Novel technique for measuring dispersion and detuning of a UV written silica-on-silicon waveguide

We shall present a new method of measuring the dispersive properties of UV written waveguides in the silica-on-silicon platform used to fabricate planar Bragg gratings. The technique involves direct measurement of the modal refractive index of a waveguide produced in the material. The data obtained also provides additional information about the spectral range of Bragg grating inscription. This direct writing technique reported previously differs from fibre Bragg grating fabrication by the small spot size of the writing beam and permits detuning of the Bragg wavelength from 1250nm to 1625nm. The fabrication technique provides the exact period of the grating and thus interrogation of the gratings produces information on the effective index of the mode. A series of integrated gratings were fabricated in a direct UV written waveguide via the direct grating writing technique in order to measure the wavelength dependence of the refractive index of the material. The Sellmeier curve obtained is shown

Prevalent Behavior of Strongly Order Preserving Semiflows

Classical results in the theory of monotone semiflows give sufficient conditions for the generic solution to converge toward an equilibrium or towards the set of equilibria (quasiconvergence). In this paper, we provide new formulations of these results in terms of the measure-theoretic notion of prevalence. For monotone reaction-diffusion systems with Neumann boundary conditions on convex domains, we show that the set of continuous initial data corresponding to solutions that converge to a spatially homogeneous equilibrium is prevalent. We also extend a previous generic convergence result to allow its use on Sobolev spaces. Careful attention is given to the measurability of the various sets involved.Comment: 18 page

Solution of the Quasispecies Model for an Arbitrary Gene Network

In this paper, we study the equilibrium behavior of Eigen's quasispecies equations for an arbitrary gene network. We consider a genome consisting of $N$ genes, so that each gene sequence $\sigma$ may be written as $\sigma = \sigma_1 \sigma_2 ... \sigma_N$. We assume a single fitness peak (SFP) model for each gene, so that gene $i$ has some ``master'' sequence $\sigma_{i, 0}$ for which it is functioning. The fitness landscape is then determined by which genes in the genome are functioning, and which are not. The equilibrium behavior of this model may be solved in the limit of infinite sequence length. The central result is that, instead of a single error catastrophe, the model exhibits a series of localization to delocalization transitions, which we term an ``error cascade.'' As the mutation rate is increased, the selective advantage for maintaining functional copies of certain genes in the network disappears, and the population distribution delocalizes over the corresponding sequence spaces. The network goes through a series of such transitions, as more and more genes become inactivated, until eventually delocalization occurs over the entire genome space, resulting in a final error catastrophe. This model provides a criterion for determining the conditions under which certain genes in a genome will lose functionality due to genetic drift. It also provides insight into the response of gene networks to mutagens. In particular, it suggests an approach for determining the relative importance of various genes to the fitness of an organism, in a more accurate manner than the standard ``deletion set'' method. The results in this paper also have implications for mutational robustness and what C.O. Wilke termed ``survival of the flattest.''Comment: 29 pages, 5 figures, to be submitted to Physical Review

Simple planar Bragg grating devices for photonic Hilbert transform

Hilbert transformers are important devices widely used in information processing and signal analysis in the electronic domain. For example, for spectral efficiency improvement, it is used to construct the analytic signal for single sideband (SSB) modulation from a real signal. Photonic Hilbert transformers (PHTs) are proposed for a similar range of applications and would allow the direct processing of optical signals at bandwidths far beyond current electronic technologies

Realisation of photonic Hilbert transformer with a simple planar Bragg grating

Photonic Hilbert transformers (PHTs) are desirable for the direct processing of optical signals at high speeds and operation bandwidths, allowing optical networks to outperform current electronic technologies. We practically demonstrate a photonic Hilbert transformer in planar geometry; utilising a pi-phase shift planar Bragg grating with proper apodization profile. The device is fabricated by direct UV grating writing technology in silica-on-silicon [1]. The PHT has a pi-phase shift at the zero point of the frequency response, whereas the amplitude remains constant. The pi-phase shift in PHT is simply induced by placing a pi-phase shift in the refractive index modulation. The constant amplitude is achieved by precise apodization of the grating coupling strength, while the apodization profile is given by [2]. With our current direct UV writing technology, the proposed grating can be fabricated in a much higher accuracy then the conventional fibre Bragg grating manufacturing technique. We will present our latest work on more complex apodized gratings to obtain the ideal realisable frequency and temporal responses for PHTs

Towards an ecological network for the Carpathians

The Carpathian Biodiversity Information System (CBIS) and the proposal for an ecological network for the eastern part of the Carpathians are the two main outcomes of the project funded by the BBI Matra program of the Dutch government. This brochure presents information on how the CBIS was designed, and how the data stored can be retrieved and used. It also clarifies how the CBIS data were used to design the ecological network and, last but not least, it offers recommendations for the use of the proposed ecological network in supporting sustainable developmentin the Carpathians. Due to funding restrictions, the project focused on three east Carpathian countries: Romania, Serbia and Ukraine, which together host the largest area of the Carpathians (Fig. 2). Geographically, the Eastern Carpathians also include parts of the Carpathians located in Poland and Slovakia. Data collection in the Western Carpathians (Czech Republic, Poland, Slovakia and Hungary) will be completed by 2010 and is funded by a parallel project

Strategies for the evolution of sex

We find that the hypothesis made by Jan, Stauffer and Moseley [Theory in Biosc., 119, 166 (2000)] for the evolution of sex, namely a strategy devised to escape extinction due to too many deleterious mutations, is sufficient but not necessary for the successful evolution of a steady state population of sexual individuals within a finite population. Simply allowing for a finite probability for conversion to sex in each generation also gives rise to a stable sexual population, in the presence of an upper limit on the number of deleterious mutations per individual. For large values of this probability, we find a phase transition to an intermittent, multi-stable regime. On the other hand, in the limit of extremely slow drive, another transition takes place to a different steady state distribution, with fewer deleterious mutations within the asexual population.Comment: RevTeX, 11 pages, multicolumn, including 12 figure

Improved model identification for non-linear systems using a random subsampling and multifold modelling (RSMM) approach

In non-linear system identification, the available observed data are conventionally partitioned into two parts: the training data that are used for model identification and the test data that are used for model performance testing. This sort of 'hold-out' or 'split-sample' data partitioning method is convenient and the associated model identification procedure is in general easy to implement. The resultant model obtained from such a once-partitioned single training dataset, however, may occasionally lack robustness and generalisation to represent future unseen data, because the performance of the identified model may be highly dependent on how the data partition is made. To overcome the drawback of the hold-out data partitioning method, this study presents a new random subsampling and multifold modelling (RSMM) approach to produce less biased or preferably unbiased models. The basic idea and the associated procedure are as follows. First, generate K training datasets (and also K validation datasets), using a K-fold random subsampling method. Secondly, detect significant model terms and identify a common model structure that fits all the K datasets using a new proposed common model selection approach, called the multiple orthogonal search algorithm. Finally, estimate and refine the model parameters for the identified common-structured model using a multifold parameter estimation method. The proposed method can produce robust models with better generalisation performance