Incoherent fibre supercontinuum generation for all-optical random number generation

Random number generation is a central component of modern information technology, with crucial applications in ensuring communications and information security. The development of new physical mechanisms suitable to directly generate random bit sequences is thus a subject of intense current research, with particular interest in alloptical techniques suitable for the generation of data sequences with high bit rate. One such promising technique that has received much recent attention is the chaotic semiconductor laser systems producing high quality random output as a result of the intrinsic nonlinear dynamics of its architecture [1]. Here we propose a novel complementary concept of all-optical technique that might dramatically increase the generation rate of random bits by using simultaneously multiple spectral channels with uncorrelated signals - somewhat similar to use of wave-division-multiplexing in communications. We propose to exploit the intrinsic nonlinear dynamics of extreme spectral broadening and supercontinuum (SC) generation in optical fibre, a process known to be often associated with non-deterministic fluctuations [2]. In this paper, we report proof-of concept results indicating that the fluctuations in highly nonlinear fibre SC generation can potentially be used for random number generation.

A randomised controlled trial investigating the effect of lutein and antioxidant dietary supplementation on visual function in healthy eyes

Background & aims It has been suggested that retinal lutein may improve visual acuity for images that are illuminated by white light. Our aim was to determine the effect of a lutein and antioxidant dietary supplement on visual function. Methods A prospective, 9- and 18-month, double-masked randomised controlled trial. For the 9-month trial, 46 healthy participants were randomised (using a random number generator) to placebo (n=25) or active (n=21) groups. Twenty-nine of these subjects went on to complete 18 months of supplementation, 15 from the placebo group, and 14 from the active group. The active group supplemented daily with 6mg lutein combined with vitamins and minerals. Outcome measures were distance and near visual acuity, contrast sensitivity, and photostress recovery time. The study had 80% power at the 5% significance level for each outcome measure. Data were collected at baseline, 9, and 18 months. Results There were no statistically significant differences between groups for any of the outcome measures over 9 or 18 months. Conclusion There was no evidence of effect of 9 or 18 months of daily supplementation with a lutein-based nutritional supplement on visual function in this group of people with healthy eyes. ISRCTN78467674.

Effect of lutein and antioxidant dietary supplementation on contrast sensitivity in age-related macular disease:A randomized controlled trial

Objective: The aim of the study is to determine the effect of lutein combined with vitamin and mineral supplementation on contrast sensitivity in people with age-related macular disease (ARMD). Design: A prospective, 9-month, double-masked randomized controlled trial. Setting: Aston University, Birmingham, UK and a UK optometric clinical practice. Subjects: Age-related maculopathy (ARM) and atrophic age-related macular degeneration (AMD) participants were randomized (using a random number generator) to either placebo (n = 10) or active (n=15) groups. Three of the placebo group and two of the active group dropped out. Interventions: The active group supplemented daily with 6 mg lutein combined with vitamins and minerals. The outcome measure was contrast sensitivity (CS) measured using the Pelli-Robson chart, for which the study had 80% power at the 5% significance level to detect a change of 0.3log units. Results: The CS score increased by 0.07 ± 0.07 and decreased by 0.02 ± 0.18 log units for the placebo and active groups, respectively. The difference between these values is not statistically significant (z = 0.903, P = 0.376). Conclusion: The results suggest that 6 mg of lutein supplementation in combination with other antioxidants is not beneficial for this group. Further work is required to establish optimum dosage levels.

A randomised controlled trial investigating the effect of nutritional supplementation on visual function in normal, and age-related macular disease affected eyes:design and methodology [ISRCTN78467674]

Background: Age-related macular disease is the leading cause of blind registration in the developed world. One aetiological hypothesis involves oxidation, and the intrinsic vulnerability of the retina to damage via this process. This has prompted interest in the role of antioxidants, particularly the carotenoids lutein and zeaxanthin, in the prevention and treatment of this eye disease. Methods: The aim of this randomised controlled trial is to determine the effect of a nutritional supplement containing lutein, vitamins A, C and E, zinc, and copper on measures of visual function in people with and without age-related macular disease. Outcome measures are distance and near visual acuity, contrast sensitivity, colour vision, macular visual field, glare recovery, and fundus photography. Randomisation is achieved via a random number generator, and masking achieved by third party coding of the active and placebo containers. Data collection will take place at nine and 18 months, and statistical analysis will employ Student's t test. Discussion: A paucity of treatment modalities for age-related macular disease has prompted research into the development of prevention strategies. A positive effect on normals may be indicative of a role of nutritional supplementation in preventing or delaying onset of the condition. An observed benefit in the age-related macular disease group may indicate a potential role of supplementation in prevention of progression, or even a degree reversal of the visual effects caused by this condition.

