Fast Inverse Nonlinear Fourier Transform For Generating Multi-Solitons In Optical Fiber

The achievable data rates of current fiber-optic wavelength-division-multiplexing (WDM) systems are limited by nonlinear interactions between different subchannels. Recently, it was thus proposed to replace the conventional Fourier transform in WDM systems with an appropriately defined nonlinear Fourier transform (NFT). The computational complexity of NFTs is a topic of current research. In this paper, a fast inverse NFT algorithm for the important special case of multi-solitonic signals is presented. The algorithm requires only $\mathcal{O}(D\log^{2}D)$ floating point operations to compute $D$ samples of a multi-soliton. To the best of our knowledge, this is the first algorithm for this problem with $\log^{2}$-linear complexity. The paper also includes a many samples analysis of the generated nonlinear Fourier spectra.Comment: Submitted to IEEE ISIT 2015 (fixed a few typos

Simulations of the formation and evolution of isolated dwarf galaxies

We present new fully self-consistent models of the formation and evolution of isolated dwarf galaxies. We have used the publicly available N-body/SPH code HYDRA, to which we have added a set of star formation criteria, and prescriptions for chemical enrichment (taking into account contributions from both SNIa and SNII), supernova feedback, and gas cooling. The models follow the evolution of an initially homogeneous gas cloud collapsing in a pre-existing dark-matter halo. These simplified initial conditions are supported by the merger trees of isolated dwarf galaxies extracted from the milli-Millennium Simulation. The star-formation histories of the model galaxies exhibit burst-like behaviour. These bursts are a consequence of the blow-out and subsequent in-fall of gas. The amount of gas that leaves the galaxy for good is found to be small, in absolute numbers, ranging between 3x10^7 Msol and 6x10^7 Msol . For the least massive models, however, this is over 80 per cent of their initial gas mass. The local fluctuations in gas density are strong enough to trigger star-bursts in the massive models, or to inhibit anything more than small residual star formation for the less massive models. Between these star-bursts there can be time intervals of several Gyrs. We have compared model predictions with available data for the relations between luminosity and surface brightness profile, half-light radius, central velocity dispersion, broad band colour (B-V) and metallicity, as well as the location relative to the fundamental plane. The properties of the model dwarf galaxies agree quite well with those of observed dwarf galaxies.Comment: 16 pages, 20 figures, accepted for publication in MNRA

Matched wideband low-noise amplifiers for radio astronomy

Two packaged low noise amplifiers for the 0.3–4 GHz frequency range are described. The amplifiers can be operated at temperatures of 300–4 K and achieve noise temperatures in the 5 K range (<0.1 dB noise figure) at 15 K physical temperature. One amplifier utilizes commercially available, plastic-packaged SiGe transistors for first and second stages; the second amplifier is identical except it utilizes an experimental chip transistor as the first stage. Both amplifiers use resistive feedback to provide input reflection coefficient S11<−10 dB over a decade bandwidth with gain over 30 dB. The amplifiers can be used as rf amplifiers in very low noise radio astronomy systems or as i.f. amplifiers following superconducting mixers operating in the millimeter and submillimeter frequency range

Efficient Computation in Adaptive Artificial Spiking Neural Networks

Artificial Neural Networks (ANNs) are bio-inspired models of neural computation that have proven highly effective. Still, ANNs lack a natural notion of time, and neural units in ANNs exchange analog values in a frame-based manner, a computationally and energetically inefficient form of communication. This contrasts sharply with biological neurons that communicate sparingly and efficiently using binary spikes. While artificial Spiking Neural Networks (SNNs) can be constructed by replacing the units of an ANN with spiking neurons, the current performance is far from that of deep ANNs on hard benchmarks and these SNNs use much higher firing rates compared to their biological counterparts, limiting their efficiency. Here we show how spiking neurons that employ an efficient form of neural coding can be used to construct SNNs that match high-performance ANNs and exceed state-of-the-art in SNNs on important benchmarks, while requiring much lower average firing rates. For this, we use spike-time coding based on the firing rate limiting adaptation phenomenon observed in biological spiking neurons. This phenomenon can be captured in adapting spiking neuron models, for which we derive the effective transfer function. Neural units in ANNs trained with this transfer function can be substituted directly with adaptive spiking neurons, and the resulting Adaptive SNNs (AdSNNs) can carry out inference in deep neural networks using up to an order of magnitude fewer spikes compared to previous SNNs. Adaptive spike-time coding additionally allows for the dynamic control of neural coding precision: we show how a simple model of arousal in AdSNNs further halves the average required firing rate and this notion naturally extends to other forms of attention. AdSNNs thus hold promise as a novel and efficient model for neural computation that naturally fits to temporally continuous and asynchronous applications

Modelling with measures: Approximation of a mass-emitting object by a point source

We consider a linear diffusion equation on $\Omega:=\mathbb{R}^2\setminus\bar{\Omega_\mathcal{O}}$, where $\Omega_\mathcal{O}$ is a bounded domain. The time-dependent flux on the boundary $\Gamma:=\partial\Omega_\mathcal{O}$ is prescribed. The aim of the paper is to approximate the dynamics by the solution of the diffusion equation on the whole of $\mathbb{R}^2$ with a measure-valued point source in the origin and provide estimates for the quality of approximation. For all time $t$, we derive an $L^2([0,t];L^2(\Gamma))$-bound on the difference in flux on the boundary. Moreover, we derive for all $t>0$ an $L^2(\Omega)$-bound and an $L^2([0,t];H^1(\Omega))$-bound for the difference of the solutions to the two models

Proving Termination of Graph Transformation Systems using Weighted Type Graphs over Semirings

We introduce techniques for proving uniform termination of graph transformation systems, based on matrix interpretations for string rewriting. We generalize this technique by adapting it to graph rewriting instead of string rewriting and by generalizing to ordered semirings. In this way we obtain a framework which includes the tropical and arctic type graphs introduced in a previous paper and a new variant of arithmetic type graphs. These type graphs can be used to assign weights to graphs and to show that these weights decrease in every rewriting step in order to prove termination. We present an example involving counters and discuss the implementation in the tool Grez

The metallicity dependence of WR winds

Wolf-Rayet (WR) stars are the most advanced stage in the evolution of the most massive stars. The strong feedback provided by these objects and their subsequent supernova (SN) explosions are decisive for a variety of astrophysical topics such as the cosmic matter cycle. Consequently, understanding the properties of WR stars and their evolution is indispensable. A crucial but still not well known quantity determining the evolution of WR stars is their mass-loss rate. Since the mass loss is predicted to increase with metallicity, the feedback provided by these objects and their spectral appearance are expected to be a function of the metal content of their host galaxy. This has severe implications for the role of massive stars in general and the exploration of low metallicity environments in particular. Hitherto, the metallicity dependence of WR star winds was not well studied. In this contribution, we review the results from our comprehensive spectral analyses of WR stars in environments of different metallicities, ranging from slightly super-solar to SMC-like metallicities. Based on these studies, we derived empirical relations for the dependence of the WN mass-loss rates on the metallicity and iron abundance, respectively.Comment: 5 pages, 4 figures, to be published in the Proceedings of the IAU Symposium No. 329 "The lives and death-throes of massive stars