28 resultados para mean-field model


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Based on dynamic renormalization group techniques, this letter analyzes the effects of external stochastic perturbations on the dynamical properties of cholesteric liquid crystals, studied in presence of a random magnetic field. Our analysis quantifies the nature of the temperature dependence of the dynamics; the results also highlight a hitherto unexplored regime in cholesteric liquid crystal dynamics. We show that stochastic fluctuations drive the system to a second-ordered Kosterlitz-Thouless phase transition point, eventually leading to a Kardar-Parisi-Zhang (KPZ) universality class. The results go beyond quasi-first order mean-field theories, and provides the first theoretical understanding of a KPZ phase in distorted nematic liquid crystal dynamics.

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We employ the methods presented in the previous chapter for decoding corrupted codewords, encoded using sparse parity check error correcting codes. We show the similarity between the equations derived from the TAP approach and those obtained from belief propagation, and examine their performance as practical decoding methods.

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This work introduces a new variational Bayes data assimilation method for the stochastic estimation of precipitation dynamics using radar observations for short term probabilistic forecasting (nowcasting). A previously developed spatial rainfall model based on the decomposition of the observed precipitation field using a basis function expansion captures the precipitation intensity from radar images as a set of ‘rain cells’. The prior distributions for the basis function parameters are carefully chosen to have a conjugate structure for the precipitation field model to allow a novel variational Bayes method to be applied to estimate the posterior distributions in closed form, based on solving an optimisation problem, in a spirit similar to 3D VAR analysis, but seeking approximations to the posterior distribution rather than simply the most probable state. A hierarchical Kalman filter is used to estimate the advection field based on the assimilated precipitation fields at two times. The model is applied to tracking precipitation dynamics in a realistic setting, using UK Met Office radar data from both a summer convective event and a winter frontal event. The performance of the model is assessed both traditionally and using probabilistic measures of fit based on ROC curves. The model is shown to provide very good assimilation characteristics, and promising forecast skill. Improvements to the forecasting scheme are discussed

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This thesis was focused on theoretical models of synchronization to cortical dynamics as measured by magnetoencephalography (MEG). Dynamical systems theory was used in both identifying relevant variables for brain coordination and also in devising methods for their quantification. We presented a method for studying interactions of linear and chaotic neuronal sources using MEG beamforming techniques. We showed that such sources can be accurately reconstructed in terms of their location, temporal dynamics and possible interactions. Synchronization in low-dimensional nonlinear systems was studied to explore specific correlates of functional integration and segregation. In the case of interacting dissimilar systems, relevant coordination phenomena involved generalized and phase synchronization, which were often intermittent. Spatially-extended systems were then studied. For locally-coupled dissimilar systems, as in the case of cortical columns, clustering behaviour occurred. Synchronized clusters emerged at different frequencies and their boundaries were marked through oscillation death. The macroscopic mean field revealed sharp spectral peaks at the frequencies of the clusters and broader spectral drops at their boundaries. These results question existing models of Event Related Synchronization and Desynchronization. We re-examined the concept of the steady-state evoked response following an AM stimulus. We showed that very little variability in the AM following response could be accounted by system noise. We presented a methodology for detecting local and global nonlinear interactions from MEG data in order to account for residual variability. We found crosshemispheric nonlinear interactions of ongoing cortical rhythms concurrent with the stimulus and interactions of these rhythms with the following AM responses. Finally, we hypothesized that holistic spatial stimuli would be accompanied by the emergence of clusters in primary visual cortex resulting in frequency-specific MEG oscillations. Indeed, we found different frequency distributions in induced gamma oscillations for different spatial stimuli, which was suggestive of temporal coding of these spatial stimuli. Further, we addressed the bursting character of these oscillations, which was suggestive of intermittent nonlinear dynamics. However, we did not observe the characteristic-3/2 power-law scaling in the distribution of interburst intervals. Further, this distribution was only seldom significantly different to the one obtained in surrogate data, where nonlinear structure was destroyed. In conclusion, the work presented in this thesis suggests that advances in dynamical systems theory in conjunction with developments in magnetoencephalography may facilitate a mapping between levels of description int he brain. this may potentially represent a major advancement in neuroscience.

