Role of coupling delay in oscillatory activity in autonomous networks of excitable neurons with dissipation.

We study numerically effects of time delay in networks of delay-coupled excitable FitzHugh-Nagumo systems with dissipation. Generation of periodic self-sustained oscillations and its threshold are analyzed depending on the dissipation of a single neuron, the delay time, and random initial conditions. The peculiarities of spatiotemporal dynamics of time-delayed bidirectional ring-structured FitzHugh-Nagumo neuronal systems are investigated in cases of local and nonlocal coupling topology between the nodes, and a first-order nonequilibrium phase transition to synchrony is established. It is shown that the emergence of an oscillatory activity in delay-coupled FitzHugh-Nagumo neurons is observed for smaller values of the coupling strength as the dissipation parameter decreases. This can provide the possibility of controlling the spatiotemporal behavior of the considered neuronal networks. The observed effects are quantified by plotting distributions of the maximal Lyapunov exponent and the global order parameter in terms of delay and coupling strength.

Nonlinear down-conversion in a single quantum dot.

Tailored nanoscale quantum light sources, matching the specific needs of use cases, are crucial building blocks for photonic quantum technologies. Several different approaches to realize solid-state quantum emitters with high performance have been pursued and different concepts for energy tuning have been established. However, the properties of the emitted photons are always defined by the individual quantum emitter and can therefore not be controlled with full flexibility. Here we introduce an all-optical nonlinear method to tailor and control the single photon emission. We demonstrate a laser-controlled down-conversion process from an excited state of a semiconductor quantum three-level system. Based on this concept, we realize energy tuning and polarization control of the single photon emission with a control-laser field. Our results mark an important step towards tailored single photon emission from a photonic quantum system based on quantum optical principles.

Control of electron and electron-hole pair dynamics on nonlinear lattice bilayers by strong solitons.

We consider the dynamics of electrons and holes moving in two-dimensional lattice layers and bilayers. As an example, we study triangular lattices with units interacting via anharmonic Morse potentials and investigate the dynamics of excess electrons and electron-hole pairs according to the Schrödinger equation in the tight binding approximation. We show that when single-site lattice solitons or M-solitons are excited in one of the layers, those lattice deformations are capable of trapping excess electrons or electron-hole pairs, thus forming quasiparticle compounds moving approximately with the velocity of the solitons. We study the temporal and spatial nonlinear dynamical evolution of localized excitations on coupled triangular double layers. Furthermore, we find that the motion of electrons or electron-hole pairs on a bilayer is slaved by solitons. By case studies of the dynamics of charges bound to solitons, we demonstrate that the slaving effect may be exploited for controlling the motion of the electrons and holes in lattice layers, including also bosonic electron-hole-soliton compounds in lattice bilayers, which represent a novel form of quasiparticles.

Escherichia ruysiae sp. nov., a novel Gram-stain-negative bacterium, isolated from a faecal sample of an international traveller.

The genus Escherichia comprises five species and at least five lineages currently not assigned to any species, termed 'Escherichia cryptic clades'. We isolated an Escherichia strain from an international traveller and resolved the complete DNA sequence of the chromosome and an IncI multidrug resistance plasmid using Illumina and Nanopore whole-genome sequencing (WGS). Strain OPT1704T can be differentiated from existing Escherichia species using biochemical (VITEK2) and genomic tests [average nucleotide identity (ANI) and digital DNA-DNA hybridization (dDDH)]. Phylogenetic analysis based on alignment of 16S rRNA sequences and 682 concatenated core genes showed similar results. Our analysis further revealed that strain OPT1704T falls within Escherichia cryptic clade IV and is closely related to cryptic clade III. Combining our analyses with publicly available WGS data of cryptic clades III and IV from Enterobase confirmed the close relationship between clades III and IV (>96 % interclade ANI), warranting assignment of both clades to the same novel species. We propose Escherichia ruysiae sp. nov. as a novel species, encompassing Escherichia cryptic clades III and IV (type strain OPT1704T=NCCB 100732T=NCTC 14359T).

Structural anomalies in brain networks induce dynamical pacemaker effects.

