Time-delayed Kuramoto model in the Watts-Strogatz small-world networks.

We study the synchronization of small-world networks of identical coupled phase oscillators through the Kuramoto interaction and uniform time delay. For a given intrinsic frequency and coupling constant, we observe synchronization enhancement in a range of time delays and discontinuous transition from the partially synchronized state with defect patterns to a glassy phase, characterized by a distribution of randomly frozen phase-locked oscillators. By further increasing the time delay, this phase undergoes a discontinuous transition to another partially synchronized state. We found the bimodal frequency distributions and hysteresis loops as indicators of the discontinuous nature of these transitions. Moreover, we found the existence of Chimera states at the onset of transitions.

Neuronal avalanches: Where temporal complexity and criticality meet.

The model of the current paper is an extension of a previous publication, wherein we have used the leaky integrate-and-fire model on a regular lattice with periodic boundary conditions, and introduced the temporal complexity as a genuine signature of criticality. In that work, the power-law distribution of neural avalanches was a manifestation of supercriticality rather than criticality. Here, however, we show that the continuous solution of the model and replacing the stochastic noise with a Gaussian zero-mean noise leads to the coincidence of power-law display of temporal complexity, and spatiotemporal patterns of neural avalanches at the critical point. We conclude that the source of inconsistency may be a numerical artifact originated by the discrete description of the model which may imply a slow numerical convergence of the avalanche distribution compared to temporal complexity.

Phase of neural oscillations as a reference frame for attention-based routing in visual cortex.

Selective attention allows the brain to efficiently process the image projected onto the retina, selectively focusing neural processing resources on behaviorally relevant visual information. While previous studies have documented the crucial role of the action potential rate of single neurons in relaying such information, little is known about how the activity of single neurons relative to their neighboring network contributes to the efficient representation of attended stimuli and transmission of this information to downstream areas. Here, we show in the dorsal visual pathway of monkeys (medial superior temporal area) that neurons fire spikes preferentially at a specific phase of the ongoing population beta (∼20 Hz) oscillations of the surrounding local network. This preferred spiking phase shifts towards a later phase when monkeys selectively attend towards (rather than away from) the receptive field of the neuron. This shift of the locking phase is positively correlated with the speed at which animals report a visual change. Furthermore, our computational modeling suggests that neural networks can manipulate the preferred phase of coupling by imposing differential synaptic delays on postsynaptic potentials. This distinction between the locking phase of neurons activated by the spatially attended stimulus vs. that of neurons activated by the unattended stimulus, may enable the neural system to discriminate relevant from irrelevant sensory inputs and consequently filter out distracting stimuli information by aligning the spikes which convey relevant/irrelevant information to distinct phases linked to periods of better/worse perceptual sensitivity for higher cortices. This strategy may be used to reserve the narrow windows of highest perceptual efficacy to the processing of the most behaviorally relevant information, ensuring highly efficient responses to attended sensory events.

Contrariety and inhibition enhance synchronization in a small-world network of phase oscillators.

We numerically study Kuramoto model synchronization consisting of the two groups of conformist-contrarian and excitatory-inhibitory phase oscillators with equal intrinsic frequency. We consider random and small-world (SW) topologies for the connectivity network of the oscillators. In random networks, regardless of the contrarian to conformist connection strength ratio, we found a crossover from the π-state to the blurred π-state and then a continuous transition to the incoherent state by increasing the fraction of contrarians. However, for the excitatory-inhibitory model in a random network, we found that for all the values of the fraction of inhibitors, the two groups remain in phase and the transition point of fully synchronized to an incoherent state reduced by strengthening the ratio of inhibitory to excitatory links. In the SW networks we found that the order parameters for both models do not show monotonic behavior in terms of the fraction of contrarians and inhibitors. Up to the optimal fraction of contrarians and inhibitors, the synchronization rises by introducing the number of contrarians and inhibitors and then falls. We discuss that the nonmonotonic behavior in synchronization is due to the weakening of the defects already formed in the pure conformist and excitatory agent model in SW networks. We found that in SW networks, the optimal fraction of contrarians and inhibitors remain unchanged for the rewiring probabilities up to ∼0.15, above which synchronization falls monotonically, like the random network. We also showed that in the conformist-contrarian model, the optimal fraction of contrarians is independent of the strength of contrarian links. However, in the excitatory-inhibitory model, the optimal fraction of inhibitors is approximately proportional to the inverse of inhibition strength.

Nodes with the highest control power play an important role at the final level of cooperation in directed networks.

