Characteristic distribution of finite-time Lyapunov exponents for chimera states

It is shown that probability densities of finite-time Lyapunov exponents, corresponding to chimera states, have a characteristic shape. Such distributions could be used as a signature of chimera states, particularly in systems for which the phases of all the oscillators cannot be measured directly. In such cases, the characteristic distribution may be obtained indirectly, via embedding techniques, thus making it possible to detect chimera states in systems where they could otherwise exist, unnoticed

A new family of solutions of the force-free field equation

A new family of solutions has been found for force-free magnetic fields and Beltrami flows, which admits a complete classification in terms of the eigenvalues of the problem. In the absence of boundary values to determine them uniquely, the eigenvalues correspond to the entire set of real numbers, except for zero. The eigenvalues are degenerate in that each eigenvalue has many eigensolutions associated with it. For each eigensolution we have been able to identify sets of equilibrium or null points and lines. The linear mappings of these null points and lines are all unstable. Finally, we derive the first integral of energy associated with this family of solutions

Compositional Morphology for Word Representations and Language Modelling

This paper presents a scalable method for integrating compositional morphological representations into a vector-based probabilistic language model. Our approach is evaluated in the context of log-bilinear language models, rendered suitably efficient for implementation inside a machine translation decoder by factoring the vocabulary. We perform both intrinsic and extrinsic evaluations, presenting results on a range of languages which demonstrate that our model learns morphological representations that both perform well on word similarity tasks and lead to substantial reductions in perplexity. When used for translation into morphologically rich languages with large vocabularies, our models obtain improvements of up to 1.2 BLEU points relative to a baseline system using back-off n-gram models.Comment: Proceedings of the 31st International Conference on Machine Learning (ICML

Extreme ultraviolet emission lines of Ni xii in laboratory and solar spectra

A linear force-free field solution is presented in cylindrical coordinates, formulated in terms of trigonometric and Bessel functions. A numerical exploration has revealed that this solution describes magnetic field lines that meander in Cartesian space, as well as field lines that lie on toroidal flux surfaces. These tori are in (or close to) the plane perpendicular to the cylindrical axis. Nested tori, as well as tori with shells that have finite thickness, were found. The parameter space of the solution shows that the tori exist within a bounded range of values

Optimized shooting method for finding periodic orbits of nonlinear dynamical systems

An alternative numerical method is developed to find stable and unstable periodic orbits of nonlinear dynamical systems. The method exploits the high-efficiency of the Levenberg-Marquardt algorithm for medium-sized problems and has the additional advantage of being relatively simple to implement. It is also applicable to both autonomous and non-autonomous systems. As an example of its use, it is employed to find periodic orbits in the R\"ossler system, a coupled R\"ossler system, as well as an eight-dimensional model of a flexible rotor-bearing; problems which have been treated previously via two related methods. The results agree with the previous methods and are seen to be more accurate in some cases. A simple implementation of the method, written in the Python programming language, is provided as an Appendix.Comment: 21 pages, 7 figure

The structure of force-free magnetic fields

Incontrovertible evidence is presented that the force-free magnetic fields exhibit strong stochastic behavior. Arnold’s solution is given with the associated first integral of energy. A subset of the solution is shown to be non-ergodic whereas the full solution is shown to be ergodic. The first integral of energy is applied to the study of these fields to prove that the equilibrium points of such magnetic configurations are saddle points. Finally, the potential function of the first integral of energy is shown to be a member of the Helmholtz family of solutions. Numerical results corroborate the theoretical conclusions and demonstrate the robustness of the energy integral, which remains constant for arbitrarily long computing time

Suicides on Commuter Rail in California: Possible Patterns — A Case Study, Research Report 10-05

Suicides on rail systems constitute a significant social concern. Reports in local media, whether in newspapers, television, or radio, have brought awareness to this very sensitive and personal subject. This is also true for the San Francisco Bay Area. These events also cause severe trauma for the train operators and staff of the system as well as disruption and cost to society. The overall objective of this project was to conduct a pilot study to identify possible patterns in suicides associated with urban commuter rail systems in California. The Caltrain commuter rail system in the San Francisco Bay Area was used as the subject system for the pilot study. The primary intent of the data analysis was to determine whether suicides along the Caltrain tracks exhibited patterns. Pattern detection in this study was conducted primarily on the basis of time and location. Because the data were readily available, the gender factor was also included in the analysis, although this is not a factor that is connected to the rail system. It was concluded that the data did show some patterns for suicides with respect to time and location. Some of the patterns can be explained while the reasons for some are not immediately obvious. However, the patterns in the latter category did not indicate a particularly attractive location or possible source for suicides

Extreme ultraviolet emission lines of Ni XII in laboratory and solar spectra

Wavelengths for emission lines arising from 3s23p5-3s3p6 and 3s23p5-3s23p43d transitions in Ni XII have been measured in extreme ultraviolet spectra of the Joint European Torus(JET) tokamak. The 3s23p5 2P1/2-3s23p4(3P)3d 2D3/2 line is found to lie at 152.90 ± 0.02 A, a significant improvement over the previous experimental determination of 152.95 ± 0.5 A. This new wavelength is in good agreement with a solar identification at 152.84 ± 0.06 A, confirming the presence of this line in the solar spectrum. The Ni XII feature at 152.15 A may be a result only of the 3s23p5 2P3/2-3s23p4(3P)3d 2D5/2 transition, rather than a blend of this line with 3s23p5 2P3/2-3s23p (3P)3d 2P1/2, as previously suggested. Unidentified emission lines at 295.32 and 317.61 A in solar flare spectra from the Skylab mission are tentatively identified as the 3s23p5 2P3/2-3s3p6 2S1/2 and 3s23p5 2P1/2-3s3p6 2S1/2 transitions in Ni XII, which have laboratory wavelengths of 295.33 and 317.50 A, respectively. Additional support for these identifications is provided by the line intensity ratio for the solar features, which shows good agreement between theory and observation