Harvested populations are more variable only in more variable environments

Acknowledgments This work was funded by NERC grant NE/C510467/1 (T. G. Benton and S. B. Piertney) and a University of Leeds Faculty Postdoctoral Fellowship (T. C. Cameron). Data Accessibility The original time series and body size data from these experiments are available to download from DRYAD entry number http://dx.doi.org/10.5061/dryad.bq135.

Critical transport properties of random metals in large magnetic fields

The threshold behavior of the transport properties of a random metal in the critical region near a metal–insulator transition is strongly affected by the measuring electromagnetic fields. In spite of the randomness, the electrical conductivity exhibits striking phase-coherent effects due to broken symmetry, which greatly sharpen the transition compared with the predictions of effective medium theories, as previously explained for electrical conductivities. Here broken symmetry explains the sign reversal of the T → 0 magnetoconductance of the metal–insulator transition in Si(B,P), also previously not understood by effective medium theories. Finally, the symmetry-breaking features of quantum percolation theory explain the unexpectedly very small electrical conductivity temperature exponent α = 0.22(2) recently observed in Ni(S,Se)2 alloys at the antiferromagnetic metal–insulator transition below T = 0.8 K.

The phasevarion: A genetic system controlling coordinated, random switching of expression of multiple genes

Several host-adapted bacterial pathogens contain methyltransferases associated with type III restriction-modification (R-M) systems that are subject to reversible, high-frequency on/off switching of expression (phase variation). To investigate the role of phase-variable expression of R-M systems, we made a mutant strain lacking the methyltransferase (mod) associated with a type III R-M system of Haemophilus influenzae and analyzed its phenotype. By microarray analysis, we identified a number of genes that were either up- or down-regulated in the mod mutant strain. This system reports the coordinated random switching of a set of genes in a bacterial pathogen and may represent a widely used mechanism.

Coherent-state quantum key distribution without random basis switching

The random switching of measurement bases is commonly assumed to be a necessary step of quantum key distribution protocols. In this paper we present a no-switching protocol and show that switching is not required for coherent-state continuous-variable quantum key distribution. Further, this protocol achieves higher information rates and a simpler experimental setup compared to previous protocols that rely on switching. We propose an optimal eavesdropping attack against this protocol, assuming individual Gaussian attacks. Finally, we investigate and compare the no-switching protocol applied to the original Bennett-Brassard 1984 scheme.

Testing the niche apportionment hypothesis with parasite communities: is random assortment always the rule?

Niche apportionment models have only been applied once to parasite communities. Only the random assortment model (RA), which indicates that species abundances are independent from each other and that interspecific competition is unimportant, provided a good fit to 3 out of 6 parasite communities investigated. The generality of this result needs to be validated, however. In this study we apply 5 niche apportionment models to the parasite communities of 14 fish species from the Great Barrier Reef. We determined which model fitted the data when using either numerical abundance or biomass as an estimate of parasite abundance, and whether the fit of niche apportionment models depends on how the parasite community is defined (e.g. ecto, endoparasites or all parasites considered together). The RA model provided a good fit for the whole community of parasites in 7 fish species when using biovolume (as a surrogate of biomass) as a measure of species abundance. The RA model also fitted observed data when ecto- and endoparasites were considered separately, using abundance or biovolume, but less frequently. Variation in fish sizes among species was not associated with the probability of a model fitting the data. Total numerical abundance and biovolume of parasites were not related across host species, suggesting that they capture different aspects of abundance. Biovolume is not only a better measurement to use with niche-orientated models, it should also be the preferred descriptor to analyse parasite community structure in other contexts. Most of the biological assumptions behind the RA model, i.e. randomness in apportioning niche space, lack of interspecific competition, independence of abundance among different species, and species with variable niches in changeable environments, are in accordance with some previous findings on parasite communities. Thus, parasite communities may generally be unsaturated with species, with empty niches, and interspecific interactions may generally be unimportant in determining parasite community structure.

