When long-range zero-lag synchronization is feasible in cortical networks

Many studies have reported long-range synchronization of neuronal activity between brain areas, in particular in the beta and gamma bands with frequencies in the range of 14–30 and 40–80 Hz, respectively. Several studies have reported synchrony with zero phase lag, which is remarkable considering the synaptic and conduction delays inherent in the connections between distant brain areas. This result has led to many speculations about the possible functional role of zero-lag synchrony, such as for neuronal communication, attention, memory, and feature binding. However, recent studies using recordings of single-unit activity and local field potentials report that neuronal synchronization may occur with non-zero phase lags. This raises the questions whether zero-lag synchrony can occur in the brain and, if so, under which conditions. We used analytical methods and computer simulations to investigate which connectivity between neuronal populations allows or prohibits zero-lag synchrony. We did so for a model where two oscillators interact via a relay oscillator. Analytical results and computer simulations were obtained for both type I Mirollo–Strogatz neurons and type II Hodgkin–Huxley neurons. We have investigated the dynamics of the model for various types of synaptic coupling and importantly considered the potential impact of Spike-Timing Dependent Plasticity (STDP) and its learning window. We confirm previous results that zero-lag synchrony can be achieved in this configuration. This is much easier to achieve with Hodgkin–Huxley neurons, which have a biphasic phase response curve, than for type I neurons. STDP facilitates zero-lag synchrony as it adjusts the synaptic strengths such that zero-lag synchrony is feasible for a much larger range of parameters than without STDP.

On Hamiltonian balanced dynamics and the slowest invariant manifold

The concept of a slowest invariant manifold is investigated for the five-component model of Lorenz under conservative dynamics. It is shown that Lorenz's model is a two-degree-of-freedom canonical Hamiltonian system, consisting of a nonlinear vorticity-triad oscillator coupled to a linear gravity wave oscillator, whose solutions consist of regular and chaotic orbits. When either the Rossby number or the rotational Froude number is small, there is a formal separation of timescales, and one can speak of fast and slow motion. In the same regime, the coupling is weak, and the Kolmogorov–Arnold-Moser theorem is shown to apply. The chaotic orbits are inherently unbalanced and are confined to regions sandwiched between invariant tori consisting of quasi-periodic regular orbits. The regular orbits generally contain free fast motion, but a slowest invariant manifold may be geometrically defined as the set of all slow cores of invariant tori (defined by zero fast action) that are smoothly related to such cores in the uncoupled system. This slowest invariant manifold is not global; in fact, its structure is fractal; but it is of nearly full measure in the limit of weak coupling. It is also nonlinearly stable. As the coupling increases, the slowest invariant manifold shrinks until it disappears altogether. The results clarify previous definitions of a slowest invariant manifold and highlight the ambiguity in the definition of “slowness.” An asymptotic procedure, analogous to standard initialization techniques, is found to yield nonzero free fast motion even when the core solutions contain none. A hierarchy of Hamiltonian balanced models preserving the symmetries in the original low-order model is formulated; these models are compared with classic balanced models, asymptotically initialized solutions of the full system and the slowest invariant manifold defined by the core solutions. The analysis suggests that for sufficiently small Rossby or rotational Froude numbers, a stable slowest invariant manifold can be defined for this system, which has zero free gravity wave activity, but it cannot be defined everywhere. The implications of the results for more complex systems are discussed.

Quantifying errors due to frequency changes and target location uncertainty for radar refractivity retrievals