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Substantial altimetry datasets collected by different satellites have only become available during the past five years, but the future will bring a variety of new altimetry missions, both parallel and consecutive in time. The characteristics of each produced dataset vary with the different orbital heights and inclinations of the spacecraft, as well as with the technical properties of the radar instrument. An integral analysis of datasets with different properties offers advantages both in terms of data quantity and data quality. This thesis is concerned with the development of the means for such integral analysis, in particular for dynamic solutions in which precise orbits for the satellites are computed simultaneously. The first half of the thesis discusses the theory and numerical implementation of dynamic multi-satellite altimetry analysis. The most important aspect of this analysis is the application of dual satellite altimetry crossover points as a bi-directional tracking data type in simultaneous orbit solutions. The central problem is that the spatial and temporal distributions of the crossovers are in conflict with the time-organised nature of traditional solution methods. Their application to the adjustment of the orbits of both satellites involved in a dual crossover therefore requires several fundamental changes of the classical least-squares prediction/correction methods. The second part of the thesis applies the developed numerical techniques to the problems of precise orbit computation and gravity field adjustment, using the altimetry datasets of ERS-1 and TOPEX/Poseidon. Although the two datasets can be considered less compatible that those of planned future satellite missions, the obtained results adequately illustrate the merits of a simultaneous solution technique. In particular, the geographically correlated orbit error is partially observable from a dataset consisting of crossover differences between two sufficiently different altimetry datasets, while being unobservable from the analysis of altimetry data of both satellites individually. This error signal, which has a substantial gravity-induced component, can be employed advantageously in simultaneous solutions for the two satellites in which also the harmonic coefficients of the gravity field model are estimated.

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The transport of a spherical solute through a long circular cylindrical pore filled with an electrolyte solution is studied numerically, in the presence of constant surface charge on the solute and the pore wall. Fluid dynamic analyses were carried out to calculate the flow field around the solute in the pore to evaluate the drag coefficients exerted on the solute. Electrical potentials around the solute in the electrolyte solution were computed based on a mean-field theory to provide the interaction energy between the charged solute and the pore wall. Combining the results of the fluid dynamic and electrostatic analyses, we estimated the rate of the diffusive and convective transport of the solute across the pore. Although the present estimates of the drag coefficients on the solute suggest more than 10% difference from existing studies, depending on the radius ratio of the solute relative to the pore and the radial position of the solute center in the pore, this difference leads to a minor effect on the hindrance factors. It was found that even at rather large ion concentrations, the repulsive electrostatic interaction between the charged solute and the pore wall of like charge could significantly reduce the transport rate of the solute.

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Recent modelling studies (Hadjipapas et al. [2009]: Neuroimage 44:1290-1303) have shown that it may be possible to distinguish between different neuronal populations on the basis of their macroscopically measured (EEG/MEG) mean field. We set out to test whether the different orientation columns contributing to a signal at a specific cortical location could be identified based on the measured MEG signal. We used 1.5deg square, static, obliquely oriented grating stimuli to generate sustained gamma oscillations in a focal region of primary visual cortex. We then used multivariate classifier methods to predict the orientation (left or right oblique) of the stimuli based purely on the time-series data from this one location. Both the single trial evoked response (0-300 ms) and induced post-transient power spectra (300-2,300 ms, 20-70 Hz band) due to the different stimuli were classifiable significantly above chance in 11/12 and 10/12 datasets respectively. Interestingly, stimulus-specific information is preserved in the sustained part of the gamma oscillation, long after perception has occurred and all neuronal transients have decayed. Importantly, the classification of this induced oscillation was still possible even when the power spectra were rank-transformed showing that the different underlying networks give rise to different characteristic temporal signatures. © 2009 Wiley-Liss, Inc.

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We study theoretically and numerically the dynamics of a passive optical fiber ring cavity pumped by a highly incoherent wave: an incoherently injected fiber laser. The theoretical analysis reveals that the turbulent dynamics of the cavity is dominated by the Raman effect. The forced-dissipative nature of the fiber cavity is responsible for a large diversity of turbulent behaviors: Aside from nonequilibrium statistical stationary states, we report the formation of a periodic pattern of spectral incoherent solitons, or the formation of different types of spectral singularities, e.g., dispersive shock waves and incoherent spectral collapse behaviors. We derive a mean-field kinetic equation that describes in detail the different turbulent regimes of the cavity and whose structure is formally analogous to the weak Langmuir turbulence kinetic equation in the presence of forcing and damping. A quantitative agreement is obtained between the simulations of the nonlinear Schrödinger equation with cavity boundary conditions and those of the mean-field kinetic equation and the corresponding singular integrodifferential reduction, without using adjustable parameters. We discuss the possible realization of a fiber cavity experimental setup in which the theoretical predictions can be observed and studied.

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A technique is presented for the development of a high precision and resolution Mean Sea Surface (MSS) model. The model utilises Radar altimetric sea surface heights extracted from the geodetic phase of the ESA ERS-1 mission. The methodology uses a modified Le Traon et al. (1995) cubic-spline fit of dual ERS-1 and TOPEX/Poseidon crossovers for the minimisation of radial orbit error. The procedure then uses Fourier domain processing techniques for spectral optimal interpolation of the mean sea surface in order to reduce residual errors within the model. Additionally, a multi-satellite mean sea surface integration technique is investigated to supplement the first model with additional enhanced data from the GEOSAT geodetic mission.The methodology employs a novel technique that combines the Stokes' and Vening-Meinsz' transformations, again in the spectral domain. This allows the presentation of a new enhanced GEOSAT gravity anomaly field.

