|1- G. Esfahani, Z., Gollo, L., Valizadeh, A., "Stimulus-dependent synchronization in delayed-coupled neuronal networks", Scientific Reports: (6), 23471-1-23471-10, (2016).|
Time delay is a general feature of all interactions. Although the effects of delayed interaction are often neglected when the intrinsic dynamics is much slower than the coupling delay, they can be crucial otherwise. We show that delayed coupled neuronal networks support transitions between synchronous and asynchronous states when the level of input to the network changes. The level of input determines the oscillation period of neurons and hence whether time-delayed connections are synchronizing or desynchronizing. We find that synchronizing connections lead to synchronous dynamics, whereas desynchronizing connections lead to out-of-phase oscillations in network motifs and to frustrated states with asynchronous dynamics in large networks. Since the impact of a neuronal network to downstream neurons increases when spikes are synchronous, networks with delayed connections can serve as gatekeeper layers mediating the firing transfer to other regions. This mechanism can regulate the opening and closing of communicating channels between cortical layers on demand.
|2- Bolhasani, E., Valizadeh, A., "Stabilizing synchrony by inhomogeneity", Scientific Reports, 5, 13854-1-13854-7, (2015).|
We show that for two weakly coupled identical neuronal oscillators with strictly positive phase resetting curve, isochronous synchrony can only be seen in the absence of noise and an arbitrarily weak noise can destroy entrainment and generate intermittent phase slips. Small inhomogeneity–mismatch in the intrinsic firing rate of the neurons–can stabilize the phase locking and lead to more precise relative spike timing of the two neurons. The results can explain how for a class of neuronal models, including leaky integrate-fire model, inhomogeneity can increase correlation of spike trains when the neurons are synaptically connected.
|3- Zarepour, M., D. Niry, M., Valizadeh, A., "Functional scale-free networks in the two-dimensional Abelian sandpile model", Phys. Rew. E., 92: (1), 012822-1-012822-6, (2015).|
Recently, the similarity of the functional network of the brain and the Ising model was investigated by Chialvo [Nat. Phys. 6, 744 (2010)]. This similarity supports the idea that the brain is a self-organized critical system. In this study we derive a functional network of the two-dimensional Bak-Tang-Wiesenfeld sandpile model as a self-organized critical model, and compare its characteristics with those of the functional network of the brain, obtained from functional magnetic resonance imaging.
|4- Bayati, M., Valizadeh, A., Abbasian, A., Cheng, S., "Self-organization of synchronous activity propagation in neuronal networks driven by local excitation", Front. Comput. Neurosci, 9, 1-15, (2015).|
Many experimental and theoretical studies have suggested that the reliable propagation of synchronous neural activity is crucial for neural information processing. The propagation of synchronous firing activity in so-called synfire chains has been studied extensively in feed-forward networks of spiking neurons. However, it remains unclear how such neural activity could emerge in recurrent neuronal networks through synaptic plasticity. In this study, we investigate whether local excitation, i.e., neurons that fire at a higher frequency than the other, spontaneously active neurons in the network, can shape a network to allow for synchronous activity propagation. We use two-dimensional, locally connected and heterogeneous neuronal networks with spike-timing dependent plasticity (STDP). We find that, in our model, local excitation drives profound network changes within seconds. In the emergent network, neural activity propagates synchronously through the network. This activity originates from the site of the local excitation and propagates through the network. The synchronous activity propagation persists, even when the local excitation is removed, since it derives from the synaptic weight matrix. Importantly, once this connectivity is established it remains stable even in the presence of spontaneous activity. Our results suggest that synfire-chain-like activity can emerge in a relatively simple way in realistic neural networks by locally exciting the desired origin of the neuronal sequence.
|5- Ghasemi Esfahani, Z., Valizadeh , A., "Zero-Lag Synchronization Despite Inhomogeneities in a Relay System
", PLoS ONE, 9: (12), 1-22, (2014).|
A novel proposal for the zero-lag synchronization of the delayed coupled neurons, is to connect them indirectly via a third relay neuron. In this study, we develop a Poincaré map to investigate the robustness of the synchrony in such a relay system against inhomogeneity in the neurons and synaptic parameters. We show that when the inhomogeneity does not violate the symmetry of the system, synchrony is maintained and in some cases inhomogeneity enhances synchrony. On the other hand if the inhomogeneity breaks the symmetry of the system, zero lag synchrony can not be preserved. In this case we give analytical results for the phase lag of the spiking of the neurons in the stable state.
|1- Goodarzi Nick, A., Niry, M. D., Valizadeh, A., "Scale-free functional networks of 2D Ising model are highly robust against structural defects: neuroscience implications/ Sharpee, et al., BMC Neuroscience 17 (Suppl 1), 54, P41", 25th Annual Computational Neuroscience
Seogwipo City, Jeju-do, South Korea. 2–7 July 2016, 33-, (2016).|
In recent years, several experimental observations have confirmed the emergence of self-organized criticality (SOC) in the brain at different scales . At large scale, functional brain networks obtained from fMRI data have shown that node-degree distributions and probability of finding a link versus distance are indicative of scale-free and small-world networks regardless of the tasks in which the subjects were involved . At small scale, the study of neuronal avalanches in networks of living neurons revealed power-law behavior in both spatial and temporal scales . It is also shown that functional networks of the brain are strikingly similar to those derived from the 2D Ising model at critical temperature  and the 2D abelian sandpile model 
|2- Pariz, A., Sadat Parsi, S., Valizadeh, A., "High frequency neuron can facilitate propagation of signal in neural networks/Sharpee, et al., BMC Neuroscience 17 (Suppl 1), 54, P42", 25th Annual Computational Neuroscience
Seogwipo City, Jeju-do, South Korea. 2–7 July 2016, 33-, (2016).|
Signal transmission is of interest from both fundamental and clinical perspective and has been well studied in nonlinear science and complex networks [1, 2]. In particular, in nervous systems, cognitive processing involves signal propagation through multiple brain regions and the activation of large numbers of specific neurons [3–6]. In information propagation through brain regions, each part, known as generator, activated locally as information comes to it from neighboring generators. Although the problem is well studied in the context of complex networks, our focus here is on the effect of the intrinsic dynamical properties of the reciprocal generators on the propagation of signal