Emulation of random output simulators

Computer models, or simulators, are widely used in a range of scientific fields to aid understanding of the processes involved and make predictions. Such simulators are often computationally demanding and are thus not amenable to statistical analysis. Emulators provide a statistical approximation, or surrogate, for the simulators accounting for the additional approximation uncertainty. This thesis develops a novel sequential screening method to reduce the set of simulator variables considered during emulation. This screening method is shown to require fewer simulator evaluations than existing approaches. Utilising the lower dimensional active variable set simplifies subsequent emulation analysis. For random output, or stochastic, simulators the output dispersion, and thus variance, is typically a function of the inputs. This work extends the emulator framework to account for such heteroscedasticity by constructing two new heteroscedastic Gaussian process representations and proposes an experimental design technique to optimally learn the model parameters. The design criterion is an extension of Fisher information to heteroscedastic variance models. Replicated observations are efficiently handled in both the design and model inference stages. Through a series of simulation experiments on both synthetic and real world simulators, the emulators inferred on optimal designs with replicated observations are shown to outperform equivalent models inferred on space-filling replicate-free designs in terms of both model parameter uncertainty and predictive variance.

Solvable model for distribution networks on random graphs

We propose a simple model that captures the salient properties of distribution networks, and study the possible occurrence of blackouts, i.e., sudden failings of large portions of such networks. The model is defined on a random graph of finite connectivity. The nodes of the graph represent hubs of the network, while the edges of the graph represent the links of the distribution network. Both, the nodes and the edges carry dynamical two state variables representing the functioning or dysfunctional state of the node or link in question. We describe a dynamical process in which the breakdown of a link or node is triggered when the level of maintenance it receives falls below a given threshold. This form of dynamics can lead to situations of catastrophic breakdown, if levels of maintenance are themselves dependent on the functioning of the net, once maintenance levels locally fall below a critical threshold due to fluctuations. We formulate conditions under which such systems can be analyzed in terms of thermodynamic equilibrium techniques, and under these conditions derive a phase diagram characterizing the collective behavior of the system, given its model parameters. The phase diagram is confirmed qualitatively and quantitatively by simulations on explicit realizations of the graph, thus confirming the validity of our approach. © 2007 The American Physical Society.

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.

Modeling of the spectrum in a random distributed feedback fiber laser within the power balance modes

The simplest model for a description of the random distributed feedback (RDFB) Raman fiber laser is a power balance model describing the evolution of the intensities of the waves over the fiber length. The model predicts well the power performances of the RDFB fiber laser including the generation threshold, the output power and pump and generation wave intensity distributions along the fiber. In the present work, we extend the power balance model and modify equations in such a way that they describe now frequency dependent spectral power density instead of integral over the spectrum intensities. We calculate the generation spectrum by using the depleted pump wave longitudinal distribution derived from the conventional power balance model. We found the spectral balance model to be sufficient to account for the spectral narrowing in the RDFB laser above the threshold of the generation. © 2014 SPIE.

High-efficiency generation in a short random fiber laser

We demonstrate a high-efficiency random lasing in a 850 m span of a phosphosilicate fiber. Random distributed feedback owing to the Rayleigh backscattering in the fiber enables narrowband generation with output power of up to 7.3 W at the Stokes wavelength λS = 1308 nm from 11 Wof the pump power at λP = 1115 nm. The laser demonstrates unique generation efficiency. Near the generation threshold, more than 2 W of output power is generated from only 0.5 W of pump power excess over the generation threshold. At high pump power, the quantum conversion efficiency defined as a ratio of generated and pump photons at the laser output exceeds 100%. Itis explained by the fact that every pump photon is converted into the Stokes photon far from the output fiber end, while the Stokes photons have lower attenuation than the pump photons. © 2014 Astro Ltd.

Random distributed feedback fiber laser of ultimate efficiency

We demonstrate a random fiber laser of ultimate efficiency. More than 2 Watts are generated from 0.5W of pump excess over the generation threshold. At higher power, an optical efficiency corresponds to the quantum limit.

Random distributed feedback Raman fiber laser with polarized pumping

In this letter, the polarization properties of a random fiber laser operating via Raman gain and random distributed feedback owing to Rayleigh scattering are investigated for the first time. Using polarized pump, the partially polarized generation is obtained with a generation spectrum exhibiting discrete narrow spectral features contrary to the smooth spectrum observed for the depolarized pump. The threshold, output power, degree of polarization and the state of polarization (SOP) of the lasing can be significantly influenced by the SOP of the pump. Fine narrow spectral components are also sensitive to the SOP of the pump wave. Furthermore, we found that random lasing's longitudinal power distributions are different in the case of polarized and depolarized pumping that results in considerable reduction of the generation slope efficiency for the polarized radiation. Our results indicate that polarization effects play an important role on the performance of the random fiber laser. This work improves the understanding of the physics of random lasing in fibers and makes a step forward towards the establishment of the vector model of random fiber lasers.