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PURPOSE: To validate a new miniaturised, open-field wavefront device which has been developed with the capacity to be attached to an ophthalmic surgical microscope or slit-lamp. SETTING: Solihull Hospital and Aston University, Birmingham, UK DESIGN: Comparative non-interventional study. METHODS: The dynamic range of the Aston Aberrometer was assessed using a calibrated model eye. The validity of the Aston Aberrometer was compared to a conventional desk mounted Shack-Hartmann aberrometer (Topcon KR1W) by measuring the refractive error and higher order aberrations of 75 dilated eyes with both instruments in random order. The Aston Aberrometer measurements were repeated five times to assess intra-session repeatability. Data was converted to vector form for analysis. RESULTS: The Aston Aberrometer had a large dynamic range of at least +21.0 D to -25.0 D. It gave similar measurements to a conventional aberrometer for mean spherical equivalent (mean difference ± 95% confidence interval: 0.02 ± 0.49D; correlation: r=0.995, p<0.001), astigmatic components (J0: 0.02 ± 0.15D; r=0.977, p<0.001; J45: 0.03 ± 0.28; r=0.666, p<0.001) and higher order aberrations RMS (0.02 ± 0.20D; r=0.620, p<0.001). Intraclass correlation coefficient assessments of intra-sessional repeatability for the Aston Aberrometer were excellent (spherical equivalent =1.000, p<0.001; astigmatic components J0 =0.998, p<0.001, J45=0.980, p<0.01; higher order aberrations RMS =0.961, p<0.001). CONCLUSIONS: The Aston Aberrometer gives valid and repeatable measures of refractive error and higher order aberrations over a large range. As it is able to measure continuously, it can provide direct feedback to surgeons during intraocular lens implantations and corneal surgery as to the optical status of the visual system.

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This article develops a model of practice-driven institutional change - or change that originates in the everyday work of individuals but results in a shift in field-level logic. In demonstrating how improvisations at work can generate institutional change, we attend to the earliest moments of change, which extant research has neglected; and we contrast existing accounts that focus on active entrepreneurship and the contested nature of change. We outline the specific mechanisms by which change emerges from everyday work, becomes justified, and diffuses within an organization and field, as well as precipitating and enabling dynamics that trigger and condition these mechanisms. © Academy of Management Journal.

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Purpose: The aims of this study were to develop an algorithm to accurately quantify Vigabatrin (VGB)-induced central visual field loss and to investigate the relationship between visual field loss and maximum daily dose, cumulative dose and duration of dose. Methods: The sample comprised 31 patients (mean age 37.9 years; SD 14.4 years) diagnosed with epilepsy and exposed to VGB. Each participant underwent standard automated static visual field examination of the central visual field. Central visual field loss was determined using continuous scales quantifying severity in terms of area and depth of defect and additionally by symmetry of defect between the two eyes. A simultaneous multiple regression model was used to explore the relationship between these visual field parameters and the drug predictor variables. Results: The regression model indicated that maximum VGB dose was the only factor to be significantly correlated with individual eye severity (right eye: p = 0.020; left eye: p = 0.012) and symmetry of visual field defect (p = 0.024). Conclusions: Maximum daily dose was the single most reliable indicator of those patients likely to exhibit visual field defects due to VGB. These findings suggest that high maximum dose is more likely to result in visual field defects than high cumulative doses or those of long duration.

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Background: Vigabatrin (VGB) is an anti-epileptic medication which has been linked to peripheral constriction of the visual field. Documenting the natural history associated with continued VGB exposure is important when making decisions about the risk and benefits associated with the treatment. Due to its speed the Swedish Interactive Threshold Algorithm (SITA) has become the algorithm of choice when carrying out Full Threshold automated static perimetry. SITA uses prior distributions of normal and glaucomatous visual field behaviour to estimate threshold sensitivity. As the abnormal model is based on glaucomatous behaviour this algorithm has not been validated for VGB recipients. We aim to assess the clinical utility of the SITA algorithm for accurately mapping VGB attributed field loss. Methods: The sample comprised one randomly selected eye of 16 patients diagnosed with epilepsy, exposed to VGB therapy. A clinical diagnosis of VGB attributed visual field loss was documented in 44% of the group. The mean age was 39.3 years∈±∈14.5 years and the mean deviation was -4.76 dB ±4.34 dB. Each patient was examined with the Full Threshold, SITA Standard and SITA Fast algorithm. Results: SITA Standard was on average approximately twice as fast (7.6 minutes) and SITA Fast approximately 3 times as fast (4.7 minutes) as examinations completed using the Full Threshold algorithm (15.8 minutes). In the clinical environment, the visual field outcome with both SITA algorithms was equivalent to visual field examination using the Full Threshold algorithm in terms of visual inspection of the grey scale plots, defect area and defect severity. Conclusions: Our research shows that both SITA algorithms are able to accurately map visual field loss attributed to VGB. As patients diagnosed with epilepsy are often vulnerable to fatigue, the time saving offered by SITA Fast means that this algorithm has a significant advantage for use with VGB recipients.