Deformed Gaussian-orthogonal-ensemble description of small-world networks

The study of spectral behavior of networks has gained enthusiasm over the last few years. In particular, random matrix theory (RMT) concepts have proven to be useful. In discussing transition from regular behavior to fully chaotic behavior it has been found that an extrapolation formula of the Brody type can be used. In the present paper we analyze the regular to chaotic behavior of small world (SW) networks using an extension of the Gaussian orthogonal ensemble. This RMT ensemble, coined the deformed Gaussian orthogonal ensemble (DGOE), supplies a natural foundation of the Brody formula. SW networks follow GOE statistics until a certain range of eigenvalue correlations depending upon the strength of random connections. We show that for these regimes of SW networks where spectral correlations do not follow GOE beyond a certain range, DGOE statistics models the correlations very well. The analysis performed in this paper proves the utility of the DGOE in network physics, as much as it has been useful in other physical systems.

Finding Quasi-Optimal Network Topologies for Information Transmission in Active Networks

This work clarifies the relation between network circuit (topology) and behaviour (information transmission and synchronization) in active networks, e.g. neural networks. As an application, we show how one can find network topologies that are able to transmit a large amount of information, possess a large number of communication channels, and are robust under large variations of the network coupling configuration. This theoretical approach is general and does not depend on the particular dynamic of the elements forming the network, since the network topology can be determined by finding a Laplacian matrix (the matrix that describes the connections and the coupling strengths among the elements) whose eigenvalues satisfy some special conditions. To illustrate our ideas and theoretical approaches, we use neural networks of electrically connected chaotic Hindmarsh-Rose neurons.

Chaotic advection in blood flow

In this paper we argue that the effects of irregular chaotic motion of particles transported by blood can play a major role in the development of serious circulatory diseases. Vessel wall irregularities modify the flow field, changing in a nontrivial way the transport and activation of biochemically active particles. We argue that blood particle transport is often chaotic in realistic physiological conditions. We also argue that this chaotic behavior of the flow has crucial consequences for the dynamics of important processes in the blood, such as the activation of platelets which are involved in the thrombus formation.

Transition to chaotic scattering: Signatures in the differential cross section

We show that bifurcations in chaotic scattering manifest themselves through the appearance of an infinitely fine-scale structure of singularities in the cross section. These ""rainbow singularities"" are created in a cascade, which is closely related to the bifurcation cascade undergone by the set of trapped orbits (the chaotic saddle). This cascade provides a signature in the differential cross section of the complex pattern of bifurcations of orbits underlying the transition to chaotic scattering. We show that there is a power law with a universal coefficient governing the sequence of births of rainbow singularities and we verify this prediction by numerical simulations.

Sensorless synchronization method for thin-film direct optical broadband monitoring system

Optical monitoring systems are necessary to manufacture multilayer thin-film optical filters with low tolerance on spectrum specification. Furthermore, to have better accuracy on the measurement of film thickness, direct monitoring is a must. Direct monitoring implies acquiring spectrum data from the optical component undergoing the film deposition itself, in real time. In making film depositions on surfaces of optical components, the high vacuum evaporator chamber is the most popular equipment. Inside the evaporator, at the top of the chamber, there is a metallic support with several holes where the optical components are assembled. This metallic support has rotary motion to promote film homogenization. To acquire a measurement of the spectrum of the film in deposition, it is necessary to pass a light beam through a glass witness undergoing the film deposition process, and collect a sample of the light beam using a spectrometer. As both the light beam and the light collector are stationary, a synchronization system is required to identify the moment at which the optical component passes through the light beam.