From rogue waves to random walks:nonlinear instabilities in supercontinuum generation

The noise properties of supercontinuum generation continue to be a subject of wide interest within both pure and applied physics. Aside from immediate applications in supercontinuum source development, detailed studies of supercontinuum noise mechanisms have attracted interdisciplinary attention because of links with extreme instabilities in other physical systems, especially the infamous and destructive oceanic rogue waves. But the instabilities inherent in supercontinuum generation can also be interpreted in terms of natural links with the general field of random processes, and this raises new possibilities for applications in areas such as random number generation. In this contribution we will describe recent work where we interpret supercontinuum intensity and phase fluctuations in this way.

Random walks and random numbers from supercontinuum generation

We report a numerical study showing how the random intensity and phase fluctuations across the bandwidth of a broadband optical supercontinuum can be interpreted in terms of the random processes of random walks and Lévy flights. We also describe how the intensity fluctuations can be applied to physical random number generation. We conclude that the optical supercontinuum provides a highly versatile means of studying and generating a wide class of random processes at optical wavelengths. © 2012 Optical Society of America.

Typical kernel size and number of sparse random matrices over Galois fields: a statistical physics approach

Using methods of statistical physics, we study the average number and kernel size of general sparse random matrices over GF(q), with a given connectivity profile, in the thermodynamical limit of large matrices. We introduce a mapping of GF(q) matrices onto spin systems using the representation of the cyclic group of order q as the q-th complex roots of unity. This representation facilitates the derivation of the average kernel size of random matrices using the replica approach, under the replica symmetric ansatz, resulting in saddle point equations for general connectivity distributions. Numerical solutions are then obtained for particular cases by population dynamics. Similar techniques also allow us to obtain an expression for the exact and average number of random matrices for any general connectivity profile. We present numerical results for particular distributions.

Coloring random graphs and maximizing local diversity

We study a variation of the graph coloring problem on random graphs of finite average connectivity. Given the number of colors, we aim to maximize the number of different colors at neighboring vertices (i.e. one edge distance) of any vertex. Two efficient algorithms, belief propagation and Walksat are adapted to carry out this task. We present experimental results based on two types of random graphs for different system sizes and identify the critical value of the connectivity for the algorithms to find a perfect solution. The problem and the suggested algorithms have practical relevance since various applications, such as distributed storage, can be mapped onto this problem.

Fast response static var generator for improving the power system performance of an electric arc furnace (EAF)

Cascaded multilevel inverters-based Static Var Generators (SVGs) are FACTS equipment introduced for active and reactive power flow control. They eliminate the need for zigzag transformers and give a fast response. However, with regard to their application for flicker reduction in using Electric Arc Furnace (EAF), the existing multilevel inverter-based SVGs suffer from the following disadvantages. (1) To control the reactive power, an off-line calculation of Modulation Index (MI) is required to adjust the SVG output voltage. This slows down the transient response to the changes of reactive power; and (2) Random active power exchange may cause unbalance to the voltage of the d.c. link (HBI) capacitor when the reactive power control is done by adjusting the power angle d alone. To resolve these problems, a mathematical model of 11-level cascaded SVG, was developed. A new control strategy involving both MI (modulation index) and power angle (d) is proposed. A selected harmonics elimination method (SHEM) is taken for switching pattern calculations. To shorten the response time and simplify the controls system, feed forward neural networks are used for on-line computation of the switching patterns instead of using look-up tables. The proposed controller updates the MI and switching patterns once each line-cycle according to the sampled reactive power Qs. Meanwhile, the remainder reactive power (compensated by the MI) and the reactive power variations during the line-cycle will be continuously compensated by adjusting the power angles, d. The scheme senses both variables MI and d, and takes action through the inverter switching angle, qi. As a result, the proposed SVG is expected to give a faster and more accurate response than present designs allow. In support of the proposal there is a mathematical model for reactive powered distribution and a sensitivity matrix for voltage regulation assessment, MATLAB simulation results are provided to validate the proposed schemes. The performance with non-linear time varying loads is analysed and refers to a general review of flicker, of methods for measuring flickers due to arc furnace and means for mitigation.

