficiency and economy principles combine up to shape all these systems. Received 6 November 2002 / Received in final form 24 January 2003 Published online 1st April 2003 RID="a" ID="a"e-mail: latora@ct.infn.it     

How effective delays shape oscillatory dynamics in neuronal networks

Synaptic, dendritic and single-cell kinetics generate significant time delays that shape the dynamics of large networks of spiking neurons. Previous work has shown that such effective delays can be taken into account with a rate model through the addition of an explicit, fixed delay (Roxin et al. (2005,2006) [29] and [30]). Here we extend this work to account for arbitrary symmetric patterns of synaptic connectivity and generic nonlinear transfer functions. Specifically, we conduct a weakly nonlinear analysis of the dynamical states arising via primary instabilities of the asynchronous state. In this way we determine analytically how the nature and stability of these states depend on the choice of transfer function and connectivity. We arrive at two general observations of physiological relevance that could not be explained in previous work. These are: 1 — fast oscillations are always supercritical for realistic transfer functions and 2 — traveling waves are preferred over standing waves given plausible patterns of local connectivity. We finally demonstrate that these results show good agreement with those obtained performing numerical simulations of a network of Hodgkin-Huxley neurons.     

不同耦合下混沌神经元网络的同步

采用Hindmarsh-Rose神经元动力学模型, 对二维点阵上的神经元网络的同步进行了研究. 为了解不同耦合对网络同步的影响, 提出了一般反馈耦合、分层反馈耦合和分层局域平均场反馈耦合三种方案.研究表明:在耦合强度较小的近邻耦合下, 一般反馈耦合不能使网络达到完全同步, 而分层反馈耦合和分层局域平均场反馈耦合可以使网络出现局部同步和全局同步. 不同形式的耦合会导致网络出现不同的斑图, 随着耦合强度的增大, 网络从不同步到同步的过程也不相同, 一般反馈耦合和分层反馈耦合网络是突然出现全局同步, 同步之前网络出现非周期性的相干斑图; 对于分层局域平均场反馈耦合网络, 同层神经元之间先出现从簇放电同步到同步的转变, 形成靶波, 然后同步区由中心向外逐渐扩大, 最终达到网络的全局同步. 这些结果表明, 只有适当的耦合才能实现信号的无损耗的传递. 此外我们发现分层局域平均场反馈耦合可以促进网络的同步.