Controllability of complex networks aims to seek the lowest number of nodes (the driver nodes) that can control all the nodes by receiving the input signals. The concept of control centrality is used to determine the power of each node to control the network. The more a node controls the nodes through connections in the network, the more it has the power to control. Although the cooperative and free-rider strategies and the final level of cooperation in a population are considered and studied in the public goods game. However, it is yet to determine a solution to indicate the effectiveness of each member in changing the strategies of the other members. In a network, the choice of nodes effective in changing the other nodes' strategies, as free-riders, will lead to lower cooperation and vice versa. This paper uses simulated and real networks to investigate that the nodes with the highest control power are more effective than the hubs, local, and random nodes in changing the strategies of the other nodes and the final level of cooperation. Results indicate that the nodes with the highest control power as free-riders, compared to the other sets being under consideration, can lead to a lower level of cooperation and are, therefore, more effective in changing the strategies of the other nodes. The obtained results can be considered in the treatment of cancer. So that, destroying the tumoral cells with the highest control power should be a priority as these cells have a higher capability to change the strategies of the other cells from cooperators to free-riders (healthy to tumoral).

Spike-phase coupling as an order parameter in a leaky integrate-and-fire model.

It is known that the leaky integrate-and-fire neural model shows a transition from irregular to synchronous firing by increasing the coupling between the neurons. However, a quantitative characterization of this order-disorder transition, that is, the determination of the order of transition and also the critical exponents in the case of continuous transition, is not entirely known. In this work, we consider a network of N excitatory neurons with local connections, residing on a square lattice with periodic boundary conditions. The cooperation between neurons K plays the role of the control parameter that generates criticality when the critical cooperation strength K_{c} is adopted. We introduce the population-averaged voltage (PAV) as a representative value of the network's cooperative activity. Then, we show that the coupling between the timing of spikes and the phase of temporal fluctuations of PAV defined as m resorts to identify a Kuramoto order parameter. By increasing K, we find a continuous transition from irregular spiking to a phase-locked state at the critical point K_{c}. We deploy the finite-size scaling analysis to calculate the critical exponents of this transition. To explore the formal indicator of criticality, we study the neuronal avalanches profile at this critical point and find a scaling behavior with the exponents in a fair agreement with the experimental values both in vivo and in vitro.

Emergence of hexatic and threefold hidden order in two-dimensional smectic liquid crystals: A Monte Carlo study.

Using a high resolution Monte Carlo simulation technique based on a multihistogram method and cluster algorithm, we have investigated the critical properties of a coupled XY model, consisting of a sixfold symmetric hexatic and a hidden order parameter of threefold symmetry in two dimensions. The simulation results demonstrate a series of continuous transitions in which both kinds of orderings are established simultaneously. It is found that the specific-heat anomaly exponents for some regions in coupling constants space are in excellent agreement with the experimentally measured exponents extracted from heat-capacity data near the smectic- A -hexatic- B transition of two-layer free standing films.

Exactly solvable spin chain models corresponding to BDI class of topological superconductors.

We present an exactly solvable extension of the quantum XY chain with longer range multi-spin interactions. Topological phase transitions of the model are classified in terms of the number of Majorana zero modes, nM which are in turn related to an integer winding number, nW. The present class of exactly solvable models belong to the BDI class in the Altland-Zirnbauer classification of topological superconductors. We show that time reversal symmetry of the spin variables translates into a sliding particle-hole (PH) transformation in the language of Jordan-Wigner fermions - a PH transformation followed by a π shift in the wave vector which we call it the πPH. Presence of πPH symmetry restricts the nW (nM) of time-reversal symmetric extensions of XY to odd (even) integers. The πPH operator may serve in further detailed classification of topological superconductors in higher dimensions as well.

Quantum phase diagram of distorted J 1 - J 2 Heisenberg S = 1/2 antiferromagnet in honeycomb lattice: a modified spin wave study.

Using the modified spin wave method, we study the [Formula: see text] Heisenberg model with first and second neighbor antiferromagnetic exchange interactions. For a symmetric S = 1/2 model, with the same couplings for all the equivalent neighbors, we find three phases in terms of the frustration parameter [Formula: see text]: (1) a commensurate collinear ordering with staggered magnetization (Néel.I state) for [Formula: see text], (2) a magnetically gapped disordered state for [Formula: see text], preserving all the symmetries of the Hamiltonian and lattice, which by definition is a quantum spin liquid (QSL) state and (3) a commensurate collinear ordering in which two out of the three nearest neighbor magnetizations are antiparallel and the remaining pair are parallel (Néel.II state), for [Formula: see text]. We also explore the phase diagram of a distorted [Formula: see text] model with S = 1/2. Distortion is introduced as an inequality of one nearest neighbor coupling with the other two. This yields a richer phase diagram by the appearance of a new gapped QSL, a gapless QSL and also a valence bond crystal phase in addition to the previous three phases found for the undistorted model.

The Physical Mechanism for Retinal Discrete Dark Noise: Thermal Activation or Cellular Ultraweak Photon Emission?