Radar refractivity retrievals can capture near-surface humidity changes, but noisy phase changes of the ground clutter returns limit the accuracy for both klystron- and magnetron-based systems. Observations with a C-band (5.6 cm) magnetron weather radar indicate that the correction for phase changes introduced by local oscillator frequency changes leads to refractivity errors no larger than 0.25 N units: equivalent to a relative humidity change of only 0.25% at 20°C. Requested stable local oscillator (STALO) frequency changes were accurate to 0.002 ppm based on laboratory measurements. More serious are the random phase change errors introduced when targets are not at the range-gate center and there are changes in the transmitter frequency (ΔfTx) or the refractivity (ΔN). Observations at C band with a 2-μs pulse show an additional 66° of phase change noise for a ΔfTx of 190 kHz (34 ppm); this allows the effect due to ΔN to be predicted. Even at S band with klystron transmitters, significant phase change noise should occur when a large ΔN develops relative to the reference period [e.g., ~55° when ΔN = 60 for the Next Generation Weather Radar (NEXRAD) radars]. At shorter wavelengths (e.g., C and X band) and with magnetron transmitters in particular, refractivity retrievals relative to an earlier reference period are even more difficult, and operational retrievals may be restricted to changes over shorter (e.g., hourly) periods of time. Target location errors can be reduced by using a shorter pulse or identified by a new technique making alternate measurements at two closely spaced frequencies, which could even be achieved with a dual–pulse repetition frequency (PRF) operation of a magnetron transmitter.

Power transfer in velocity-vortex acceleration

A theoretical model is presented of an electron acceleration-as-oscillator method derived from the work of Joseph Larmor unified with J. Clerk Maxwell’s theory of vorticity for the displacement of radiation into free-space at an antenna interface.

The lifecycle of the North Atlantic storm track

The North Atlantic eddy-driven jet exhibits latitudinal variability, with evidence of three preferred latitudinal locations: south, middle and north. Here we examine the drivers of this variability and the variability of the associated storm track. We investigate the changes in the storm track characteristics for the three jet locations, and propose a mechanism by which enhanced storm track activity, as measured by upstream heat flux, is responsible for cyclical downstream latitudinal shifts in the jet. This mechanism is based on a nonlinear oscillator relationship between the enhanced meridional temperature gradient (and thus baroclinicity) and the meridional high-frequency (periods of shorter than 10 days) eddy heat flux. Such oscillations in baroclinicity and heat flux induce variability in eddy anisotropy which is associated with the changes in the dominant type of wave breaking and a different latitudinal deflection of the jet. Our results suggest that high heat flux is conducive to a northward deflection of the jet, whereas low heat flux is conducive to a more zonal jet. This jet deflecting effect was found to operate most prominently downstream of the storm track maximum, while the storm track and the jet remain anchored at a fixed latitudinal location at the beginning of the storm track. These cyclical changes in storm track characteristics can be viewed as different stages of the storm track’s spatio-temporal lifecycle.

Dissociation of circadian and light inhibition of melatonin release through forced desynchronization in the rat

Pineal melatonin release exhibits a circadian rhythm with a tight nocturnal pattern. Melatonin synthesis is regulated by the master circadian clock within the hypothalamic suprachiasmatic nucleus (SCN) and is also directly inhibited by light. The SCN is necessary for both circadian regulation and light inhibition of melatonin synthesis and thus it has been difficult to isolate these two regulatory limbs to define the output pathways by which the SCN conveys circadian and light phase information to the pineal. A 22-h light-dark (LD) cycle forced desynchrony protocol leads to the stable dissociation of rhythmic clock gene expression within the ventrolateral SCN (vlSCN) and the dorsomedial SCN (dmSCN). In the present study, we have used this protocol to assess the pattern of melatonin release under forced desynchronization of these SCN subregions. In light of our reported patterns of clock gene expression in the forced desynchronized rat, we propose that the vlSCN oscillator entrains to the 22-h LD cycle whereas the dmSCN shows relative coordination to the light-entrained vlSCN, and that this dual-oscillator configuration accounts for the pattern of melatonin release. We present a simple mathematical model in which the relative coordination of a single oscillator within the dmSCN to a single light-entrained oscillator within the vlSCN faithfully portrays the circadian phase, duration and amplitude of melatonin release under forced desynchronization. Our results underscore the importance of the SCN`s subregional organization to both photic input processing and rhythmic output control.

