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Recent experimental and theoretical studies have indicated that the putative criticality of cortical dynamics may correspond to a synchronization phase transition. The critical dynamics near such a critical point needs further investigation specifically when compared to the critical behavior near the standard absorbing state phase transition. Since the phenomena of learning and self-organized criticality (SOC) at the edge of synchronization transition can emerge jointly in spiking neural networks due to the presence of spike-timing dependent plasticity (STDP), it is tempting to ask the following: what is the relationship between synchronization and learning in neural networks? Further, does learning benefit from SOC at the edge of synchronization transition? In this paper, we intend to address these important issues. Accordingly, we construct a biologically inspired model of a cognitive system which learns to perform stimulus-response tasks. We train this system using a reinforcement learning rule implemented through dopamine-modulated STDP. We find that the system exhibits a continuous transition from synchronous to asynchronous neural oscillations upon increasing the average axonal time delay. We characterize the learning performance of the system and observe that it is optimized near the synchronization transition. We also study neuronal avalanches in the system and provide evidence that optimized learning is achieved in a slightly supercritical state.

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Within the context of social balance theory, much attention has been paid to the attainment and stability of unipolar or bipolar societies. However, multipolar societies are commonplace in the real world, despite the fact that the mechanism of their emergence is much less explored. Here, we investigate the evolution of a society of interacting agents with friendly (positive) and enmity (negative) relations into a final stable multipolar state. Triads are assigned energy according to the degree of tension they impose on the network. Agents update their connections to decrease the total energy (tension) of the system, on average. Our approach is to consider a variable energy ε∈[0,1] for triads which are entirely made of negative relations. We show that the final state of the system depends on the initial density of the friendly links ρ_{0}. For initial densities greater than an ε-dependent threshold ρ_{0}^{c}(ε), a unipolar (paradise) state is reached. However, for ρ_{0}≤ρ_{0}^{c}(ε), multipolar and bipolar states can emerge. We observe that the number of stable final poles increases with decreasing ε where the first transition from bipolar to multipolar society occurs at ε^{*}≈0.67. We end the paper by providing a mean-field calculation that provides an estimate for the critical (ε dependent) initial positive link density, which is consistent with our simulations.

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Recently, we introduced a stochastic social balance model with Glauber dynamics which takes into account the role of randomness in the individual's behavior [Phys. Rev. E 100, 022303 (2019)2470-004510.1103/PhysRevE.100.022303]. One important finding of our study was a phase transition from a balance state to an imbalance state as the randomness crosses a critical value, which was shown to vanish in the thermodynamic limit. In a similar study [Malarz and Kulakowski, Phys. Rev. E 103, 066301 (2021)10.1103/PhysRevE.103.066301], it was shown that the critical randomness tends to infinity as the system size diverges. This led the authors to question the appropriateness of the results in our Monte Carlo simulations, when compared with the non-normalized form, used in their work. The normalized form of energy in our model is, in fact, a common choice when one deals with systems comprising long-range interactions. Here, we show how their probabilistic definition leads to vanishing possibility of forming negative bonds, thus leading to a frozen ordered (paradise) state for any amount of finite randomness (temperature) for large enough system size. On the other hand, in the same large system size limit, our model is unstable to thermal randomness due to global, long-range effect of changing a bond's sign. We also address the rule of different updating mechanisms (synchronous vs sequential) in the two models. We finally discuss the distinction between the balanced states reached by each model and provide arguments for social relevance of our model.

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Critical brain hypothesis has been intensively studied both in experimental and theoretical neuroscience over the past two decades. However, some important questions still remain: (i) What is the critical point the brain operates at? (ii) What is the regulatory mechanism that brings about and maintains such a critical state? (iii) The critical state is characterized by scale-invariant behavior which is seemingly at odds with definitive brain oscillations? In this work we consider a biologically motivated model of Izhikevich neuronal network with chemical synapses interacting via spike-timing-dependent plasticity (STDP) as well as axonal time delay. Under generic and physiologically relevant conditions we show that the system is organized and maintained around a synchronization transition point as opposed to an activity transition point associated with an absorbing state phase transition. However, such a state exhibits experimentally relevant signs of critical dynamics including scale-free avalanches with finite-size scaling as well as critical branching ratios. While the system displays stochastic oscillations with highly correlated fluctuations, it also displays dominant frequency modes seen as sharp peaks in the power spectrum. The role of STDP as well as time delay is crucial in achieving and maintaining such critical dynamics, while the role of inhibition is not as crucial. In this way we provide possible answers to all three questions posed above. We also show that one can achieve supercritical or subcritical dynamics if one changes the average time delay associated with axonal conduction.