For several decades the physical mechanism underlying discrete dark noise of photoreceptors in the eye has remained highly controversial and poorly understood. It is known that the Arrhenius equation, which is based on the Boltzmann distribution for thermal activation, can model only a part (e.g. half of the activation energy) of the retinal dark noise experimentally observed for vertebrate rod and cone pigments. Using the Hinshelwood distribution instead of the Boltzmann distribution in the Arrhenius equation has been proposed as a solution to the problem. Here, we show that the using the Hinshelwood distribution does not solve the problem completely. As the discrete components of noise are indistinguishable in shape and duration from those produced by real photon induced photo-isomerization, the retinal discrete dark noise is most likely due to 'internal photons' inside cells and not due to thermal activation of visual pigments. Indeed, all living cells exhibit spontaneous ultraweak photon emission (UPE), mainly in the optical wavelength range, i.e., 350-700 nm. We show here that the retinal discrete dark noise has a similar rate as UPE and therefore dark noise is most likely due to spontaneous cellular UPE and not due to thermal activation.

Monte Carlo simulation of a strongly coupled XY model in three dimensions.

Many experimental studies, over the past two decades, have constantly reported a critical behavior for the transition from the smectic- A phase of liquid crystals to the hexatic- B phase with non- XY critical exponents. However, according to symmetry arguments this transition must belong to the XY universality class. Using an optimized Monte Carlo simulation technique based on the multihistogram method, we have investigated the phase diagram of a coupled XY model, proposed by Bruinsma and Aeppli [Phys. Rev. Lett. 48, 1625 (1982)], in three dimensions. The simulation results demonstrate the existence of a tricritical point for this model, in which two different orderings are established simultaneously. This result verifies the accepted idea that the large specific heat anomaly exponent observed for the SmA-HexB transition could be due to the occurrence of this transition in the vicinity of a tricritical point.

Noise assisted excitation energy transfer in a linear model of a selectivity filter backbone strand.

In this paper, we investigate the effect of noise and disorder on the efficiency of excitation energy transfer (EET) in a N = 5 sites linear chain with 'static' dipole-dipole couplings. In fact, here, the disordered chain is a toy model for one strand of the selectivity filter backbone in ion channels. It has recently been discussed that the presence of quantum coherence in the selectivity filter is possible and can play a role in mediating ion-conduction and ion-selectivity in the selectivity filter. The question is 'how a quantum coherence can be effective in such structures while the environment of the channel is dephasing (i.e. noisy)?' Basically, we expect that the presence of the noise should have a destructive effect in the quantum transport. In fact, we show that such expectation is valid for ordered chains. However, our results indicate that introducing the dephasing in the disordered chains leads to the weakening of the localization effects, arising from the multiple back-scatterings due to the randomness, and then increases the efficiency of quantum energy transfer. Thus, the presence of noise is crucial for the enhancement of EET efficiency in disordered chains. We also show that the contribution of both classical and quantum mechanical effects are required to improve the speed of energy transfer along the chain. Our analysis may help for better understanding of fast and efficient functioning of the selectivity filters in ion channels.

Valence bond phases in S = 1/2 Kane-Mele-Heisenberg model.

The phase diagram of the Kane-Mele-Heisenberg model in a classical limit [47] contains disordered regions in the coupling space, as the result of competition between different terms in the Hamiltonian, leading to frustration in finding a unique ground state. In this work we explore the nature of these phases in the quantum limit, for a S = 1/2. Employing exact diagonalization in Sz and nearest neighbour valence bond bases, and bond and plaquette valence bond mean field theories, we show that the disordered regions are divided into ordered quantum states in the form of plaquette valence bond crystals and staggered dimerized phases.

Noise-induced synchronization in small world networks of phase oscillators.

A small-world (SW) network of similar phase oscillators, interacting according to the Kuramoto model, is studied numerically. It is shown that deterministic Kuramoto dynamics on SW networks has various stable stationary states. This can be attributed to the so-called defect patterns in an SW network, which it inherits from deformation of helical patterns in its regular parent. Turning on an uncorrelated random force causes vanishing of the defect patterns, hence increasing the synchronization among oscillators for moderate noise intensities. This phenomenon, called stochastic synchronization, is generally observed in some natural networks such as the brain neural network.

Anderson transition in disordered bilayer graphene.

Employing the kernel polynomial method (KPM), we study the electronic properties of the graphene bilayers with Bernal stacking in the presence of diagonal disorder, within the tight-binding approximation and nearest neighbor interactions. The KPM method enables us to calculate local density of states (LDOS) without the need to exactly diagonalize the Hamiltonian. We use the geometrical averaging of the LDOS at different lattice sites as a criterion to distinguish the localized states from extended ones. We find that this model undergoes an Anderson metal-insulator transition at a critical value of disorder strength.