A Random Evolution Inclusion of Subdifferential Type in Hilbert Spaces

In this paper we study a nonlinear evolution inclusion of subdifferential type in Hilbert spaces. The perturbation term is Hausdorff continuous in the state variable and has closed but not necessarily convex values. Our result is a stochastic generalization of an existence theorem proved by Kravvaritis and Papageorgiou in [6].

On-off and multistate intermittencies in cascaded random distributed feedback fibre laser

A range of physical and engineering systems exhibit an irregular complex dynamics featuring alternation of quiet and burst time intervals called the intermittency. The intermittent dynamics most popular in laser science is the on-off intermittency [1]. The on-off intermittency can be understood as a conversion of the noise in a system close to an instability threshold into effective time-dependent fluctuations which result in the alternation of stable and unstable periods. The on-off intermittency has been recently demonstrated in semiconductor, Erbium doped and Raman lasers [2-5]. Recently demonstrated random distributed feedback (random DFB) fiber laser has an irregular dynamics near the generation threshold [6,7]. Here we show the intermittency in the cascaded random DFB fiber laser. We study intensity fluctuations in a random DFB fiber laser based on nitrogen doped fiber. The laser generates first and second Stokes components 1120 nm and 1180 nm respectively under an appropriate pumping. We study the intermittency in the radiation of the second Stokes wave. The typical time trace near the generation threshold of the second Stokes wave (Pth) is shown at Fig. 1a. From the number of long enough time-traces we calculate statistical distribution between major spikes in time dynamics, Fig. 1b. To eliminate contribution of high frequency components of spikes we use a low pass filter along with the reference value of the output power. Experimental data is fitted by power law, ~(P-Pth)y, where is a mean time between pikes. There are two different intermittency regimes. Just above Pth, the mean time is approximated by the -3/2 power law. The -3/2 power law is typical to the on-off intermittency with hopping between two states (first and second Stokes waves in our case) [7]. At higher power, the mean time is approximated by -4 power law, that indicates a change in intermittency type to multistate. Multistable dynamics is observed in erbium-doped fiber lasers [8]. The origin of multiples states in our system could be probably connected with polarization hopping or other reasons and should be further investigated. We have presented a first experimental statistical characterisation of the on-off and multistate intermittencies that occur in the generation of the second Stokes wave in nitrogen doped random DFB fiber laser. References [1] H. Fujisaka and T. Yamada, “A New Intermittency in Coupled Dynamical Systems,” Prog. Theor. Phys. 74, 918 (1985). [2] S. Osborne, A. Amann, D. Bitauld, and S. O’Brien, “On-off intermittency in an optically injected semiconductor laser,” Phys. Rev. E 85, 056204 (2012). [3] S. Sergeyev, K. O'Mahoney, S. Popov, and A. T. Friberg, “Coherence and anticoherence resonance in high-concentration erbium-doped fiber laser,” Opt. Lett. 35, 3736 (2010). [4] A.E. El-Taher, S.V. Sergeyev, E.G. Turitsyna, P. Harper, and S. K. Turitsyn, “Intermittent Self-Pulsing in a Fiber Raman Laser”, In proc. Conf. Nonlin. Photon., paper ID 1367139, Colorado Springs, USA, 2012 [5] S.K. Turitsyn, S.A. Babin, A.E. El-Taher, P. Harper, D.V. Churkin, S.I. Kablukov, J.D. Ania-Castañón, V. Karalekas, and E.V. Podivilov, “Random distributed feedback fibre laser”, Nat. Photon..4, 231 (2010). [6] I. D. Vatnik, D. V. Churkin, S. A. Babin, and S. K. Turitsyn, "Cascaded random distributed feedback Raman fiber laser operating at 1.2 μm," Opt. Express 19, 18486 (2011). [7] W. Feller, An introduction to probability theory and its applications, Vol. 1, 3rd ed. (Wiley, New-York, 1968). [8] G. Huerta-Cuellar, A.N. Pisarchik, and Y.O. Barmenkov, “Experimental characterization of hopping dynamics in a multistable fiber laser,” Phys. Rev. E 78, 035202(R) (2008).

Power optimization of random distributed feedback fiber lasers

We present a comprehensive study of power output characteristics of random distributed feedback Raman fiber lasers. The calculated optimal slope efficiency of the backward wave generation in the one-arm configuration is shown to be as high as ∼90% for 1 W threshold. Nevertheless, in real applications a presence of a small reflection at fiber ends can appreciably deteriorate the power performance. The developed numerical model well describes the experimental data. © 2012 Optical Society of America.