An Extension of the Invariance Principle for a Class of Differential Equations with Finite Delay

An extension of the uniform invariance principle for ordinary differential equations with finite delay is developed. The uniform invariance principle allows the derivative of the auxiliary scalar function V to be positive in some bounded sets of the state space while the classical invariance principle assumes that. V <= 0. As a consequence, the uniform invariance principle can deal with a larger class of problems. The main difficulty to prove an invariance principle for functional differential equations is the fact that flows are defined on an infinite dimensional space and, in such spaces, bounded solutions may not be precompact. This difficulty is overcome by imposing the vector field taking bounded sets into bounded sets.

Anticipation of pain enhances the nociceptive transmission and functional connectivity within pain network in rats

Background: Expectation is a very potent pain modulator in both humans and animals. There is evidence that pain transmission neurons are modulated by expectation preceding painful stimuli. Nonetheless, few studies have examined the influence of pain expectation on the pain-related neuronal activity and the functional connectivity within the central nociceptive network. Results: This study used a tone-laser conditioning paradigm to establish the pain expectation in rats, and simultaneously recorded the anterior cingulate cortex (ACC), the medial dorsal thalamus (MD), and the primary somatosensory cortex (SI) to investigate the effect of pain expectation on laser-induced neuronal responses. Cross-correlation and partial directed coherence analysis were used to determine the functional interactions within and between the recorded areas during nociceptive transmission. The results showed that under anticipation condition, the neuronal activity to the auditory cue was significantly increased in the ACC area, whereas those to actual noxious stimuli were enhanced in all the recorded areas. Furthermore, neuronal correlations within and between these areas were significantly increased under conditions of expectation compared to those under non-expectation conditions, indicating an enhanced synchronization of neural activity within the pain network. In addition, information flow from the medial (ACC and MD) to the lateral (SI cortex) pain pathway increased, suggesting that the emotion-related neural circuits may modulate the neuronal activity in the somatosensory pathway during nociceptive transmission. Conclusion: These results demonstrate that the nociceptive processing in both medial and lateral pain systems is modulated by the expectation of pain.

Border figure detection using a phase oscillator network with dynamical coupling

Oscillator networks have been developed in order to perform specific tasks related to image processing. Here we analytically investigate the existence of synchronism in a pair of phase oscillators that are short-range dynamically coupled. Then, we use these analytical results to design a network able of detecting border of black-and-white figures. Each unit composing this network is a pair of such phase oscillators and is assigned to a pixel in the image. The couplings among the units forming the network are also dynamical. Border detection emerges from the network activity.

Fully Connected PLL Networks: How Filter Determines the Number of Nodes

Synchronization plays an important role in telecommunication systems, integrated circuits, and automation systems. Formerly, the masterslave synchronization strategy was used in the great majority of cases due to its reliability and simplicity. Recently, with the wireless networks development, and with the increase of the operation frequency of integrated circuits, the decentralized clock distribution strategies are gaining importance. Consequently, fully connected clock distribution systems with nodes composed of phase-locked loops (PLLs) appear as a convenient engineering solution. In this work, the stability of the synchronous state of these networks is studied in two relevant situations: when the node filters are first-order lag-lead low-pass or when the node filters are second-order low-pass. For first-order filters, the synchronous state of the network shows to be stable for any number of nodes. For second-order filter, there is a superior limit for the number of nodes, depending on the PLL parameters. Copyright (C) 2009 Atila Madureira Bueno et al.

In vitro development of cloned bovine embryos produced by handmade cloning using somatic cells from distinct levels of cell culture confluence

The relationship between the level of cell confluence near the plateau phase of growth and blastocyst yield following somatic cell cloning is not well understood. We examined the effect of distinct cell culture confluence levels on in vitro development of cloned bovine embryos. In vitro-matured bovine oocytes were manually bisected and selected by DNA staining. One or two enucleated hemi-cytoplasts were paired and fused with an adult skin somatic cell. Cultured skin cells from an adult Nellore cow harvested at three distinct culture confluence levels (70-80, 80-90, and > 95%) were used for construction of embryos and hemi-embryos. After activation, structures were cultured in vitro as one embryo (1 x 100%) or as aggregates of two hemi-embryos (2 x 50%) per microwell. Fusion, cleavage and blastocyst rates were compared using the chi(2) test. The fusion rate for hemi-embryos (51.4%) was lower than for embryos (67.6%), with no influence of degree of cell confluence. However, blastocyst rates improved linearly (7.0, 17.5, and 29.4%) with increases in cell confluence. We conclude that degree of cell culture confluence significantly influences subsequent embryo development; use of a cell population in high confluence (> 90%) for nuclear transfer significantly improved blastocyst yield after cloning.