Dynamical effects on healthy brains and brains affected by tumor are investigated via numerical simulations. The brains are modeled as multilayer networks consisting of neuronal oscillators whose connectivities are extracted from Magnetic Resonance Imaging (MRI) data. The numerical results demonstrate that the healthy brain presents chimera-like states where regions with high white matter concentrations in the direction connecting the two hemispheres act as the coherent domain, while the rest of the brain presents incoherent oscillations. To the contrary, in brains with destructed structures, traveling waves are produced initiated at the region where the tumor is located. These areas act as the pacemaker of the waves sweeping across the brain. The numerical simulations are performed using two neuronal models: (a) the FitzHugh-Nagumo model and (b) the leaky integrate-and-fire model. Both models give consistent results regarding the chimera-like oscillations in healthy brains and the pacemaker effect in the tumorous brains. These results are considered a starting point for further investigation in the detection of tumors with small sizes before becoming discernible on MRI recordings as well as in tumor development and evolution.

Relay and complete synchronization in heterogeneous multiplex networks of chaotic maps.

We study relay and complete synchronization in a heterogeneous triplex network of discrete-time chaotic oscillators. A relay layer and two outer layers, which are not directly coupled but interact via the relay layer, represent rings of nonlocally coupled two-dimensional maps. We consider for the first time the case when the spatiotemporal dynamics of the relay layer is completely different from that of the outer layers. Two different configurations of the triplex network are explored: when the relay layer consists of Lozi maps while the outer layers are given by Henon maps and vice versa. Phase and amplitude chimera states are observed in the uncoupled Henon map ring, while solitary state regimes are typical for the isolated Lozi map ring. We show for the first time relay synchronization of amplitude and phase chimeras, a solitary state chimera, and solitary state regimes in the outer layers. We reveal regimes of complete synchronization for the chimera structures and solitary state modes in all the three layers. We also analyze how the synchronization effects depend on the spatiotemporal dynamics of the relay layer and construct phase diagrams in the parameter plane of inter-layer vs intra-layer coupling strength of the relay layer.

Complex partial synchronization patterns in networks of delay-coupled neurons.

We study the spatio-temporal dynamics of a multiplex network of delay-coupled FitzHugh-Nagumo oscillators with non-local and fractal connectivities. Apart from chimera states, a new regime of coexistence of slow and fast oscillations is found. An analytical explanation for the emergence of such coexisting partial synchronization patterns is given. Furthermore, we propose a control scheme for the number of fast and slow neurons in each layer. This article is part of the theme issue 'Nonlinear dynamics of delay systems'.

Synchronization of spiral wave patterns in two-layer 2D lattices of nonlocally coupled discrete oscillators.

The paper describes the effects of mutual and external synchronization of spiral wave structures in two coupled two-dimensional lattices of coupled discrete-time oscillators. Each lattice is given by a 2D N×N network of nonlocally coupled Nekorkin maps which model neuronal activity. We show numerically that spiral wave structures, including spiral wave chimeras, can be synchronized and establish the mechanism of the synchronization scenario. Our numerical studies indicate that when the coupling strength between the lattices is sufficiently weak, only a certain part of oscillators of the interacting networks is imperfectly synchronized, while the other part demonstrates a partially synchronous behavior. If the spatiotemporal patterns in the lattices do not include incoherent cores, imperfect synchronization is realized for most oscillators above a certain value of the coupling strength. In the regime of spiral wave chimeras, the imperfect synchronization of all oscillators cannot be achieved even for sufficiently large values of the coupling strength.

Two-dimensional spatiotemporal complexity in dual-delayed nonlinear feedback systems: Chimeras and dissipative solitons.

We demonstrate for a photonic nonlinear system that two highly asymmetric feedback delays can induce a variety of emergent patterns which are highly robust during the system's global evolution. Explicitly, two-dimensional chimeras and dissipative solitons become visible upon a space-time transformation. Switching between chimeras and dissipative solitons requires only adjusting two system parameters, demonstrating self-organization exclusively based on the system's dynamical properties. Experiments were performed using a tunable semiconductor laser's transmission through a Fabry-Pérot resonator resulting in an Airy function as nonlinearity. Resulting dynamics were bandpass filtered and propagated along two feedback paths whose time delays differ by two orders of magnitude. An excellent agreement between experimental results and the theoretical model given by modified Ikeda equations was achieved.

Erratum: The Dynamics of Coalition Formation on Complex Networks.