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We study the evolution of a social network with friendly or enmity connections into a balanced state by introducing a dynamical model with an intrinsic randomness, similar to Glauber dynamics in statistical mechanics. We include the possibility of the tension promotion as well as the tension reduction in our model. Such a more realistic situation enables the system to escape from local minima in its energy landscape and thus to exit out of frozen imbalanced states, which are unwanted outcomes observed in previous models. On the other hand, in finite networks the dynamics takes the system into a balanced phase, if the randomness is lower than a critical value. For large networks, we also find a sharp phase transition at the initial positive link density of ρ_{0}^{*}=1/2, where the system transitions from a bipolar state into a paradise. This modifies the gradual phase transition at a nontrivial value of ρ_{0}^{*}≃0.65, observed in recent studies.

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Scale-free behavior as well as oscillations are frequently observed in the activity of many natural systems. One important example is the cortical tissues of mammalian brain where both phenomena are simultaneously observed. Rhythmic oscillations as well as critical (scale-free) dynamics are thought to be important, but theoretically incompatible, features of a healthy brain. Motivated by the above, we study the possibility of the coexistence of scale-free avalanches along with rhythmic behavior within the framework of self-organized criticality. In particular, we add an oscillatory perturbation to local threshold condition of the continuous Zhang model and characterize the subsequent activity of the system. We observe regular oscillations embedded in well-defined avalanches which exhibit scale-free size and duration in line with observed neuronal avalanches. The average amplitude of such oscillations are shown to decrease with increasing frequency consistent with real brain oscillations. Furthermore, it is shown that optimal amplification of oscillations occur at the critical point, further providing evidence for functional advantages of criticality.

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Despite their significant functional roles, beta-band oscillations are least understood. Synchronization in neuronal networks have attracted much attention in recent years with the main focus on transition type. Whether one obtains explosive transition or a continuous transition is an important feature of the neuronal network which can depend on network structure as well as synaptic types. In this study we consider the effect of synaptic interaction (electrical and chemical) as well as structural connectivity on synchronization transition in network models of Izhikevich neurons which spike regularly with beta rhythms. We find a wide range of behavior including continuous transition, explosive transition, as well as lack of global order. The stronger electrical synapses are more conducive to synchronization and can even lead to explosive synchronization. The key network element which determines the order of transition is found to be the clustering coefficient and not the small world effect, or the existence of hubs in a network. These results are in contrast to previous results which use phase oscillator models such as the Kuramoto model. Furthermore, we show that the patterns of synchronization changes when one goes to the gamma band. We attribute such a change to the change in the refractory period of Izhikevich neurons which changes significantly with frequency.

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Networks of excitable nodes have recently attracted much attention particularly in regards to neuronal dynamics, where criticality has been argued to be a fundamental property. Refractory behavior, which limits the excitability of neurons is thought to be an important dynamical property. We therefore consider a simple model of excitable nodes which is known to exhibit a transition to instability at a critical point (λ = 1), and introduce refractory period into its dynamics. We use mean-field analytical calculations as well as numerical simulations to calculate the activity dependent branching ratio that is useful to characterize the behavior of critical systems. We also define avalanches and calculate probability distribution of their size and duration. We find that in the presence of refractory period the dynamics stabilizes while various parameter regimes become accessible. A sub-critical regime with λ < 1.0, a standard critical behavior with exponents close to critical branching process for λ = 1, a regime with 1 < λ < 2 that exhibits an interesting scaling behavior, and an oscillating regime with λ > 2.0. We have therefore shown that refractory behavior leads to a wide range of scaling as well as periodic behavior which are relevant to real neuronal dynamics.

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Critical dynamics of cortical neurons have been intensively studied over the past decade. Neuronal avalanches provide the main experimental as well as theoretical tools to consider criticality in such systems. Experimental studies show that critical neuronal avalanches show mean-field behavior. There are structural as well as recently proposed [Phys. Rev. E 89, 052139 (2014)] dynamical mechanisms that can lead to mean-field behavior. In this work we consider a simple model of neuronal dynamics based on threshold self-organized critical models with synaptic noise. We investigate the role of high-average connectivity, random long-range connections, as well as synaptic noise in achieving mean-field behavior. We employ finite-size scaling in order to extract critical exponents with good accuracy. We conclude that relevant structural mechanisms responsible for mean-field behavior cannot be justified in realistic models of the cortex. However, strong dynamical noise, which can have realistic justifications, always leads to mean-field behavior regardless of the underlying structure. Our work provides a different (dynamical) origin than the conventionally accepted (structural) mechanisms for mean-field behavior in neuronal avalanches.

