Dynamics and scaling of noise-induced domain growth

The domain growth processes originating from noise-induced nonequilibrium phase transitions are analyzed, both for non-conserved and conserved dynamics. The existence of a dynamical scaling regime is established in the two cases, and the corresponding growth laws are determined. The resulting universal dynamical scaling scenarios are those of Allen-Cahn and Lifshitz-Slyozov, respectively. Additionally, the effect of noise sources on the behaviour of the pair correlation function at short distances is studied. Received 28 June 2000 and Received in final form 29 September 2000     

A new universality for random sequential deposition of needles

Percolation and jamming phenomena are investigated for random sequential deposition of rectangular needles on d=2 square lattices. Associated thresholds and are determined for various needle sizes. Their ratios are found to be a constant for all sizes. In addition the ratio of jamming thresholds for respectively square blocks and needles is also found to be a constant . These constants exhibit some universal connexion in the geometry of jamming and percolation for both anisotropic shapes (needles versus square lattices) and isotropic shapes (square blocks on square lattices). A universal empirical law is proposed for all three thresholds as a function of a. Received 27 January 2000 and Received in final form 2 February 2000     

Van Douwen's problem on 0-dimensional images of ordered compacta

A compact 0-dimensional space has a -separating rank 1 family of clopen sets iff it is the continuous image of a compact 0-dimensional linearly ordered space.

     

Preservation of the Range under Perturbations of an Operator

A sufficient condition for the stability of the range of a positive operator in a Hilbert space is given. As a consequence, we get a class of additive perturbations which preserve regularity of the critical point of a positive operator in a Krein space.

     

Phase noise suppression in a DPSK transmission system by the use of an attenuation-imbalanced NOLM

A nonlinear optical loop mirror (NOLM) imbalanced by attenuation has been used for the suppression of nonlinear phase noise in a DPSK transmission system. It has been experimentally shown that such a passive, NOLM-based regenerator can significantly improve the performance of a phase-encoded transmission when it is limited by nonlinear phase noise. A brief overview over the advantages und limitations of different NOLM-based phase-preserving amplitude regenerators is also given.     

Partially coherent optical processor for enhancement of partial second order derivatives of an image: Analysis and implementation

We present an optical processor capable to perform partial second derivatives of an image working with partially coherent illumination. The proposed system utilizes a liquid crystal display, onto which images to be derived are displayed. The method is based on the capacity of these devices to generate simultaneously a contrast reverted replica of the image displayed on it. A positive replica of original image is obtained when the LCD is between crossed polarizers, while the negative one is obtained with the LCD is between parallel polarizers. Since the LCD is a diffraction element, both polarizer arrangements may be simultaneously implemented, for example, in a 4f optical processor using polarization filtering of the different diffraction orders. When three images (two replicas of original image displaced in opposite direction and the other one with contrast reverted and centered at the origin.) are imagined across a slightly defocused plane, one obtains an image with enhanced second derivatives in a given direction. No other incoherent (or partially coherent) optical system is presently known which can perform partial second-order derivatives of an image. Experimental results obtained are presented.     

Shot noise suppression in a series graphene tunnel barrier structure

The shot noise properties in a graphene-based multi-quantum well structure are investigated theoretically. It is found that when the number of the potential barriers (quantum wells) is big enough and the width of the barriers and the wells is shorter than the mean free path, another Dirac-like point at which the Fermi energy equals half of the barrier height appears. The transport is almost forbidden at this new Dirac-like point, the conductivity gets the minimum, and the Fano factor approaches 1/3. With the random potential barrier being taken into consideration, the conductance enhances clearly, meanwhile the Fano factor is suppressed much more.     

Diffusion-weighted MRI: influence of intravoxel fat signal and breast density on breast tumor conspicuity and apparent diffusion coefficient measurements

Promising recent investigations have shown that breast malignancies exhibit restricted diffusion on diffusion-weighted imaging (DWI) and may be distinguished from normal tissue and benign lesions in the breast based on differences in apparent diffusion coefficient (ADC) values. In this study, we assessed the influence of intravoxel fat signal on breast diffusion measures by comparing ADC values obtained using a diffusion-weighted single shot fast spin-echo sequence with and without fat suppression. The influence of breast density on ADC measures was also evaluated. ADC values were calculated for both tumor and normal fibroglandular tissue in a group of 21 women with diagnosed breast cancer. There were systematic underestimations of ADC for both tumor and normal breast tissue due to intravoxel contribution from fat signal on non–fat-suppressed DWI. This ADC underestimation was more pronounced for normal tissue values (mean difference=40%) than for tumors (mean difference=27%, P<.001) and was worse in women with low breast tissue density vs. those with extremely dense breasts (P<.05 for both tumor and normal tissue). Tumor conspicuity measured by contrast-to-noise ratio was significantly higher on ADC maps created with fat suppression and was not significantly associated with breast density. In summary, robust fat suppression is important for accurate breast ADC measures and optimal lesion conspicuity on DWI.     

The relationship between BOLD signal and autonomic nervous system functions: implications for processing of "physiological noise"

Functional magnetic resonance imaging (fMRI) research has revealed not only important aspects of the neural basis of cognitive and perceptual functions, but also important information on the relation between high-level brain functions and physiology. One of the central outstanding questions, given the features of the blood oxygenation level-dependent (BOLD) signal, is whether and how autonomic nervous system (ANS) functions are related to changes in brain states as measured in the human brain. A straightforward way to address this question has been to acquire external measurements of ANS activity such as cardiac and respiratory data, and examine their relation to the BOLD signal. In this article, we describe two conceptual approaches to the treatment of ANS measures in the context of BOLD fMRI analysis. On the one hand, several research lines have treated ANS activity measures as noise, considering them as nothing but a confounding factor that reduces the power of fMRI analysis or its validity. Work in this line has developed powerful methods to remove ANS effects from the BOLD signal. On the other hand, a different line of work has made important progress in showing that ANS functions such as cardiac pulsation, heart rate variability and breathing rate could be considered as a theoretically meaningful component of the signal that is useful for understanding brain function. Work within this latter framework suggests that caution should be exercised when employing procedures to remove correlations between BOLD data and physiological measures. We discuss these two positions and the reasoning underlying them. Thereafter, we draw on the reviewed literature in presenting practical guidelines for treatment of ANS data, which are based on the premise that ANS data should be considered as theoretically meaningful information. This holds particularly when studying cortical systems involved in regulation, monitoring and/or generation of ANS activity, such as those involved in decision making, conflict resolution and the experience of emotion.     

Asymptotic compactness and absorbing sets for 2D stochastic Navier-Stokes equations on some unbounded domains

We introduce a notion of an asymptotically compact (AC) random dynamical system (RDS). We prove that for an AC RDS the -limit set of any bounded set is nonempty, compact, strictly invariant and attracts the set . We establish that the D Navier Stokes Equations (NSEs) in a domain satisfying the Poincaré inequality perturbed by an additive irregular noise generate an AC RDS in the energy space . As a consequence we deduce existence of an invariant measure for such NSEs. Our study generalizes on the one hand the earlier results by Flandoli-Crauel (1994) and Schmalfuss (1992) obtained in the case of bounded domains and regular noise, and on the other hand the results by Rosa (1998) for the deterministic NSEs.