Properties of sparse random matrices over finite fields

Typical properties of sparse random matrices over finite (Galois) fields are studied, in the limit of large matrices, using techniques from the physics of disordered systems. For the case of a finite field GF(q) with prime order q, we present results for the average kernel dimension, average dimension of the eigenvector spaces and the distribution of the eigenvalues. The number of matrices for a given distribution of entries is also calculated for the general case. The significance of these results to error-correcting codes and random graphs is also discussed.

Contrast sensitivity for complex and random gratings

This thesis studied the effect of (i) the number of grating components and (ii) parameter randomisation on root-mean-square (r.m.s.) contrast sensitivity and spatial integration. The effectiveness of spatial integration without external spatial noise depended on the number of equally spaced orientation components in the sum of gratings. The critical area marking the saturation of spatial integration was found to decrease when the number of components increased from 1 to 5-6 but increased again at 8-16 components. The critical area behaved similarly as a function of the number of grating components when stimuli consisted of 3, 6 or 16 components with different orientations and/or phases embedded in spatial noise. Spatial integration seemed to depend on the global Fourier structure of the stimulus. Spatial integration was similar for sums of two vertical cosine or sine gratings with various Michelson contrasts in noise. The critical area for a grating sum was found to be a sum of logarithmic critical areas for the component gratings weighted by their relative Michelson contrasts. The human visual system was modelled as a simple image processor where the visual stimuli is first low-pass filtered by the optical modulation transfer function of the human eye and secondly high-pass filtered, up to the spatial cut-off frequency determined by the lowest neural sampling density, by the neural modulation transfer function of the visual pathways. The internal noise is then added before signal interpretation occurs in the brain. The detection is mediated by a local spatially windowed matched filter. The model was extended to include complex stimuli and its applicability to the data was found to be successful. The shape of spatial integration function was similar for non-randomised and randomised simple and complex gratings. However, orientation and/or phase randomised reduced r.m.s contrast sensitivity by a factor of 2. The effect of parameter randomisation on spatial integration was modelled under the assumption that human observers change the observer strategy from cross-correlation (i.e., a matched filter) to auto-correlation detection when uncertainty is introduced to the task. The model described the data accurately.

The throughput order of multicast traffics with physical-layer network coding in random wireless ad hoc networks

This paper attempts to address the effectiveness of physical-layer network coding (PNC) on the throughput improvement for multi-hop multicast in random wireless ad hoc networks (WAHNs). We prove that the per session throughput order with PNC is tightly bounded as T((nvmR (n))-1) if m = O(R-2 (n)), where n is the total number of nodes, R(n) is the communication range, and m is the number of destinations for each multicast session. We also show that per-session throughput order with PNC is tight bounded as T(n-1), when m = O(R-2(n)). The results of this paper imply that PNC cannot improve the throughput order of multicast in random WAHNs, which is different from the intuition that PNC may improve the throughput order as it allows simultaneous signal access and combination.

The dawn of the RNA World:toward functional complexity through ligation of random RNA oligomers

A main unsolved problem in the RNA World scenario for the origin of life is how a template-dependent RNA polymerase ribozyme emerged from short RNA oligomers obtained by random polymerization on mineral surfaces. A number of computational studies have shown that the structural repertoire yielded by that process is dominated by topologically simple structures, notably hairpin-like ones. A fraction of these could display RNA ligase activity and catalyze the assembly of larger, eventually functional RNA molecules retaining their previous modular structure: molecular complexity increases but template replication is absent. This allows us to build up a stepwise model of ligation- based, modular evolution that could pave the way to the emergence of a ribozyme with RNA replicase activity, step at which information-driven Darwinian evolution would be triggered. Copyright © 2009 RNA Society.