Serum-Starved Apoptotic Fibroblasts Reduce Blastocyst Production but Enable Development to Term after SCNT in Cattle

Cell cycle synchronization by serum starvation (SS) induces apoptosis in somatic cells. This side effect of SS is hypothesized to negatively affect the outcome of somatic cell nuclear transfer (SCNT). We determined whether apoptotic fibroblasts affect SCNT yields. Serum-starved, adult, bovine fibroblasts were stained with annexin V-FITC/propidium iodide to allow apoptosis detection by flow cytometry. Positive and negative cells sorted by fluorescence activated cell sorting (FACS) and an unsorted control group were used as nuclear donors for SCNT. Reconstructed embryos were cultured in vitro and transferred to synchronized recipients. Apoptosis had no effect on fusion and cleavage rates; however, it resulted in reductions in blastocyst production and quality measured by apoptotic index. However, reconstructed embryos with apoptotic cells resulted in pregnancy rates similar to that of the control on day 30, and generated one live female calf. In conclusion, we showed that apoptotic cells present in serum-starved cultures negatively affect embryo production after SCNT without compromising full-term development. Further studies will evaluate the ability of the oocyte to reprogram cells in specific phases of apoptosis.

Modeling Two-Oscillator Circadian Systems Entrained by Two Environmental Cycles

Several experimental studies have altered the phase relationship between photic and non-photic environmental, 24 h cycles (zeitgebers) in order to assess their role in the synchronization of circadian rhythms. To assist in the interpretation of the complex activity patterns that emerge from these ""conflicting zeitgeber'' protocols, we present computer simulations of coupled circadian oscillators forced by two independent zeitgebers. This circadian system configuration was first employed by Pittendrigh and Bruce (1959), to model their studies of the light and temperature entrainment of the eclosion oscillator in Drosophila. Whereas most of the recent experiments have restricted conflicting zeitgeber experiments to two experimental conditions, by comparing circadian oscillator phases under two distinct phase relationships between zeitgebers (usually 0 and 12 h), Pittendrigh and Bruce compared eclosion phase under 12 distinct phase relationships, spanning the 24 h interval. Our simulations using non-linear differential equations replicated complex non-linear phenomena, such as ""phase jumps'' and sudden switches in zeitgeber preferences, which had previously been difficult to interpret. Our simulations reveal that these phenomena generally arise when inter-oscillator coupling is high in relation to the zeitgeber strength. Manipulations in the structural symmetry of the model indicated that these results can be expected to apply to a wide range of system configurations. Finally, our studies recommend the use of the complete protocol employed by Pittendrigh and Bruce, because different system configurations can generate similar results when a ""conflicting zeitgeber experiment'' incorporates only two phase relationships between zeitgebers.

Hormone-regulated expression and distribution of versican in mouse uterine tissues

Background: Remodeling of the extracellular matrix is one of the most striking features observed in the uterus during the estrous cycle and after hormone replacement. Versican (VER) is a hyaluronan-binding proteoglycan that undergoes RNA alternative splicing, generating four distinct isoforms. This study analyzed the synthesis and distribution of VER in mouse uterine tissues during the estrous cycle, in ovariectomized (OVX) animals and after 17beta-estradiol (E2) and medroxyprogesterone (MPA) treatments, either alone or in combination. Methods: Uteri from mice in all phases of the estrous cycle, and animals subjected to ovariectomy and hormone replacement were collected for immunoperoxidase staining for versican, as well as PCR and quantitative Real Time PCR. Results: In diestrus and proestrus, VER was exclusively expressed in the endometrial stroma. In estrus and metaestrus, VER was present in both endometrial stroma and myometrium. In OVX mice, VER immunoreaction was abolished in all uterine tissues. VER expression was restored by E2, MPA and E2+MPA treatments. Real Time PCR analysis showed that VER expression increases considerably in the MPA-treated group. Analysis of mRNA identified isoforms V0, V1 and V3 in the mouse uterus. Conclusion: These results show that the expression of versican in uterine tissues is modulated by ovarian steroid hormones, in a tissue-specific manner. VER is induced in the myometrium exclusively by E2, whereas MPA induces VER deposition only in the endometrial stroma.

Modulation of small leucine-rich proteoglycans (SLRPs) expression in the mouse uterus by estradiol and progesterone

Background: We have previously demonstrated that four members of the family of small leucine-rich-proteoglycans (SLRPs) of the extracellular matrix (ECM), named decorin, biglycan, lumican and fibromodulin, are deeply remodeled in mouse uterine tissues along the estrous cycle and early pregnancy. It is known that the combined action of estrogen (E2) and progesterone (P4) orchestrates the estrous cycle and prepares the endometrium for pregnancy, modulating synthesis, deposition and degradation of various molecules. Indeed, we showed that versican, another proteoglycan of the ECM, is under hormonal control in the uterine tissues. Methods: E2 and/or medroxiprogesterone acetate (MPA) were used to demonstrate, by real time PCR and immunoperoxidase staining, respectively, their effects on mRNA expression and protein deposition of these SLRPs, in the uterine tissues. Results: Decorin and lumican were constitutively expressed and deposited in the ECM in the absence of the ovarian hormones, whereas deposition of biglycan and fibromodulin were abolished from the uterine ECM in the non-treated group. Interestingly, ovariectomy promoted an increase in decorin, lumican and fibromodulin mRNA levels, while biglycan mRNA conspicuously decreased. Hormone replacement with E2 and/or MPA differentially modulates their expression and deposition. Conclusions: The patterns of expression of these SLRPs in the uterine tissues were found to be hormone-dependent and uterine compartment-related. These results reinforce the existence of subpopulations of endometrial fibroblasts, localized into distinct functional uterine compartments, resembling the organization into basal and functional layers of the human endometrium.