Circadian Pattern of Wheel-Running Activity of a South American Subterranean Rodent (Ctenomys cf knightii)

Circadian rhythms are regarded as essentially ubiquitous features of animal behavior and are thought to confer important adaptive advantages. However, although circadian systems of rodents have been among the most extensively studied, most comparative biology is restricted to a few related species. In this study, the circadian organization of locomotor activity was studied in the subterranean, solitary north Argentinean rodent, Ctenomys knightii. The genus, Ctenomys, commonly known as Tuco-tucos, comprises more than 50 known species over a range that extends from 12S latitude into Patagonia, and includes at least one social species. The genus, therefore, is ideal for comparative and ecological studies of circadian rhythms. Ctenomys knightii is the first of these to be studied for its circadian behavior. All animals were wild caught but adapted quickly to laboratory conditions, with clear and precise activity-rest rhythms in a light-dark (LD) cycle and strongly nocturnal wheel running behavior. In constant dark (DD), the rhythm expression persisted with free-running periods always longer than 24h. Upon reinstatement of the LD cycle, rhythms resynchronized rapidly with large phase advances in 7/8 animals. In constant light (LL), six animals had free-running periods shorter than in DD, and 4/8 showed evidence of splitting. We conclude that under laboratory conditions, in wheel-running cages, this species shows a clear nocturnal rhythmic organization controlled by an endogenous circadian oscillator that is entrained to 24h LD cycles, predominantly by light-induced advances, and shows the same interindividual variable responses to constant light as reported in other non-subterranean species. These data are the first step toward understanding the chronobiology of the largest genus of subterranean rodents.

Patterns of fos activation in rat raphe nuclei during feeding behavior

To analyze the differential recruitment of the raphe nuclei during different phases of feeding behavior, rats were subjected to a food restriction schedule (food for 2 h/day, during 15 days). The animals were submitted to different feeding conditions, constituting the experimental groups: search for food (MFS), food ingestion (MFI), satiety (MFSa) and food restriction control (MFC). A baseline condition (BC) group was included as further control. The MFI and MFC groups, which presented greater autonomic and somatic activation, had more FOS-immunoreactive (FOS-IR) neurons. The MFI group presented more labeled cells in the linear (LRN) and dorsal (DRN) nuclei; the MFC group showed more labeling in the median (MRN), pontine (PRN), magnus (NRM) and obscurus (NRO) nuclei; and the MFSa group had more labeled cells in the pallidus (NRP). The BC exhibited the lowest number of reactive cells. The PRN presented the highest percentage of activation in the raphe while the DRN the lowest. Additional experiments revealed few double-labeled (FOS-IR+ 5-HT-IR) cells within the raphe nuclei in the MFI group, suggesting little serotonergic activation in the raphe during food ingestion. These findings suggest a differential recruitment of raphe nuclei during various phases of feeding behavior. Such findings may reflect changes in behavioral state (e.g., food-induced arousal versus sleep) that lead to greater motor activation, and consequently increased FOS expression. While these data are consistent with the idea that the raphe system acts as gain setter for autonomic and somatic activities, the functional complexity of the raphe is not completely understood. (c) 2008 Elsevier B.V. All rights reserved.

Semiclassical evolution of dissipative Markovian systems

A semiclassical approximation for an evolving density operator, driven by a `closed` Hamiltonian operator and `open` Markovian Lindblad operators, is obtained. The theory is based on the chord function, i.e. the Fourier transform of the Wigner function. It reduces to an exact solution of the Lindblad master equation if the Hamiltonian operator is a quadratic function and the Lindblad operators are linear functions of positions and momenta. Initially, the semiclassical formulae for the case of Hermitian Lindblad operators are reinterpreted in terms of a (real) double phase space, generated by an appropriate classical double Hamiltonian. An extra `open` term is added to the double Hamiltonian by the non-Hermitian part of the Lindblad operators in the general case of dissipative Markovian evolution. The particular case of generic Hamiltonian operators, but linear dissipative Lindblad operators, is studied in more detail. A Liouville-type equivariance still holds for the corresponding classical evolution in double phase space, but the centre subspace, which supports the Wigner function, is compressed, along with expansion of its conjugate subspace, which supports the chord function. Decoherence narrows the relevant region of double phase space to the neighbourhood of a caustic for both the Wigner function and the chord function. This difficulty is avoided by a propagator in a mixed representation, so that a further `small-chord` approximation leads to a simple generalization of the quadratic theory for evolving Wigner functions.