This corrects the article DOI: 10.1038/srep13386.

Self-organized emergence of multilayer structure and chimera states in dynamical networks with adaptive couplings.

We report the phenomenon of self-organized emergence of hierarchical multilayered structures and chimera states in dynamical networks with adaptive couplings. This process is characterized by a sequential formation of subnetworks (layers) of densely coupled elements, the size of which is ordered in a hierarchical way, and which are weakly coupled between each other. We show that the hierarchical structure causes the decoupling of the subnetworks. Each layer can exhibit either a two-cluster state, a periodic traveling wave, or an incoherent state, and these states can coexist on different scales of subnetwork sizes.

Synchronization in heterogeneous FitzHugh-Nagumo networks with hierarchical architecture.

We study synchronization in heterogeneous FitzHugh-Nagumo networks. It is well known that heterogeneities in the nodes hinder synchronization when becoming too large. Here we develop a controller to counteract the impact of these heterogeneities. We first analyze the stability of the equilibrium point in a ring network of heterogeneous nodes. We then derive a sufficient condition for synchronization in the absence of control. Based on these results we derive the controller providing synchronization for parameter values where synchronization without control is absent. We demonstrate our results in networks with different topologies. Particular attention is given to hierarchical (fractal) topologies, which are relevant for the architecture of the brain.

The Dynamics of Coalition Formation on Complex Networks.

Complex networks describe the structure of many socio-economic systems. However, in studies of decision-making processes the evolution of the underlying social relations are disregarded. In this report, we aim to understand the formation of self-organizing domains of cooperation ("coalitions") on an acquaintance network. We include both the network's influence on the formation of coalitions and vice versa how the network adapts to the current coalition structure, thus forming a social feedback loop. We increase complexity from simple opinion adaptation processes studied in earlier research to more complex decision-making determined by costs and benefits, and from bilateral to multilateral cooperation. We show how phase transitions emerge from such coevolutionary dynamics, which can be interpreted as processes of great transformations. If the network adaptation rate is high, the social dynamics prevent the formation of a grand coalition and therefore full cooperation. We find some empirical support for our main results: Our model develops a bimodal coalition size distribution over time similar to those found in social structures. Our detection and distinguishing of phase transitions may be exemplary for other models of socio-economic systems with low agent numbers and therefore strong finite-size effects.

Quantum signatures of chimera states.

Chimera states are complex spatiotemporal patterns in networks of identical oscillators, characterized by the coexistence of synchronized and desynchronized dynamics. Here we propose to extend the phenomenon of chimera states to the quantum regime, and uncover intriguing quantum signatures of these states. We calculate the quantum fluctuations about semiclassical trajectories and demonstrate that chimera states in the quantum regime can be characterized by bosonic squeezing, weighted quantum correlations, and measures of mutual information. Our findings reveal the relation of chimera states to quantum information theory, and give promising directions for experimental realization of chimera states in quantum systems.

Localization and expression of CaBP1/caldendrin in the mouse brain.

Ca(2+) binding protein 1 (CaBP1) and caldendrin are alternatively spliced variants of a subfamily of CaBPs with high homology to calmodulin. Although CaBP1 and caldendrin regulate effectors including plasma membrane and intracellular Ca(2+) channels in heterologous expression systems, little is known about their functions in vivo. Therefore, we generated mice deficient in CaBP1/caldendrin expression (C-KO) and analyzed the expression and cellular localization of CaBP1 and caldendrin in the mouse brain. Immunoperoxidase labeling with antibodies recognizing both CaBP1 and caldendrin was absent in the brain of C-KO mice, but was intense in multiple brain regions of wild-type mice. By Western blot, the antibodies detected two proteins that were absent in the C-KO mouse and consistent in size with caldendrin variants originating from alternative translation initiation sites. By quantitative PCR, caldendrin transcript levels were far greater than those for CaBP1, particularly in the cerebral cortex and hippocampus. In the frontal cortex but not in the hippocampus, caldendrin expression increased steadily from birth. By double-label immunofluorescence, CaBP1/caldendrin was localized in principal neurons and parvalbumin-positive interneurons. In the cerebellum, CaBP1/caldendrin antibodies labeled interneurons in the molecular layer and in basket cell terminals surrounding the soma and axon initial segment of Purkinje neurons, but immunolabeling was absent in Purkinje neurons. We conclude that CaBP1/caldendrin is localized both pre- and postsynaptically where it may regulate Ca(2+) signaling and excitability in select groups of excitatory and inhibitory neurons.

