Finite-connectivity spin-glass phase diagrams and low-density parity check codes

We obtain phase diagrams of regular and irregular finite-connectivity spin glasses. Contact is first established between properties of the phase diagram and the performance of low-density parity check (LDPC) codes within the replica symmetric (RS) ansatz. We then study the location of the dynamical and critical transition points of these systems within the one step replica symmetry breaking theory (RSB), extending similar calculations that have been performed in the past for the Bethe spin-glass problem. We observe that the location of the dynamical transition line does change within the RSB theory, in comparison with the results obtained in the RS case. For LDPC decoding of messages transmitted over the binary erasure channel we find, at zero temperature and rate R=14, an RS critical transition point at pc 0.67 while the critical RSB transition point is located at pc 0.7450±0.0050, to be compared with the corresponding Shannon bound 1-R. For the binary symmetric channel we show that the low temperature reentrant behavior of the dynamical transition line, observed within the RS ansatz, changes its location when the RSB ansatz is employed; the dynamical transition point occurs at higher values of the channel noise. Possible practical implications to improve the performance of the state-of-the-art error correcting codes are discussed. © 2006 The American Physical Society.

Phase transitions and memory effects in the dynamics of Boolean networks

The generating functional method is employed to investigate the synchronous dynamics of Boolean networks, providing an exact result for the system dynamics via a set of macroscopic order parameters. The topology of the networks studied and its constituent Boolean functions represent the system's quenched disorder and are sampled from a given distribution. The framework accommodates a variety of topologies and Boolean function distributions and can be used to study both the noisy and noiseless regimes; it enables one to calculate correlation functions at different times that are inaccessible via commonly used approximations. It is also used to determine conditions for the annealed approximation to be valid, explore phases of the system under different levels of noise and obtain results for models with strong memory effects, where existing approximations break down. Links between Boolean networks and general Boolean formulas are identified and results common to both system types are highlighted. © 2012 Copyright Taylor and Francis Group, LLC.

The Riesz transform and simultaneous representations of phase, energy and orientation in spatial vision

To represent the local orientation and energy of a 1-D image signal, many models of early visual processing employ bandpass quadrature filters, formed by combining the original signal with its Hilbert transform. However, representations capable of estimating an image signal's 2-D phase have been largely ignored. Here, we consider 2-D phase representations using a method based upon the Riesz transform. For spatial images there exist two Riesz transformed signals and one original signal from which orientation, phase and energy may be represented as a vector in 3-D signal space. We show that these image properties may be represented by a Singular Value Decomposition (SVD) of the higher-order derivatives of the original and the Riesz transformed signals. We further show that the expected responses of even and odd symmetric filters from the Riesz transform may be represented by a single signal autocorrelation function, which is beneficial in simplifying Bayesian computations for spatial orientation. Importantly, the Riesz transform allows one to weight linearly across orientation using both symmetric and asymmetric filters to account for some perceptual phase distortions observed in image signals - notably one's perception of edge structure within plaid patterns whose component gratings are either equal or unequal in contrast. Finally, exploiting the benefits that arise from the Riesz definition of local energy as a scalar quantity, we demonstrate the utility of Riesz signal representations in estimating the spatial orientation of second-order image signals. We conclude that the Riesz transform may be employed as a general tool for 2-D visual pattern recognition by its virtue of representing phase, orientation and energy as orthogonal signal quantities.

In situ studies of phase separation and crystallization directed by Marangoni instabilities during spin-coating

Results of a pioneering study are presented in which for the first time, crystallization, phase separation and Marangoni instabilities occurring during the spin-coating of polymer blends are directly visualized, in real-space and real-time. The results provide exciting new insights into the process of self-assembly, taking place during spin-coating, paving the way for the rational design of processing conditions, to allow desired morphologies to be obtained. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Phase discrimination and simultaneous frequency conversion of the orthogonal components of an optical signal by four-wave mixing in an SOA

Simultaneous conversion of the two orthogonal phase components of an optical input to different output frequencies has been demonstrated by simulation and experiment. A single stage of four-wave mixing between the input signal and four pumps derived from a frequency comb was employed. The nonlinear device was a semiconductor optical amplifier, which provided overall signal gain and sufficient contrast for phase sensitive signal processing. The decomposition of a quadrature phase-shift keyed signal into a pair of binary phase-shift keyed outputs at different frequencies was also demonstrated by simulation.

Optical regeneration using self-phase modulation and quasi-continuous filtering

We propose a scheme for 211 optical regeneration based on self-phase modulation in fiber and quasi-continuous filtering. Numerical simulations demonstrate the possibility of increasing the transmission reach from 3500 to more than 6000 km at 10 Gb/s using 100-km spans. Spectral broadening is shown to be small using this technique, indicating its suitability for wavelength-division-multiplexing regeneration.

Power-controlled phase-matching and instability of CW propagation in multicore optical fibers with a central core

We present modulation instability analysis including azimuthal perturbations of steady-state continuous wave (CW) propagation in multicore-fiber configurations with a central core. In systems with a central core, a steady CW evolution regime requires power-controlled phase matching, which offers interesting spatial-division applications. Our results have general applicability and are relevant to a range of physical and engineering systems, including high-power fiber lasers, optical transmission in multicore fiber, and systems of coupled nonlinear waveguides. © 2013 Optical Society of America.