Chaotic synchronization in general network topology for scene segmentation

Chaotic synchronization has been discovered to be an important property of neural activities, which in turn has encouraged many researchers to develop chaotic neural networks for scene and data analysis. In this paper, we study the synchronization role of coupled chaotic oscillators in networks of general topology. Specifically, a rigorous proof is presented to show that a large number of oscillators with arbitrary geometrical connections can be synchronized by providing a sufficiently strong coupling strength. Moreover, the results presented in this paper not only are valid to a wide class of chaotic oscillators, but also cover the parameter mismatch case. Finally, we show how the obtained result can be applied to construct an oscillatory network for scene segmentation.

Chaotic synchronization in 2D lattice for scene segmentation

Synchronization and chaos play important roles in neural activities and have been applied in oscillatory correlation modeling for scene and data analysis. Although it is an extensively studied topic, there are still few results regarding synchrony in locally coupled systems. In this paper we give a rigorous proof to show that large numbers of coupled chaotic oscillators with parameter mismatch in a 2D lattice can be synchronized by providing a sufficiently large coupling strength. We demonstrate how the obtained result can be applied to construct an oscillatory network for scene segmentation. (C) 2007 Elsevier B.V. All rights reserved.

Suppressing grazing chaos in impacting system by structural nonlinearity

In this note we investigate the influence of structural nonlinearity of a simple cantilever beam impacting system on its dynamic responses close to grazing incidence by a means of numerical simulation. To obtain a clear picture of this effect we considered two systems exhibiting impacting motion, where the primary stiffness is either linear (piecewise linear system) or nonlinear (piecewise nonlinear system). Two systems were studied by constructing bifurcation diagrams, basins of attractions, Lyapunov exponents and parameter plots. In our analysis we focused on the grazing transitions from no impact to impact motion. We observed that the dynamic responses of these two similar systems are qualitatively different around the grazing transitions. For the piecewise linear system, we identified on the parameter space a considerable region with chaotic behaviour, while for the piecewise nonlinear system we found just periodic attractors. We postulate that the structural nonlinearity of the cantilever impacting beam suppresses chaos near grazing. (C) 2007 Elsevier Ltd. All rights reserved.

Borel-Leroy summability of a nonpolynomial potential

We investigate the perturbation series for the spectrum of a class of Schrodinger operators with potential V = 1/2 x(2) + g(m-1)x(2m)/(1 + alpha gx(2)) which generalize particular cases investigated in the literature in connection with models in laser theory and quantum field theory of particles and fields. It is proved that the series obey a modified strong asymptotic condition of order (m - 1) and have an order (m - 1) strong asymptotic series in g which are shown to be summable in the sense of Borel-Leroy method.

An analytical relation between entropy production and quantum Lyapunov exponents for Gaussian bipartite systems

We study and compare the information loss of a large class of Gaussian bipartite systems. It includes the usual Caldeira-Leggett-type model as well as Anosov models ( parametric oscillators, the inverted oscillator environment, etc), which exhibit instability, one of the most important characteristics of chaotic systems. We establish a rigorous connection between the quantum Lyapunov exponents and coherence loss, and show that in the case of unstable environments coherence loss is completely determined by the upper quantum Lyapunov exponent, a behavior which is more universal than that of the Caldeira-Leggett-type model.

Optical Properties and Charge-Transfer Excitations in Edge-Functionalized All-Graphene Nanojunctions

We investigate the optical properties of edge-fiinctionalized graphene nanosystems, focusing on the formation of junctions and charge-transfer excitons. We consider a class of graphene structures that combine the main electronic features of graphene with the wide tunability of large polycyclic aromatic hydrocarbons. By investigating prototypical ribbon-like systems, we show that, upon convenient choice of functional groups, low-energy excitations with remarkable charge-transfer character and large oscillator strength are obtained. These properties can be further modulated through an appropriate width variation, thus spanning a wide range in the low-energy region of the UV-vis spectra. Our results are relevant in view of designing all-graphene optoelectronic nanodevices, which take advantage of the versatility of molecular functionalization, together with the stability and the electronic properties of graphene nanostructures.