On the structural repertoire of pools of short, random RNA sequences

A detailed knowledge of the mapping between sequence and structure spaces in populations of RNA molecules is essential to better understand their present-day functional properties, to envisage a plausible early evolution of RNA in a prebiotic chemical environment and to improve the design of in vitro evolution experiments, among others. Analysis of natural RNAs, as well as in vitro and computational studies, show that certain RNA structural motifs are much more abundant than others, pointing out a complex relation between sequence and structure. Within this framework, we have investigated computationally the structural properties of a large pool (10 molecules) of single-stranded, 35 nt-long, random RNA sequences. The secondary structures obtained are ranked and classified into structure families. The number of structures in main families is analytically calculated and compared with the numerical results. This permits a quantification of the fraction of structure space covered by a large pool of sequences. We further show that the number of structural motifs and their frequency is highly unbalanced with respect to the nucleotide composition: simple structures such as stem-loops and hairpins arise from sequences depleted in G, while more complex structures require an enrichment of G. In general, we observe a strong correlation between subfamilies-characterized by a fixed number of paired nucleotides-and nucleotide composition. Our results are compared to the structural repertoire obtained in a second pool where isolated base pairs are prohibited. © 2008 Elsevier Ltd. All rights reserved.

Random distributed feedback fibre lasers

The concept of random lasers exploiting multiple scattering of photons in an amplifying disordered medium in order to generate coherent light without a traditional laser resonator has attracted a great deal of attention in recent years. This research area lies at the interface of the fundamental theory of disordered systems and laser science. The idea was originally proposed in the context of astrophysics in the 1960s by V.S. Letokhov, who studied scattering with "negative absorption" of the interstellar molecular clouds. Research on random lasers has since developed into a mature experimental and theoretical field. A simple design of such lasers would be promising for potential applications. However, in traditional random lasers the properties of the output radiation are typically characterized by complex features in the spatial, spectral and time domains, making them less attractive than standard laser systems in terms of practical applications. Recently, an interesting and novel type of one-dimensional random laser that operates in a conventional telecommunication fibre without any pre-designed resonator mirrors-random distributed feedback fibre laser-was demonstrated. The positive feedback required for laser generation in random fibre lasers is provided by the Rayleigh scattering from the inhomogeneities of the refractive index that are naturally present in silica glass. In the proposed laser concept, the randomly backscattered light is amplified through the Raman effect, providing distributed gain over distances up to 100km. Although an effective reflection due to the Rayleigh scattering is extremely small (~0.1%), the lasing threshold may be exceeded when a sufficiently large distributed Raman gain is provided. Such a random distributed feedback fibre laser has a number of interesting and attractive features. The fibre waveguide geometry provides transverse confinement, and effectively one-dimensional random distributed feedback leads to the generation of a stationary near-Gaussian beam with a narrow spectrum. A random distributed feedback fibre laser has efficiency and performance that are comparable to and even exceed those of similar conventional fibre lasers. The key features of the generated radiation of random distributed feedback fibre lasers include: a stationary narrow-band continuous modeless spectrum that is free of mode competition, nonlinear power broadening, and an output beam with a Gaussian profile in the fundamental transverse mode (generated both in single mode and multi-mode fibres).This review presents the current status of research in the field of random fibre lasers and shows their potential and perspectives. We start with an introductory overview of conventional distributed feedback lasers and traditional random lasers to set the stage for discussion of random fibre lasers. We then present a theoretical analysis and experimental studies of various random fibre laser configurations, including widely tunable, multi-wavelength, narrow-band generation, and random fibre lasers operating in different spectral bands in the 1-1.6μm range. Then we discuss existing and future applications of random fibre lasers, including telecommunication and distributed long reach sensor systems. A theoretical description of random lasers is very challenging and is strongly linked with the theory of disordered systems and kinetic theory. We outline two key models governing the generation of random fibre lasers: the average power balance model and the nonlinear Schrödinger equation based model. Recently invented random distributed feedback fibre lasers represent a new and exciting field of research that brings together such diverse areas of science as laser physics, the theory of disordered systems, fibre optics and nonlinear science. Stable random generation in optical fibre opens up new possibilities for research on wave transport and localization in disordered media. We hope that this review will provide background information for research in various fields and will stimulate cross-disciplinary collaborations on random fibre lasers. © 2014 Elsevier B.V.