Design constraints for third-order PLL nodes in master-slave clock distribution networks

Clock signal distribution in telecommunication commercial systems usually adopts a master-slave architecture, with a precise time basis generator as a master and phase-locked loops (PLLs) as slaves. In the majority of the networks, second-order PLLs are adopted due to their simplicity and stability. Nevertheless, in some applications better transient responses are necessary and, consequently, greater order PLLs need to be used, in spite of the possibility of bifurcations and chaotic attractors. Here a master-slave network with third-order PLLs is analyzed and conditions for the stability of the synchronous state are derived, providing design constraints for the node parameters, in order to guarantee stability and reachability of the synchronous state for the whole network. Numerical simulations are carried out in order to confirm the analytical results. (C) 2009 Elsevier B.V. All rights reserved.

Network of phase-locking oscillators and a possible model for neural synchronization

In order to model the synchronization of brain signals, a three-node fully-connected network is presented. The nodes are considered to be voltage control oscillator neurons (VCON) allowing to conjecture about how the whole process depends on synaptic gains, free-running frequencies and delays. The VCON, represented by phase-locked loops (PLL), are fully-connected and, as a consequence, an asymptotically stable synchronous state appears. Here, an expression for the synchronous state frequency is derived and the parameter dependence of its stability is discussed. Numerical simulations are performed providing conditions for the use of the derived formulae. Model differential equations are hard to be analytically treated, but some simplifying assumptions combined with simulations provide an alternative formulation for the long-term behavior of the fully-connected VCON network. Regarding this kind of network as models for brain frequency signal processing, with each PLL representing a neuron (VCON), conditions for their synchronization are proposed, considering the different bands of brain activity signals and relating them to synaptic gains, delays and free-running frequencies. For the delta waves, the synchronous state depends strongly on the delays. However, for alpha, beta and theta waves, the free-running individual frequencies determine the synchronous state. (C) 2011 Elsevier B.V. All rights reserved.

Spectral properties of chaotic signals generated by the skew tent map

Chaotic signals have been considered potentially attractive in many signal processing applications ranging from wideband communication systems to cryptography and watermarking. Besides, some devices as nonlinear adaptive filters and phase-locked loops can present chaotic behavior. In this paper, we derive analytical expressions for the autocorrelation sequence, power spectral density and essential bandwidth of chaotic signals generated by the skew tent map. From these results, we suggest possible applications in communication systems. (C) 2009 Elsevier B.V. All rights reserved.

Spectral properties of chaotic signals with applications in communications

This paper investigates the characteristics of the Power Spectral Density (PSD) of chaotic signals generated by skew tent maps. The influence of the Lyapunov exponent on the autocorrelation sequence and on the PSD is evaluated via computational simulations. We conclude that the essential bandwidth of these signals is strongly related to this exponent and they can be low-pass or high-pass depending on the family`s parameter. This way, the PSD of a chaotic signal is a function of the generating map although this is not a one-to-one relationship. (C) 2009 Elsevier Ltd. All rights reserved.

Optimized network structure for full-synchronization

A network of Kuramoto oscillators with different natural frequencies is optimized for enhanced synchronizability. All node inputs are normalized by the node connectivity and some important properties of the network Structure are determined in this case: (i) optimized networks present a strong anti-correlation between natural frequencies of adjacent nodes: (ii) this anti-correlation should be as high as possible since the average path length between nodes is maintained as small as in random networks: and (iii) high anti-correlation is obtained without any relation between nodes natural frequencies and the degree of connectivity. We also propose a network construction model with which it is shown that high anti-correlation and small average paths may be achieved by randomly rewiring a fraction of the links of a totally anti-correlated network, and that these networks present optimal synchronization properties. (C) 2008 Elsevier B.V. All rights reserved.