Phase-disorder-induced double resonance of neuronal activity

It is well known that resonance can be induced by external noise or diversity. Here we show that resonance can be induced even by a phase disorder in coupled excitable neurons with subthreshold activity. In contrast to the case of identical phase, we find that phase disorder plays an active role in enhancing neuronal activity. We also uncover that the presence of phase disorder can induce a double resonance phenomenon: phase disorder and coupling strength both can enhance neuronal firing activity. A physical theory is formulated to help understand the mechanism behind this double resonance phenomenon.

Bicoherence in electrostatic turbulence driven by high magnetohydrodynamic activity in Tokamak Chauffage Alfven Bresilien

During some discharges in Tokamak Chauffage Alfven Bresilien [R. M. O. Galvao et al., Plasma Phys. Controlled Fusion 43, 1181 (2001)] high magnetohydrodynamic activity may appear with a peaked frequency spectrum. Whenever this peak occurs, the ambient broadband electrostatic turbulence is remarkably modified, synchronizing into the dominant magnetic fluctuation frequency and presenting high bicoherence in the whole plasma edge with a maximum bicoherence inside the plasma. A phenomenological model is introduced to investigate this driven turbulence bicoherence, consisting of nonlinearly coupled phase-randomized drift modes with time-periodic external driving at the dominant magnetic fluctuation frequency. The bicoherence spectrum of this model can mimic features of the experimental results. (C) 2009 American Institute of Physics. [DOI: 10.1063/1.3099701]

Electrostatic turbulence driven by high magnetohydrodynamic activity in Tokamak Chauffage Alfven Bresilien

In Tokamak Chauffage Alfven Bresilien [R. M. O. Galvao , Plasma Phys. Controlled Fusion 43, 1181 (2001)], high magnetohydrodynamic (MHD) activity may appear spontaneously or during discharges with a voltage biased electrode inserted at the plasma edge. The turbulent electrostatic fluctuations, measured by Langmuir probes, are modulated by Mirnov oscillations presenting a dominant peak with a common frequency around 10 kHz. We report the occurrence of phase locking of the turbulent potential fluctuations driven by MHD activity at this frequency. Using wavelet cross-spectral analysis, we characterized the phase and frequency synchronization in the plasma edge region. We introduced an order parameter to characterize the radial dependence of the phase-locking intensity. (c) 2008 American Institute of Physics.

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.

Soil nitrous oxide emissions in long-term cover crops-based rotations under subtropical climate

It has been shown that cover crops can enhance soil nitrous oxide (N(2)O) emissions, but the magnitude of increase depends on the quantity and quality of the crop residues. Therefore, this study aimed to evaluate the effect of long-term (19 and 21 years) no-till maize crop rotations including grass [black oat (Avena strigosa Schreb)] and legume cover crops [vetch (Vigna sativa L), cowpea (Vigna unguiculata L. Walp), pigeon pea (Cajanus cajan L. Millsp.) and lablab (Dolichos lablab)] on annual soil N(2)O emissions in a subtropical Acrisol in Southern Brazil. Greater soil N(2)O emissions were observed in the first 45 days after the cover crop residue management in all crop rotations, varying from -20.2 +/- 1.9 to 163.9 +/- 24.3 mu g N m(-2) h(-1). Legume-based crop rotations had the largest cumulative emissions in this period, which were directly related to the quantity of N (r(2) = 0.60, p = 0.13)and inversely related to the lignin:N ratio(r(2) = 0.89,p = 0.01) of the cover crop residues. After this period, the mean fluxes were smaller and were closely related to the total soil N stocks (r(2) = 0.96, p = 0.002). The annual soil N(2)O emission represented 0.39-0.75% of the total N added by the legume cover crops. Management-control led soil variables such as mineral N (NO(3)(-) and NH(4)(+)) and dissolved organic C influenced more the N(2)O fluxes than environmental-related variables as water-filled pore space and air and soil temperature. Consequently, the synchronization between N mineralization and N uptake by plants seems to be the main challenge to reduce N(2)O emissions while maintaining the environmental and agronomic services provided by legume cover crops in agricultural systems. (C) 2009 Elsevier B.V. All rights reserved.