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.

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.

Algorithms for solving large random graphs

DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT

Investigations into responses of cylindrical shells to random acoustic excitation

DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT

Changes in neural complexity during the perception of 3D images using random dot stereograms

One developing theme in consciousness research is that consciousness is not the product of any specific component of the brain, rather it is an emergent property of the changing patterns of connectivity between different specialised functional components. For example, the dynamic core hypothesis proposes that conscious experience requires high levels of neural complexity, where complexity is defined in terms of functional connectivity. To test this hypothesis, electroencephalography was recorded while participants were shown random dot-stereograms. Consistent with the dynamic core hypothesis, neural complexity increased as the participants changed from simply viewing the stereogram to consciously perceiving the hidden 3D image.

Dynamics of linear polymers in random media

We study phenomenological scaling theories of the polymer dynamics in random media, employing the existing scaling theories of polymer chains and the percolation statistics. We investigate both the Rouse and the Zimm model for Brownian dynamics and estimate the diffusion constant of the center-of-mass of the chain in such disordered media. For internal dynamics of the chain, we estimate the dynamic exponents. We propose similar scaling theory for the reptation dynamics of the chain in the framework of Flory theory for the disordered medium. The modifications in the case of correlated disorders are also discussed. .

Random walks in local dynamics of network losses

We suggest a model for data losses in a single node (memory buffer) of a packet-switched network (like the Internet) which reduces to one-dimensional discrete random walks with unusual boundary conditions. By construction, the model has critical behavior with a sharp transition from exponentially small to finite losses with increasing data arrival rate. We show that for a finite-capacity buffer at the critical point the loss rate exhibits strong fluctuations and non-Markovian power-law correlations in time, in spite of the Markovian character of the data arrival process.

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.

Lagrangian and Eulerian descriptions of inertial particles in random flows

We study how the spatial distribution of inertial particles evolves with time in a random flow. We describe an explosive appearance of caustics and show how they influence an exponential growth of clusters due to smooth parts of the flow, leading in particular to an exponential growth of the average distance between particles. We demonstrate how caustics restrict applicability of Lagrangian description to inertial particles.

Multiwavelength generation in a random distributed feedback fiber laser using an all fiber Lyot filter

Multiwavelength lasing in the random distributed feedback fiber laser is demonstrated by employing an all fiber Lyot filter. Stable multiwavelength generation is obtained, with each line exhibiting subnanometer line-widths. A flat power distribution over multiple lines is obtained, which indicates that the power between lines is redistributed in nonlinear mixing processes. The multiwavelength generation is observed both in first and second Stokes waves. © 2014 Optical Society of America.

Narrow-band generation in random distributed feedback fiber laser

Narrow-band emission of spectral width down to ∼0.05 nm linewidth is achieved in the random distributed feedback fiber laser employing narrow-band fiber Bragg grating or fiber Fabry-Perot interferometer filters. The observed line-width is ∼10 times less than line-width of other demonstrated up to date random distributed feedback fiber lasers. The random DFB laser with Fabry-Perot interferometer filter provides simultaneously multi-wavelength and narrow-band (within each line) generation with possibility of further wavelength tuning. © 2013 Optical Society of America.

Modeling of spectral and statistical properties of a random distributed feedback fiber laser

For the first time we report full numerical NLSE-based modeling of generation properties of random distributed feedback fiber laser based on Rayleigh scattering. The model which takes into account the random backscattering via its average strength only describes well power and spectral properties of random DFB fiber lasers. The influence of dispersion and nonlinearity on spectral and statistical properties is investigated. The evidence of non-gaussian intensity statistics is found. © 2013 Optical Society of America.

How optical spectrum of random fiber laser is formed

We experimentally and theoretically describe formation of random fiber laser's optical spectrum. We propose a new concept of active cycled wave kinetics from which we derive first ever nonlinear kinetic theory describing laser spectrum. © OSA 2015.

On reliable computation by noisy random Boolean formulas

We study noisy computation in randomly generated k-ary Boolean formulas. We establish bounds on the noise level above which the results of computation by random formulas are not reliable. This bound is saturated by formulas constructed from a single majority-like gate. We show that these gates can be used to compute any Boolean function reliably below the noise bound.