Influence of La-doping on phase transformation and photocatalytic properties of ZnTiO3 nanoparticles synthesized via modified sol-gel method

Non-doped and La-doped ZnTiO3 nanoparticles were successfully synthesized via a modified sol–gel method. The synthesized nanoparticles were structurally characterized by PXRD, UV-vis DRS, FT-IR, SEM-EDS, TEM, Raman and photoluminescence spectroscopy. The results show that doping of La into the framework of ZnTiO3 has a strong influence on the physico-chemical properties of the synthesized nanoparticles. XRD results clearly show that the non-doped ZnTiO3 exhibits a hexagonal phase at 800 °C, whereas the La-doped ZnTiO3 exhibits a cubic phase under similar experimental conditions. In spite of the fact that it has a large ionic radius, the La is efficiently involved in the evolution process by blocking the crystal growth and the cubic to hexagonal transformation in ZnTiO3. Interestingly the absorption edge of the La-doped ZnTiO3 nanoparticles shifted from the UV region to the visible region. The photocatalytic activity of the La-doped ZnTiO3 nanoparticles was evaluated for the degradation of Rhodamine B under sunlight irradiation. The optimum photocatalytic activity was obtained for 2 atom% La-doped ZnTiO3, which is much higher than that of the non-doped ZnTiO3 as well as commercial N-TiO2. A possible mechanism for the degradation of Rhodamine B over La-doped ZnTiO3 was also discussed by trapping experiments. More importantly, the reusability of these nanoparticles is high. Hence La-doped ZnTiO3 nanoparticles can be used as efficient photocatalysts for environmental applications.

Dimensioning BCH codes for coherent DQPSK systems with laser phase noise and cycle slips

Forward error correction (FEC) plays a vital role in coherent optical systems employing multi-level modulation. However, much of coding theory assumes that additive white Gaussian noise (AWGN) is dominant, whereas coherent optical systems have significant phase noise (PN) in addition to AWGN. This changes the error statistics and impacts FEC performance. In this paper, we propose a novel semianalytical method for dimensioning binary Bose-Chaudhuri-Hocquenghem (BCH) codes for systems with PN. Our method involves extracting statistics from pre-FEC bit error rate (BER) simulations. We use these statistics to parameterize a bivariate binomial model that describes the distribution of bit errors. In this way, we relate pre-FEC statistics to post-FEC BER and BCH codes. Our method is applicable to pre-FEC BER around 10-3 and any post-FEC BER. Using numerical simulations, we evaluate the accuracy of our approach for a target post-FEC BER of 10-5. Codes dimensioned with our bivariate binomial model meet the target within 0.2-dB signal-to-noise ratio.

The impact of pump phase-modulation and filtering on WDM signals in a fibre optical parametric amplifier

WDM signal degradation from pump phase-modulation in a one-pump 20dB net-gain fibre optical parametric amplifier is experimentally and numerically characterised for the first time using 10x59Gb/s QPSK signals.

Solid-phase combinatorial chemistry and scintillation proximity assays

The Scintillation Proximity Assay (SPA) is a method that is frequently used to detect and quantify the strength of intermolecular interactions between a biological receptor and ligand molecule in aqueous media. This thesis describes the synthesis of scintillant-tagged-compounds for application in a novel cell-based SPA. A series of 4-functianlised-2,5-diphenyloxazole molecules were synthesised. These 4-functionalised-2,5-diphenyloxazoles were evaluated by Sense Proteomic Ltd. Accordingly, the molecules were evaluated for the ability to scintillate in the presence of ionising radiation. In addition, the molecules were incorporated into liposomal preparations which were subsequently evaluated for the ability to scintillate in the presence of ionising radiation. The optimal liposomal preparation was introduced into the membrane of HeLa cells that were used successfully in a cell-based SPA to detect and quantify the uptake of [14C]methionine. This thesis also describes the synthesis and subsequent polymerisation of novel poly(oxyethylene glycol)-based monomers to form a series of new polymer supports. These Poly(oxyethylene glycol)-polymer (POP) supports were evaluated for the ability to swell and mass-uptake in a variety of solvents, demonstrating that POP-supports exhibit enhanced solvent compatibilities over several commercial resins. The utility of POP-supports in solid-phase synthesis was also demonstrated successfully. The incorporation of (4’-vinyl)-4-benzyl-2,5-diphenyloxazole in varying mole percentage into the monomer composition resulted in the production of chemically functionalised scintillant-containing poly(oxyethylene glycol) polymer (POP-Sc) supports. These materials are compatible with both aqueous and organic solvents and scintillate efficiently in the presence of ionising radiation. The utility of POP-Sc supports in solid-phase synthesis and subsequent in-situ SPA to detect and quantify, in real-time, the kinetic progress of a solid-phase reaction was exemplified successfully.In addition, POP-Sc supports were used successfully both in solid-phase combinatorial synthesis of a peptide nucleic acid (PNA)-library and subsequent screening of this library for the ability to hybridise with DNA, which was labelled with a suitable radio-isotape. This data was used to identify the dependence of the number and position of complimentary codon pairs upon the extent of hybridisation. Finally, a further SPA was used to demonstrate the excellent compatibility of POP-Sc supports for use in the detection and quantification of enzyme assays conducted within the matrix of the POP-Sc support.