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Motivated by recent experiments in neuroscience which indicate that neuronal avalanches exhibit scale invariant behavior similar to self-organized critical systems, we study the role of noisy (nonconservative) local dynamics on the critical behavior of a sandpile model which can be taken to mimic the dynamics of neuronal avalanches. We find that despite the fact that noise breaks the strict local conservation required to attain criticality, our system exhibits true criticality for a wide range of noise in various dimensions, given that conservation is respected on the average. Although the system remains critical, exhibiting finite-size scaling, the value of critical exponents change depending on the intensity of local noise. Interestingly, for a sufficiently strong noise level, the critical exponents approach and saturate at their mean-field values, consistent with empirical measurements of neuronal avalanches. This is confirmed for both two and three dimensional models. However, the addition of noise does not affect the exponents at the upper critical dimension (D = 4). In addition to an extensive finite-size scaling analysis of our systems, we also employ a useful time-series analysis method to establish true criticality of noisy systems. Finally, we discuss the implications of our work in neuroscience as well as some implications for the general phenomena of criticality in nonequilibrium systems.

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Recent advances in brain and cognitive science studies have revolutionized concepts in neural dynamics, regulating mechanisms, coding systems and information processing networks which govern our function and behavior. Hidden aspects of neurological and psychiatric diseases are being understood and hopes for their treatment are emerging. Although the two comprehensive mega-projects on brain mapping are in place in the United States and Europe; the proportion of science contributed by the developing countries should not be downsized. With the granted supports from the Cognitive Sciences and Technologies Council (CSTC), Iran can take its role in research on brain and cognition further. The idea of research and development in Cognitive Sciences and Technologies (CST) is being disseminated across the country by CSTC. Towards this goal, the first Shiraz interdisciplinary meeting on CST was held on 9 January 2014 in Namazi hospital, Shiraz. CST research priorities, infrastructure development, education and promotion were among the main topics discussed during this interactive meeting. The steering committee of the first CST meeting in Shiraz decided to frame future research works within the "Brain and Cognition Study Group-Shiraz" (BCSG-Shiraz). The study group comprises scientific leaders from various allied disciplines including neuroscience, neurosurgery, neurology, psychiatry, psychology, radiology, physiology, bioengineering, biophysics, applied physics and telecommunication. As the headquarter for CST in the southern Iran, BCSG-Shiraz is determined to advocate "brain and cognition" awareness, education and research in close collaboration with CSTC. Together with CSTC, Shiraz Neuroscience Research center (SNRC) will take the initiative to cross boundaries in interdisciplinary works and multi-centric research projects within the study group.

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In this paper we consider the effect of different time parametrizations on the stationary velocity distribution function for a relativistic gas. We clarify the distinction between two such distributions, namely, the Jüttner and the Modified Jüttner distributions. Using a recently proposed model of a relativistic gas, we show that the obtained results for the proper-time averaging does not lead to the Modified Jüttner distribution (as recently conjectured), but introduces a Lorentz factor γ(v) (i.e., energy) to the well-known Jüttner function which results from observer-time averaging. These two modifications (i.e., Modified Jüttner function or Jüttner divided by energy) are identical in the rest frame; however, their distinction comes to light when one considers a moving frame. We obtain results for rest frame as well as moving frame in order to support our claim. We finally conclude that reparametrizing time simply rescales stationary (Jüttner) distribution function according to a well-defined frame-independent relation.

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In this paper we study a fully relativistic model of a two-dimensional hard-disk gas. This model avoids the general problems associated with relativistic particle collisions and is therefore an ideal system to study relativistic effects in statistical thermodynamics. We study this model using molecular-dynamics simulation, concentrating on the velocity distribution functions. We obtain results for x and y components of velocity in the rest frame (Gamma) as well as the moving frame (Gamma;{'}) . Our results confirm that Jüttner distribution is the correct generalization of Maxwell-Boltzmann distribution. We obtain the same "temperature" parameter beta for both frames consistent with a recent study of a limited one-dimensional model. We also address the controversial topic of temperature transformation. We show that while local thermal equilibrium holds in the moving frame, relying on statistical methods such as distribution functions or equipartition theorem are ultimately inconclusive in deciding on a correct temperature transformation law (if any).