Synchronization of networks of oscillators with distributed delay coupling.

This paper studies the stability of synchronized states in networks, where couplings between nodes are characterized by some distributed time delay, and develops a generalized master stability function approach. Using a generic example of Stuart-Landau oscillators, it is shown how the stability of synchronized solutions in networks with distributed delay coupling can be determined through a semi-analytic computation of Floquet exponents. The analysis of stability of fully synchronized and of cluster or splay states is illustrated for several practically important choices of delay distributions and network topologies.

Amplitude and phase dynamics in oscillators with distributed-delay coupling.

This paper studies the effects of distributed-delay coupling on the dynamics in a system of non-identical coupled Stuart-Landau oscillators. For uniform and gamma delay distribution kernels, the conditions for amplitude death are obtained in terms of average frequency, frequency detuning and the parameters of the coupling, including coupling strength and phase, as well as the mean time delay and the width of the delay distribution. To gain further insights into the dynamics inside amplitude death regions, the eigenvalues of the corresponding characteristic equations are computed numerically. Oscillatory dynamics of the system is also investigated, using amplitude and phase representation. Various branches of phase-locked solutions are identified, and their stability is analysed for different types of delay distributions.

Neuronal degeneration is observed in multiple regions outside the hippocampus after lithium pilocarpine-induced status epilepticus in the immature rat.

Although hippocampal sclerosis is frequently identified as a possible epileptic focus in patients with temporal lobe epilepsy, neuronal loss has also been observed in additional structures, including areas outside the temporal lobe. The claim from several researchers using animal models of acquired epilepsy that the immature brain can develop epilepsy without evidence of hippocampal neuronal death raises the possibility that neuronal death in some of these other regions may also be important for epileptogenesis. The present study used the lithium pilocarpine model of acquired epilepsy in immature animals to assess which structures outside the hippocampus are injured acutely after status epilepticus. Sprague-Dawley rat pups were implanted with surface EEG electrodes, and status epilepticus was induced at 20 days of age with lithium pilocarpine. After 72 h, brain tissue from 12 animals was examined with Fluoro-Jade B, a histochemical marker for degenerating neurons. All animals that had confirmed status epilepticus demonstrated Fluoro-Jade B staining in areas outside the hippocampus. The most prominent staining was seen in the thalamus (mediodorsal, paratenial, reuniens, and ventral lateral geniculate nuclei), amygdala (ventral lateral, posteromedial, and basomedial nuclei), ventral premammillary nuclei of hypothalamus, and paralimbic cortices (perirhinal, entorhinal, and piriform) as well as parasubiculum and dorsal endopiriform nuclei. These results demonstrate that lithium pilocarpine-induced status epilepticus in the immature rat brain consistently results in neuronal injury in several distinct areas outside of the hippocampus. Many of these regions are similar to areas damaged in patients with temporal lobe epilepsy, thus suggesting a possible role in epileptogenesis.

Time-domain model of quantum-dot semiconductor optical amplifiers for wideband optical signals.

We present a novel theoretical time-domain model for a quantum dot semiconductor optical amplifier, that allows to simulate subpicosecond pulse propagation including power-based and phase-based effects. Static results including amplified spontaneous emission spectra, continuous wave amplification, and four-wave mixing experiments in addition to dynamic pump-probe simulations are presented for different injection currents. The model uses digital filters to describe the frequency dependent gain and microscopically calculated carrier-carrier scattering rates for the interband carrier dynamics. It can be used to calculate the propagation of multiple signals with different wavelengths or one wideband signal with high bitrate.

Towards easier realization of time-delayed feedback control of odd-number orbits.

We develop generalized time-delayed feedback schemes for the stabilization of periodic orbits with an odd number of positive Floquet exponents, which are particularly well suited for experimental realization. We construct the parameter regimes of successful control and validate these by numerical simulations and numerical continuation methods. In particular, it is shown how periodic orbits can be stabilized with symmetric feedback matrices by introducing an additional latency time in the control loop. Finally, we show using normal form analysis and numerical simulations how our results could be implemented in a laser setup using optoelectronic feedback.