Effect of follicular wave synchronization on in vitro embryo production in heifers

Aiming to achieve the ideal time of ovum pick-up (OPU) for in vitro embryo production (IVP) in crossbred heifers, two Latin square design studies investigated the effect of ovarian follicular wave synchronization with estradiol benzoate (EB) and progestins. For each experiment, crossbred heifers stage of estrous cycle was synchronized either with a norgestomet ear implant (Experiment 1) or a progesterone intravaginal device (Experiment 2) for 7d, followed by the administration of 150 mu g D-cloprostenol. On Day 7, all follicles >3 mm in diameter were aspirated and implants/devices were replaced by new ones. Afterwards, implant/device replacement was conducted every 14 d. Each experiment had three treatment groups. In Experiment I (n = 12), heifers in Group 2X had their follicles aspirated twice a week and those in Groups 1X and 1X-EB were submitted to OPU once a week for a period of 28 d. Heifers from Group 1X-EB also received 2 mg EB i.m. immediately after each OPU session. In Experiment 2 (n = 11), animals from Group 0EB did not receive EB while heifers in Groups 2EB and 5EB received 2 and 5 mg of EB respectively, immediately after OPU. The OPU sessions were performed once weekly for 28 d. Therefore, in both experiments, four OPU sessions were performed in heifers aspirated once a week and in Experiment 1, eight OPU sessions were done in heifers aspirated twice a week. Additionally, during the 7-d period following follicular aspiration, ovarian ultrasonography examinations were conducted to measure diameter of the largest follicle and blood samples were collected for FSH quantification by RIA. In Experiment 1, all viable oocytes recovered were in vitro matured and fertilized. Results indicated that while progestin and EB altered follicular wave patterns, this treatment did not prevent establishment of follicular dominance on the ovaries of heifers during OPU at 7-d intervals. Furthermore, the proposed stage of follicular wave synchronization strategies did not improve the number and quality of the recovered oocytes, or the number of in vitro produced embryos. (C) 2009 Elsevier B.V. All rights reserved.

Experimental evidence of frequency entrainment between coupled chaotic oscillations

The nonlinear response of a chaotic system to a chaotic variation in a system parameter is investigated experimentally. Clear experimental evidence of frequency entrainment of the chaotic oscillations is observed. We show that analogous to the frequency locking between coupled periodic oscillations, this effect is generic for coupled chaotic systems.

Chaotic dynamics of cold atoms in far-off-resonant donut beams

We describe the classical two-dimensional nonlinear dynamics of cold atoms in far-off-resonant donut beams. We show that chaotic dynamics exists there for charge greater than unity, when the intensity of the beam is periodically modulated. The two-dimensional distributions of atoms in the (x,y) plant for charge 2 are simulated. We show that the atoms will accumulate on several ring regions when the system enters a regime of global chaos. [S1063-651X(99)03903-3].

Synchronization of estrus and fertility in zebu beef heifers treated with three estrus synchronization protocols

The effects on estrus and fertility of 3 estrus synchronization protocols were studied in Brahman beef heifers. In Treatment 1 (PGF protocol; n=234), heifers received 7.5 mg, im prostianol on Day 0 and were inseminated after observed estrus until Day 5. Treatment 2 (10-d NOR protocol; n=220) consisted of norgestomet (NOR; 3 mg, sc implant and 3 mg, im) and estradiol valerate (5 mg, im) treatment on Day -10, NOR implant removal and 400 IU, im PMSG on Day 0, and AI after observed estrus through to Day 5. Treatment 3 (14-d NOR+PGF protocol; n=168) constituted a NOR implant (3 mg, sc) on Day -14, NOR implant removal on Day 0, PGF on Day 16, and AI after observed estrus through to Day 21. All heifers were examined for return to estrus at the next cycle and inseminated after observed estrus. The heifers were then exposed to bulls for at least 21 d. During the period of estrus observation (5 d) after treatment, those heifers treated with the PGF protocol had a lower (P

Controlling chaos in a Lorenz-like system using feedback

We demonstrate that the dynamics of an autonomous chaotic laser can be controlled to a periodic or steady state under self-synchronization. In general, past the chaos threshold the dependence of the laser output on feedback applied to the pump is submerged in the Lorenz-like chaotic pulsation. However there exist specific feedback delays that stabilize the chaos to periodic behavior or even steady state. The range of control depends critically on the feedback delay time and amplitude. Our experimental results are compared with the complex Lorenz equations which show good agreement.